Exploring Text and Icon Graph Interpretation in Students with Dyslexia: An Eye-tracking Study.

Science.gov (United States)

Kim, Sunjung; Wiseheart, Rebecca

2017-02-01

A growing body of research suggests that individuals with dyslexia struggle to use graphs efficiently. Given the persistence of orthographic processing deficits in dyslexia, this study tested whether graph interpretation deficits in dyslexia are directly related to difficulties processing the orthographic components of graphs (i.e. axes and legend labels). Participants were 80 college students with and without dyslexia. Response times and eye movements were recorded as students answered comprehension questions about simple data displayed in bar graphs. Axes and legends were labelled either with words (mixed-modality graphs) or icons (orthography-free graphs). Students also answered informationally equivalent questions presented in sentences (orthography-only condition). Response times were slower in the dyslexic group only for processing sentences. However, eye tracking data revealed group differences for processing mixed-modality graphs, whereas no group differences were found for the orthography-free graphs. When processing bar graphs, students with dyslexia differ from their able reading peers only when graphs contain orthographic features. Implications for processing informational text are discussed. Copyright © 2017 John Wiley & Sons, Ltd. Copyright © 2017 John Wiley & Sons, Ltd.

Deciding the On-line Chromatic Number of a Graph with Pre-coloring is PSPACE-complete

DEFF Research Database (Denmark)

Kudahl, Christian

2015-01-01

In an on-line coloring, the vertices of a graph are revealed one by one. An algorithm assigns a color to each vertex after it is revealed. When a vertex is revealed, it is also revealed which of the previous vertices it is adjacent to. The on-line chromatic number of a graph, G, is the smallest...... number of colors an algorithm will need when on-line-coloring G. The algorithm may know G, but not the order in which the vertices are revealed. The problem of determining if the on-line chromatic number of a graph is less than or equal to k, given a pre-coloring, is shown to be PSPACE-complete....

The Use of Graphing Technology to Promote Transfer of Learning: the Interpretation of Graphs in Physics.

Science.gov (United States)

Nichols, Jeri Ann

This study examined the relationship between mathematics background and performance on graph-related problems in physics before and after instruction on the graphical analysis of motion and several microcomputer-based laboratory experiences. Students identified as either having or not having a graphing technology enhanced precalculus mathematics background were further categorized into one of four groups according to mathematics placement at the university. The performances of these groups were compared to identity differences. Pre- and Post-test data were collected from 589 students and 312 students during Autumn Quarter 1990 and Winter Quarter 1991 respectively. Background information was collected from each student. Significant differences were found between students with the technology enhanced mathematics background and those without when considering the entire populations both quarters. The students with the technology background were favored Autumn quarter and students without the technology background were favored Winter quarter. However, the entire population included an underrepresentation of students at the highest and lowest placements; hence, these were eliminated from the analyses. No significant differences were found between the technology/no technology groups after the elimination of the underrepresented groups. All categories of students increased their mean scores from pretest to post-test; the average increase was 8.23 points Autumn Quarter and 11.41 points Winter Quarter. Males consistently outperformed females on both the pretest and the post-test Autumn 1990. All students found questions involving the concept of acceleration more difficult than questions involving velocity or distance. Questions requiring students to create graphs were more difficult than questions requiring students to interpret graphs. Further research involving a qualitative component is recommended to identify the specific skills students use when solving graph

Spreadsheets, Graphing Calculators and the Line of Best Fit

Directory of Open Access Journals (Sweden)

Bernie O'Sullivan

2003-07-01

One technique that can now be done, almost mindlessly, is the line of best fit. Both the graphing calculator and the Excel spreadsheet produce models for collected data that appear to be very good fits, but upon closer scrutiny, are revealed to be quite poor. This article will examine one such case. I will couch the paper within the framework of a very good classroom investigation that will help generate students’ understanding of the basic principles of curve fitting and will enable them to produce a very accurate model of collected data by combining the technology of the graphing calculator and the spreadsheet.

Component efficient solutions in line-graph games with applications

NARCIS (Netherlands)

van den Brink, J.R.; van der Laan, G.; Vasil'ev, V.

2007-01-01

Recently, applications of cooperative game theory to economic allocation problems have gained popularity. We investigate a class of cooperative games that generalizes some economic applications with a similar structure. These are the so-called line-graph games being cooperative TU-games in which the

Modeling and interpretation of line observations*

Directory of Open Access Journals (Sweden)

Kamp Inga

2015-01-01

Full Text Available Models for the interpretation of line observations from protoplanetary disks are summarized. The spectrum ranges from 1D LTE slab models to 2D thermo-chemical radiative transfer models and their use depends largely on the type/nature of observational data that is analyzed. I discuss the various types of observational data and their interpretation in the context of disk physical and chemical properties. The most simple spatially and spectral unresolved data are line fluxes, which can be interpreted using so-called Boltzmann diagrams. The interpretation is often tricky due to optical depth and non-LTE effects and requires care. Line profiles contain kinematic information and thus indirectly the spatial origin of the emission. Using series of line profiles, we can for example deduce radial temperature gradients in disks (CO pure rotational ladder. Spectro-astrometry of e.g. CO ro-vibrational line profiles probes the disk structure in the 1–30 AU region, where planet formation through core accretion should be most efficient. Spatially and spectrally resolved line images from (submm interferometers are the richest datasets we have to date and they enable us to unravel exciting details of the radial and vertical disk structure such as winds and asymmetries.

Lung Tumor Segmentation Using Electric Flow Lines for Graph Cuts

DEFF Research Database (Denmark)

Hollensen, Christian; Cannon, George; Cannon, Donald

2012-01-01

are normally only used for correction of movements. The method uses graphs based on electric flow lines. The method offers several advantages when trying to replicate manual segmentations. The method gave a dice coefficient of 0.85 and performed better than level set methods and deformable registration....

Integrating concepts and skills: Slope and kinematics graphs

Science.gov (United States)

Tonelli, Edward P., Jr.

The concept of force is a foundational idea in physics. To predict the results of applying forces to objects, a student must be able to interpret data representing changes in distance, time, speed, and acceleration. Comprehension of kinematics concepts requires students to interpret motion graphs, where rates of change are represented as slopes of line segments. Studies have shown that majorities of students who show proficiency with mathematical concepts fail accurately to interpret motion graphs. The primary aim of this study was to examine how students apply their knowledge of slope when interpreting kinematics graphs. To answer the research questions a mixed methods research design, which included a survey and interviews, was adopted. Ninety eight (N=98) high school students completed surveys which were quantitatively analyzed along with qualitative information collected from interviews of students (N=15) and teachers ( N=2). The study showed that students who recalled methods for calculating slopes and speeds calculated slopes accurately, but calculated speeds inaccurately. When comparing the slopes and speeds, most students resorted to calculating instead of visual inspection. Most students recalled and applied memorized rules. Students who calculated slopes and speeds inaccurately failed to recall methods of calculating slopes and speeds, but when comparing speeds, these students connected the concepts of distance and time to the line segments and the rates of change they represented. This study's findings will likely help mathematics and science educators to better assist their students to apply their knowledge of the definition of slope and skills in kinematics concepts.

Study of Chromatic parameters of Line, Total, Middle graphs and Graph operators of Bipartite graph

Science.gov (United States)

Nagarathinam, R.; Parvathi, N.

2018-04-01

Chromatic parameters have been explored on the basis of graph coloring process in which a couple of adjacent nodes receives different colors. But the Grundy and b-coloring executes maximum colors under certain restrictions. In this paper, Chromatic, b-chromatic and Grundy number of some graph operators of bipartite graph has been investigat

A signal-flow-graph approach to on-line gradient calculation.

Science.gov (United States)

Campolucci, P; Uncini, A; Piazza, F

2000-08-01

A large class of nonlinear dynamic adaptive systems such as dynamic recurrent neural networks can be effectively represented by signal flow graphs (SFGs). By this method, complex systems are described as a general connection of many simple components, each of them implementing a simple one-input, one-output transformation, as in an electrical circuit. Even if graph representations are popular in the neural network community, they are often used for qualitative description rather than for rigorous representation and computational purposes. In this article, a method for both on-line and batch-backward gradient computation of a system output or cost function with respect to system parameters is derived by the SFG representation theory and its known properties. The system can be any causal, in general nonlinear and time-variant, dynamic system represented by an SFG, in particular any feedforward, time-delay, or recurrent neural network. In this work, we use discrete-time notation, but the same theory holds for the continuous-time case. The gradient is obtained in a straightforward way by the analysis of two SFGs, the original one and its adjoint (obtained from the first by simple transformations), without the complex chain rule expansions of derivatives usually employed. This method can be used for sensitivity analysis and for learning both off-line and on-line. On-line learning is particularly important since it is required by many real applications, such as digital signal processing, system identification and control, channel equalization, and predistortion.

My Bar Graph Tells a Story

Science.gov (United States)

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…

Flexibility in data interpretation: effects of representational format.

Science.gov (United States)

Braithwaite, David W; Goldstone, Robert L

2013-01-01

Graphs and tables differentially support performance on specific tasks. For tasks requiring reading off single data points, tables are as good as or better than graphs, while for tasks involving relationships among data points, graphs often yield better performance. However, the degree to which graphs and tables support flexibility across a range of tasks is not well-understood. In two experiments, participants detected main and interaction effects in line graphs and tables of bivariate data. Graphs led to more efficient performance, but also lower flexibility, as indicated by a larger discrepancy in performance across tasks. In particular, detection of main effects of variables represented in the graph legend was facilitated relative to detection of main effects of variables represented in the x-axis. Graphs may be a preferable representational format when the desired task or analytical perspective is known in advance, but may also induce greater interpretive bias than tables, necessitating greater care in their use and design.

Proving termination of graph transformation systems using weighted type graphs over semirings

NARCIS (Netherlands)

Bruggink, H.J.S.; König, B.; Nolte, D.; Zantema, H.; Parisi-Presicce, F.; Westfechtel, B.

2015-01-01

We introduce techniques for proving uniform termination of graph transformation systems, based on matrix interpretations for string rewriting. We generalize this technique by adapting it to graph rewriting instead of string rewriting and by generalizing to ordered semirings. In this way we obtain a

On 4-critical t-perfect graphs

OpenAIRE

Benchetrit, Yohann

2016-01-01

It is an open question whether the chromatic number of $t$-perfect graphs is bounded by a constant. The largest known value for this parameter is 4, and the only example of a 4-critical $t$-perfect graph, due to Laurent and Seymour, is the complement of the line graph of the prism $\\Pi$ (a graph is 4-critical if it has chromatic number 4 and all its proper induced subgraphs are 3-colorable). In this paper, we show a new example of a 4-critical $t$-perfect graph: the complement of the line gra...

Price competition on graphs

NARCIS (Netherlands)

Soetevent, A.R.

2010-01-01

This paper extends Hotelling's model of price competition with quadratic transportation costs from a line to graphs. I propose an algorithm to calculate firm-level demand for any given graph, conditional on prices and firm locations. One feature of graph models of price competition is that spatial

How accurate are interpretations of curriculum-based measurement progress monitoring data? Visual analysis versus decision rules.

Science.gov (United States)

Van Norman, Ethan R; Christ, Theodore J

2016-10-01

Curriculum based measurement of oral reading (CBM-R) is used to monitor the effects of academic interventions for individual students. Decisions to continue, modify, or terminate these interventions are made by interpreting time series CBM-R data. Such interpretation is founded upon visual analysis or the application of decision rules. The purpose of this study was to compare the accuracy of visual analysis and decision rules. Visual analysts interpreted 108 CBM-R progress monitoring graphs one of three ways: (a) without graphic aids, (b) with a goal line, or (c) with a goal line and a trend line. Graphs differed along three dimensions, including trend magnitude, variability of observations, and duration of data collection. Automated trend line and data point decision rules were also applied to each graph. Inferential analyses permitted the estimation of the probability of a correct decision (i.e., the student is improving - continue the intervention, or the student is not improving - discontinue the intervention) for each evaluation method as a function of trend magnitude, variability of observations, and duration of data collection. All evaluation methods performed better when students made adequate progress. Visual analysis and decision rules performed similarly when observations were less variable. Results suggest that educators should collect data for more than six weeks, take steps to control measurement error, and visually analyze graphs when data are variable. Implications for practice and research are discussed. Copyright © 2016 Society for the Study of School Psychology. Published by Elsevier Ltd. All rights reserved.

Fuzzy Graph Language Recognizability

OpenAIRE

Kalampakas , Antonios; Spartalis , Stefanos; Iliadis , Lazaros

2012-01-01

Part 5: Fuzzy Logic; International audience; Fuzzy graph language recognizability is introduced along the lines of the established theory of syntactic graph language recognizability by virtue of the algebraic structure of magmoids. The main closure properties of the corresponding class are investigated and several interesting examples of fuzzy graph languages are examined.

Graphs and matrices

CERN Document Server

Bapat, Ravindra B

2014-01-01

This new edition illustrates the power of linear algebra in the study of graphs. The emphasis on matrix techniques is greater than in other texts on algebraic graph theory. Important matrices associated with graphs (for example, incidence, adjacency and Laplacian matrices) are treated in detail. Presenting a useful overview of selected topics in algebraic graph theory, early chapters of the text focus on regular graphs, algebraic connectivity, the distance matrix of a tree, and its generalized version for arbitrary graphs, known as the resistance matrix. Coverage of later topics include Laplacian eigenvalues of threshold graphs, the positive definite completion problem and matrix games based on a graph. Such an extensive coverage of the subject area provides a welcome prompt for further exploration. The inclusion of exercises enables practical learning throughout the book. In the new edition, a new chapter is added on the line graph of a tree, while some results in Chapter 6 on Perron-Frobenius theory are reo...

Simplicial complexes of graphs

CERN Document Server

Jonsson, Jakob

2008-01-01

A graph complex is a finite family of graphs closed under deletion of edges. Graph complexes show up naturally in many different areas of mathematics, including commutative algebra, geometry, and knot theory. Identifying each graph with its edge set, one may view a graph complex as a simplicial complex and hence interpret it as a geometric object. This volume examines topological properties of graph complexes, focusing on homotopy type and homology. Many of the proofs are based on Robin Forman's discrete version of Morse theory. As a byproduct, this volume also provides a loosely defined toolbox for attacking problems in topological combinatorics via discrete Morse theory. In terms of simplicity and power, arguably the most efficient tool is Forman's divide and conquer approach via decision trees; it is successfully applied to a large number of graph and digraph complexes.

A cognitive architecture-based model of graph comprehension

OpenAIRE

Peebles, David

2012-01-01

I present a model of expert comprehension performance for 2 × 2 "interaction" graphs typically used to present data from two-way factorial research designs. Developed using the ACT-R cognitive architecture, the model simulates the cognitive and perceptual operations involved in interpreting interaction graphs and provides a detailed characterisation of the information extracted from the diagram, the prior knowledge required to interpret interaction graphs, and the knowledge generated during t...

A Graph is Worth a Thousand Words: How Overconfidence and Graphical Disclosure of Numerical Information Influence Financial Analysts Accuracy on Decision Making.

Directory of Open Access Journals (Sweden)

Ricardo Lopes Cardoso

Full Text Available Previous researches support that graphs are relevant decision aids to tasks related to the interpretation of numerical information. Moreover, literature shows that different types of graphical information can help or harm the accuracy on decision making of accountants and financial analysts. We conducted a 4×2 mixed-design experiment to examine the effects of numerical information disclosure on financial analysts' accuracy, and investigated the role of overconfidence in decision making. Results show that compared to text, column graph enhanced accuracy on decision making, followed by line graphs. No difference was found between table and textual disclosure. Overconfidence harmed accuracy, and both genders behaved overconfidently. Additionally, the type of disclosure (text, table, line graph and column graph did not affect the overconfidence of individuals, providing evidence that overconfidence is a personal trait. This study makes three contributions. First, it provides evidence from a larger sample size (295 of financial analysts instead of a smaller sample size of students that graphs are relevant decision aids to tasks related to the interpretation of numerical information. Second, it uses the text as a baseline comparison to test how different ways of information disclosure (line and column graphs, and tables can enhance understandability of information. Third, it brings an internal factor to this process: overconfidence, a personal trait that harms the decision-making process of individuals. At the end of this paper several research paths are highlighted to further study the effect of internal factors (personal traits on financial analysts' accuracy on decision making regarding numerical information presented in a graphical form. In addition, we offer suggestions concerning some practical implications for professional accountants, auditors, financial analysts and standard setters.

A Graph is Worth a Thousand Words: How Overconfidence and Graphical Disclosure of Numerical Information Influence Financial Analysts Accuracy on Decision Making.

Science.gov (United States)

Cardoso, Ricardo Lopes; Leite, Rodrigo Oliveira; de Aquino, André Carlos Busanelli

2016-01-01

Previous researches support that graphs are relevant decision aids to tasks related to the interpretation of numerical information. Moreover, literature shows that different types of graphical information can help or harm the accuracy on decision making of accountants and financial analysts. We conducted a 4×2 mixed-design experiment to examine the effects of numerical information disclosure on financial analysts' accuracy, and investigated the role of overconfidence in decision making. Results show that compared to text, column graph enhanced accuracy on decision making, followed by line graphs. No difference was found between table and textual disclosure. Overconfidence harmed accuracy, and both genders behaved overconfidently. Additionally, the type of disclosure (text, table, line graph and column graph) did not affect the overconfidence of individuals, providing evidence that overconfidence is a personal trait. This study makes three contributions. First, it provides evidence from a larger sample size (295) of financial analysts instead of a smaller sample size of students that graphs are relevant decision aids to tasks related to the interpretation of numerical information. Second, it uses the text as a baseline comparison to test how different ways of information disclosure (line and column graphs, and tables) can enhance understandability of information. Third, it brings an internal factor to this process: overconfidence, a personal trait that harms the decision-making process of individuals. At the end of this paper several research paths are highlighted to further study the effect of internal factors (personal traits) on financial analysts' accuracy on decision making regarding numerical information presented in a graphical form. In addition, we offer suggestions concerning some practical implications for professional accountants, auditors, financial analysts and standard setters.

Crystal Graph Convolutional Neural Networks for an Accurate and Interpretable Prediction of Material Properties

Science.gov (United States)

Xie, Tian; Grossman, Jeffrey C.

2018-04-01

The use of machine learning methods for accelerating the design of crystalline materials usually requires manually constructed feature vectors or complex transformation of atom coordinates to input the crystal structure, which either constrains the model to certain crystal types or makes it difficult to provide chemical insights. Here, we develop a crystal graph convolutional neural networks framework to directly learn material properties from the connection of atoms in the crystal, providing a universal and interpretable representation of crystalline materials. Our method provides a highly accurate prediction of density functional theory calculated properties for eight different properties of crystals with various structure types and compositions after being trained with 1 04 data points. Further, our framework is interpretable because one can extract the contributions from local chemical environments to global properties. Using an example of perovskites, we show how this information can be utilized to discover empirical rules for materials design.

Price Competition on Graphs

OpenAIRE

Adriaan R. Soetevent

2010-01-01

This paper extends Hotelling's model of price competition with quadratic transportation costs from a line to graphs. I propose an algorithm to calculate firm-level demand for any given graph, conditional on prices and firm locations. One feature of graph models of price competition is that spatial discontinuities in firm-level demand may occur. I show that the existence result of D'Aspremont et al. (1979) does not extend to simple star graphs. I conjecture that this non-existence result holds...

Price Competition on Graphs

OpenAIRE

Pim Heijnen; Adriaan Soetevent

2014-01-01

This paper extends Hotelling's model of price competition with quadratic transportation costs from a line to graphs. We derive an algorithm to calculate firm-level demand for any given graph, conditional on prices and firm locations. These graph models of price competition may lead to spatial discontinuities in firm-level demand. We show that the existence result of D'Aspremont et al. (1979) does not extend to simple star graphs and conjecture that this non-existence result holds more general...

Graph transformation tool contest 2008

NARCIS (Netherlands)

Rensink, Arend; van Gorp, Pieter

This special section is the outcome of the graph transformation tool contest organised during the Graph-Based Tools (GraBaTs) 2008 workshop, which took place as a satellite event of the International Conference on Graph Transformation (ICGT) 2008. The contest involved two parts: three “off-line case

The on-line graph processing study on phase separation of two-phase flow in T-tube

International Nuclear Information System (INIS)

Qian Yong; Xu Jijun; Yang Zhilin; Chen Yifen

1997-01-01

The on-line graph processing measure system is equipped with and experimental study of phase separation of air-water bubbly flow in the horizontal T-junction is carried out. For the first time, the author have found and defined the new type of complete phase separation, by the visual experiment, which shows that under certain conditions, the air flow entering the T junction will flow into the run outlet completely, which had never been reported in the literature Also, the pressure wave feed back effect and the branch bubble flow reorganization effect were found and analyzed. The complexity of this phase separation phenomenon in the T junction has been further revealed via the on-line graph processing technology. Meanwhile the influences of the inlet mass flow rate W1, the inlet mass quality X1, and the mass extraction rate G3/G1 on phase separation were analyzed

Graph theoretical model of a sensorimotor connectome in zebrafish.

Science.gov (United States)

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

2012-01-01

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

Graphs in kinematics—a need for adherence to principles of algebraic functions

Science.gov (United States)

Sokolowski, Andrzej

2017-11-01

Graphs in physics are central to the analysis of phenomena and to learning about a system’s behavior. The ways students handle graphs are frequently researched. Students’ misconceptions are highlighted, and methods of improvement suggested. While kinematics graphs are to represent a real motion, they are also algebraic entities that must satisfy conditions for being algebraic functions. To be algebraic functions, they must pass certain tests before they can be used to infer more about motion. A preliminary survey of some physics resources has revealed that little attention is paid to verifying if the position, velocity and acceleration versus time graphs, that are to depict real motion, satisfy the most critical condition for being an algebraic function; the vertical line test. The lack of attention to this adherence shows as vertical segments in piecewise graphs. Such graphs generate unrealistic interpretations and may confuse students. A group of 25 college physics students was provided with such a graph and asked to analyse its adherence to reality. The majority of the students (N  =  16, 64%) questioned the graph’s validity. It is inferred that such graphs might not only jeopardize the function principles studied in mathematics but also undermine the purpose of studying these principles. The aim of this study was to bring this idea forth and suggest a better alignment of physics and mathematics methods.

THE APPLICATION OF DIGITAL LINE GRAPHS AND MAP IN THE NETWORK ENVIRONMENT

Directory of Open Access Journals (Sweden)

X. Guo

2012-07-01

Full Text Available WebGIS is an important research field in GIS. W3C organization established SVG standard, which laid a foundation for WebGIS based on vector data. In China, Digital Line Graphs(DLG is a significant GIS product and it has been used in many medium and large WebGIS system. Geographic information-portrayal is the common method of DLG visualization. However, the inherent characteristics of Geographic information-portrayal may lead to a relatively higher data production input, still, the visualization effect is not ideal. We put forward a new product named Digital Line Graphs and Map(DLGM, which consists of DLG and DLG's cartographic presentation data. It provides visualization data based on the cartographic standards. Due to the manufacture and management of DLGM data that are independent from software and platform, its data can be used in many fields. Network application is one of them. This paper is to use DLGM in the network applications. First it reveals the connotation and characteristics of DLGM then analyses the model that DLGM organizes, manages DLG and map symbol data. After that, combined with SVG standards, we put forward DLGM’s SVG encoding method without any information loss. Finally we provide a web map system based on local area network by using 1：10000 DLGM data of a certain area. Based on this study, we conclude that DLGM can be used in the network environment providing high quality DLG and cartographic data for WebGIS.

Interaction graphs

DEFF Research Database (Denmark)

Seiller, Thomas

2016-01-01

Interaction graphs were introduced as a general, uniform, construction of dynamic models of linear logic, encompassing all Geometry of Interaction (GoI) constructions introduced so far. This series of work was inspired from Girard's hyperfinite GoI, and develops a quantitative approach that should...... be understood as a dynamic version of weighted relational models. Until now, the interaction graphs framework has been shown to deal with exponentials for the constrained system ELL (Elementary Linear Logic) while keeping its quantitative aspect. Adapting older constructions by Girard, one can clearly define...... "full" exponentials, but at the cost of these quantitative features. We show here that allowing interpretations of proofs to use continuous (yet finite in a measure-theoretic sense) sets of states, as opposed to earlier Interaction Graphs constructions were these sets of states were discrete (and finite...

Graph theoretical model of a sensorimotor connectome in zebrafish.

Directory of Open Access Journals (Sweden)

Michael Stobb

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

Supplantation of Mental Operations on Graphs

Science.gov (United States)

Vogel, Markus; Girwidz, Raimund; Engel, Joachim

2007-01-01

Research findings show the difficulties younger students have in working with graphs. Higher mental operations are necessary for a skilled interpretation of abstract representations. We suggest connecting a concrete representation of the modeled problem with the related graph. The idea is to illustrate essential mental operations externally. This…

Generalizing a categorization of students’ interpretations of linear kinematics graphs

Directory of Open Access Journals (Sweden)

Laurens Bollen

2016-02-01

Full Text Available We have investigated whether and how a categorization of responses to questions on linear distance-time graphs, based on a study of Irish students enrolled in an algebra-based course, could be adopted and adapted to responses from students enrolled in calculus-based physics courses at universities in Flanders, Belgium (KU Leuven and the Basque Country, Spain (University of the Basque Country. We discuss how we adapted the categorization to accommodate a much more diverse student cohort and explain how the prior knowledge of students may account for many differences in the prevalence of approaches and success rates. Although calculus-based physics students make fewer mistakes than algebra-based physics students, they encounter similar difficulties that are often related to incorrectly dividing two coordinates. We verified that a qualitative understanding of kinematics is an important but not sufficient condition for students to determine a correct value for the speed. When comparing responses to questions on linear distance-time graphs with responses to isomorphic questions on linear water level versus time graphs, we observed that the context of a question influences the approach students use. Neither qualitative understanding nor an ability to find the slope of a context-free graph proved to be a reliable predictor for the approach students use when they determine the instantaneous speed.

Generalizing a categorization of students' interpretations of linear kinematics graphs

Science.gov (United States)

Bollen, Laurens; De Cock, Mieke; Zuza, Kristina; Guisasola, Jenaro; van Kampen, Paul

2016-06-01

We have investigated whether and how a categorization of responses to questions on linear distance-time graphs, based on a study of Irish students enrolled in an algebra-based course, could be adopted and adapted to responses from students enrolled in calculus-based physics courses at universities in Flanders, Belgium (KU Leuven) and the Basque Country, Spain (University of the Basque Country). We discuss how we adapted the categorization to accommodate a much more diverse student cohort and explain how the prior knowledge of students may account for many differences in the prevalence of approaches and success rates. Although calculus-based physics students make fewer mistakes than algebra-based physics students, they encounter similar difficulties that are often related to incorrectly dividing two coordinates. We verified that a qualitative understanding of kinematics is an important but not sufficient condition for students to determine a correct value for the speed. When comparing responses to questions on linear distance-time graphs with responses to isomorphic questions on linear water level versus time graphs, we observed that the context of a question influences the approach students use. Neither qualitative understanding nor an ability to find the slope of a context-free graph proved to be a reliable predictor for the approach students use when they determine the instantaneous speed.

Potential-controlled filtering in quantum star graphs

International Nuclear Information System (INIS)

Turek, Ondřej; Cheon, Taksu

2013-01-01

We study the scattering in a quantum star graph with a Fülöp–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 Fülöp–Tsutsui couplings and demonstrate that the couplings needed for the construction of the proposed quantum devices can be approximated by simple graphs carrying only δ potentials. - Highlights: ► Spectral filtering devices based on quantum graphs are designed theoretically. ► The passband is controlled by the application of macroscopic potentials on lines. ► The filters are built upon special Fulop–Tsutsui type couplings at graph vertices. ► A method of construction of Fulop–Tsutsui vertices from delta potentials is devised.

Neural complexity: A graph theoretic interpretation

Science.gov (United States)

Barnett, L.; Buckley, C. L.; Bullock, S.

2011-04-01

One of the central challenges facing modern neuroscience is to explain the ability of the nervous system to coherently integrate information across distinct functional modules in the absence of a central executive. To this end, Tononi [Proc. Natl. Acad. Sci. USA.PNASA60027-842410.1073/pnas.91.11.5033 91, 5033 (1994)] proposed a measure of neural complexity that purports to capture this property based on mutual information between complementary subsets of a system. Neural complexity, so defined, is one of a family of information theoretic metrics developed to measure the balance between the segregation and integration of a system’s dynamics. One key question arising for such measures involves understanding how they are influenced by network topology. Sporns [Cereb. Cortex53OPAV1047-321110.1093/cercor/10.2.127 10, 127 (2000)] employed numerical models in order to determine the dependence of neural complexity on the topological features of a network. However, a complete picture has yet to be established. While De Lucia [Phys. Rev. EPLEEE81539-375510.1103/PhysRevE.71.016114 71, 016114 (2005)] made the first attempts at an analytical account of this relationship, their work utilized a formulation of neural complexity that, we argue, did not reflect the intuitions of the original work. In this paper we start by describing weighted connection matrices formed by applying a random continuous weight distribution to binary adjacency matrices. This allows us to derive an approximation for neural complexity in terms of the moments of the weight distribution and elementary graph motifs. In particular, we explicitly establish a dependency of neural complexity on cyclic graph motifs.

A Feynman graph selection tool in GRACE system

International Nuclear Information System (INIS)

Yuasa, Fukuko; Ishikawa, Tadashi; Kaneko, Toshiaki

2001-01-01

We present a Feynman graph selection tool grcsel, which is an interpreter written in C language. In the framework of GRACE, it enables us to get a subset of Feynman graphs according to given conditions

Mechatronic modeling and simulation using bond graphs

CERN Document Server

Das, Shuvra

2009-01-01

Introduction to Mechatronics and System ModelingWhat Is Mechatronics?What Is a System and Why Model Systems?Mathematical Modeling Techniques Used in PracticeSoftwareBond Graphs: What Are They?Engineering SystemsPortsGeneralized VariablesBond GraphsBasic Components in SystemsA Brief Note about Bond Graph Power DirectionsSummary of Bond Direction RulesDrawing Bond Graphs for Simple Systems: Electrical and MechanicalSimplification Rules for Junction StructureDrawing Bond Graphs for Electrical SystemsDrawing Bond Graphs for Mechanical SystemsCausalityDrawing Bond Graphs for Hydraulic and Electronic Components and SystemsSome Basic Properties and Concepts for FluidsBond Graph Model of Hydraulic SystemsElectronic SystemsDeriving System Equations from Bond GraphsSystem VariablesDeriving System EquationsTackling Differential CausalityAlgebraic LoopsSolution of Model Equations and Their InterpretationZeroth Order SystemsFirst Order SystemsSecond Order SystemTransfer Functions and Frequency ResponsesNumerical Solution ...

On a conjecture concerning helly circle graphs

Directory of Open Access Journals (Sweden)

Durán Guillermo

2003-01-01

Full Text Available We say that G is an e-circle graph if there is a bijection between its vertices and straight lines on the cartesian plane such that two vertices are adjacent in G if and only if the corresponding lines intersect inside the circle of radius one. This definition suggests a method for deciding whether a given graph G is an e-circle graph, by constructing a convenient system S of equations and inequations which represents the structure of G, in such a way that G is an e-circle graph if and only if S has a solution. In fact, e-circle graphs are exactly the circle graphs (intersection graphs of chords in a circle, and thus this method provides an analytic way for recognizing circle graphs. A graph G is a Helly circle graph if G is a circle graph and there exists a model of G by chords such that every three pairwise intersecting chords intersect at the same point. A conjecture by Durán (2000 states that G is a Helly circle graph if and only if G is a circle graph and contains no induced diamonds (a diamond is a graph formed by four vertices and five edges. Many unsuccessful efforts - mainly based on combinatorial and geometrical approaches - have been done in order to validate this conjecture. In this work, we utilize the ideas behind the definition of e-circle graphs and restate this conjecture in terms of an equivalence between two systems of equations and inequations, providing a new, analytic tool to deal with it.

Quantum snake walk on graphs

International Nuclear Information System (INIS)

Rosmanis, Ansis

2011-01-01

I introduce a continuous-time quantum walk on graphs called the quantum snake walk, the basis states of which are fixed-length paths (snakes) in the underlying graph. First, I analyze the quantum snake walk on the line, and I show that, even though most states stay localized throughout the evolution, there are specific states that most likely move on the line as wave packets with momentum inversely proportional to the length of the snake. Next, I discuss how an algorithm based on the quantum snake walk might potentially be able to solve an extended version of the glued trees problem, which asks to find a path connecting both roots of the glued trees graph. To the best of my knowledge, no efficient quantum algorithm solving this problem is known yet.

RJSplot: Interactive Graphs with R.

Science.gov (United States)

Barrios, David; Prieto, Carlos

2018-03-01

Data visualization techniques provide new methods for the generation of interactive graphs. These graphs allow a better exploration and interpretation of data but their creation requires advanced knowledge of graphical libraries. Recent packages have enabled the integration of interactive graphs in R. However, R provides limited graphical packages that allow the generation of interactive graphs for computational biology applications. The present project has joined the analytical power of R with the interactive graphical features of JavaScript in a new R package (RJSplot). It enables the easy generation of interactive graphs in R, provides new visualization capabilities, and contributes to the advance of computational biology analytical methods. At present, 16 interactive graphics are available in RJSplot, such as the genome viewer, Manhattan plots, 3D plots, heatmaps, dendrograms, networks, and so on. The RJSplot package is freely available online at http://rjsplot.net. © 2018 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

Graph-based semi-supervised learning

CERN Document Server

Subramanya, Amarnag

2014-01-01

While labeled data is expensive to prepare, ever increasing amounts of unlabeled data is becoming widely available. In order to adapt to this phenomenon, several semi-supervised learning (SSL) algorithms, which learn from labeled as well as unlabeled data, have been developed. In a separate line of work, researchers have started to realize that graphs provide a natural way to represent data in a variety of domains. Graph-based SSL algorithms, which bring together these two lines of work, have been shown to outperform the state-of-the-art in many applications in speech processing, computer visi

Applied and computational harmonic analysis on graphs and networks

Science.gov (United States)

Irion, Jeff; Saito, Naoki

2015-09-01

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

Towards a theory of geometric graphs

CERN Document Server

Pach, Janos

2004-01-01

The early development of graph theory was heavily motivated and influenced by topological and geometric themes, such as the Konigsberg Bridge Problem, Euler's Polyhedral Formula, or Kuratowski's characterization of planar graphs. In 1936, when Denes Konig published his classical Theory of Finite and Infinite Graphs, the first book ever written on the subject, he stressed this connection by adding the subtitle Combinatorial Topology of Systems of Segments. He wanted to emphasize that the subject of his investigations was very concrete: planar figures consisting of points connected by straight-line segments. However, in the second half of the twentieth century, graph theoretical research took an interesting turn. In the most popular and most rapidly growing areas (the theory of random graphs, Ramsey theory, extremal graph theory, algebraic graph theory, etc.), graphs were considered as abstract binary relations rather than geometric objects. Many of the powerful techniques developed in these fields have been su...

Dynamic planar embeddings of dynamic graphs

DEFF Research Database (Denmark)

Holm, Jacob; Rotenberg, Eva

2017-01-01

query, one-flip- linkable(u,v) providing a suggestion for a flip that will make them linkable if one exists. We support all updates and queries in O(log 2 n) time. Our time bounds match those of Italiano et al. for a static (flipless) embedding of a dynamic graph. Our new algorithm is simpler......, exploiting that the complement of a spanning tree of a connected plane graph is a spanning tree of the dual graph. The primal and dual trees are interpreted as having the same Euler tour, and a main idea of the new algorithm is an elegant interaction between top trees over the two trees via their common...

Strategy and pattern recognition in expert\\ud comprehension of 2 × 2 interaction graphs

OpenAIRE

Peebles, David

2013-01-01

I present a model of expert comprehension performance for 2 × 2 "interaction" graphs typically used to present data from two-way factorial research designs. Developed using the ACT-R cognitive architecture, the model simulates the cognitive and perceptual operations involved in interpreting interaction graphs and provides a detailed characterisation of the information\\ud extracted from the diagram, the prior knowledge required to interpret interaction graphs, and the knowledge generated durin...

Interpretation of the [ClIII] Lines in Gaseous Nebulae.

Science.gov (United States)

Aller, L H; Czyzak, S J; Walker, M F; Krueger, T K

1970-05-01

The intensity ratio of the green lambdalambda5517 and 5537 lines of [ClIII] serves as an indicatrix of the electron density in many gaseous nebulae whose spectra can be observed with an image converter. Quantitative interpretation of the line ratio requires accurate values of the collisional strengths and transition probabilities. With improved values of these parameters we have revised electron densities for a number of nebulae; the results seem to be in good accord with those derived from other criteria.

Three Syntactic Theories for Combinatory Graph Reduction

DEFF Research Database (Denmark)

Danvy, Olivier; Zerny, Ian

2013-01-01

, as a store-based reduction semantics of combinatory term graphs. We then refocus this store-based reduction semantics into a store-based abstract machine. The architecture of this store-based abstract machine coincides with that of Turner's original reduction machine. The three syntactic theories presented......We present a purely syntactic theory of graph reduction for the canonical combinators S, K, and I, where graph vertices are represented with evaluation contexts and let expressions. We express this rst syntactic theory as a storeless reduction semantics of combinatory terms. We then factor out...... the introduction of let expressions to denote as many graph vertices as possible upfront instead of on demand . The factored terms can be interpreted as term graphs in the sense of Barendregt et al. We express this second syntactic theory, which we prove equivalent to the rst, as a storeless reduction semantics...

A Characterization of 2-Tree Probe Interval Graphs

Directory of Open Access Journals (Sweden)

Brown David E.

2014-08-01

Full Text Available A graph is a probe interval graph if its vertices correspond to some set of intervals of the real line and can be partitioned into sets P and N so that vertices are adjacent if and only if their corresponding intervals intersect and at least one belongs to P. We characterize the 2-trees which are probe interval graphs and extend a list of forbidden induced subgraphs for such graphs created by Pržulj and Corneil in [2-tree probe interval graphs have a large obstruction set, Discrete Appl. Math. 150 (2005 216-231

Dynamic planar embeddings of dynamic graphs

DEFF Research Database (Denmark)

Holm, Jacob; Rotenberg, Eva

2015-01-01

-flip-linkable(u, v) providing a suggestion for a flip that will make them linkable if one exists. We will support all updates and queries in O(log2 n) time. Our time bounds match those of Italiano et al. for a static (flipless) embedding of a dynamic graph. Our new algorithm is simpler, exploiting...... that the complement of a spanning tree of a connected plane graph is a spanning tree of the dual graph. The primal and dual trees are interpreted as having the same Euler tour, and a main idea of the new algorithm is an elegant interaction between top trees over the two trees via their common Euler tour....

Applying graphs and complex networks to football metric interpretation.

Science.gov (United States)

Arriaza-Ardiles, E; Martín-González, J M; Zuniga, M D; Sánchez-Flores, J; de Saa, Y; García-Manso, J M

2018-02-01

This work presents a methodology for analysing the interactions between players in a football team, from the point of view of graph theory and complex networks. We model the complex network of passing interactions between players of a same team in 32 official matches of the Liga de Fútbol Profesional (Spain), using a passing/reception graph. This methodology allows us to understand the play structure of the team, by analysing the offensive phases of game-play. We utilise two different strategies for characterising the contribution of the players to the team: the clustering coefficient, and centrality metrics (closeness and betweenness). We show the application of this methodology by analyzing the performance of a professional Spanish team according to these metrics and the distribution of passing/reception in the field. Keeping in mind the dynamic nature of collective sports, in the future we will incorporate metrics which allows us to analyse the performance of the team also according to the circumstances of game-play and to different contextual variables such as, the utilisation of the field space, the time, and the ball, according to specific tactical situations. Copyright © 2017 Elsevier B.V. All rights reserved.

Higher-Order Minimal Functional Graphs

DEFF Research Database (Denmark)

Jones, Neil D; Rosendahl, Mads

1994-01-01

We present a minimal function graph semantics for a higher-order functional language with applicative evaluation order. The semantics captures the intermediate calls performed during the evaluation of a program. This information may be used in abstract interpretation as a basis for proving...

Generative Graph Grammar of Neo-Vaiśeṣika Formal Ontology (NVFO)

Science.gov (United States)

Tavva, Rajesh; Singh, Navjyoti

NLP applications for Sanskrit so far work within computational paradigm of string grammars. However, to compute 'meanings', as in traditional śā bdabodha prakriyā-s, there is a need to develop suitable graph grammars. Ontological structures are fundamentally graphs. We work within the formal framework of Neo-Vaiśeṣika Formal Ontology (NVFO) to propose a generative graph grammar. The proposed formal grammar only produces well-formed graphs that can be readily interpreted in accordance with Vaiśeṣ ika Ontology. We show that graphs not permitted by Vaiśeṣ ika ontology are not generated by the proposed grammar. Further, we write Interpreter of these graphical structures. This creates computational environment which can be deployed for writing computational applications of Vaiśeṣ ika ontology. We illustrate how this environment can be used to create applications like computing śā bdabodha of sentences.

Calculating Graph Algorithms for Dominance and Shortest Path

DEFF Research Database (Denmark)

Sergey, Ilya; Midtgaard, Jan; Clarke, Dave

2012-01-01

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

Isomorphisms and traversability of directed path graphs

NARCIS (Netherlands)

Broersma, Haitze J.; Li, Xueliang; Li, X.

1998-01-01

The concept of a line digraph is generalized to that of a directed path graph. The directed path graph $\\forw P_k(D)$ of a digraph $D$ is obtained by representing the directed paths on $k$ vertices of $D$ by vertices. Two vertices are joined by an arc whenever the corresponding directed paths in $D$

VT Digital Line Graph Railroads

Data.gov (United States)

Vermont Center for Geographic Information — (Link to Metadata) This datalayer is comprised of major railroad lines for the state of Vermont. These railroad lines line up well along quadrangle boundaries, but...

Large-scale Graph Computation on Just a PC

Science.gov (United States)

2014-05-01

edges for several vertices simultaneously). We compared the performance of GraphChi-DB to Neo4j using their Java API (we discuss MySQL comparison in the...75 4.7.6 Comparison to RDBMS ( MySQL ) . . . . . . . . . . . . . . . . . . . . . 75 4.7.7 Summary of the...Windows method, GraphChi. The C++ implementation has circa 8,000 lines of code. We have also de- veloped a Java -version of GraphChi, but it does not

A NON-ISOTHERMAL THEORY FOR INTERPRETING SODIUM LINES IN TRANSMISSION SPECTRA OF EXOPLANETS

Energy Technology Data Exchange (ETDEWEB)

Heng, Kevin; Lavie, Baptiste [University of Bern, Physics Institute, Center for Space and Habitability, Sidlerstrasse 5, CH-3012 Bern (Switzerland); Wyttenbach, Aurélien; Ehrenreich, David; Lovis, Christophe [Observatoire de l’Université de Genève, 51 chemin des Maillettes, CH-1290 Sauverny (Switzerland); Sing, David K., E-mail: kevin.heng@csh.unibe.ch [Astrophysics Group, School of Physics, University of Exeter, Stocker Road, Exeter EX4 4QL (United Kingdom)

2015-04-10

We present a theory for interpreting the sodium lines detected in transmission spectra of exoplanetary atmospheres. Previous analyses employed the isothermal approximation and dealt only with the transit radius. By recognizing the absorption depth and the transit radius as being independent observables, we develop a theory for jointly interpreting both quantities, which allows us to infer the temperatures and number densities associated with the sodium lines. We are able to treat a non-isothermal situation with a constant temperature gradient. Our novel diagnostics take the form of simple-to-use algebraic formulae and require measurements of the transit radii (and their corresponding absorption depths) at line center and in the line wing for both sodium lines. We apply our diagnostics to the HARPS data of HD 189733b, confirm the upper atmospheric heating reported by Huitson et al., derive a temperature gradient of 0.4376 ± 0.0154 K km{sup −1}, and find densities ∼1–10{sup 4} cm{sup −3}.

Generalizing a Categorization of Students' Interpretations of Linear Kinematics Graphs

Science.gov (United States)

Bollen, Laurens; De Cock, Mieke; Zuza, Kristina; Guisasola, Jenaro; van Kampen, Paul

2016-01-01

We have investigated whether and how a categorization of responses to questions on linear distance-time graphs, based on a study of Irish students enrolled in an algebra-based course, could be adopted and adapted to responses from students enrolled in calculus-based physics courses at universities in Flanders, Belgium (KU Leuven) and the Basque…

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

Science.gov (United States)

Szyjka, Sebastian P.

The purpose of this study was to determine the extent to which six cognitive and attitudinal variables predicted pre-service elementary teachers' performance on line graphing. Predictors included Illinois teacher education basic skills sub-component scores in reading comprehension and mathematics, logical thinking performance scores, as well as measures of attitudes toward science, mathematics and graphing. This study also determined the strength of the relationship between each prospective predictor variable and the line graphing performance variable, as well as the extent to which measures of attitude towards science, mathematics and graphing mediated relationships between scores on mathematics, reading, logical thinking and line graphing. Ninety-four pre-service elementary education teachers enrolled in two different elementary science methods courses during the spring 2009 semester at Southern Illinois University Carbondale participated in this study. Each subject completed five different instruments designed to assess science, mathematics and graphing attitudes as well as logical thinking and graphing ability. Sixty subjects provided copies of primary basic skills score reports that listed subset scores for both reading comprehension and mathematics. The remaining scores were supplied by a faculty member who had access to a database from which the scores were drawn. Seven subjects, whose scores could not be found, were eliminated from final data analysis. Confirmatory factor analysis (CFA) was conducted in order to establish validity and reliability of the Questionnaire of Attitude Toward Line Graphs in Science (QALGS) instrument. CFA tested the statistical hypothesis that the five main factor structures within the Questionnaire of Attitude Toward Statistical Graphs (QASG) would be maintained in the revised QALGS. Stepwise Regression Analysis with backward elimination was conducted in order to generate a parsimonious and precise predictive model. This

The One Universal Graph — a free and open graph database

Science.gov (United States)

Ng, Liang S.; Champion, Corbin

2016-02-01

Recent developments in graph database mostly are huge projects involving big organizations, big operations and big capital, as the name Big Data attests. We proposed the concept of One Universal Graph (OUG) which states that all observable and known objects and concepts (physical, conceptual or digitally represented) can be connected with only one single graph; furthermore the OUG can be implemented with a very simple text file format with free software, capable of being executed on Android or smaller devices. As such the One Universal Graph Data Exchange (GOUDEX) modules can potentially be installed on hundreds of millions of Android devices and Intel compatible computers shipped annually. Coupled with its open nature and ability to connect to existing leading search engines and databases currently in operation, GOUDEX has the potential to become the largest and a better interface for users and programmers to interact with the data on the Internet. With a Web User Interface for users to use and program in native Linux environment, Free Crowdware implemented in GOUDEX can help inexperienced users learn programming with better organized documentation for free software, and is able to manage programmer's contribution down to a single line of code or a single variable in software projects. It can become the first practically realizable “Internet brain” on which a global artificial intelligence system can be implemented. Being practically free and open, One Universal Graph can have significant applications in robotics, artificial intelligence as well as social networks.

Overlapping communities detection based on spectral analysis of line graphs

Science.gov (United States)

Gui, Chun; Zhang, Ruisheng; Hu, Rongjing; Huang, Guoming; Wei, Jiaxuan

2018-05-01

Community in networks are often overlapping where one vertex belongs to several clusters. Meanwhile, many networks show hierarchical structure such that community is recursively grouped into hierarchical organization. In order to obtain overlapping communities from a global hierarchy of vertices, a new algorithm (named SAoLG) is proposed to build the hierarchical organization along with detecting the overlap of community structure. SAoLG applies the spectral analysis into line graphs to unify the overlap and hierarchical structure of the communities. In order to avoid the limitation of absolute distance such as Euclidean distance, SAoLG employs Angular distance to compute the similarity between vertices. Furthermore, we make a micro-improvement partition density to evaluate the quality of community structure and use it to obtain the more reasonable and sensible community numbers. The proposed SAoLG algorithm achieves a balance between overlap and hierarchy by applying spectral analysis to edge community detection. The experimental results on one standard network and six real-world networks show that the SAoLG algorithm achieves higher modularity and reasonable community number values than those generated by Ahn's algorithm, the classical CPM and GN ones.

The hamiltonian index of a graph and its branch-bonds

NARCIS (Netherlands)

Xiong, Liming; Broersma, Haitze J.; Li, Xueliang; Li, Xueliang; Li, MingChu

2004-01-01

Let G be an undirected and loopless finite graph that is not a path. The smallest integer m such that the iterated line graph Lm(G) is hamiltonian is called the hamiltonian index of G, denoted by h(G). A reduction method to determine the hamiltonian index of a graph G with h(G) ≤ 2 is given here. We

jsGraph and jsNMR—Advanced Scientific Charting

Directory of Open Access Journals (Sweden)

Norman Pellet

2014-09-01

Full Text Available The jsGraph library is a versatile javascript library that allows advanced charting to be rendered interactively in web browsers without relying on server-side image processing. jsGraph is released under the MIT license and is free of charge. While being highly customizable through an intuitive javascript API, jsGraph is optimized to render a large quantity of data in a short amount of time. jsGraphs can display line, scatter, contour or zone series. Examples can be consulted on the project home page [1]. Customization of the chart, its axis and its series is achieved through simple but comprehensive JSON configurations.

The One Universal Graph — a free and open graph database

International Nuclear Information System (INIS)

Ng, Liang S.; Champion, Corbin

2016-01-01

Recent developments in graph database mostly are huge projects involving big organizations, big operations and big capital, as the name Big Data attests. We proposed the concept of One Universal Graph (OUG) which states that all observable and known objects and concepts (physical, conceptual or digitally represented) can be connected with only one single graph; furthermore the OUG can be implemented with a very simple text file format with free software, capable of being executed on Android or smaller devices. As such the One Universal Graph Data Exchange (GOUDEX) modules can potentially be installed on hundreds of millions of Android devices and Intel compatible computers shipped annually. Coupled with its open nature and ability to connect to existing leading search engines and databases currently in operation, GOUDEX has the potential to become the largest and a better interface for users and programmers to interact with the data on the Internet. With a Web User Interface for users to use and program in native Linux environment, Free Crowdware implemented in GOUDEX can help inexperienced users learn programming with better organized documentation for free software, and is able to manage programmer's contribution down to a single line of code or a single variable in software projects. It can become the first practically realizable “Internet brain” on which a global artificial intelligence system can be implemented. Being practically free and open, One Universal Graph can have significant applications in robotics, artificial intelligence as well as social networks. (paper)

Optimal graph based segmentation using flow lines with application to airway wall segmentation

DEFF Research Database (Denmark)

Petersen, Jens; Nielsen, Mads; Lo, Pechin Chien Pau

2011-01-01

This paper introduces a novel optimal graph construction method that is applicable to multi-dimensional, multi-surface segmentation problems. Such problems are often solved by refining an initial coarse surface within the space given by graph columns. Conventional columns are not well suited...

Parallel algorithms for finding cliques in a graph

International Nuclear Information System (INIS)

Szabo, S

2011-01-01

A clique is a subgraph in a graph that is complete in the sense that each two of its nodes are connected by an edge. Finding cliques in a given graph is an important procedure in discrete mathematical modeling. The paper will show how concepts such as splitting partitions, quasi coloring, node and edge dominance are related to clique search problems. In particular we will discuss the connection with parallel clique search algorithms. These concepts also suggest practical guide lines to inspect a given graph before starting a large scale search.

Optimal graph based segmentation using flow lines with application to airway wall segmentation

DEFF Research Database (Denmark)

Petersen, Jens; Nielsen, Mads; Lo, Pechin

2011-01-01

This paper introduces a novel optimal graph construction method that is applicable to multi-dimensional, multi-surface segmentation problems. Such problems are often solved by refining an initial coarse surface within the space given by graph columns. Conventional columns are not well suited for ...

Embedded graph invariants in Chern-Simons theory

International Nuclear Information System (INIS)

Major, Seth A.

1999-01-01

Chern-Simons gauge theory, since its inception as a topological quantum field theory, has proved to be a rich source of understanding for knot invariants. In this work the theory is used to explore the definition of the expectation value of a network of Wilson lines -- an embedded graph invariant. Using a generalization of the variational method, lowest-order results for invariants for graphs of arbitrary valence and general vertex tangent space structure are derived. Gauge invariant operators are introduced. Higher order results are found. The method used here provides a Vassiliev-type definition of graph invariants which depend on both the embedding of the graph and the group structure of the gauge theory. It is found that one need not frame individual vertices. However, without a global projection of the graph there is an ambiguity in the relation of the decomposition of distinct vertices. It is suggested that framing may be seen as arising from this ambiguity -- as a way of relating frames at distinct vertices

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

Directory of Open Access Journals (Sweden)

Tomasz Kajdanowicz

2016-09-01

Full Text Available Over the years, several theoretical graph generation models have been proposed. Among the most prominent are: the Erdős–Renyi random graph model, Watts–Strogatz small world model, Albert–Barabási preferential attachment model, Price citation model, and many more. Often, researchers working with real-world data are interested in understanding the generative phenomena underlying their empirical graphs. They want to know which of the theoretical graph generation models would most probably generate a particular empirical graph. In other words, they expect some similarity assessment between the empirical graph and graphs artificially created from theoretical graph generation models. Usually, in order to assess the similarity of two graphs, centrality measure distributions are compared. For a theoretical graph model this means comparing the empirical graph to a single realization of a theoretical graph model, where the realization is generated from the given model using an arbitrary set of parameters. The similarity between centrality measure distributions can be measured using standard statistical tests, e.g., the Kolmogorov–Smirnov test of distances between cumulative distributions. However, this approach is both error-prone and leads to incorrect conclusions, as we show in our experiments. Therefore, we propose a new method for graph comparison and type classification by comparing the entropies of centrality measure distributions (degree centrality, betweenness centrality, closeness centrality. We demonstrate that our approach can help assign the empirical graph to the most similar theoretical model using a simple unsupervised learning method.

On the graph turnpike problem

KAUST Repository

Feder, Tomá s; Motwani, Rajeev

2009-01-01

Results on graph turnpike problem without distinctness, including its NP-completeness, and an O(m+n log n) algorithm, is presented. The usual turnpike problem has all pairwise distances given, but does not specify which pair of vertices w e corresponds to. There are two other problems that can be viewed as special cases of the graph turnpike problem, including the bandwidth problem and the low-distortion graph embedding problem. The aim for the turnpike problem in the NP-complete is to orient the edges with weights w i in either direction so that when the whole cycle is transversed in the real line, it returns to a chosen starting point for the cycle. An instance of the turnpike problem with or without distinctness is uniquely mappable if there exists at most one solution up to translation and choice of orientation.

On the graph turnpike problem

KAUST Repository

Feder, Tomás

2009-06-01

Results on graph turnpike problem without distinctness, including its NP-completeness, and an O(m+n log n) algorithm, is presented. The usual turnpike problem has all pairwise distances given, but does not specify which pair of vertices w e corresponds to. There are two other problems that can be viewed as special cases of the graph turnpike problem, including the bandwidth problem and the low-distortion graph embedding problem. The aim for the turnpike problem in the NP-complete is to orient the edges with weights w i in either direction so that when the whole cycle is transversed in the real line, it returns to a chosen starting point for the cycle. An instance of the turnpike problem with or without distinctness is uniquely mappable if there exists at most one solution up to translation and choice of orientation.

Decisiveness of the spectral gaps of periodic Schrödinger operators on the dumbbell-like metric graph

Directory of Open Access Journals (Sweden)

Hiroaki Niikuni

2015-01-01

Full Text Available In this paper, we consider periodic Schrödinger operators on the dumbbell-like metric graph, which is a periodic graph consisting of lines and rings. Let one line and two rings be in the basic period. We see the relationship between the structure of graph and the band-gap spectrum.

Generalizing a categorization of students' interpretations of linear kinematics graphs

OpenAIRE

Bollen, Laurens; De Cock, Mieke; Zuza, Kristina; Guisasola, Jenaro; van Kampen, Paul

2016-01-01

We have investigated whether and how a categorization of responses to questions on linear distance-time graphs, based on a study of Irish students enrolled in an algebra-based course, could be adopted and adapted to responses from students enrolled in calculus-based physics courses at universities in Flanders, Belgium (KU Leuven) and the Basque Country, Spain (University of the Basque Country). We discuss how we adapted the categorization to accommodate a much more diverse student cohort and ...

Isotropic covariance functions on graphs and their edges

DEFF Research Database (Denmark)

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

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

Infrared Fe II lines in Eta Carinae and a possible interpretation of infrared excesses

International Nuclear Information System (INIS)

Thackeray, A.D.

1978-01-01

The identification of very strong emission lines in the near infrared spectrum of Eta Carinae with newly recognised high-level transitions of Fe II raises the possibility that the infrared excesses of hot emission-line stars may be due to dielectronic recombination of Fe II. Johansson's Fe II lines also need to be considered in the interpretation of the infrared spectra of supernovae. (author)

Network Graph Analysis of Gene-Gene Interactions in Genome-Wide Association Study Data

Directory of Open Access Journals (Sweden)

Sungyoung Lee

2012-12-01

Full Text Available Most common complex traits, such as obesity, hypertension, diabetes, and cancers, are known to be associated with multiple genes, environmental factors, and their epistasis. Recently, the development of advanced genotyping technologies has allowed us to perform genome-wide association studies (GWASs. For detecting the effects of multiple genes on complex traits, many approaches have been proposed for GWASs. Multifactor dimensionality reduction (MDR is one of the powerful and efficient methods for detecting high-order gene-gene (GxG interactions. However, the biological interpretation of GxG interactions identified by MDR analysis is not easy. In order to aid the interpretation of MDR results, we propose a network graph analysis to elucidate the meaning of identified GxG interactions. The proposed network graph analysis consists of three steps. The first step is for performing GxG interaction analysis using MDR analysis. The second step is to draw the network graph using the MDR result. The third step is to provide biological evidence of the identified GxG interaction using external biological databases. The proposed method was applied to Korean Association Resource (KARE data, containing 8838 individuals with 327,632 single-nucleotide polymorphisms, in order to perform GxG interaction analysis of body mass index (BMI. Our network graph analysis successfully showed that many identified GxG interactions have known biological evidence related to BMI. We expect that our network graph analysis will be helpful to interpret the biological meaning of GxG interactions.

Network graph analysis of gene-gene interactions in genome-wide association study data.

Science.gov (United States)

Lee, Sungyoung; Kwon, Min-Seok; Park, Taesung

2012-12-01

Most common complex traits, such as obesity, hypertension, diabetes, and cancers, are known to be associated with multiple genes, environmental factors, and their epistasis. Recently, the development of advanced genotyping technologies has allowed us to perform genome-wide association studies (GWASs). For detecting the effects of multiple genes on complex traits, many approaches have been proposed for GWASs. Multifactor dimensionality reduction (MDR) is one of the powerful and efficient methods for detecting high-order gene-gene (GxG) interactions. However, the biological interpretation of GxG interactions identified by MDR analysis is not easy. In order to aid the interpretation of MDR results, we propose a network graph analysis to elucidate the meaning of identified GxG interactions. The proposed network graph analysis consists of three steps. The first step is for performing GxG interaction analysis using MDR analysis. The second step is to draw the network graph using the MDR result. The third step is to provide biological evidence of the identified GxG interaction using external biological databases. The proposed method was applied to Korean Association Resource (KARE) data, containing 8838 individuals with 327,632 single-nucleotide polymorphisms, in order to perform GxG interaction analysis of body mass index (BMI). Our network graph analysis successfully showed that many identified GxG interactions have known biological evidence related to BMI. We expect that our network graph analysis will be helpful to interpret the biological meaning of GxG interactions.

Interferometric measurement of lines shift in flames in connection with interpretation of lined absorption method in atomic absorption spectroscopy

International Nuclear Information System (INIS)

L'vov, B.V.; Polzik, L.K.; Katskov, D.A.; Kruglikova, L.P.

1975-01-01

This paper is concerned with interferometric measuring of the line shift in flames in the view of interpretation of absorption lines in the atomic absorption spectroscopy. The newly measured line shifts were compared to the known data on Lorentz broadening of the same lines obtained by methods free of the systematic errors. The resonant lines of the alkaline earth elements (Sr, Ca, Ba) were investigated. To reduce self-absorption in the flame the solutions with minimum concentrations of the elements were used. The computation scheme includes the spectrometer apparatus width and line broadening due to the self-absorption. Formulae are given for computing the values studied. Good agreement was observed between the computed and experimental results. Error analysis was performed. It was concluded that any line shifts in the hydrocarbons were correctly taken into an account in the absolute computations of absorption

A graph rewriting programming language for graph drawing

OpenAIRE

Rodgers, Peter

1998-01-01

This paper describes Grrr, a prototype visual graph drawing tool. Previously there were no visual languages for programming graph drawing algorithms despite the inherently visual nature of the process. The languages which gave a diagrammatic view of graphs were not computationally complete and so could not be used to implement complex graph drawing algorithms. Hence current graph drawing tools are all text based. Recent developments in graph rewriting systems have produced computationally com...

Pathfinding in graph-theoretic sabotage models. I. Simultaneous attack by several teams

International Nuclear Information System (INIS)

Hulme, B.L.

1976-07-01

Graph models are developed for fixed-site safeguards systems. The problem of finding optimal routes for several sabotage teams is cast as a problem of finding shortest paths in a graph. The motivation, rationale, and interpretation of the mathematical models are discussed in detail, and an algorithm for efficiently solving the associated path problem is described

Reproducibility of graph metrics in fMRI networks

Directory of Open Access Journals (Sweden)

Qawi K Telesford

2010-12-01

Full Text Available The reliability of graph metrics calculated in network analysis is essential to the interpretation of complex network organization. These graph metrics are used to deduce the small-world properties in networks. In this study, we investigated the test-retest reliability of graph metrics from functional magnetic resonance imaging (fMRI data collected for two runs in 45 healthy older adults. Graph metrics were calculated on data for both runs and compared using intraclass correlation coefficient (ICC statistics and Bland-Altman (BA plots. ICC scores describe the level of absolute agreement between two measurements and provide a measure of reproducibility. For mean graph metrics, ICC scores were high for clustering coefficient (ICC=0.86, global efficiency (ICC=0.83, path length (ICC=0.79, and local efficiency (ICC=0.75; the ICC score for degree was found to be low (ICC=0.29. ICC scores were also used to generate reproducibility maps in brain space to test voxel-wise reproducibility for unsmoothed and smoothed data. Reproducibility was uniform across the brain for global efficiency and path length, but was only high in network hubs for clustering coefficient, local efficiency and degree. BA plots were used to test the measurement repeatability of all graph metrics. All graph metrics fell within the limits for repeatability. Together, these results suggest that with exception of degree, mean graph metrics are reproducible and suitable for clinical studies. Further exploration is warranted to better understand reproducibility across the brain on a voxel-wise basis.

Graph Aggregation

NARCIS (Netherlands)

Endriss, U.; Grandi, U.

Graph aggregation is the process of computing a single output graph that constitutes a good compromise between several input graphs, each provided by a different source. One needs to perform graph aggregation in a wide variety of situations, e.g., when applying a voting rule (graphs as preference

Proxy Graph: Visual Quality Metrics of Big Graph Sampling.

Science.gov (United States)

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

2017-06-01

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

A Clustering Graph Generator

Energy Technology Data Exchange (ETDEWEB)

Winlaw, Manda [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); De Sterck, Hans [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Sanders, Geoffrey [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

2015-10-26

In very simple terms a network can be de ned as a collection of points joined together by lines. Thus, networks can be used to represent connections between entities in a wide variety of elds including engi- neering, science, medicine, and sociology. Many large real-world networks share a surprising number of properties, leading to a strong interest in model development research and techniques for building synthetic networks have been developed, that capture these similarities and replicate real-world graphs. Modeling these real-world networks serves two purposes. First, building models that mimic the patterns and prop- erties of real networks helps to understand the implications of these patterns and helps determine which patterns are important. If we develop a generative process to synthesize real networks we can also examine which growth processes are plausible and which are not. Secondly, high-quality, large-scale network data is often not available, because of economic, legal, technological, or other obstacles [7]. Thus, there are many instances where the systems of interest cannot be represented by a single exemplar network. As one example, consider the eld of cybersecurity, where systems require testing across diverse threat scenarios and validation across diverse network structures. In these cases, where there is no single exemplar network, the systems must instead be modeled as a collection of networks in which the variation among them may be just as important as their common features. By developing processes to build synthetic models, so-called graph generators, we can build synthetic networks that capture both the essential features of a system and realistic variability. Then we can use such synthetic graphs to perform tasks such as simulations, analysis, and decision making. We can also use synthetic graphs to performance test graph analysis algorithms, including clustering algorithms and anomaly detection algorithms.

Chromatic graph theory

CERN Document Server

Chartrand, Gary; Rosen, Kenneth H

2008-01-01

Beginning with the origin of the four color problem in 1852, the field of graph colorings has developed into one of the most popular areas of graph theory. Introducing graph theory with a coloring theme, Chromatic Graph Theory explores connections between major topics in graph theory and graph colorings as well as emerging topics. This self-contained book first presents various fundamentals of graph theory that lie outside of graph colorings, including basic terminology and results, trees and connectivity, Eulerian and Hamiltonian graphs, matchings and factorizations, and graph embeddings. The remainder of the text deals exclusively with graph colorings. It covers vertex colorings and bounds for the chromatic number, vertex colorings of graphs embedded on surfaces, and a variety of restricted vertex colorings. The authors also describe edge colorings, monochromatic and rainbow edge colorings, complete vertex colorings, several distinguishing vertex and edge colorings, and many distance-related vertex coloring...

MadGraph/MadEvent. The new web generation

International Nuclear Information System (INIS)

Alwall, J.

2007-01-01

The new web-based version of the automatized process and event generator MadGraph/MadEvent is now available. Recent developments are: New models, notably MSSM, 2HDM and a framework for addition of user-defined models, inclusive sample generation and on-line hadronization and detector simulation. Event generation can be done on-line on any of our clusters. (author)

Cross Talk Analysis on Multiple Coupled Transmission Lines; (The calculation of transfer functions on multiple coupled tansmission lines in an inhomogeneous dielectric medium)

DEFF Research Database (Denmark)

Dalby, Arne Brejning

1994-01-01

A flow graph relating voltages and the forward and reflected propagation modes (¿ TEM) on multiple coupled transmission lines in an inhomogeneous dielectric medium is presented. This flow graph directy gives the different transfer functions, including S-parameters, in matrix form needed to calcul......A flow graph relating voltages and the forward and reflected propagation modes (¿ TEM) on multiple coupled transmission lines in an inhomogeneous dielectric medium is presented. This flow graph directy gives the different transfer functions, including S-parameters, in matrix form needed...

Graph sampling

OpenAIRE

Zhang, L.-C.; Patone, M.

2017-01-01

We synthesise the existing theory of graph sampling. We propose a formal definition of sampling in finite graphs, and provide a classification of potential graph parameters. We develop a general approach of Horvitz–Thompson estimation to T-stage snowball sampling, and present various reformulations of some common network sampling methods in the literature in terms of the outlined graph sampling theory.

Voice-Centric LTE Femtocells and Improper Graph Colorings

DEFF Research Database (Denmark)

Garcia, Luis Guilherme Uzeda; Pedersen, Klaus; Mogensen, Preben

2012-01-01

. The investigation revolves around the sensible definition of the underlying graph, i.e. the network model, rather than focusing on the coloring algorithms and their properties. Ultimately, we posit that improper online graph-coloring suffices and is actually preferable. In short, settling for less......This paper addresses carrier-based inter-cell interference coordination (CB-ICIC) among LTE femtocells operating on a single carrier. CB-ICIC is in many ways linked to the widely investigated dynamic channel assignment problem, which is often studied in the context of graph coloring......-than-optimal configurations avoids uncontrolled service interruptions. Such disruptions tend to raise understandable concerns when it comes to fully autonomous selection of operational CCs. Our results dispel such concerns by showing that conservative methods can achieve most of the benefits of unrestricted off-line coloring...

Algorithms for Planar Graphs and Graphs in Metric Spaces

DEFF Research Database (Denmark)

Wulff-Nilsen, Christian

structural properties that can be exploited. For instance, a road network or a wire layout on a microchip is typically (near-)planar and distances in the network are often defined w.r.t. the Euclidean or the rectilinear metric. Specialized algorithms that take advantage of such properties are often orders...... of magnitude faster than the corresponding algorithms for general graphs. The first and main part of this thesis focuses on the development of efficient planar graph algorithms. The most important contributions include a faster single-source shortest path algorithm, a distance oracle with subquadratic...... for geometric graphs and graphs embedded in metric spaces. Roughly speaking, the stretch factor is a real value expressing how well a (geo-)metric graph approximates the underlying complete graph w.r.t. distances. We give improved algorithms for computing the stretch factor of a given graph and for augmenting...

Edge compression techniques for visualization of dense directed graphs.

Science.gov (United States)

Dwyer, Tim; Henry Riche, Nathalie; Marriott, Kim; Mears, Christopher

2013-12-01

We explore the effectiveness of visualizing dense directed graphs by replacing individual edges with edges connected to 'modules'-or groups of nodes-such that the new edges imply aggregate connectivity. We only consider techniques that offer a lossless compression: that is, where the entire graph can still be read from the compressed version. The techniques considered are: a simple grouping of nodes with identical neighbor sets; Modular Decomposition which permits internal structure in modules and allows them to be nested; and Power Graph Analysis which further allows edges to cross module boundaries. These techniques all have the same goal--to compress the set of edges that need to be rendered to fully convey connectivity--but each successive relaxation of the module definition permits fewer edges to be drawn in the rendered graph. Each successive technique also, we hypothesize, requires a higher degree of mental effort to interpret. We test this hypothetical trade-off with two studies involving human participants. For Power Graph Analysis we propose a novel optimal technique based on constraint programming. This enables us to explore the parameter space for the technique more precisely than could be achieved with a heuristic. Although applicable to many domains, we are motivated by--and discuss in particular--the application to software dependency analysis.

The effect of four instructional methods, gender, and time of testing on the achievement of sixth graders learning to interpret graphs

Science.gov (United States)

Young, Jerry Wayne

The purpose of this study was to determine the effects of four instructional methods (direct instruction, computer-aided instruction, video observation, and microcomputer-based lab activities), gender, and time of testing (pretest, immediate posttest for determining the immediate effect of instruction, and a delayed posttest two weeks later to determine the retained effect of the instruction) on the achievement of sixth graders who were learning to interpret graphs of displacement and velocity. The dependent variable of achievement was reflected in the scores earned by students on a testing instrument of established validity and reliability. The 107 students participating in the study were divided by gender and were then randomly assigned to the four treatment groups, each taught by a different teacher. Each group had approximately equal numbers of males and females. The students were pretested and then involved in two class periods of the instructional method which was unique to their group. Immediately following treatment they were posttested and two weeks later they were posttested again. The data in the form of test scores were analyzed with a two-way split-plot analysis of variance to determine if there was significant interaction among technique, gender, and time of testing. When significant interaction was indicated, the Tukey HSD test was used to determine specific mean differences. The results of the analysis indicated no gender effect. Only students in the direct instruction group and the microcomputer-based laboratory group had significantly higher posttest-1 scores than pretest scores. They also had significantly higher posttest-2 scores than pretest scores. This suggests that the learning was retained. The other groups experienced no significant differences among pretest, posttest-1, and posttest-2 scores. Recommendations are that direct instruction and microcomputer-based laboratory activities should be considered as effective stand-alone methods for

Degree Associated Edge Reconstruction Number of Graphs with Regular Pruned Graph

Directory of Open Access Journals (Sweden)

P. Anusha Devi

2015-10-01

Full Text Available An ecard of a graph $G$ is a subgraph formed by deleting an edge. A da-ecard specifies the degree of the deleted edge along with the ecard. The degree associated edge reconstruction number of a graph $G,~dern(G,$ is the minimum number of da-ecards that uniquely determines $G.$  The adversary degree associated edge reconstruction number of a graph $G, adern(G,$ is the minimum number $k$ such that every collection of $k$ da-ecards of $G$ uniquely determines $G.$ The maximal subgraph without end vertices of a graph $G$ which is not a tree is the pruned graph of $G.$ It is shown that $dern$ of complete multipartite graphs and some connected graphs with regular pruned graph is $1$ or $2.$ We also determine $dern$ and $adern$ of corona product of standard graphs.

Learning about Science Graphs and Word Games. Superific Science Book V. A Good Apple Science Activity Book for Grades 5-8+.

Science.gov (United States)

Conway, Lorraine

This packet of student materials contains a variety of worksheet activities dealing with science graphs and science word games. These reproducible materials deal with: (1) bar graphs; (2) line graphs; (3) circle graphs; (4) pictographs; (5) histograms; (6) artgraphs; (7) designing your own graphs; (8) medical prefixes; (9) color prefixes; (10)…

Introduction to graph theory

CERN Document Server

Trudeau, Richard J

1994-01-01

Preface1. Pure Mathematics Introduction; Euclidean Geometry as Pure Mathematics; Games; Why Study Pure Mathematics?; What's Coming; Suggested Reading2. Graphs Introduction; Sets; Paradox; Graphs; Graph diagrams; Cautions; Common Graphs; Discovery; Complements and Subgraphs; Isomorphism; Recognizing Isomorphic Graphs; Semantics The Number of Graphs Having a Given nu; Exercises; Suggested Reading3. Planar Graphs Introduction; UG, K subscript 5, and the Jordan Curve Theorem; Are there More Nonplanar Graphs?; Expansions; Kuratowski's Theorem; Determining Whether a Graph is Planar or

Graph Theory. 2. Vertex Descriptors and Graph Coloring

Directory of Open Access Journals (Sweden)

Lorentz JÄNTSCHI

2002-12-01

Full Text Available This original work presents the construction of a set of ten sequence matrices and their applications for ordering vertices in graphs. For every sequence matrix three ordering criteria are applied: lexicographic ordering, based on strings of numbers, corresponding to every vertex, extracted as rows from sequence matrices; ordering by the sum of path lengths from a given vertex; and ordering by the sum of paths, starting from a given vertex. We also examine a graph that has different orderings for the above criteria. We then proceed to demonstrate that every criterion induced its own partition of graph vertex. We propose the following theoretical result: both LAVS and LVDS criteria generate identical partitioning of vertices in any graph. Finally, a coloring of graph vertices according to introduced ordering criteria was proposed.

Graphs cospectral with a friendship graph or its complement

Directory of Open Access Journals (Sweden)

Alireza Abdollahi

2013-12-01

Full Text Available Let $n$ be any positive integer and let $F_n$ be the friendship (or Dutch windmill graph with $2n+1$ vertices and $3n$ edges. Here we study graphs with the same adjacency spectrum as the $F_n$. Two graphs are called cospectral if the eigenvalues multiset of their adjacency matrices are the same. Let $G$ be a graph cospectral with $F_n$. Here we prove that if $G$ has no cycle of length $4$ or $5$, then $Gcong F_n$. Moreover if $G$ is connected and planar then $Gcong F_n$.All but one of connected components of $G$ are isomorphic to $K_2$.The complement $overline{F_n}$ of the friendship graph is determined by its adjacency eigenvalues, that is, if $overline{F_n}$ is cospectral with a graph $H$, then $Hcong overline{F_n}$.

Performance analysis of chi models using discrete-time probabilistic reward graphs

NARCIS (Netherlands)

Trcka, N.; Georgievska, S.; Markovski, J.; Andova, S.; Vink, de E.P.

2008-01-01

We propose the model of discrete-time probabilistic reward graphs (DTPRGs) for performance analysis of systems exhibiting discrete deterministic time delays and probabilistic behavior, via their interpretation as discrete-time Markov reward chains, full-fledged platform for qualitative and

Combining Vertex-centric Graph Processing with SPARQL for Large-scale RDF Data Analytics

KAUST Repository

Abdelaziz, Ibrahim

2017-06-27

Modern applications, such as drug repositioning, require sophisticated analytics on RDF graphs that combine structural queries with generic graph computations. Existing systems support either declarative SPARQL queries, or generic graph processing, but not both. We bridge the gap by introducing Spartex, a versatile framework for complex RDF analytics. Spartex extends SPARQL to support programs that combine seamlessly generic graph algorithms (e.g., PageRank, Shortest Paths, etc.) with SPARQL queries. Spartex builds on existing vertex-centric graph processing frameworks, such as Graphlab or Pregel. It implements a generic SPARQL operator as a vertex-centric program that interprets SPARQL queries and executes them efficiently using a built-in optimizer. In addition, any graph algorithm implemented in the underlying vertex-centric framework, can be executed in Spartex. We present various scenarios where our framework simplifies significantly the implementation of complex RDF data analytics programs. We demonstrate that Spartex scales to datasets with billions of edges, and show that our core SPARQL engine is at least as fast as the state-of-the-art specialized RDF engines. For complex analytical tasks that combine generic graph processing with SPARQL, Spartex is at least an order of magnitude faster than existing alternatives.

Resolvent expansion for the Schrödinger operator on a graph with infinite rays

DEFF Research Database (Denmark)

Ito, Kenichi; Jensen, Arne

2018-01-01

We consider the Schrödinger operator on a combinatorial graph consisting of a finite graph and a finite number of discrete half-lines, all jointed together, and compute an asymptotic expansion of its resolvent around the threshold 0. Precise expressions are obtained for the first few coefficients...

Novel Ontologies-based Optical Character Recognition-error Correction Cooperating with Graph Component Extraction

Directory of Open Access Journals (Sweden)

Sarunya Kanjanawattana

2017-01-01

Full Text Available literature. Extracting graph information clearly contributes to readers, who are interested in graph information interpretation, because we can obtain significant information presenting in the graph. A typical tool used to transform image-based characters to computer editable characters is optical character recognition (OCR. Unfortunately, OCR cannot guarantee perfect results, because it is sensitive to noise and input quality. This becomes a serious problem because misrecognition provides misunderstanding information to readers and causes misleading communication. In this study, we present a novel method for OCR-error correction based on bar graphs using semantics, such as ontologies and dependency parsing. Moreover, we used a graph component extraction proposed in our previous study to omit irrelevant parts from graph components. It was applied to clean and prepare input data for this OCR-error correction. The main objectives of this paper are to extract significant information from the graph using OCR and to correct OCR errors using semantics. As a result, our method provided remarkable performance with the highest accuracies and F-measures. Moreover, we examined that our input data contained less of noise because of an efficiency of our graph component extraction. Based on the evidence, we conclude that our solution to the OCR problem achieves the objectives.

Graph embedding with rich information through heterogeneous graph

KAUST Repository

Sun, Guolei

2017-11-12

Graph embedding, aiming to learn low-dimensional representations for nodes in graphs, has attracted increasing attention due to its critical application including node classification, link prediction and clustering in social network analysis. Most existing algorithms for graph embedding only rely on the topology information and fail to use the copious information in nodes as well as edges. As a result, their performance for many tasks may not be satisfactory. In this thesis, we proposed a novel and general framework for graph embedding with rich text information (GERI) through constructing a heterogeneous network, in which we integrate node and edge content information with graph topology. Specially, we designed a novel biased random walk to explore the constructed heterogeneous network with the notion of flexible neighborhood. Our sampling strategy can compromise between BFS and DFS local search on heterogeneous graph. To further improve our algorithm, we proposed semi-supervised GERI (SGERI), which learns graph embedding in an discriminative manner through heterogeneous network with label information. The efficacy of our method is demonstrated by extensive comparison experiments with 9 baselines over multi-label and multi-class classification on various datasets including Citeseer, Cora, DBLP and Wiki. It shows that GERI improves the Micro-F1 and Macro-F1 of node classification up to 10%, and SGERI improves GERI by 5% in Wiki.

Graph run-length matrices for histopathological image segmentation.

Science.gov (United States)

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.

Topics in graph theory graphs and their Cartesian product

CERN Document Server

Imrich, Wilfried; Rall, Douglas F

2008-01-01

From specialists in the field, you will learn about interesting connections and recent developments in the field of graph theory by looking in particular at Cartesian products-arguably the most important of the four standard graph products. Many new results in this area appear for the first time in print in this book. Written in an accessible way, this book can be used for personal study in advanced applications of graph theory or for an advanced graph theory course.

Identifying Stages in a Learning Hierarchy for Use in Formative Assessment--The Example of Line Graphs

Science.gov (United States)

Stacey, Kaye; Price, Beth; Steinle, Vicki

2012-01-01

This paper discusses issues arising in the design of questions to use in an on-line computer-based formative assessment system, focussing on how best to identify the stages of a learning hierarchy for reporting to teachers. Data from several hundred students is used to illustrate how design decisions have been made for a test on interpreting line…

Handbook of graph grammars and computing by graph transformation

CERN Document Server

Engels, G; Kreowski, H J; Rozenberg, G

1999-01-01

Graph grammars originated in the late 60s, motivated by considerations about pattern recognition and compiler construction. Since then, the list of areas which have interacted with the development of graph grammars has grown quite impressively. Besides the aforementioned areas, it includes software specification and development, VLSI layout schemes, database design, modeling of concurrent systems, massively parallel computer architectures, logic programming, computer animation, developmental biology, music composition, visual languages, and many others.The area of graph grammars and graph tran

Structuring heterogeneous biological information using fuzzy clustering of k-partite graphs

Directory of Open Access Journals (Sweden)

Theis Fabian J

2010-10-01

Full Text Available Abstract Background Extensive and automated data integration in bioinformatics facilitates the construction of large, complex biological networks. However, the challenge lies in the interpretation of these networks. While most research focuses on the unipartite or bipartite case, we address the more general but common situation of k-partite graphs. These graphs contain k different node types and links are only allowed between nodes of different types. In order to reveal their structural organization and describe the contained information in a more coarse-grained fashion, we ask how to detect clusters within each node type. Results Since entities in biological networks regularly have more than one function and hence participate in more than one cluster, we developed a k-partite graph partitioning algorithm that allows for overlapping (fuzzy clusters. It determines for each node a degree of membership to each cluster. Moreover, the algorithm estimates a weighted k-partite graph that connects the extracted clusters. Our method is fast and efficient, mimicking the multiplicative update rules commonly employed in algorithms for non-negative matrix factorization. It facilitates the decomposition of networks on a chosen scale and therefore allows for analysis and interpretation of structures on various resolution levels. Applying our algorithm to a tripartite disease-gene-protein complex network, we were able to structure this graph on a large scale into clusters that are functionally correlated and biologically meaningful. Locally, smaller clusters enabled reclassification or annotation of the clusters' elements. We exemplified this for the transcription factor MECP2. Conclusions In order to cope with the overwhelming amount of information available from biomedical literature, we need to tackle the challenge of finding structures in large networks with nodes of multiple types. To this end, we presented a novel fuzzy k-partite graph partitioning

Utilization of graph theory in security analysis of power grid

Directory of Open Access Journals (Sweden)

Dalibor Válek

2014-12-01

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

A Qualitative Interpretation of Residual Magnetic Anomaly using ...

African Journals Online (AJOL)

A Qualitative Interpretation of Residual Magnetic Anomaly using Ground ... The magnetic data was collected using a G816 proton precision magnetometer. ... Analysis of residual anomaly graph reveals the existence of some structural features ...

Centrosymmetric Graphs And A Lower Bound For Graph Energy Of Fullerenes

Directory of Open Access Journals (Sweden)

Katona Gyula Y.

2014-11-01

Full Text Available The energy of a molecular graph G is defined as the summation of the absolute values of the eigenvalues of adjacency matrix of a graph G. In this paper, an infinite class of fullerene graphs with 10n vertices, n ≥ 2, is considered. By proving centrosymmetricity of the adjacency matrix of these fullerene graphs, a lower bound for its energy is given. Our method is general and can be extended to other class of fullerene graphs.

Graphs and Homomorphisms

CERN Document Server

Hell, Pavol

2004-01-01

This is a book about graph homomorphisms. Graph theory is now an established discipline but the study of graph homomorphisms has only recently begun to gain wide acceptance and interest. The subject gives a useful perspective in areas such as graph reconstruction, products, fractional and circular colourings, and has applications in complexity theory, artificial intelligence, telecommunication, and, most recently, statistical physics.Based on the authors' lecture notes for graduate courses, this book can be used as a textbook for a second course in graph theory at 4th year or master's level an

Expert and Novice Approaches to Using Graphs: Evidence from Eye-Track Experiments

Science.gov (United States)

Wirth, K. R.; Lindgren, J. M.

2015-12-01

Professionals and students in geology use an array of graphs to study the earth, but relatively little detail is known about how users interact with these graphs. Comprehension of graphical information in the earth sciences is further complicated by the common use of non-traditional formats (e.g., inverted axes, logarithmic scales, normalized plots, ternary diagrams). Many educators consider graph-reading skills an important outcome of general education science curricula, so it is critical that we understand both the development of graph-reading skills and the instructional practices that are most efficacious. Eye-tracking instruments provide quantitative information about eye movements and offer important insights into the development of expertise in graph use. We measured the graph reading skills and eye movements of novices (students with a variety of majors and educational attainment) and experts (faculty and staff from a variety of disciplines) while observing traditional and non-traditional graph formats. Individuals in the expert group consistently demonstrated significantly greater accuracy in responding to questions (e.g., retrieval, interpretation, prediction) about graphs. Among novices, only the number of college math and science courses correlated with response accuracy. Interestingly, novices and experts exhibited similar eye-tracks when they first encountered a new graph; they typically scanned through the title, x and y-axes, and data regions in the first 5-15 seconds. However, experts are readily distinguished from novices by a greater number of eye movements (20-35%) between the data and other graph elements (e.g., title, x-axis, y-axis) both during and after the initial orientation phase. We attribute the greater eye movements between the different graph elements an outcome of the generally better-developed self-regulation skills (goal-setting, monitoring, self-evaluation) that likely characterize individuals in our expert group.

Generating QCD amplitudes in the color-flow basis with MadGraph

International Nuclear Information System (INIS)

Hagiwara, Kaoru; Takaesu, Yoshitaro

2011-01-01

We propose to make use of the off-shell recursive relations with the color-flow decomposition in the calculation of QCD amplitudes on MadGraph. We introduce colored quarks and their interactions with nine gluons in the color-flow basis plus an Abelian gluon on MadGraph, such that it generates helicity amplitudes in the color-flow basis with off-shell recursive formulae for multi-gluon sub-amplitudes. We demonstrate calculations of up to 5-jet processes such as gg→5g, u anti u→5g and uu→uuggg. Although our demonstration is limited, it paves the way to evaluate amplitudes with more quark lines and gluons with MadGraph. (orig.)

Approximating centrality in evolving graphs: toward sublinearity

Science.gov (United States)

Priest, Benjamin W.; Cybenko, George

2017-05-01

The identification of important nodes is a ubiquitous problem in the analysis of social networks. Centrality indices (such as degree centrality, closeness centrality, betweenness centrality, PageRank, and others) are used across many domains to accomplish this task. However, the computation of such indices is expensive on large graphs. Moreover, evolving graphs are becoming increasingly important in many applications. It is therefore desirable to develop on-line algorithms that can approximate centrality measures using memory sublinear in the size of the graph. We discuss the challenges facing the semi-streaming computation of many centrality indices. In particular, we apply recent advances in the streaming and sketching literature to provide a preliminary streaming approximation algorithm for degree centrality utilizing CountSketch and a multi-pass semi-streaming approximation algorithm for closeness centrality leveraging a spanner obtained through iteratively sketching the vertex-edge adjacency matrix. We also discuss possible ways forward for approximating betweenness centrality, as well as spectral measures of centrality. We provide a preliminary result using sketched low-rank approximations to approximate the output of the HITS algorithm.

Decomposing Oriented Graphs into Six Locally Irregular Oriented Graphs

DEFF Research Database (Denmark)

Bensmail, Julien; Renault, Gabriel

2016-01-01

An undirected graph G is locally irregular if every two of its adjacent vertices have distinct degrees. We say that G is decomposable into k locally irregular graphs if there exists a partition E1∪E2∪⋯∪Ek of the edge set E(G) such that each Ei induces a locally irregular graph. It was recently co...

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

Directory of Open Access Journals (Sweden)

K. Vasudevan

2010-10-01

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

Tangent Lines without Derivatives for Quadratic and Cubic Equations

Science.gov (United States)

Carroll, William J.

2009-01-01

In the quadratic equation, y = ax[superscript 2] + bx + c, the equation y = bx + c is identified as the equation of the line tangent to the parabola at its y-intercept. This is extended to give a convenient method of graphing tangent lines at any point on the graph of a quadratic or a cubic equation. (Contains 5 figures.)

Non-heuristic reduction of the graph in graph-cut optimization

International Nuclear Information System (INIS)

Malgouyres, François; Lermé, Nicolas

2012-01-01

During the last ten years, graph cuts had a growing impact in shape optimization. In particular, they are commonly used in applications of shape optimization such as image processing, computer vision and computer graphics. Their success is due to their ability to efficiently solve (apparently) difficult shape optimization problems which typically involve the perimeter of the shape. Nevertheless, solving problems with a large number of variables remains computationally expensive and requires a high memory usage since underlying graphs sometimes involve billion of nodes and even more edges. Several strategies have been proposed in the literature to improve graph-cuts in this regards. In this paper, we give a formal statement which expresses that a simple and local test performed on every node before its construction permits to avoid the construction of useless nodes for the graphs typically encountered in image processing and vision. A useless node is such that the value of the maximum flow in the graph does not change when removing the node from the graph. Such a test therefore permits to limit the construction of the graph to a band of useful nodes surrounding the final cut.

Graph embedding with rich information through heterogeneous graph

KAUST Repository

Sun, Guolei

2017-01-01

Graph embedding, aiming to learn low-dimensional representations for nodes in graphs, has attracted increasing attention due to its critical application including node classification, link prediction and clustering in social network analysis. Most

Graphing trillions of triangles.

Science.gov (United States)

Burkhardt, Paul

2017-07-01

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

Adaptive Graph Convolutional Neural Networks

OpenAIRE

Li, Ruoyu; Wang, Sheng; Zhu, Feiyun; Huang, Junzhou

2018-01-01

Graph Convolutional Neural Networks (Graph CNNs) are generalizations of classical CNNs to handle graph data such as molecular data, point could and social networks. Current filters in graph CNNs are built for fixed and shared graph structure. However, for most real data, the graph structures varies in both size and connectivity. The paper proposes a generalized and flexible graph CNN taking data of arbitrary graph structure as input. In that way a task-driven adaptive graph is learned for eac...

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

Directory of Open Access Journals (Sweden)

Mehmet Fatih Öçal

2017-01-01

Full Text Available Graphing function is an important issue in mathematics education due to its use in various areas of mathematics and its potential roles for students to enhance learning mathematics. The use of some graphing software assists students’ learning during graphing functions. However, the display of graphs of functions that students sketched by hand may be relatively different when compared to the correct forms sketched using graphing software. The possible misleading effects of this situation brought a discussion of a misconception (asymptote misconception on graphing functions. The purpose of this study is two- fold. First of all, this study investigated whether using graphing software (GeoGebra in this case helps students to determine and resolve this misconception in calculus classrooms. Second, the reasons for this misconception are sought. The multiple case study was utilized in this study. University students in two calculus classrooms who received instructions with (35 students or without GeoGebra assisted instructions (32 students were compared according to whether they fell into this misconception on graphing basic functions (1/x, lnx, ex. In addition, students were interviewed to reveal the reasons behind this misconception. Data were analyzed by means of descriptive and content analysis methods. The findings indicated that those who received GeoGebra assisted instruction were better in resolving it. In addition, the reasons behind this misconception were found to be teacher-based, exam-based and some other factors.

High Dimensional Spectral Graph Theory and Non-backtracking Random Walks on Graphs

Science.gov (United States)

Kempton, Mark

This thesis has two primary areas of focus. First we study connection graphs, which are weighted graphs in which each edge is associated with a d-dimensional rotation matrix for some fixed dimension d, in addition to a scalar weight. Second, we study non-backtracking random walks on graphs, which are random walks with the additional constraint that they cannot return to the immediately previous state at any given step. Our work in connection graphs is centered on the notion of consistency, that is, the product of rotations moving from one vertex to another is independent of the path taken, and a generalization called epsilon-consistency. We present higher dimensional versions of the combinatorial Laplacian matrix and normalized Laplacian matrix from spectral graph theory, and give results characterizing the consistency of a connection graph in terms of the spectra of these matrices. We generalize several tools from classical spectral graph theory, such as PageRank and effective resistance, to apply to connection graphs. We use these tools to give algorithms for sparsification, clustering, and noise reduction on connection graphs. In non-backtracking random walks, we address the question raised by Alon et. al. concerning how the mixing rate of a non-backtracking random walk to its stationary distribution compares to the mixing rate for an ordinary random walk. Alon et. al. address this question for regular graphs. We take a different approach, and use a generalization of Ihara's Theorem to give a new proof of Alon's result for regular graphs, and to extend the result to biregular graphs. Finally, we give a non-backtracking version of Polya's Random Walk Theorem for 2-dimensional grids.

X-Graphs: Language and Algorithms for Heterogeneous Graph Streams

Science.gov (United States)

2017-09-01

are widely used by academia and industry. 15. SUBJECT TERMS Data Analytics, Graph Analytics, High-Performance Computing 16. SECURITY CLASSIFICATION...form the core of the DeepDive Knowledge Construction System. 2 INTRODUCTION The goal of the X-Graphs project was to develop computational techniques...memory multicore machine. Ringo is based on Snap.py and SNAP, and uses Python . Ringo now allows the integration of Delite DSL Framework Graph

On the sizes of expander graphs and minimum distances of graph codes

DEFF Research Database (Denmark)

Høholdt, Tom; Justesen, Jørn

2014-01-01

We give lower bounds for the minimum distances of graph codes based on expander graphs. The bounds depend only on the second eigenvalue of the graph and the parameters of the component codes. We also give an upper bound on the size of a degree regular graph with given second eigenvalue....

Similarity Measure of Graphs

Directory of Open Access Journals (Sweden)

Amine Labriji

2017-07-01

Full Text Available The topic of identifying the similarity of graphs was considered as highly recommended research field in the Web semantic, artificial intelligence, the shape recognition and information research. One of the fundamental problems of graph databases is finding similar graphs to a graph query. Existing approaches dealing with this problem are usually based on the nodes and arcs of the two graphs, regardless of parental semantic links. For instance, a common connection is not identified as being part of the similarity of two graphs in cases like two graphs without common concepts, the measure of similarity based on the union of two graphs, or the one based on the notion of maximum common sub-graph (SCM, or the distance of edition of graphs. This leads to an inadequate situation in the context of information research. To overcome this problem, we suggest a new measure of similarity between graphs, based on the similarity measure of Wu and Palmer. We have shown that this new measure satisfies the properties of a measure of similarities and we applied this new measure on examples. The results show that our measure provides a run time with a gain of time compared to existing approaches. In addition, we compared the relevance of the similarity values obtained, it appears that this new graphs measure is advantageous and  offers a contribution to solving the problem mentioned above.

Multiplex visibility graphs to investigate recurrent neural network dynamics

Science.gov (United States)

Bianchi, Filippo Maria; Livi, Lorenzo; Alippi, Cesare; Jenssen, Robert

2017-03-01

A recurrent neural network (RNN) is a universal approximator of dynamical systems, whose performance often depends on sensitive hyperparameters. Tuning them properly may be difficult and, typically, based on a trial-and-error approach. In this work, we adopt a graph-based framework to interpret and characterize internal dynamics of a class of RNNs called echo state networks (ESNs). We design principled unsupervised methods to derive hyperparameters configurations yielding maximal ESN performance, expressed in terms of prediction error and memory capacity. In particular, we propose to model time series generated by each neuron activations with a horizontal visibility graph, whose topological properties have been shown to be related to the underlying system dynamics. Successively, horizontal visibility graphs associated with all neurons become layers of a larger structure called a multiplex. We show that topological properties of such a multiplex reflect important features of ESN dynamics that can be used to guide the tuning of its hyperparamers. Results obtained on several benchmarks and a real-world dataset of telephone call data records show the effectiveness of the proposed methods.

Spectra of Graphs

NARCIS (Netherlands)

Brouwer, A.E.; Haemers, W.H.

2012-01-01

This book gives an elementary treatment of the basic material about graph spectra, both for ordinary, and Laplace and Seidel spectra. The text progresses systematically, by covering standard topics before presenting some new material on trees, strongly regular graphs, two-graphs, association

The impact of home care nurses' numeracy and graph literacy on comprehension of visual display information: implications for dashboard design.

Science.gov (United States)

Dowding, Dawn; Merrill, Jacqueline A; Onorato, Nicole; Barrón, Yolanda; Rosati, Robert J; Russell, David

2018-02-01

To explore home care nurses' numeracy and graph literacy and their relationship to comprehension of visualized data. A multifactorial experimental design using online survey software. Nurses were recruited from 2 Medicare-certified home health agencies. Numeracy and graph literacy were measured using validated scales. Nurses were randomized to 1 of 4 experimental conditions. Each condition displayed data for 1 of 4 quality indicators, in 1 of 4 different visualized formats (bar graph, line graph, spider graph, table). A mixed linear model measured the impact of numeracy, graph literacy, and display format on data understanding. In all, 195 nurses took part in the study. They were slightly more numerate and graph literate than the general population. Overall, nurses understood information presented in bar graphs most easily (88% correct), followed by tables (81% correct), line graphs (77% correct), and spider graphs (41% correct). Individuals with low numeracy and low graph literacy had poorer comprehension of information displayed across all formats. High graph literacy appeared to enhance comprehension of data regardless of numeracy capabilities. Clinical dashboards are increasingly used to provide information to clinicians in visualized format, under the assumption that visual display reduces cognitive workload. Results of this study suggest that nurses' comprehension of visualized information is influenced by their numeracy, graph literacy, and the display format of the data. Individual differences in numeracy and graph literacy skills need to be taken into account when designing dashboard technology. © The Author 2017. Published by Oxford University Press on behalf of the American Medical Informatics Association. All rights reserved. For Permissions, please email: journals.permissions@oup.com

Pattern graph rewrite systems

Directory of Open Access Journals (Sweden)

Aleks Kissinger

2014-03-01

Full Text Available String diagrams are a powerful tool for reasoning about physical processes, logic circuits, tensor networks, and many other compositional structures. Dixon, Duncan and Kissinger introduced string graphs, which are a combinatoric representations of string diagrams, amenable to automated reasoning about diagrammatic theories via graph rewrite systems. In this extended abstract, we show how the power of such rewrite systems can be greatly extended by introducing pattern graphs, which provide a means of expressing infinite families of rewrite rules where certain marked subgraphs, called !-boxes ("bang boxes", on both sides of a rule can be copied any number of times or removed. After reviewing the string graph formalism, we show how string graphs can be extended to pattern graphs and how pattern graphs and pattern rewrite rules can be instantiated to concrete string graphs and rewrite rules. We then provide examples demonstrating the expressive power of pattern graphs and how they can be applied to study interacting algebraic structures that are central to categorical quantum mechanics.

On middle cube graphs

Directory of Open Access Journals (Sweden)

C. Dalfo

2015-10-01

Full Text Available We study a family of graphs related to the $n$-cube. The middle cube graph of parameter k is the subgraph of $Q_{2k-1}$ induced by the set of vertices whose binary representation has either $k-1$ or $k$ number of ones. The middle cube graphs can be obtained from the well-known odd graphs by doubling their vertex set. Here we study some of the properties of the middle cube graphs in the light of the theory of distance-regular graphs. In particular, we completely determine their spectra (eigenvalues and their multiplicities, and associated eigenvectors.

Discrete Morse functions for graph configuration spaces

International Nuclear Information System (INIS)

Sawicki, A

2012-01-01

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

Graph visualization (Invited talk)

NARCIS (Netherlands)

Wijk, van J.J.; Kreveld, van M.J.; Speckmann, B.

2012-01-01

Black and white node link diagrams are the classic method to depict graphs, but these often fall short to give insight in large graphs or when attributes of nodes and edges play an important role. Graph visualization aims obtaining insight in such graphs using interactive graphical representations.

Adventures in graph theory

CERN Document Server

Joyner, W David

2017-01-01

This textbook acts as a pathway to higher mathematics by seeking and illuminating the connections between graph theory and diverse fields of mathematics, such as calculus on manifolds, group theory, algebraic curves, Fourier analysis, cryptography and other areas of combinatorics. An overview of graph theory definitions and polynomial invariants for graphs prepares the reader for the subsequent dive into the applications of graph theory. To pique the reader’s interest in areas of possible exploration, recent results in mathematics appear throughout the book, accompanied with examples of related graphs, how they arise, and what their valuable uses are. The consequences of graph theory covered by the authors are complicated and far-reaching, so topics are always exhibited in a user-friendly manner with copious graphs, exercises, and Sage code for the computation of equations. Samples of the book’s source code can be found at github.com/springer-math/adventures-in-graph-theory. The text is geared towards ad...

Polarization of X-ray lines emitted from plasma-focus discharges; Problems of interpretation

International Nuclear Information System (INIS)

Jakubowski, L.

2002-01-01

In high current pulse discharges of the Plasma Focus (PF) type, inside the collapsing pinch column, there are formed local micro-regions of high-density and high-temperature plasma, so-called hot spots. Individual hot spots are separated in space and time. Each hot spot is characterized by its specific electron concentration and temperature, as well as by the emission of X-ray lines with different polarization. When numerous hot spots are produced it is impossible to determine local plasma parameters and to interpret the polarization effects. To eliminate this problem this study was devoted to the realization of PF-type discharges with single hot spot only. It has been achieved by a choice of the electrode configuration, which facilitated the formation of a single hot spot emitting intense X-ray lines. At the chosen experimental conditions it was possible to determine local plasma parameters and to demonstrate evident differences in the polarization of the observed X-ray lines. (author)

Polarization of x-ray lines emitted from plasma-focus discharges; Problems of interpretation

International Nuclear Information System (INIS)

Jakubowski, L.; Sadowski, M.J.; Baronova, E.O.

2003-01-01

In high current pulse discharges of the Plasma Focus (PF) type, inside the collapsing pinch column, there are formed local micro-regions of high-density and high-temperature plasma, so-called hot spots. Individual hot spots are separated in space and time. Each hot spot is characterized by its specific electron concentration and temperature, as well as by the emission of X-ray lines with different polarization. When numerous hot spots are produced it is impossible to determine local plasma parameters and to interpretate the polarization effects. To eliminate this problem this study was devoted to the realization of PF-type discharges with single hot spot only. It has been achieved by a choice of the electrode configuration, which facilitated the formation of a single hot spot emitting intense X-ray lines. At the chosen experimental conditions it was possible to determine local plasma parameters and to demonstrate evident differences in the polarization of the observed X-ray lines. (author)

Distance-regular graphs

NARCIS (Netherlands)

van Dam, Edwin R.; Koolen, Jack H.; Tanaka, Hajime

2016-01-01

This is a survey of distance-regular graphs. We present an introduction to distance-regular graphs for the reader who is unfamiliar with the subject, and then give an overview of some developments in the area of distance-regular graphs since the monograph 'BCN'[Brouwer, A.E., Cohen, A.M., Neumaier,

Geometric covers, graph orientations, counter games

DEFF Research Database (Denmark)

Berglin, Edvin

-directed graph is dynamic (can be altered by some outside actor), some orientations may need to be reversed in order to maintain the low out-degree. We present a new algorithm that is simpler than earlier work, yet matches or outperforms the efficiency of these results with very few exceptions. Counter games...... example is Line Cover, also known as Point-Line Cover, where a set of points in a geometric space are to be covered by placing a restricted number of lines. We present new FPT algorithms for the sub-family Curve Cover (which includes Line Cover), as well as for Hyperplane Cover restricted to R 3 (i...... are a type of abstract game played over a set of counters holding values, and these values may be moved between counters according to some set of rules. Typically they are played between two players: the adversary who tries to concentrate the greatest value possible in a single counter, and the benevolent...

On the strong metric dimension of generalized butterfly graph, starbarbell graph, and {C}_{m}\\odot {P}_{n} graph

Science.gov (United States)

Yunia Mayasari, Ratih; Atmojo Kusmayadi, Tri

2018-04-01

Let G be a connected graph with vertex set V(G) and edge set E(G). For every pair of vertices u,v\\in V(G), the interval I[u, v] between u and v to be the collection of all vertices that belong to some shortest u ‑ v path. A vertex s\\in V(G) strongly resolves two vertices u and v if u belongs to a shortest v ‑ s path or v belongs to a shortest u ‑ s path. A vertex set S of G is a strong resolving set of G if every two distinct vertices of G are strongly resolved by some vertex of S. The strong metric basis of G is a strong resolving set with minimal cardinality. The strong metric dimension sdim(G) of a graph G is defined as the cardinality of strong metric basis. In this paper we determine the strong metric dimension of a generalized butterfly graph, starbarbell graph, and {C}mȯ {P}n graph. We obtain the strong metric dimension of generalized butterfly graph is sdim(BFn ) = 2n ‑ 2. The strong metric dimension of starbarbell graph is sdim(S{B}{m1,{m}2,\\ldots,{m}n})={\\sum }i=1n({m}i-1)-1. The strong metric dimension of {C}mȯ {P}n graph are sdim({C}mȯ {P}n)=2m-1 for m > 3 and n = 2, and sdim({C}mȯ {P}n)=2m-2 for m > 3 and n > 2.

Subgraph detection using graph signals

KAUST Repository

Chepuri, Sundeep Prabhakar

2017-03-06

In this paper we develop statistical detection theory for graph signals. In particular, given two graphs, namely, a background graph that represents an usual activity and an alternative graph that represents some unusual activity, we are interested in answering the following question: To which of the two graphs does the observed graph signal fit the best? To begin with, we assume both the graphs are known, and derive an optimal Neyman-Pearson detector. Next, we derive a suboptimal detector for the case when the alternative graph is not known. The developed theory is illustrated with numerical experiments.

Subgraph detection using graph signals

KAUST Repository

Chepuri, Sundeep Prabhakar; Leus, Geert

2017-01-01

In this paper we develop statistical detection theory for graph signals. In particular, given two graphs, namely, a background graph that represents an usual activity and an alternative graph that represents some unusual activity, we are interested in answering the following question: To which of the two graphs does the observed graph signal fit the best? To begin with, we assume both the graphs are known, and derive an optimal Neyman-Pearson detector. Next, we derive a suboptimal detector for the case when the alternative graph is not known. The developed theory is illustrated with numerical experiments.

Graph spectrum

NARCIS (Netherlands)

Brouwer, A.E.; Haemers, W.H.; Brouwer, A.E.; Haemers, W.H.

2012-01-01

This chapter presents some simple results on graph spectra.We assume the reader is familiar with elementary linear algebra and graph theory. Throughout, J will denote the all-1 matrix, and 1 is the all-1 vector.

Pragmatic Graph Rewriting Modifications

OpenAIRE

Rodgers, Peter; Vidal, Natalia

1999-01-01

We present new pragmatic constructs for easing programming in visual graph rewriting programming languages. The first is a modification to the rewriting process for nodes the host graph, where nodes specified as 'Once Only' in the LHS of a rewrite match at most once with a corresponding node in the host graph. This reduces the previously common use of tags to indicate the progress of matching in the graph. The second modification controls the application of LHS graphs, where those specified a...

The STAPL Parallel Graph Library

KAUST Repository

Harshvardhan,

2013-01-01

This paper describes the stapl Parallel Graph Library, a high-level framework that abstracts the user from data-distribution and parallelism details and allows them to concentrate on parallel graph algorithm development. It includes a customizable distributed graph container and a collection of commonly used parallel graph algorithms. The library introduces pGraph pViews that separate algorithm design from the container implementation. It supports three graph processing algorithmic paradigms, level-synchronous, asynchronous and coarse-grained, and provides common graph algorithms based on them. Experimental results demonstrate improved scalability in performance and data size over existing graph libraries on more than 16,000 cores and on internet-scale graphs containing over 16 billion vertices and 250 billion edges. © Springer-Verlag Berlin Heidelberg 2013.

Topic Model for Graph Mining.

Science.gov (United States)

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.

Modern graph theory

CERN Document Server

Bollobás, Béla

1998-01-01

The time has now come when graph theory should be part of the education of every serious student of mathematics and computer science, both for its own sake and to enhance the appreciation of mathematics as a whole. This book is an in-depth account of graph theory, written with such a student in mind; it reflects the current state of the subject and emphasizes connections with other branches of pure mathematics. The volume grew out of the author's earlier book, Graph Theory -- An Introductory Course, but its length is well over twice that of its predecessor, allowing it to reveal many exciting new developments in the subject. Recognizing that graph theory is one of several courses competing for the attention of a student, the book contains extensive descriptive passages designed to convey the flavor of the subject and to arouse interest. In addition to a modern treatment of the classical areas of graph theory such as coloring, matching, extremal theory, and algebraic graph theory, the book presents a detailed ...

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

Science.gov (United States)

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.

On-line Ramsey Numbers for Paths and Stars

Directory of Open Access Journals (Sweden)

Jaroslaw Grytczuk

2008-08-01

Full Text Available We study on-line version of size-Ramsey numbers of graphs defined via a game played between Builder and Painter: in one round Builder joins two vertices by an edge and Painter paints it red or blue. The goal of Builder is to force Painter to create a monochromatic copy of a fixed graph H in as few rounds as possible. The minimum number of rounds (assuming both players play perfectly is the on-line Ramsey number r(H of the graph H. We determine exact values of r(H for a few short paths and obtain a general upper bound r(Pn ≤ 4n-7. We also study asymmetric version of this parameter when one of the target graphs is a star Sn with n edges. We prove that r(Sn,H≤n ·e(H when H is any tree, cycle or clique.

Introduction to quantum graphs

CERN Document Server

Berkolaiko, Gregory

2012-01-01

A "quantum graph" is a graph considered as a one-dimensional complex and equipped with a differential operator ("Hamiltonian"). Quantum graphs arise naturally as simplified models in mathematics, physics, chemistry, and engineering when one considers propagation of waves of various nature through a quasi-one-dimensional (e.g., "meso-" or "nano-scale") system that looks like a thin neighborhood of a graph. Works that currently would be classified as discussing quantum graphs have been appearing since at least the 1930s, and since then, quantum graphs techniques have been applied successfully in various areas of mathematical physics, mathematics in general and its applications. One can mention, for instance, dynamical systems theory, control theory, quantum chaos, Anderson localization, microelectronics, photonic crystals, physical chemistry, nano-sciences, superconductivity theory, etc. Quantum graphs present many non-trivial mathematical challenges, which makes them dear to a mathematician's heart. Work on qu...

Graph Generator Survey

Energy Technology Data Exchange (ETDEWEB)

Lothian, Joshua [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Powers, Sarah S. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Sullivan, Blair D. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Baker, Matthew B. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Schrock, Jonathan [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Poole, Stephen W. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

2013-10-01

The benchmarking effort within the Extreme Scale Systems Center at Oak Ridge National Laboratory seeks to provide High Performance Computing benchmarks and test suites of interest to the DoD sponsor. The work described in this report is a part of the effort focusing on graph generation. A previously developed benchmark, SystemBurn, allowed the emulation of different application behavior profiles within a single framework. To complement this effort, similar capabilities are desired for graph-centric problems. This report examines existing synthetic graph generator implementations in preparation for further study on the properties of their generated synthetic graphs.

Functions and graphs

CERN Document Server

Gelfand, I M; Shnol, E E

1969-01-01

The second in a series of systematic studies by a celebrated mathematician I. M. Gelfand and colleagues, this volume presents students with a well-illustrated sequence of problems and exercises designed to illuminate the properties of functions and graphs. Since readers do not have the benefit of a blackboard on which a teacher constructs a graph, the authors abandoned the customary use of diagrams in which only the final form of the graph appears; instead, the book's margins feature step-by-step diagrams for the complete construction of each graph. The first part of the book employs simple fu

Loose Graph Simulations

DEFF Research Database (Denmark)

Mansutti, Alessio; Miculan, Marino; Peressotti, Marco

2017-01-01

We introduce loose graph simulations (LGS), a new notion about labelled graphs which subsumes in an intuitive and natural way subgraph isomorphism (SGI), regular language pattern matching (RLPM) and graph simulation (GS). Being a unification of all these notions, LGS allows us to express directly...... also problems which are “mixed” instances of previous ones, and hence which would not fit easily in any of them. After the definition and some examples, we show that the problem of finding loose graph simulations is NP-complete, we provide formal translation of SGI, RLPM, and GS into LGSs, and we give...

Guidelines for Graphing Data with Microsoft[R] Office 2007[TM], Office 2010[TM], and Office for Mac[TM] 2008 and 2011

Science.gov (United States)

Barton, Erin E.; Reichow, Brian

2012-01-01

The interpretation of single-case data requires systematic visual analysis across and within conditions. Graphs are a vital component for analyzing and communicating single-case design data and a necessary tool for applied researchers and practitioners. Several articles have been published with task analyses for graphing data with the new versions…

From modular invariants to graphs: the modular splitting method

International Nuclear Information System (INIS)

Isasi, E; Schieber, G

2007-01-01

We start with a given modular invariant M of a two-dimensional su-hat(n) k conformal field theory (CFT) and present a general method for solving the Ocneanu modular splitting equation and then determine, in a step-by-step explicit construction (1) the generalized partition functions corresponding to the introduction of boundary conditions and defect lines; (2) the quantum symmetries of the higher ADE graph G associated with the initial modular invariant M. Note that one does not suppose here that the graph G is already known, since it appears as a by-product of the calculations. We analyse several su-hat(3) k exceptional cases at levels 5 and 9

Interactive graphics for the Macintosh: software review of FlexiGraphs.

Science.gov (United States)

Antonak, R F

1990-01-01

While this product is clearly unique, its usefulness to individuals outside small business environments is somewhat limited. FlexiGraphs is, however, a reasonable first attempt to design a microcomputer software package that controls data through interactive editing within a graph. Although the graphics capabilities of mainframe programs such as MINITAB (Ryan, Joiner, & Ryan, 1981) and the graphic manipulations available through exploratory data analysis (e.g., Velleman & Hoaglin, 1981) will not be surpassed anytime soon by this program, a researcher may want to add this program to a software library containing other Macintosh statistics, drawing, and graphics programs if only to obtain the easy-to-obtain curve fitting and line smoothing options. I welcome the opportunity to review the enhanced "scientific" version of FlexiGraphs that the author of the program indicates is currently under development. An MS-DOS version of the program should be available within the year.

Graph Design via Convex Optimization: Online and Distributed Perspectives

Science.gov (United States)

Meng, De

Network and graph have long been natural abstraction of relations in a variety of applications, e.g. transportation, power system, social network, communication, electrical circuit, etc. As a large number of computation and optimization problems are naturally defined on graphs, graph structures not only enable important properties of these problems, but also leads to highly efficient distributed and online algorithms. For example, graph separability enables the parallelism for computation and operation as well as limits the size of local problems. More interestingly, graphs can be defined and constructed in order to take best advantage of those problem properties. This dissertation focuses on graph structure and design in newly proposed optimization problems, which establish a bridge between graph properties and optimization problem properties. We first study a new optimization problem called Geodesic Distance Maximization Problem (GDMP). Given a graph with fixed edge weights, finding the shortest path, also known as the geodesic, between two nodes is a well-studied network flow problem. We introduce the Geodesic Distance Maximization Problem (GDMP): the problem of finding the edge weights that maximize the length of the geodesic subject to convex constraints on the weights. We show that GDMP is a convex optimization problem for a wide class of flow costs, and provide a physical interpretation using the dual. We present applications of the GDMP in various fields, including optical lens design, network interdiction, and resource allocation in the control of forest fires. We develop an Alternating Direction Method of Multipliers (ADMM) by exploiting specific problem structures to solve large-scale GDMP, and demonstrate its effectiveness in numerical examples. We then turn our attention to distributed optimization on graph with only local communication. Distributed optimization arises in a variety of applications, e.g. distributed tracking and localization, estimation

Sequential Optimization of Paths in Directed Graphs Relative to Different Cost Functions

KAUST Repository

Mahayni, Malek A.

2011-07-01

Finding optimal paths in directed graphs is a wide area of research that has received much of attention in theoretical computer science due to its importance in many applications (e.g., computer networks and road maps). Many algorithms have been developed to solve the optimal paths problem with different kinds of graphs. An algorithm that solves the problem of paths’ optimization in directed graphs relative to different cost functions is described in [1]. It follows an approach extended from the dynamic programming approach as it solves the problem sequentially and works on directed graphs with positive weights and no loop edges. The aim of this thesis is to implement and evaluate that algorithm to find the optimal paths in directed graphs relative to two different cost functions ( , ). A possible interpretation of a directed graph is a network of roads so the weights for the function represent the length of roads, whereas the weights for the function represent a constraint of the width or weight of a vehicle. The optimization aim for those two functions is to minimize the cost relative to the function and maximize the constraint value associated with the function. This thesis also includes finding and proving the relation between the two different cost functions ( , ). When given a value of one function, we can find the best possible value for the other function. This relation is proven theoretically and also implemented and experimented using Matlab®[2].

Methods of filtering the graph images of the functions

Directory of Open Access Journals (Sweden)

Олександр Григорович Бурса

2017-06-01

Full Text Available The theoretical aspects of cleaning raster images of scanned graphs of functions from digital, chromatic and luminance distortions by using computer graphics techniques have been considered. The basic types of distortions characteristic of graph images of functions have been stated. To suppress the distortion several methods, providing for high-quality of the resulting images and saving their topological features, were suggested. The paper describes the techniques developed and improved by the authors: the method of cleaning the image of distortions by means of iterative contrasting, based on the step-by-step increase in image contrast in the graph by 1%; the method of small entities distortion restoring, based on the thinning of the known matrix of contrast increase filter (the allowable dimensions of the nucleus dilution radius convolution matrix, which provide for the retention of the graph lines have been established; integration technique of the noise reduction method by means of contrasting and distortion restoring method of small entities with known σ-filter. Each method in the complex has been theoretically substantiated. The developed methods involve treatment of graph images as the entire image (global processing and its fragments (local processing. The metrics assessing the quality of the resulting image with the global and local processing have been chosen, the substantiation of the choice as well as the formulas have been given. The proposed complex methods of cleaning the graphs images of functions from grayscale image distortions is adaptive to the form of an image carrier, the distortion level in the image and its distribution. The presented results of testing the developed complex of methods for a representative sample of images confirm its effectiveness

Autoregressive Moving Average Graph Filtering

OpenAIRE

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

2016-01-01

One of the cornerstones of the field of signal processing on graphs are graph filters, direct analogues of classical filters, but intended for signals defined on graphs. This work brings forth new insights on the distributed graph filtering problem. We design a family of autoregressive moving average (ARMA) recursions, which (i) are able to approximate any desired graph frequency response, and (ii) give exact solutions for tasks such as graph signal denoising and interpolation. The design phi...

On cyclic orthogonal double covers of circulant graphs by special infinite graphs

Directory of Open Access Journals (Sweden)

R. El-Shanawany

2017-12-01

Full Text Available In this article, a technique to construct cyclic orthogonal double covers (CODCs of regular circulant graphs by certain infinite graph classes such as complete bipartite and tripartite graphs and disjoint union of butterfly and K1,2n−10 is introduced.

Quantum walks on quotient graphs

International Nuclear Information System (INIS)

Krovi, Hari; Brun, Todd A.

2007-01-01

A discrete-time quantum walk on a graph Γ is the repeated application of a unitary evolution operator to a Hilbert space corresponding to the graph. If this unitary evolution operator has an associated group of symmetries, then for certain initial states the walk will be confined to a subspace of the original Hilbert space. Symmetries of the original graph, given by its automorphism group, can be inherited by the evolution operator. We show that a quantum walk confined to the subspace corresponding to this symmetry group can be seen as a different quantum walk on a smaller quotient graph. We give an explicit construction of the quotient graph for any subgroup H of the automorphism group and illustrate it with examples. The automorphisms of the quotient graph which are inherited from the original graph are the original automorphism group modulo the subgroup H used to construct it. The quotient graph is constructed by removing the symmetries of the subgroup H from the original graph. We then analyze the behavior of hitting times on quotient graphs. Hitting time is the average time it takes a walk to reach a given final vertex from a given initial vertex. It has been shown in earlier work [Phys. Rev. A 74, 042334 (2006)] that the hitting time for certain initial states of a quantum walks can be infinite, in contrast to classical random walks. We give a condition which determines whether the quotient graph has infinite hitting times given that they exist in the original graph. We apply this condition for the examples discussed and determine which quotient graphs have infinite hitting times. All known examples of quantum walks with hitting times which are short compared to classical random walks correspond to systems with quotient graphs much smaller than the original graph; we conjecture that the existence of a small quotient graph with finite hitting times is necessary for a walk to exhibit a quantum speedup

Fundamentals of algebraic graph transformation

CERN Document Server

Ehrig, Hartmut; Prange, Ulrike; Taentzer, Gabriele

2006-01-01

Graphs are widely used to represent structural information in the form of objects and connections between them. Graph transformation is the rule-based manipulation of graphs, an increasingly important concept in computer science and related fields. This is the first textbook treatment of the algebraic approach to graph transformation, based on algebraic structures and category theory. Part I is an introduction to the classical case of graph and typed graph transformation. In Part II basic and advanced results are first shown for an abstract form of replacement systems, so-called adhesive high-level replacement systems based on category theory, and are then instantiated to several forms of graph and Petri net transformation systems. Part III develops typed attributed graph transformation, a technique of key relevance in the modeling of visual languages and in model transformation. Part IV contains a practical case study on model transformation and a presentation of the AGG (attributed graph grammar) tool envir...

Graph-based modelling in engineering

CERN Document Server

Rysiński, Jacek

2017-01-01

This book presents versatile, modern and creative applications of graph theory in mechanical engineering, robotics and computer networks. Topics related to mechanical engineering include e.g. machine and mechanism science, mechatronics, robotics, gearing and transmissions, design theory and production processes. The graphs treated are simple graphs, weighted and mixed graphs, bond graphs, Petri nets, logical trees etc. The authors represent several countries in Europe and America, and their contributions show how different, elegant, useful and fruitful the utilization of graphs in modelling of engineering systems can be. .

BootGraph: probabilistic fiber tractography using bootstrap algorithms and graph theory.

Science.gov (United States)

Vorburger, Robert S; Reischauer, Carolin; Boesiger, Peter

2013-02-01

Bootstrap methods have recently been introduced to diffusion-weighted magnetic resonance imaging to estimate the measurement uncertainty of ensuing diffusion parameters directly from the acquired data without the necessity to assume a noise model. These methods have been previously combined with deterministic streamline tractography algorithms to allow for the assessment of connection probabilities in the human brain. Thereby, the local noise induced disturbance in the diffusion data is accumulated additively due to the incremental progression of streamline tractography algorithms. Graph based approaches have been proposed to overcome this drawback of streamline techniques. For this reason, the bootstrap method is in the present work incorporated into a graph setup to derive a new probabilistic fiber tractography method, called BootGraph. The acquired data set is thereby converted into a weighted, undirected graph by defining a vertex in each voxel and edges between adjacent vertices. By means of the cone of uncertainty, which is derived using the wild bootstrap, a weight is thereafter assigned to each edge. Two path finding algorithms are subsequently applied to derive connection probabilities. While the first algorithm is based on the shortest path approach, the second algorithm takes all existing paths between two vertices into consideration. Tracking results are compared to an established algorithm based on the bootstrap method in combination with streamline fiber tractography and to another graph based algorithm. The BootGraph shows a very good performance in crossing situations with respect to false negatives and permits incorporating additional constraints, such as a curvature threshold. By inheriting the advantages of the bootstrap method and graph theory, the BootGraph method provides a computationally efficient and flexible probabilistic tractography setup to compute connection probability maps and virtual fiber pathways without the drawbacks of

Equipackable graphs

DEFF Research Database (Denmark)

Vestergaard, Preben Dahl; Hartnell, Bert L.

2006-01-01

There are many results dealing with the problem of decomposing a fixed graph into isomorphic subgraphs. There has also been work on characterizing graphs with the property that one can delete the edges of a number of edge disjoint copies of the subgraph and, regardless of how that is done, the gr...

Handbook of graph drawing and visualization

CERN Document Server

Tamassia, Roberto

2013-01-01

Planarity Testing and Embedding Maurizio PatrignaniCrossings and Planarization Christoph Buchheim, Markus Chimani, Carsten Gutwenger, Michael Jünger, and Petra MutzelSymmetric Graph Drawing Peter Eades and Seok-Hee HongProximity Drawings Giuseppe LiottaTree Drawing Algorithms Adrian RusuPlanar Straight-Line Drawing Algorithms Luca VismaraPlanar Orthogonal and Polyline Drawing Algorithms Christian A. Duncan and Michael T. GoodrichSpine and Radial Drawings Emilio Di Giacomo, Walter Didimo, and Giuseppe LiottaCircular Drawing Algorithms Janet M. Six and Ioannis G. TollisRectangular Drawing Algori

Khovanov homology of graph-links

Energy Technology Data Exchange (ETDEWEB)

Nikonov, Igor M [M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)

2012-08-31

Graph-links arise as the intersection graphs of turning chord diagrams of links. Speaking informally, graph-links provide a combinatorial description of links up to mutations. Many link invariants can be reformulated in the language of graph-links. Khovanov homology, a well-known and useful knot invariant, is defined for graph-links in this paper (in the case of the ground field of characteristic two). Bibliography: 14 titles.

Semantic Health Knowledge Graph: Semantic Integration of Heterogeneous Medical Knowledge and Services

Directory of Open Access Journals (Sweden)

Longxiang Shi

2017-01-01

Full Text Available With the explosion of healthcare information, there has been a tremendous amount of heterogeneous textual medical knowledge (TMK, which plays an essential role in healthcare information systems. Existing works for integrating and utilizing the TMK mainly focus on straightforward connections establishment and pay less attention to make computers interpret and retrieve knowledge correctly and quickly. In this paper, we explore a novel model to organize and integrate the TMK into conceptual graphs. We then employ a framework to automatically retrieve knowledge in knowledge graphs with a high precision. In order to perform reasonable inference on knowledge graphs, we propose a contextual inference pruning algorithm to achieve efficient chain inference. Our algorithm achieves a better inference result with precision and recall of 92% and 96%, respectively, which can avoid most of the meaningless inferences. In addition, we implement two prototypes and provide services, and the results show our approach is practical and effective.

Generalized connectivity of graphs

CERN Document Server

Li, Xueliang

2016-01-01

Noteworthy results, proof techniques, open problems and conjectures in generalized (edge-) connectivity are discussed in this book. Both theoretical and practical analyses for generalized (edge-) connectivity of graphs are provided. Topics covered in this book include: generalized (edge-) connectivity of graph classes, algorithms, computational complexity, sharp bounds, Nordhaus-Gaddum-type results, maximum generalized local connectivity, extremal problems, random graphs, multigraphs, relations with the Steiner tree packing problem and generalizations of connectivity. This book enables graduate students to understand and master a segment of graph theory and combinatorial optimization. Researchers in graph theory, combinatorics, combinatorial optimization, probability, computer science, discrete algorithms, complexity analysis, network design, and the information transferring models will find this book useful in their studies.

Skew-adjacency matrices of graphs

NARCIS (Netherlands)

Cavers, M.; Cioaba, S.M.; Fallat, S.; Gregory, D.A.; Haemers, W.H.; Kirkland, S.J.; McDonald, J.J.; Tsatsomeros, M.

2012-01-01

The spectra of the skew-adjacency matrices of a graph are considered as a possible way to distinguish adjacency cospectral graphs. This leads to the following topics: graphs whose skew-adjacency matrices are all cospectral; relations between the matchings polynomial of a graph and the characteristic

Graph theory

CERN Document Server

Diestel, Reinhard

2017-01-01

This standard textbook of modern graph theory, now in its fifth edition, combines the authority of a classic with the engaging freshness of style that is the hallmark of active mathematics. It covers the core material of the subject with concise yet reliably complete proofs, while offering glimpses of more advanced methods in each field by one or two deeper results, again with proofs given in full detail. The book can be used as a reliable text for an introductory course, as a graduate text, and for self-study. From the reviews: “This outstanding book cannot be substituted with any other book on the present textbook market. It has every chance of becoming the standard textbook for graph theory.”Acta Scientiarum Mathematiciarum “Deep, clear, wonderful. This is a serious book about the heart of graph theory. It has depth and integrity. ”Persi Diaconis & Ron Graham, SIAM Review “The book has received a very enthusiastic reception, which it amply deserves. A masterly elucidation of modern graph theo...

Acyclicity in edge-colored graphs

DEFF Research Database (Denmark)

Gutin, Gregory; Jones, Mark; Sheng, Bin

2017-01-01

A walk W in edge-colored graphs is called properly colored (PC) if every pair of consecutive edges in W is of different color. We introduce and study five types of PC acyclicity in edge-colored graphs such that graphs of PC acyclicity of type i is a proper superset of graphs of acyclicity of type i......+1, i=1,2,3,4. The first three types are equivalent to the absence of PC cycles, PC closed trails, and PC closed walks, respectively. While graphs of types 1, 2 and 3 can be recognized in polynomial time, the problem of recognizing graphs of type 4 is, somewhat surprisingly, NP-hard even for 2-edge-colored...... graphs (i.e., when only two colors are used). The same problem with respect to type 5 is polynomial-time solvable for all edge-colored graphs. Using the five types, we investigate the border between intractability and tractability for the problems of finding the maximum number of internally vertex...

Graph Sampling for Covariance Estimation

KAUST Repository

Chepuri, Sundeep Prabhakar

2017-04-25

In this paper the focus is on subsampling as well as reconstructing the second-order statistics of signals residing on nodes of arbitrary undirected graphs. Second-order stationary graph signals may be obtained by graph filtering zero-mean white noise and they admit a well-defined power spectrum whose shape is determined by the frequency response of the graph filter. Estimating the graph power spectrum forms an important component of stationary graph signal processing and related inference tasks such as Wiener prediction or inpainting on graphs. The central result of this paper is that by sampling a significantly smaller subset of vertices and using simple least squares, we can reconstruct the second-order statistics of the graph signal from the subsampled observations, and more importantly, without any spectral priors. To this end, both a nonparametric approach as well as parametric approaches including moving average and autoregressive models for the graph power spectrum are considered. The results specialize for undirected circulant graphs in that the graph nodes leading to the best compression rates are given by the so-called minimal sparse rulers. A near-optimal greedy algorithm is developed to design the subsampling scheme for the non-parametric and the moving average models, whereas a particular subsampling scheme that allows linear estimation for the autoregressive model is proposed. Numerical experiments on synthetic as well as real datasets related to climatology and processing handwritten digits are provided to demonstrate the developed theory.

Collective Rationality in Graph Aggregation

NARCIS (Netherlands)

Endriss, U.; Grandi, U.; Schaub, T.; Friedrich, G.; O'Sullivan, B.

2014-01-01

Suppose a number of agents each provide us with a directed graph over a common set of vertices. Graph aggregation is the problem of computing a single “collective” graph that best represents the information inherent in this profile of individual graphs. We consider this aggregation problem from the

GoFFish: A Sub-Graph Centric Framework for Large-Scale Graph Analytics1

Energy Technology Data Exchange (ETDEWEB)

Simmhan, Yogesh; Kumbhare, Alok; Wickramaarachchi, Charith; Nagarkar, Soonil; Ravi, Santosh; Raghavendra, Cauligi; Prasanna, Viktor

2014-08-25

Large scale graph processing is a major research area for Big Data exploration. Vertex centric programming models like Pregel are gaining traction due to their simple abstraction that allows for scalable execution on distributed systems naturally. However, there are limitations to this approach which cause vertex centric algorithms to under-perform due to poor compute to communication overhead ratio and slow convergence of iterative superstep. In this paper we introduce GoFFish a scalable sub-graph centric framework co-designed with a distributed persistent graph storage for large scale graph analytics on commodity clusters. We introduce a sub-graph centric programming abstraction that combines the scalability of a vertex centric approach with the flexibility of shared memory sub-graph computation. We map Connected Components, SSSP and PageRank algorithms to this model to illustrate its flexibility. Further, we empirically analyze GoFFish using several real world graphs and demonstrate its significant performance improvement, orders of magnitude in some cases, compared to Apache Giraph, the leading open source vertex centric implementation. We map Connected Components, SSSP and PageRank algorithms to this model to illustrate its flexibility. Further, we empirically analyze GoFFish using several real world graphs and demonstrate its significant performance improvement, orders of magnitude in some cases, compared to Apache Giraph, the leading open source vertex centric implementation.

Graph Theory. 1. Fragmentation of Structural Graphs

Directory of Open Access Journals (Sweden)

Lorentz JÄNTSCHI

2002-12-01

Full Text Available The investigation of structural graphs has many fields of applications in engineering, especially in applied sciences like as applied chemistry and physics, computer sciences and automation, electronics and telecommunication. The main subject of the paper is to express fragmentation criteria in graph using a new method of investigation: terminal paths. Using terminal paths are defined most of the fragmentation criteria that are in use in molecular topology, but the fields of applications are more generally than that, as I mentioned before. Graphical examples of fragmentation are given for every fragmentation criteria. Note that all fragmentation is made with a computer program that implements a routine for every criterion.[1] A web routine for tracing all terminal paths in graph can be found at the address: http://vl.academicdirect.ro/molecular_topology/tpaths/ [1] M. V. Diudea, I. Gutman, L. Jäntschi, Molecular Topology, Nova Science, Commack, New York, 2001, 2002.

Introductory graph theory

CERN Document Server

Chartrand, Gary

1984-01-01

Graph theory is used today in the physical sciences, social sciences, computer science, and other areas. Introductory Graph Theory presents a nontechnical introduction to this exciting field in a clear, lively, and informative style. Author Gary Chartrand covers the important elementary topics of graph theory and its applications. In addition, he presents a large variety of proofs designed to strengthen mathematical techniques and offers challenging opportunities to have fun with mathematics. Ten major topics - profusely illustrated - include: Mathematical Models, Elementary Concepts of Grap

Creating more effective graphs

CERN Document Server

Robbins, Naomi B

2012-01-01

A succinct and highly readable guide to creating effective graphs The right graph can be a powerful tool for communicating information, improving a presentation, or conveying your point in print. If your professional endeavors call for you to present data graphically, here's a book that can help you do it more effectively. Creating More Effective Graphs gives you the basic knowledge and techniques required to choose and create appropriate graphs for a broad range of applications. Using real-world examples everyone can relate to, the author draws on her years of experience in gr

Graph Compression by BFS

Directory of Open Access Journals (Sweden)

Alberto Apostolico

2009-08-01

Full Text Available The Web Graph is a large-scale graph that does not fit in main memory, so that lossless compression methods have been proposed for it. This paper introduces a compression scheme that combines efficient storage with fast retrieval for the information in a node. The scheme exploits the properties of the Web Graph without assuming an ordering of the URLs, so that it may be applied to more general graphs. Tests on some datasets of use achieve space savings of about 10% over existing methods.

Graphing Inequalities, Connecting Meaning

Science.gov (United States)

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…

Bell inequalities for graph states

International Nuclear Information System (INIS)

Toth, G.; Hyllus, P.; Briegel, H.J.; Guehne, O.

2005-01-01

Full text: In the last years graph states have attracted an increasing interest in the field of quantum information theory. Graph states form a family of multi-qubit states which comprises many popular states such as the GHZ states and the cluster states. They also play an important role in applications. For instance, measurement based quantum computation uses graph states as resources. From a theoretical point of view, it is remarkable that graph states allow for a simple description in terms of stabilizing operators. In this contribution, we investigate the non-local properties of graph states. We derive a family of Bell inequalities which require three measurement settings for each party and are maximally violated by graph states. In turn, any graph state violates at least one of the inequalities. We show that for certain types of graph states the violation of these inequalities increases exponentially with the number of qubits. We also discuss connections to other entanglement properties such as the positively of the partial transpose or the geometric measure of entanglement. (author)

Neighbor Rupture Degree of Some Middle Graphs

Directory of Open Access Journals (Sweden)

Gökşen BACAK-TURAN

2017-12-01

Full Text Available Networks have an important place in our daily lives. Internet networks, electricity networks, water networks, transportation networks, social networks and biological networks are some of the networks we run into every aspects of our lives. A network consists of centers connected by links. A network is represented when centers and connections modelled by vertices and edges, respectively. In consequence of the failure of some centers or connection lines, measurement of the resistance of the network until the communication interrupted is called vulnerability of the network. In this study, neighbor rupture degree which is a parameter that explores the vulnerability values of the resulting graphs due to the failure of some centers of a communication network and its neighboring centers becoming nonfunctional were applied to some middle graphs and neighbor rupture degree of the $M(C_{n},$ $M(P_{n},$ $M(K_{1,n},$ $M(W_{n},$ $M(P_{n}\\times K_{2}$ and $M(C_{n}\\times K_{2}$ have been found.

Quantitative graph theory mathematical foundations and applications

CERN Document Server

Dehmer, Matthias

2014-01-01

The first book devoted exclusively to quantitative graph theory, Quantitative Graph Theory: Mathematical Foundations and Applications presents and demonstrates existing and novel methods for analyzing graphs quantitatively. Incorporating interdisciplinary knowledge from graph theory, information theory, measurement theory, and statistical techniques, this book covers a wide range of quantitative-graph theoretical concepts and methods, including those pertaining to real and random graphs such as:Comparative approaches (graph similarity or distance)Graph measures to characterize graphs quantitat

Dynamic Representations of Sparse Graphs

DEFF Research Database (Denmark)

Brodal, Gerth Stølting; Fagerberg, Rolf

1999-01-01

We present a linear space data structure for maintaining graphs with bounded arboricity—a large class of sparse graphs containing e.g. planar graphs and graphs of bounded treewidth—under edge insertions, edge deletions, and adjacency queries. The data structure supports adjacency queries in worst...... case O(c) time, and edge insertions and edge deletions in amortized O(1) and O(c+log n) time, respectively, where n is the number of nodes in the graph, and c is the bound on the arboricity....

Spectral fluctuations of quantum graphs

International Nuclear Information System (INIS)

Pluhař, Z.; Weidenmüller, H. A.

2014-01-01

We prove the Bohigas-Giannoni-Schmit conjecture in its most general form for completely connected simple graphs with incommensurate bond lengths. We show that for graphs that are classically mixing (i.e., graphs for which the spectrum of the classical Perron-Frobenius operator possesses a finite gap), the generating functions for all (P,Q) correlation functions for both closed and open graphs coincide (in the limit of infinite graph size) with the corresponding expressions of random-matrix theory, both for orthogonal and for unitary symmetry

Multiple graph regularized protein domain ranking.

Science.gov (United States)

Wang, Jim Jing-Yan; Bensmail, Halima; Gao, Xin

2012-11-19

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

Acyclicity in edge-colored graphs

DEFF Research Database (Denmark)

Gutin, Gregory; Jones, Mark; Sheng, Bin

2017-01-01

A walk W in edge-colored graphs is called properly colored (PC) if every pair of consecutive edges in W is of different color. We introduce and study five types of PC acyclicity in edge-colored graphs such that graphs of PC acyclicity of type i is a proper superset of graphs of acyclicity of type...

ON BIPOLAR SINGLE VALUED NEUTROSOPHIC GRAPHS

OpenAIRE

Said Broumi; Mohamed Talea; Assia Bakali; Florentin Smarandache

2016-01-01

In this article, we combine the concept of bipolar neutrosophic set and graph theory. We introduce the notions of bipolar single valued neutrosophic graphs, strong bipolar single valued neutrosophic graphs, complete bipolar single valued neutrosophic graphs, regular bipolar single valued neutrosophic graphs and investigate some of their related properties.

Practical graph mining with R

CERN Document Server

Hendrix, William; Jenkins, John; Padmanabhan, Kanchana; Chakraborty, Arpan

2014-01-01

Practical Graph Mining with R presents a "do-it-yourself" approach to extracting interesting patterns from graph data. It covers many basic and advanced techniques for the identification of anomalous or frequently recurring patterns in a graph, the discovery of groups or clusters of nodes that share common patterns of attributes and relationships, the extraction of patterns that distinguish one category of graphs from another, and the use of those patterns to predict the category of new graphs. Hands-On Application of Graph Data Mining Each chapter in the book focuses on a graph mining task, such as link analysis, cluster analysis, and classification. Through applications using real data sets, the book demonstrates how computational techniques can help solve real-world problems. The applications covered include network intrusion detection, tumor cell diagnostics, face recognition, predictive toxicology, mining metabolic and protein-protein interaction networks, and community detection in social networks. De...

A seminar on graph theory

CERN Document Server

Harary, Frank

2015-01-01

Presented in 1962-63 by experts at University College, London, these lectures offer a variety of perspectives on graph theory. Although the opening chapters form a coherent body of graph theoretic concepts, this volume is not a text on the subject but rather an introduction to the extensive literature of graph theory. The seminar's topics are geared toward advanced undergraduate students of mathematics.Lectures by this volume's editor, Frank Harary, include ""Some Theorems and Concepts of Graph Theory,"" ""Topological Concepts in Graph Theory,"" ""Graphical Reconstruction,"" and other introduc

Application of machine learning and expert systems to Statistical Process Control (SPC) chart interpretation

Science.gov (United States)

Shewhart, Mark

1991-01-01

Statistical Process Control (SPC) charts are one of several tools used in quality control. Other tools include flow charts, histograms, cause and effect diagrams, check sheets, Pareto diagrams, graphs, and scatter diagrams. A control chart is simply a graph which indicates process variation over time. The purpose of drawing a control chart is to detect any changes in the process signalled by abnormal points or patterns on the graph. The Artificial Intelligence Support Center (AISC) of the Acquisition Logistics Division has developed a hybrid machine learning expert system prototype which automates the process of constructing and interpreting control charts.

Uniform Single Valued Neutrosophic Graphs

Directory of Open Access Journals (Sweden)

S. Broumi

2017-09-01

Full Text Available In this paper, we propose a new concept named the uniform single valued neutrosophic graph. An illustrative example and some properties are examined. Next, we develop an algorithmic approach for computing the complement of the single valued neutrosophic graph. A numerical example is demonstrated for computing the complement of single valued neutrosophic graphs and uniform single valued neutrosophic graph.

Extremal graph theory

CERN Document Server

Bollobas, Bela

2004-01-01

The ever-expanding field of extremal graph theory encompasses a diverse array of problem-solving methods, including applications to economics, computer science, and optimization theory. This volume, based on a series of lectures delivered to graduate students at the University of Cambridge, presents a concise yet comprehensive treatment of extremal graph theory.Unlike most graph theory treatises, this text features complete proofs for almost all of its results. Further insights into theory are provided by the numerous exercises of varying degrees of difficulty that accompany each chapter. A

Multiple graph regularized protein domain ranking

KAUST Repository

Wang, Jim Jing-Yan

2012-11-19

Background: Protein domain ranking is a fundamental task in structural biology. Most protein domain ranking methods rely on the pairwise comparison of protein domains while neglecting the global manifold structure of the protein domain database. Recently, graph regularized ranking that exploits the global structure of the graph defined by the pairwise similarities has been proposed. However, the existing graph regularized ranking methods are very sensitive to the choice of the graph model and parameters, and this remains a difficult problem for most of the protein domain ranking methods.Results: To tackle this problem, we have developed the Multiple Graph regularized Ranking algorithm, MultiG-Rank. Instead of using a single graph to regularize the ranking scores, MultiG-Rank approximates the intrinsic manifold of protein domain distribution by combining multiple initial graphs for the regularization. Graph weights are learned with ranking scores jointly and automatically, by alternately minimizing an objective function in an iterative algorithm. Experimental results on a subset of the ASTRAL SCOP protein domain database demonstrate that MultiG-Rank achieves a better ranking performance than single graph regularized ranking methods and pairwise similarity based ranking methods.Conclusion: The problem of graph model and parameter selection in graph regularized protein domain ranking can be solved effectively by combining multiple graphs. This aspect of generalization introduces a new frontier in applying multiple graphs to solving protein domain ranking applications. 2012 Wang et al; licensee BioMed Central Ltd.

Multiple graph regularized protein domain ranking

KAUST Repository

Wang, Jim Jing-Yan; Bensmail, Halima; Gao, Xin

2012-01-01

Background: Protein domain ranking is a fundamental task in structural biology. Most protein domain ranking methods rely on the pairwise comparison of protein domains while neglecting the global manifold structure of the protein domain database. Recently, graph regularized ranking that exploits the global structure of the graph defined by the pairwise similarities has been proposed. However, the existing graph regularized ranking methods are very sensitive to the choice of the graph model and parameters, and this remains a difficult problem for most of the protein domain ranking methods.Results: To tackle this problem, we have developed the Multiple Graph regularized Ranking algorithm, MultiG-Rank. Instead of using a single graph to regularize the ranking scores, MultiG-Rank approximates the intrinsic manifold of protein domain distribution by combining multiple initial graphs for the regularization. Graph weights are learned with ranking scores jointly and automatically, by alternately minimizing an objective function in an iterative algorithm. Experimental results on a subset of the ASTRAL SCOP protein domain database demonstrate that MultiG-Rank achieves a better ranking performance than single graph regularized ranking methods and pairwise similarity based ranking methods.Conclusion: The problem of graph model and parameter selection in graph regularized protein domain ranking can be solved effectively by combining multiple graphs. This aspect of generalization introduces a new frontier in applying multiple graphs to solving protein domain ranking applications. 2012 Wang et al; licensee BioMed Central Ltd.

Multiple graph regularized protein domain ranking

Directory of Open Access Journals (Sweden)

Wang Jim

2012-11-01

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

Canonical Labelling of Site Graphs

Directory of Open Access Journals (Sweden)

Nicolas Oury

2013-06-01

Full Text Available We investigate algorithms for canonical labelling of site graphs, i.e. graphs in which edges bind vertices on sites with locally unique names. We first show that the problem of canonical labelling of site graphs reduces to the problem of canonical labelling of graphs with edge colourings. We then present two canonical labelling algorithms based on edge enumeration, and a third based on an extension of Hopcroft's partition refinement algorithm. All run in quadratic worst case time individually. However, one of the edge enumeration algorithms runs in sub-quadratic time for graphs with "many" automorphisms, and the partition refinement algorithm runs in sub-quadratic time for graphs with "few" bisimulation equivalences. This suite of algorithms was chosen based on the expectation that graphs fall in one of those two categories. If that is the case, a combined algorithm runs in sub-quadratic worst case time. Whether this expectation is reasonable remains an interesting open problem.

Domination criticality in product graphs

Directory of Open Access Journals (Sweden)

M.R. Chithra

2015-07-01

Full Text Available A connected dominating set is an important notion and has many applications in routing and management of networks. Graph products have turned out to be a good model of interconnection networks. This motivated us to study the Cartesian product of graphs G with connected domination number, γc(G=2,3 and characterize such graphs. Also, we characterize the k−γ-vertex (edge critical graphs and k−γc-vertex (edge critical graphs for k=2,3 where γ denotes the domination number of G. We also discuss the vertex criticality in grids.

Graph Creation, Visualisation and Transformation

Directory of Open Access Journals (Sweden)

Maribel Fernández

2010-03-01

Full Text Available We describe a tool to create, edit, visualise and compute with interaction nets - a form of graph rewriting systems. The editor, called GraphPaper, allows users to create and edit graphs and their transformation rules using an intuitive user interface. The editor uses the functionalities of the TULIP system, which gives us access to a wealth of visualisation algorithms. Interaction nets are not only a formalism for the specification of graphs, but also a rewrite-based computation model. We discuss graph rewriting strategies and a language to express them in order to perform strategic interaction net rewriting.

Graph Colouring Algorithms

DEFF Research Database (Denmark)

Husfeldt, Thore

2015-01-01

This chapter presents an introduction to graph colouring algorithms. The focus is on vertex-colouring algorithms that work for general classes of graphs with worst-case performance guarantees in a sequential model of computation. The presentation aims to demonstrate the breadth of available...

High Performance Descriptive Semantic Analysis of Semantic Graph Databases

Energy Technology Data Exchange (ETDEWEB)

Joslyn, Cliff A.; Adolf, Robert D.; al-Saffar, Sinan; Feo, John T.; Haglin, David J.; Mackey, Greg E.; Mizell, David W.

2011-06-02

As semantic graph database technology grows to address components ranging from extant large triple stores to SPARQL endpoints over SQL-structured relational databases, it will become increasingly important to be able to understand their inherent semantic structure, whether codified in explicit ontologies or not. Our group is researching novel methods for what we call descriptive semantic analysis of RDF triplestores, to serve purposes of analysis, interpretation, visualization, and optimization. But data size and computational complexity makes it increasingly necessary to bring high performance computational resources to bear on this task. Our research group built a novel high performance hybrid system comprising computational capability for semantic graph database processing utilizing the large multi-threaded architecture of the Cray XMT platform, conventional servers, and large data stores. In this paper we describe that architecture and our methods, and present the results of our analyses of basic properties, connected components, namespace interaction, and typed paths such for the Billion Triple Challenge 2010 dataset.

Graph Theoretical Analysis Reveals: Women's Brains Are Better Connected than Men's.

Directory of Open Access Journals (Sweden)

Balázs Szalkai

Full Text Available Deep graph-theoretic ideas in the context with the graph of the World Wide Web led to the definition of Google's PageRank and the subsequent rise of the most popular search engine to date. Brain graphs, or connectomes, are being widely explored today. We believe that non-trivial graph theoretic concepts, similarly as it happened in the case of the World Wide Web, will lead to discoveries enlightening the structural and also the functional details of the animal and human brains. When scientists examine large networks of tens or hundreds of millions of vertices, only fast algorithms can be applied because of the size constraints. In the case of diffusion MRI-based structural human brain imaging, the effective vertex number of the connectomes, or brain graphs derived from the data is on the scale of several hundred today. That size facilitates applying strict mathematical graph algorithms even for some hard-to-compute (or NP-hard quantities like vertex cover or balanced minimum cut. In the present work we have examined brain graphs, computed from the data of the Human Connectome Project, recorded from male and female subjects between ages 22 and 35. Significant differences were found between the male and female structural brain graphs: we show that the average female connectome has more edges, is a better expander graph, has larger minimal bisection width, and has more spanning trees than the average male connectome. Since the average female brain weighs less than the brain of males, these properties show that the female brain has better graph theoretical properties, in a sense, than the brain of males. It is known that the female brain has a smaller gray matter/white matter ratio than males, that is, a larger white matter/gray matter ratio than the brain of males; this observation is in line with our findings concerning the number of edges, since the white matter consists of myelinated axons, which, in turn, roughly correspond to the connections

The fascinating world of graph theory

CERN Document Server

Benjamin, Arthur; Zhang, Ping

2015-01-01

Graph theory goes back several centuries and revolves around the study of graphs-mathematical structures showing relations between objects. With applications in biology, computer science, transportation science, and other areas, graph theory encompasses some of the most beautiful formulas in mathematics-and some of its most famous problems. The Fascinating World of Graph Theory explores the questions and puzzles that have been studied, and often solved, through graph theory. This book looks at graph theory's development and the vibrant individuals responsible for the field's growth. Introducin

Classical dynamics on graphs

International Nuclear Information System (INIS)

Barra, F.; Gaspard, P.

2001-01-01

We consider the classical evolution of a particle on a graph by using a time-continuous Frobenius-Perron operator that generalizes previous propositions. In this way, the relaxation rates as well as the chaotic properties can be defined for the time-continuous classical dynamics on graphs. These properties are given as the zeros of some periodic-orbit zeta functions. We consider in detail the case of infinite periodic graphs where the particle undergoes a diffusion process. The infinite spatial extension is taken into account by Fourier transforms that decompose the observables and probability densities into sectors corresponding to different values of the wave number. The hydrodynamic modes of diffusion are studied by an eigenvalue problem of a Frobenius-Perron operator corresponding to a given sector. The diffusion coefficient is obtained from the hydrodynamic modes of diffusion and has the Green-Kubo form. Moreover, we study finite but large open graphs that converge to the infinite periodic graph when their size goes to infinity. The lifetime of the particle on the open graph is shown to correspond to the lifetime of a system that undergoes a diffusion process before it escapes

Interpretation of the line profiles of the 8 micron band of silicon monoxide from VY canis majoris

International Nuclear Information System (INIS)

Van Blerkom, D.; Xinjie, M.

1982-01-01

Observations of the vibration-rotation transitions of silicon monoxide from the expanding circumstellar envelope of VY Canis Majoris have previously been interpreted in terms of line formation in a thin shell of gas surrounding an opaque core of dust which emits a continuous spectrum. We show that the use of this model is the cause of the apparent displacement of the stellar velocity derived from the 8 μm lines by 14 km s -1 from the value based on the v = 0, J = 2→1 SiO line and on the midpoint of the OH maser emission. No such displacement occurs if a model of line formation is employed in which emission from the entire envelope contributes to the emergent profile. This eliminates the need to postulate asymmetries in the envelope and agrees with infrared continuum studies

Groupies in multitype random graphs

OpenAIRE

Shang, Yilun

2016-01-01

A groupie in a graph is a vertex whose degree is not less than the average degree of its neighbors. Under some mild conditions, we show that the proportion of groupies is very close to 1/2 in multitype random graphs (such as stochastic block models), which include Erd?s-R?nyi random graphs, random bipartite, and multipartite graphs as special examples. Numerical examples are provided to illustrate the theoretical results.

Quantum information processing with graph states

International Nuclear Information System (INIS)

Schlingemann, Dirk-Michael

2005-04-01

Graph states are multiparticle states which are associated with graphs. Each vertex of the graph corresponds to a single system or particle. The links describe quantum correlations (entanglement) between pairs of connected particles. Graph states were initiated independently by two research groups: On the one hand, graph states were introduced by Briegel and Raussendorf as a resource for a new model of one-way quantum computing, where algorithms are implemented by a sequence of measurements at single particles. On the other hand, graph states were developed by the author of this thesis and ReinhardWerner in Braunschweig, as a tool to build quantum error correcting codes, called graph codes. The connection between the two approaches was fully realized in close cooperation of both research groups. This habilitation thesis provides a survey of the theory of graph codes, focussing mainly, but not exclusively on the author's own research work. We present the theoretical and mathematical background for the analysis of graph codes. The concept of one-way quantum computing for general graph states is discussed. We explicitly show how to realize the encoding and decoding device of a graph code on a one-way quantum computer. This kind of implementation is to be seen as a mathematical description of a quantum memory device. In addition to that, we investigate interaction processes, which enable the creation of graph states on very large systems. Particular graph states can be created, for instance, by an Ising type interaction between next neighbor particles which sits at the points of an infinitely extended cubic lattice. Based on the theory of quantum cellular automata, we give a constructive characterization of general interactions which create a translationally invariant graph state. (orig.)

Fibonacci number of the tadpole graph

Directory of Open Access Journals (Sweden)

Joe DeMaio

2014-10-01

Full Text Available In 1982, Prodinger and Tichy defined the Fibonacci number of a graph G to be the number of independent sets of the graph G. They did so since the Fibonacci number of the path graph Pn is the Fibonacci number F(n+2 and the Fibonacci number of the cycle graph Cn is the Lucas number Ln. The tadpole graph Tn,k is the graph created by concatenating Cn and Pk with an edge from any vertex of Cn to a pendant of Pk for integers n=3 and k=0. This paper establishes formulae and identities for the Fibonacci number of the tadpole graph via algebraic and combinatorial methods.

Generalization of Binomial Coefficients to Numbers on the Nodes of Graphs

NARCIS (Netherlands)

Khmelnitskaya, A.; van der Laan, G.; Talman, Dolf

2016-01-01

The triangular array of binomial coefficients, or Pascal's triangle, is formed by starting with an apex of 1. Every row of Pascal's triangle can be seen as a line-graph, to each node of which the corresponding binomial coefficient is assigned. We show that the binomial coefficient of a node is equal

Generalization of binomial coefficients to numbers on the nodes of graphs

NARCIS (Netherlands)

Khmelnitskaya, Anna Borisovna; van der Laan, Gerard; Talman, Dolf

The triangular array of binomial coefficients, or Pascal's triangle, is formed by starting with an apex of 1. Every row of Pascal's triangle can be seen as a line-graph, to each node of which the corresponding binomial coefficient is assigned. We show that the binomial coefficient of a node is equal

Network reconstruction via graph blending

Science.gov (United States)

Estrada, Rolando

2016-05-01

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

Groupies in multitype random graphs.

Science.gov (United States)

Shang, Yilun

2016-01-01

A groupie in a graph is a vertex whose degree is not less than the average degree of its neighbors. Under some mild conditions, we show that the proportion of groupies is very close to 1/2 in multitype random graphs (such as stochastic block models), which include Erdős-Rényi random graphs, random bipartite, and multipartite graphs as special examples. Numerical examples are provided to illustrate the theoretical results.

Combinatorial and geometric aspects of Feynman graphs and Feynman integrals

Energy Technology Data Exchange (ETDEWEB)

Bergbauer, Christoph

2009-06-11

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

Combinatorial and geometric aspects of Feynman graphs and Feynman integrals

International Nuclear Information System (INIS)

Bergbauer, Christoph

2009-01-01

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

The Harary index of a graph

CERN Document Server

Xu, Kexiang; Trinajstić, Nenad

2015-01-01

This is the first book to focus on the topological index, the Harary index, of a graph, including its mathematical properties, chemical applications and some related and attractive open problems. This book is dedicated to Professor Frank Harary (1921—2005), the grandmaster of graph theory and its applications. It has be written by experts in the field of graph theory and its applications. For a connected graph G, as an important distance-based topological index, the Harary index H(G) is defined as the sum of the reciprocals of the distance between any two unordered vertices of the graph G. In this book, the authors report on the newest results on the Harary index of a graph. These results mainly concern external graphs with respect to the Harary index; the relations to other topological indices; its properties and applications to pure graph theory and chemical graph theory; and two significant variants, i.e., additively and multiplicatively weighted Harary indices. In the last chapter, we present a number o...

A Modal-Logic Based Graph Abstraction

NARCIS (Netherlands)

Bauer, J.; Boneva, I.B.; Kurban, M.E.; Rensink, Arend; Ehrig, H; Heckel, R.; Rozenberg, G.; Taentzer, G.

2008-01-01

Infinite or very large state spaces often prohibit the successful verification of graph transformation systems. Abstract graph transformation is an approach that tackles this problem by abstracting graphs to abstract graphs of bounded size and by lifting application of productions to abstract

ROC-ing along: Evaluation and interpretation of receiver operating characteristic curves.

Science.gov (United States)

Carter, Jane V; Pan, Jianmin; Rai, Shesh N; Galandiuk, Susan

2016-06-01

It is vital for clinicians to understand and interpret correctly medical statistics as used in clinical studies. In this review, we address current issues and focus on delivering a simple, yet comprehensive, explanation of common research methodology involving receiver operating characteristic (ROC) curves. ROC curves are used most commonly in medicine as a means of evaluating diagnostic tests. Sample data from a plasma test for the diagnosis of colorectal cancer were used to generate a prediction model. These are actual, unpublished data that have been used to describe the calculation of sensitivity, specificity, positive predictive and negative predictive values, and accuracy. The ROC curves were generated to determine the accuracy of this plasma test. These curves are generated by plotting the sensitivity (true-positive rate) on the y axis and 1 - specificity (false-positive rate) on the x axis. Curves that approach closest to the coordinate (x = 0, y = 1) are more highly predictive, whereas ROC curves that lie close to the line of equality indicate that the result is no better than that obtained by chance. The optimum sensitivity and specificity can be determined from the graph as the point where the minimum distance line crosses the ROC curve. This point corresponds to the Youden index (J), a function of sensitivity and specificity used commonly to rate diagnostic tests. The area under the curve is used to quantify the overall ability of a test to discriminate between 2 outcomes. By following these simple guidelines, interpretation of ROC curves will be less difficult and they can then be interpreted more reliably when writing, reviewing, or analyzing scientific papers. Copyright © 2016 Elsevier Inc. All rights reserved.

Graph mining for next generation sequencing: leveraging the assembly graph for biological insights.

Science.gov (United States)

Warnke-Sommer, Julia; Ali, Hesham

2016-05-06

The assembly of Next Generation Sequencing (NGS) reads remains a challenging task. This is especially true for the assembly of metagenomics data that originate from environmental samples potentially containing hundreds to thousands of unique species. The principle objective of current assembly tools is to assemble NGS reads into contiguous stretches of sequence called contigs while maximizing for both accuracy and contig length. The end goal of this process is to produce longer contigs with the major focus being on assembly only. Sequence read assembly is an aggregative process, during which read overlap relationship information is lost as reads are merged into longer sequences or contigs. The assembly graph is information rich and capable of capturing the genomic architecture of an input read data set. We have developed a novel hybrid graph in which nodes represent sequence regions at different levels of granularity. This model, utilized in the assembly and analysis pipeline Focus, presents a concise yet feature rich view of a given input data set, allowing for the extraction of biologically relevant graph structures for graph mining purposes. Focus was used to create hybrid graphs to model metagenomics data sets obtained from the gut microbiomes of five individuals with Crohn's disease and eight healthy individuals. Repetitive and mobile genetic elements are found to be associated with hybrid graph structure. Using graph mining techniques, a comparative study of the Crohn's disease and healthy data sets was conducted with focus on antibiotics resistance genes associated with transposase genes. Results demonstrated significant differences in the phylogenetic distribution of categories of antibiotics resistance genes in the healthy and diseased patients. Focus was also evaluated as a pure assembly tool and produced excellent results when compared against the Meta-velvet, Omega, and UD-IDBA assemblers. Mining the hybrid graph can reveal biological phenomena captured

Labelling subway lines

NARCIS (Netherlands)

Garrido, M.A.; Iturriaga, C.; Márquez, A.; Portillo, J.R.; Reyes, P.; Wolff, A.; Eades, P.; Takaoka, T.

2001-01-01

Graphical features on map, charts, diagrams and graph drawings usually must be annotated with text labels in order to convey their meaning. In this paper we focus on a problem that arises when labeling schematized maps, e.g. for subway networks. We present algorithms for labeling points on a line

Distance-transitive graphs

NARCIS (Netherlands)

Cohen, A.M.; Beineke, L.W.; Wilson, R.J.; Cameron, P.J.

2004-01-01

In this chapter we investigate the classification of distance-transitive graphs: these are graphs whose automorphism groups are transitive on each of the sets of pairs of vertices at distance i, for i = 0, 1,.... We provide an introduction into the field. By use of the classification of finite

TrajGraph: A Graph-Based Visual Analytics Approach to Studying Urban Network Centralities Using Taxi Trajectory Data.

Science.gov (United States)

Huang, Xiaoke; Zhao, Ye; Yang, Jing; Zhang, Chong; Ma, Chao; Ye, Xinyue

2016-01-01

We propose TrajGraph, a new visual analytics method, for studying urban mobility patterns by integrating graph modeling and visual analysis with taxi trajectory data. A special graph is created to store and manifest real traffic information recorded by taxi trajectories over city streets. It conveys urban transportation dynamics which can be discovered by applying graph analysis algorithms. To support interactive, multiscale visual analytics, a graph partitioning algorithm is applied to create region-level graphs which have smaller size than the original street-level graph. Graph centralities, including Pagerank and betweenness, are computed to characterize the time-varying importance of different urban regions. The centralities are visualized by three coordinated views including a node-link graph view, a map view and a temporal information view. Users can interactively examine the importance of streets to discover and assess city traffic patterns. We have implemented a fully working prototype of this approach and evaluated it using massive taxi trajectories of Shenzhen, China. TrajGraph's capability in revealing the importance of city streets was evaluated by comparing the calculated centralities with the subjective evaluations from a group of drivers in Shenzhen. Feedback from a domain expert was collected. The effectiveness of the visual interface was evaluated through a formal user study. We also present several examples and a case study to demonstrate the usefulness of TrajGraph in urban transportation analysis.

Temporal Representation in Semantic Graphs

Energy Technology Data Exchange (ETDEWEB)

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.

The complexity of the matching-cut problem for planar graphs and other graph classes

NARCIS (Netherlands)

Bonsma, P.S.

2009-01-01

The Matching-Cut problem is the problem to decide whether a graph has an edge cut that is also a matching. Previously this problem was studied under the name of the Decomposable Graph Recognition problem, and proved to be -complete when restricted to graphs with maximum degree four. In this paper it

PRIVATE GRAPHS – ACCESS RIGHTS ON GRAPHS FOR SEAMLESS NAVIGATION

Directory of Open Access Journals (Sweden)

W. Dorner

2016-06-01

Full Text Available After the success of GNSS (Global Navigational Satellite Systems and navigation services for public streets, indoor seems to be the next big development in navigational services, relying on RTLS – Real Time Locating Services (e.g. WIFI and allowing seamless navigation. In contrast to navigation and routing services on public streets, seamless navigation will cause an additional challenge: how to make routing data accessible to defined users or restrict access rights for defined areas or only to parts of the graph to a defined user group? The paper will present case studies and data from literature, where seamless and especially indoor navigation solutions are presented (hospitals, industrial complexes, building sites, but the problem of restricted access rights was only touched from a real world, but not a technical perspective. The analysis of case studies will show, that the objective of navigation and the different target groups for navigation solutions will demand well defined access rights and require solutions, how to make only parts of a graph to a user or application available to solve a navigational task. The paper will therefore introduce the concept of private graphs, which is defined as a graph for navigational purposes covering the street, road or floor network of an area behind a public street and suggest different approaches how to make graph data for navigational purposes available considering access rights and data protection, privacy and security issues as well.

The Canopy Graph and Level Statistics for Random Operators on Trees

International Nuclear Information System (INIS)

Aizenman, Michael; Warzel, Simone

2006-01-01

For operators with homogeneous disorder, it is generally expected that there is a relation between the spectral characteristics of a random operator in the infinite setup and the distribution of the energy gaps in its finite volume versions, in corresponding energy ranges. Whereas pure point spectrum of the infinite operator goes along with Poisson level statistics, it is expected that purely absolutely continuous spectrum would be associated with gap distributions resembling the corresponding random matrix ensemble. We prove that on regular rooted trees, which exhibit both spectral types, the eigenstate point process has always Poissonian limit. However, we also find that this does not contradict the picture described above if that is carefully interpreted, as the relevant limit of finite trees is not the infinite homogenous tree graph but rather a single-ended 'canopy graph.' For this tree graph, the random Schroedinger operator is proven here to have only pure-point spectrum at any strength of the disorder. For more general single-ended trees it is shown that the spectrum is always singular - pure point possibly with singular continuous component which is proven to occur in some cases

A componential model of human interaction with graphs: 1. Linear regression modeling

Science.gov (United States)

Gillan, Douglas J.; Lewis, Robert

1994-01-01

Task analyses served as the basis for developing the Mixed Arithmetic-Perceptual (MA-P) model, which proposes (1) that people interacting with common graphs to answer common questions apply a set of component processes-searching for indicators, encoding the value of indicators, performing arithmetic operations on the values, making spatial comparisons among indicators, and repsonding; and (2) that the type of graph and user's task determine the combination and order of the components applied (i.e., the processing steps). Two experiments investigated the prediction that response time will be linearly related to the number of processing steps according to the MA-P model. Subjects used line graphs, scatter plots, and stacked bar graphs to answer comparison questions and questions requiring arithmetic calculations. A one-parameter version of the model (with equal weights for all components) and a two-parameter version (with different weights for arithmetic and nonarithmetic processes) accounted for 76%-85% of individual subjects' variance in response time and 61%-68% of the variance taken across all subjects. The discussion addresses possible modifications in the MA-P model, alternative models, and design implications from the MA-P model.

Bilinear Regularized Locality Preserving Learning on Riemannian Graph for Motor Imagery BCI.

Science.gov (United States)

Xie, Xiaofeng; Yu, Zhu Liang; Gu, Zhenghui; Zhang, Jun; Cen, Ling; Li, Yuanqing

2018-03-01

In off-line training of motor imagery-based brain-computer interfaces (BCIs), to enhance the generalization performance of the learned classifier, the local information contained in test data could be used to improve the performance of motor imagery as well. Further considering that the covariance matrices of electroencephalogram (EEG) signal lie on Riemannian manifold, in this paper, we construct a Riemannian graph to incorporate the information of training and test data into processing. The adjacency and weight in Riemannian graph are determined by the geodesic distance of Riemannian manifold. Then, a new graph embedding algorithm, called bilinear regularized locality preserving (BRLP), is derived upon the Riemannian graph for addressing the problems of high dimensionality frequently arising in BCIs. With a proposed regularization term encoding prior information of EEG channels, the BRLP could obtain more robust performance. Finally, an efficient classification algorithm based on extreme learning machine is proposed to perform on the tangent space of learned embedding. Experimental evaluations on the BCI competition and in-house data sets reveal that the proposed algorithms could obtain significantly higher performance than many competition algorithms after using same filter process.

Integer Flows and Circuit Covers of Graphs and Signed Graphs

Science.gov (United States)

Cheng, Jian

The work in Chapter 2 is motivated by Tutte and Jaeger's pioneering work on converting modulo flows into integer-valued flows for ordinary graphs. For a signed graphs (G, sigma), we first prove that for each k ∈ {2, 3}, if (G, sigma) is (k - 1)-edge-connected and contains an even number of negative edges when k = 2, then every modulo k-flow of (G, sigma) can be converted into an integer-valued ( k + 1)-ow with a larger or the same support. We also prove that if (G, sigma) is odd-(2p+1)-edge-connected, then (G, sigma) admits a modulo circular (2 + 1/ p)-flows if and only if it admits an integer-valued circular (2 + 1/p)-flows, which improves all previous result by Xu and Zhang (DM2005), Schubert and Steffen (EJC2015), and Zhu (JCTB2015). Shortest circuit cover conjecture is one of the major open problems in graph theory. It states that every bridgeless graph G contains a set of circuits F such that each edge is contained in at least one member of F and the length of F is at most 7/5∥E(G)∥. This concept was recently generalized to signed graphs by Macajova et al. (JGT2015). In Chapter 3, we improve their upper bound from 11∥E( G)∥ to 14/3 ∥E(G)∥, and if G is 2-edgeconnected and has even negativeness, then it can be further reduced to 11/3 ∥E(G)∥. Tutte's 3-flow conjecture has been studied by many graph theorists in the last several decades. As a new approach to this conjecture, DeVos and Thomassen considered the vectors as ow values and found that there is a close relation between vector S1-flows and integer 3-NZFs. Motivated by their observation, in Chapter 4, we prove that if a graph G admits a vector S1-flow with rank at most two, then G admits an integer 3-NZF. The concept of even factors is highly related to the famous Four Color Theorem. We conclude this dissertation in Chapter 5 with an improvement of a recent result by Chen and Fan (JCTB2016) on the upperbound of even factors. We show that if a graph G contains an even factor, then it

Port-Hamiltonian Systems on Open Graphs

NARCIS (Netherlands)

Schaft, A.J. van der; Maschke, B.M.

2010-01-01

In this talk we discuss how to define in an intrinsic manner port-Hamiltonian dynamics on open graphs. Open graphs are graphs where some of the vertices are boundary vertices (terminals), which allow interconnection with other systems. We show that a directed graph carries two natural Dirac

From Specific Information Extraction to Inferences: A Hierarchical Framework of Graph Comprehension

Science.gov (United States)

2004-09-01

The skill to interpret the information displayed in graphs is so important to have, the National Council of Teachers of Mathematics has created...guidelines to ensure that students learn these skills ( NCTM : Standards for Mathematics , 2003). These guidelines are based primarily on the extraction of...graphical perception. Human Computer Interaction, 8, 353-388. NCTM : Standards for Mathematics . (2003, 2003). Peebles, D., & Cheng, P. C.-H. (2002

Quantum walk on a chimera graph

Science.gov (United States)

Xu, Shu; Sun, Xiangxiang; Wu, Jizhou; Zhang, Wei-Wei; Arshed, Nigum; Sanders, Barry C.

2018-05-01

We analyse a continuous-time quantum walk on a chimera graph, which is a graph of choice for designing quantum annealers, and we discover beautiful quantum walk features such as localization that starkly distinguishes classical from quantum behaviour. Motivated by technological thrusts, we study continuous-time quantum walk on enhanced variants of the chimera graph and on diminished chimera graph with a random removal of vertices. We explain the quantum walk by constructing a generating set for a suitable subgroup of graph isomorphisms and corresponding symmetry operators that commute with the quantum walk Hamiltonian; the Hamiltonian and these symmetry operators provide a complete set of labels for the spectrum and the stationary states. Our quantum walk characterization of the chimera graph and its variants yields valuable insights into graphs used for designing quantum-annealers.

Software for Graph Analysis and Visualization

Directory of Open Access Journals (Sweden)

M. I. Kolomeychenko

2014-01-01

Full Text Available This paper describes the software for graph storage, analysis and visualization. The article presents a comparative analysis of existing software for analysis and visualization of graphs, describes the overall architecture of application and basic principles of construction and operation of the main modules. Furthermore, a description of the developed graph storage oriented to storage and processing of large-scale graphs is presented. The developed algorithm for finding communities and implemented algorithms of autolayouts of graphs are the main functionality of the product. The main advantage of the developed software is high speed processing of large size networks (up to millions of nodes and links. Moreover, the proposed graph storage architecture is unique and has no analogues. The developed approaches and algorithms are optimized for operating with big graphs and have high productivity.

What Would a Graph Look Like in this Layout? A Machine Learning Approach to Large Graph Visualization.

Science.gov (United States)

Kwon, Oh-Hyun; Crnovrsanin, Tarik; Ma, Kwan-Liu

2018-01-01

Using different methods for laying out a graph can lead to very different visual appearances, with which the viewer perceives different information. Selecting a "good" layout method is thus important for visualizing a graph. The selection can be highly subjective and dependent on the given task. A common approach to selecting a good layout is to use aesthetic criteria and visual inspection. However, fully calculating various layouts and their associated aesthetic metrics is computationally expensive. In this paper, we present a machine learning approach to large graph visualization based on computing the topological similarity of graphs using graph kernels. For a given graph, our approach can show what the graph would look like in different layouts and estimate their corresponding aesthetic metrics. An important contribution of our work is the development of a new framework to design graph kernels. Our experimental study shows that our estimation calculation is considerably faster than computing the actual layouts and their aesthetic metrics. Also, our graph kernels outperform the state-of-the-art ones in both time and accuracy. In addition, we conducted a user study to demonstrate that the topological similarity computed with our graph kernel matches perceptual similarity assessed by human users.

Text-Filled Stacked Area Graphs

DEFF Research Database (Denmark)

Kraus, Martin

2011-01-01

-filled stacked area graphs; i.e., graphs that feature stacked areas that are filled with small-typed text. Since these graphs allow for computing the text layout automatically, it is possible to include large amounts of textual detail with very little effort. We discuss the most important challenges and some...... solutions for the design of text-filled stacked area graphs with the help of an exemplary visualization of the genres, publication years, and titles of a database of several thousand PC games....

On Graph Rewriting, Reduction and Evaluation

DEFF Research Database (Denmark)

Zerny, Ian

2010-01-01

We inter-derive two prototypical styles of graph reduction: reduction machines à la Turner and graph rewriting systems à la Barendregt et al. To this end, we adapt Danvy et al.'s mechanical program derivations from the world of terms to the world of graphs. We also outline how to inter-derive a t......We inter-derive two prototypical styles of graph reduction: reduction machines à la Turner and graph rewriting systems à la Barendregt et al. To this end, we adapt Danvy et al.'s mechanical program derivations from the world of terms to the world of graphs. We also outline how to inter...

On dominator colorings in graphs

Indian Academy of Sciences (India)

colors required for a dominator coloring of G is called the dominator .... Theorem 1.3 shows that the complete graph Kn is the only connected graph of order n ... Conversely, if a graph G satisfies condition (i) or (ii), it is easy to see that χd(G) =.

Computing the Maximum Detour of a Plane Graph in Subquadratic Time

DEFF Research Database (Denmark)

Wulff-Nilsen, Christian

2008-01-01

Let G be a plane graph where each edge is a line segment. We consider the problem of computing the maximum detour of G, defined as the maximum over all pairs of distinct points p and q of G of the ratio between the distance between p and q in G and the distance |pq|. The fastest known algorithm...

Graphs with branchwidth at most three

NARCIS (Netherlands)

Bodlaender, H.L.; Thilikos, D.M.

1997-01-01

In this paper we investigate both the structure of graphs with branchwidth at most three, as well as algorithms to recognise such graphs. We show that a graph has branchwidth at most three, if and only if it has treewidth at most three and does not contain the three-dimensional binary cube graph

The Little-Hopfield model on a sparse random graph

International Nuclear Information System (INIS)

Castillo, I Perez; Skantzos, N S

2004-01-01

We study the Hopfield model on a random graph in scaling regimes where the average number of connections per neuron is a finite number and the spin dynamics is governed by a synchronous execution of the microscopic update rule (Little-Hopfield model). We solve this model within replica symmetry, and by using bifurcation analysis we prove that the spin-glass/paramagnetic and the retrieval/paramagnetic transition lines of our phase diagram are identical to those of sequential dynamics. The first-order retrieval/spin-glass transition line follows by direct evaluation of our observables using population dynamics. Within the accuracy of numerical precision and for sufficiently small values of the connectivity parameter we find that this line coincides with the corresponding sequential one. Comparison with simulation experiments shows excellent agreement

Adaptation of Chain Event Graphs for use with Case-Control Studies in Epidemiology.

Science.gov (United States)

Keeble, Claire; Thwaites, Peter Adam; Barber, Stuart; Law, Graham Richard; Baxter, Paul David

2017-09-26

Case-control studies are used in epidemiology to try to uncover the causes of diseases, but are a retrospective study design known to suffer from non-participation and recall bias, which may explain their decreased popularity in recent years. Traditional analyses report usually only the odds ratio for given exposures and the binary disease status. Chain event graphs are a graphical representation of a statistical model derived from event trees which have been developed in artificial intelligence and statistics, and only recently introduced to the epidemiology literature. They are a modern Bayesian technique which enable prior knowledge to be incorporated into the data analysis using the agglomerative hierarchical clustering algorithm, used to form a suitable chain event graph. Additionally, they can account for missing data and be used to explore missingness mechanisms. Here we adapt the chain event graph framework to suit scenarios often encountered in case-control studies, to strengthen this study design which is time and financially efficient. We demonstrate eight adaptations to the graphs, which consist of two suitable for full case-control study analysis, four which can be used in interim analyses to explore biases, and two which aim to improve the ease and accuracy of analyses. The adaptations are illustrated with complete, reproducible, fully-interpreted examples, including the event tree and chain event graph. Chain event graphs are used here for the first time to summarise non-participation, data collection techniques, data reliability, and disease severity in case-control studies. We demonstrate how these features of a case-control study can be incorporated into the analysis to provide further insight, which can help to identify potential biases and lead to more accurate study results.

Planar graphs theory and algorithms

CERN Document Server

Nishizeki, T

1988-01-01

Collected in this volume are most of the important theorems and algorithms currently known for planar graphs, together with constructive proofs for the theorems. Many of the algorithms are written in Pidgin PASCAL, and are the best-known ones; the complexities are linear or 0(nlogn). The first two chapters provide the foundations of graph theoretic notions and algorithmic techniques. The remaining chapters discuss the topics of planarity testing, embedding, drawing, vertex- or edge-coloring, maximum independence set, subgraph listing, planar separator theorem, Hamiltonian cycles, and single- or multicommodity flows. Suitable for a course on algorithms, graph theory, or planar graphs, the volume will also be useful for computer scientists and graph theorists at the research level. An extensive reference section is included.

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

Science.gov (United States)

Gan, Tingyue; Cameron, Maria

2017-06-01

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

Graph Quasicontinuous Functions and Densely Continuous Forms

Directory of Open Access Journals (Sweden)

Lubica Hola

2017-07-01

Full Text Available Let $X, Y$ be topological spaces. A function $f: X \\to Y$ is said to be graph quasicontinuous if there is a quasicontinuous function $g: X \\to Y$ with the graph of $g$ contained in the closure of the graph of $f$. There is a close relation between the notions of graph quasicontinuous functions and minimal usco maps as well as the notions of graph quasicontinuous functions and densely continuous forms. Every function with values in a compact Hausdorff space is graph quasicontinuous; more generally every locally compact function is graph quasicontinuous.

CORECLUSTER: A Degeneracy Based Graph Clustering Framework

OpenAIRE

Giatsidis , Christos; Malliaros , Fragkiskos; Thilikos , Dimitrios M. ,; Vazirgiannis , Michalis

2014-01-01

International audience; Graph clustering or community detection constitutes an important task forinvestigating the internal structure of graphs, with a plethora of applications in several domains. Traditional tools for graph clustering, such asspectral methods, typically suffer from high time and space complexity. In thisarticle, we present \\textsc{CoreCluster}, an efficient graph clusteringframework based on the concept of graph degeneracy, that can be used along withany known graph clusteri...

Coloring sums of extensions of certain graphs

Directory of Open Access Journals (Sweden)

Johan Kok

2017-12-01

Full Text Available We recall that the minimum number of colors that allow a proper coloring of graph $G$ is called the chromatic number of $G$ and denoted $\\chi(G$. Motivated by the introduction of the concept of the $b$-chromatic sum of a graph the concept of $\\chi'$-chromatic sum and $\\chi^+$-chromatic sum are introduced in this paper. The extended graph $G^x$ of a graph $G$ was recently introduced for certain regular graphs. This paper furthers the concepts of $\\chi'$-chromatic sum and $\\chi^+$-chromatic sum to extended paths and cycles. Bipartite graphs also receive some attention. The paper concludes with patterned structured graphs. These last said graphs are typically found in chemical and biological structures.

Optimization Problems on Threshold Graphs

Directory of Open Access Journals (Sweden)

Elena Nechita

2010-06-01

Full Text Available During the last three decades, different types of decompositions have been processed in the field of graph theory. Among these we mention: decompositions based on the additivity of some characteristics of the graph, decompositions where the adjacency law between the subsets of the partition is known, decompositions where the subgraph induced by every subset of the partition must have predeterminate properties, as well as combinations of such decompositions. In this paper we characterize threshold graphs using the weakly decomposition, determine: density and stability number, Wiener index and Wiener polynomial for threshold graphs.

Line-based monocular graph SLAM algorithm%基于图优化的单目线特征SLAM算法

Institute of Scientific and Technical Information of China (English)

董蕊芳; 柳长安; 杨国田; 程瑞营

2017-01-01

A new line based 6-DOF monocular algorithm for using graph simultaneous localization and mapping(SLAM) algoritm was proposed.First,the straight line were applied as a feature instead of points,due to a map consisting of a sparse set of 3D points is unable to describe the structure of the surrounding world.Secondly,most of previous line-based SLAM algorithms were focused on filtering-based solutions suffering from the inconsistent when applied to the inherently non-linear SLAM problem,in contrast,the graph-based solution was used to improve the accuracy of the localization and the consistency of mapping.Thirdly,a special line representation was exploited for combining the Plücker coordinates with the Cayley representation.The Plücker coordinates were used for the 3D line projection function,and the Cayley representation helps to update the line parameters during the non-linear optimization process.Finally,the simulation experiment shows that the proposed algorithm outperforms odometry and EKF-based SLAM in terms of the pose estimation,while the sum of the squared errors (SSE) and root-mean-square error (RMSE) of proposed method are 2.5％ and 10.5％ of odometry,and 22.4％ and 33％ of EKF-based SLAM.The reprojection error is only 45.5 pixels.The real image experiment shows that the proposed algorithm obtains only 958 cm2 and 3.941 3 cm the SSE and RMSE of pose estimation.Therefore,it can be concluded that the proposed algorithm is effective and accuracy.%提出了基于图优化的单目线特征同时定位和地图构建(SLAM)的方法.首先,针对主流视觉SLAM算法因采用点作为特征而导致构建的点云地图稀疏、难以准确表达环境结构信息等缺点,采用直线作为特征来构建地图.然后,根据现有线特征的SLAM算法都是基于滤波器的SLAM框架、存在线性化及更新效率的问题,采用基于图优化的SLAM解决方案以提高定位精度及地图构建的一致性和准确性.将线特征�

Hierarchy of modular graph identities

Energy Technology Data Exchange (ETDEWEB)

D’Hoker, Eric; Kaidi, Justin [Mani L. Bhaumik Institute for Theoretical Physics, Department of Physics and Astronomy,University of California,Los Angeles, CA 90095 (United States)

2016-11-09

The low energy expansion of Type II superstring amplitudes at genus one is organized in terms of modular graph functions associated with Feynman graphs of a conformal scalar field on the torus. In earlier work, surprising identities between two-loop graphs at all weights, and between higher-loop graphs of weights four and five were constructed. In the present paper, these results are generalized in two complementary directions. First, all identities at weight six and all dihedral identities at weight seven are obtained and proven. Whenever the Laurent polynomial at the cusp is available, the form of these identities confirms the pattern by which the vanishing of the Laurent polynomial governs the full modular identity. Second, the family of modular graph functions is extended to include all graphs with derivative couplings and worldsheet fermions. These extended families of modular graph functions are shown to obey a hierarchy of inhomogeneous Laplace eigenvalue equations. The eigenvalues are calculated analytically for the simplest infinite sub-families and obtained by Maple for successively more complicated sub-families. The spectrum is shown to consist solely of eigenvalues s(s−1) for positive integers s bounded by the weight, with multiplicities which exhibit rich representation-theoretic patterns.

Hierarchy of modular graph identities

International Nuclear Information System (INIS)

D’Hoker, Eric; Kaidi, Justin

2016-01-01

The low energy expansion of Type II superstring amplitudes at genus one is organized in terms of modular graph functions associated with Feynman graphs of a conformal scalar field on the torus. In earlier work, surprising identities between two-loop graphs at all weights, and between higher-loop graphs of weights four and five were constructed. In the present paper, these results are generalized in two complementary directions. First, all identities at weight six and all dihedral identities at weight seven are obtained and proven. Whenever the Laurent polynomial at the cusp is available, the form of these identities confirms the pattern by which the vanishing of the Laurent polynomial governs the full modular identity. Second, the family of modular graph functions is extended to include all graphs with derivative couplings and worldsheet fermions. These extended families of modular graph functions are shown to obey a hierarchy of inhomogeneous Laplace eigenvalue equations. The eigenvalues are calculated analytically for the simplest infinite sub-families and obtained by Maple for successively more complicated sub-families. The spectrum is shown to consist solely of eigenvalues s(s−1) for positive integers s bounded by the weight, with multiplicities which exhibit rich representation-theoretic patterns.

Well-covered graphs and factors

DEFF Research Database (Denmark)

Randerath, Bert; Vestergaard, Preben D.

2006-01-01

A maximum independent set of vertices in a graph is a set of pairwise nonadjacent vertices of largest cardinality α. Plummer defined a graph to be well-covered, if every independent set is contained in a maximum independent set of G. Every well-covered graph G without isolated vertices has a perf...

On the centrality of some graphs

Directory of Open Access Journals (Sweden)

Vecdi Aytac

2017-10-01

Full Text Available A central issue in the analysis of complex networks is the assessment of their stability and vulnerability. A variety of measures have been proposed in the literature to quantify the stability of networks and a number of graph-theoretic parameters have been used to derive formulas for calculating network reliability. Different measures for graph vulnerability have been introduced so far to study different aspects of the graph behavior after removal of vertices or links such as connectivity, toughness, scattering number, binding number, residual closeness and integrity. In this paper, we consider betweenness centrality of a graph. Betweenness centrality of a vertex of a graph is portion of the shortest paths all pairs of vertices passing through a given vertex. In this paper, we obtain exact values for betweenness centrality for some wheel related graphs namely gear, helm, sunflower and friendship graphs.

Enabling Graph Appliance for Genome Assembly

Energy Technology Data Exchange (ETDEWEB)

Singh, Rina [ORNL; Graves, Jeffrey A [ORNL; Lee, Sangkeun (Matt) [ORNL; Sukumar, Sreenivas R [ORNL; Shankar, Mallikarjun [ORNL

2015-01-01

In recent years, there has been a huge growth in the amount of genomic data available as reads generated from various genome sequencers. The number of reads generated can be huge, ranging from hundreds to billions of nucleotide, each varying in size. Assembling such large amounts of data is one of the challenging computational problems for both biomedical and data scientists. Most of the genome assemblers developed have used de Bruijn graph techniques. A de Bruijn graph represents a collection of read sequences by billions of vertices and edges, which require large amounts of memory and computational power to store and process. This is the major drawback to de Bruijn graph assembly. Massively parallel, multi-threaded, shared memory systems can be leveraged to overcome some of these issues. The objective of our research is to investigate the feasibility and scalability issues of de Bruijn graph assembly on Cray s Urika-GD system; Urika-GD is a high performance graph appliance with a large shared memory and massively multithreaded custom processor designed for executing SPARQL queries over large-scale RDF data sets. However, to the best of our knowledge, there is no research on representing a de Bruijn graph as an RDF graph or finding Eulerian paths in RDF graphs using SPARQL for potential genome discovery. In this paper, we address the issues involved in representing a de Bruin graphs as RDF graphs and propose an iterative querying approach for finding Eulerian paths in large RDF graphs. We evaluate the performance of our implementation on real world ebola genome datasets and illustrate how genome assembly can be accomplished with Urika-GD using iterative SPARQL queries.

Local adjacency metric dimension of sun graph and stacked book graph

Science.gov (United States)

Yulisda Badri, Alifiah; Darmaji

2018-03-01

A graph is a mathematical system consisting of a non-empty set of nodes and a set of empty sides. One of the topics to be studied in graph theory is the metric dimension. Application in the metric dimension is the navigation robot system on a path. Robot moves from one vertex to another vertex in the field by minimizing the errors that occur in translating the instructions (code) obtained from the vertices of that location. To move the robot must give different instructions (code). In order for the robot to move efficiently, the robot must be fast to translate the code of the nodes of the location it passes. so that the location vertex has a minimum distance. However, if the robot must move with the vertex location on a very large field, so the robot can not detect because the distance is too far.[6] In this case, the robot can determine its position by utilizing location vertices based on adjacency. The problem is to find the minimum cardinality of the required location vertex, and where to put, so that the robot can determine its location. The solution to this problem is the dimension of adjacency metric and adjacency metric bases. Rodrguez-Velzquez and Fernau combine the adjacency metric dimensions with local metric dimensions, thus becoming the local adjacency metric dimension. In the local adjacency metric dimension each vertex in the graph may have the same adjacency representation as the terms of the vertices. To obtain the local metric dimension of values in the graph of the Sun and the stacked book graph is used the construction method by considering the representation of each adjacent vertex of the graph.

An LG-graph-based early evaluation of segmented images

International Nuclear Information System (INIS)

Tsitsoulis, Athanasios; Bourbakis, Nikolaos

2012-01-01

Image segmentation is one of the first important parts of image analysis and understanding. Evaluation of image segmentation, however, is a very difficult task, mainly because it requires human intervention and interpretation. In this work, we propose a blind reference evaluation scheme based on regional local–global (RLG) graphs, which aims at measuring the amount and distribution of detail in images produced by segmentation algorithms. The main idea derives from the field of image understanding, where image segmentation is often used as a tool for scene interpretation and object recognition. Evaluation here derives from summarization of the structural information content and not from the assessment of performance after comparisons with a golden standard. Results show measurements for segmented images acquired from three segmentation algorithms, applied on different types of images (human faces/bodies, natural environments and structures (buildings)). (paper)

DIMENSI METRIK GRAPH LOBSTER Ln (q;r

Directory of Open Access Journals (Sweden)

PANDE GDE DONY GUMILAR

2013-05-01

Full Text Available The metric dimension of connected graph G is the cardinality of minimum resolving set in graph G. In this research, we study how to find the metric dimension of lobster graph Ln (q;r. Lobster graph Ln (q;r is a regular lobster graph with vertices backbone on the main path, every backbone vertex is connected to q hand vertices and every hand vertex is connected to r finger vertices, with n, q, r element of N. We obtain the metric dimension of lobster graph L2 (1;1 is 1, the metric dimension of lobster graph L2 (1;1 for n > 2 is 2.

Summary: beyond fault trees to fault graphs

International Nuclear Information System (INIS)

Alesso, H.P.; Prassinos, P.; Smith, C.F.

1984-09-01

Fault Graphs are the natural evolutionary step over a traditional fault-tree model. A Fault Graph is a failure-oriented directed graph with logic connectives that allows cycles. We intentionally construct the Fault Graph to trace the piping and instrumentation drawing (P and ID) of the system, but with logical AND and OR conditions added. Then we evaluate the Fault Graph with computer codes based on graph-theoretic methods. Fault Graph computer codes are based on graph concepts, such as path set (a set of nodes traveled on a path from one node to another) and reachability (the complete set of all possible paths between any two nodes). These codes are used to find the cut-sets (any minimal set of component failures that will fail the system) and to evaluate the system reliability

Interactive Graph Layout of a Million Nodes

Directory of Open Access Journals (Sweden)

Peng Mi

2016-12-01

Full Text Available Sensemaking of large graphs, specifically those with millions of nodes, is a crucial task in many fields. Automatic graph layout algorithms, augmented with real-time human-in-the-loop interaction, can potentially support sensemaking of large graphs. However, designing interactive algorithms to achieve this is challenging. In this paper, we tackle the scalability problem of interactive layout of large graphs, and contribute a new GPU-based force-directed layout algorithm that exploits graph topology. This algorithm can interactively layout graphs with millions of nodes, and support real-time interaction to explore alternative graph layouts. Users can directly manipulate the layout of vertices in a force-directed fashion. The complexity of traditional repulsive force computation is reduced by approximating calculations based on the hierarchical structure of multi-level clustered graphs. We evaluate the algorithm performance, and demonstrate human-in-the-loop layout in two sensemaking case studies. Moreover, we summarize lessons learned for designing interactive large graph layout algorithms on the GPU.

Eulerian Graphs and Related Topics

CERN Document Server

Fleischner, Herbert

1990-01-01

The two volumes comprising Part 1 of this work embrace the theme of Eulerian trails and covering walks. They should appeal both to researchers and students, as they contain enough material for an undergraduate or graduate graph theory course which emphasizes Eulerian graphs, and thus can be read by any mathematician not yet familiar with graph theory. But they are also of interest to researchers in graph theory because they contain many recent results, some of which are only partial solutions to more general problems. A number of conjectures have been included as well. Various problems (such a

Degree-based graph construction

International Nuclear Information System (INIS)

Kim, Hyunju; Toroczkai, Zoltan; Erdos, Peter L; Miklos, Istvan; Szekely, Laszlo A

2009-01-01

Degree-based graph construction is a ubiquitous problem in network modelling (Newman et al 2006 The Structure and Dynamics of Networks (Princeton Studies in Complexity) (Princeton, NJ: Princeton University Press), Boccaletti et al 2006 Phys. Rep. 424 175), ranging from social sciences to chemical compounds and biochemical reaction networks in the cell. This problem includes existence, enumeration, exhaustive construction and sampling questions with aspects that are still open today. Here we give necessary and sufficient conditions for a sequence of nonnegative integers to be realized as a simple graph's degree sequence, such that a given (but otherwise arbitrary) set of connections from an arbitrarily given node is avoided. We then use this result to present a swap-free algorithm that builds all simple graphs realizing a given degree sequence. In a wider context, we show that our result provides a greedy construction method to build all the f-factor subgraphs (Tutte 1952 Can. J. Math. 4 314) embedded within K n setmn S k , where K n is the complete graph and S k is a star graph centred on one of the nodes. (fast track communication)

Downhill Domination in Graphs

Directory of Open Access Journals (Sweden)

Haynes Teresa W.

2014-08-01

Full Text Available A path π = (v1, v2, . . . , vk+1 in a graph G = (V,E is a downhill path if for every i, 1 ≤ i ≤ k, deg(vi ≥ deg(vi+1, where deg(vi denotes the degree of vertex vi ∈ V. The downhill domination number equals the minimum cardinality of a set S ⊆ V having the property that every vertex v ∈ V lies on a downhill path originating from some vertex in S. We investigate downhill domination numbers of graphs and give upper bounds. In particular, we show that the downhill domination number of a graph is at most half its order, and that the downhill domination number of a tree is at most one third its order. We characterize the graphs obtaining each of these bounds

Subsampling for graph power spectrum estimation

KAUST Repository

Chepuri, Sundeep Prabhakar; Leus, Geert

2016-01-01

In this paper we focus on subsampling stationary random signals that reside on the vertices of undirected graphs. Second-order stationary graph signals are obtained by filtering white noise and they admit a well-defined power spectrum. Estimating the graph power spectrum forms a central component of stationary graph signal processing and related inference tasks. We show that by sampling a significantly smaller subset of vertices and using simple least squares, we can reconstruct the power spectrum of the graph signal from the subsampled observations, without any spectral priors. In addition, a near-optimal greedy algorithm is developed to design the subsampling scheme.

Proving relations between modular graph functions

International Nuclear Information System (INIS)

Basu, Anirban

2016-01-01

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

Subsampling for graph power spectrum estimation

KAUST Repository

Chepuri, Sundeep Prabhakar

2016-10-06

In this paper we focus on subsampling stationary random signals that reside on the vertices of undirected graphs. Second-order stationary graph signals are obtained by filtering white noise and they admit a well-defined power spectrum. Estimating the graph power spectrum forms a central component of stationary graph signal processing and related inference tasks. We show that by sampling a significantly smaller subset of vertices and using simple least squares, we can reconstruct the power spectrum of the graph signal from the subsampled observations, without any spectral priors. In addition, a near-optimal greedy algorithm is developed to design the subsampling scheme.

Semantic graphs and associative memories

Science.gov (United States)

Pomi, Andrés; Mizraji, Eduardo

2004-12-01

Graphs have been increasingly utilized in the characterization of complex networks from diverse origins, including different kinds of semantic networks. Human memories are associative and are known to support complex semantic nets; these nets are represented by graphs. However, it is not known how the brain can sustain these semantic graphs. The vision of cognitive brain activities, shown by modern functional imaging techniques, assigns renewed value to classical distributed associative memory models. Here we show that these neural network models, also known as correlation matrix memories, naturally support a graph representation of the stored semantic structure. We demonstrate that the adjacency matrix of this graph of associations is just the memory coded with the standard basis of the concept vector space, and that the spectrum of the graph is a code invariant of the memory. As long as the assumptions of the model remain valid this result provides a practical method to predict and modify the evolution of the cognitive dynamics. Also, it could provide us with a way to comprehend how individual brains that map the external reality, almost surely with different particular vector representations, are nevertheless able to communicate and share a common knowledge of the world. We finish presenting adaptive association graphs, an extension of the model that makes use of the tensor product, which provides a solution to the known problem of branching in semantic nets.

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

Directory of Open Access Journals (Sweden)

Namhee Kim

Full Text Available Graph representations have been widely used to analyze and design various economic, social, military, political, and biological networks. In systems biology, networks of cells and organs are useful for understanding disease and medical treatments and, in structural biology, structures of molecules can be described, including RNA structures. In our RNA-As-Graphs (RAG framework, we represent RNA structures as tree graphs by translating unpaired regions into vertices and helices into edges. Here we explore the modularity of RNA structures by applying graph partitioning known in graph theory to divide an RNA graph into subgraphs. To our knowledge, this is the first application of graph partitioning to biology, and the results suggest a systematic approach for modular design in general. The graph partitioning algorithms utilize mathematical properties of the Laplacian eigenvector (µ2 corresponding to the second eigenvalues (λ2 associated with the topology matrix defining the graph: λ2 describes the overall topology, and the sum of µ2's components is zero. The three types of algorithms, termed median, sign, and gap cuts, divide a graph by determining nodes of cut by median, zero, and largest gap of µ2's components, respectively. We apply these algorithms to 45 graphs corresponding to all solved RNA structures up through 11 vertices (∼ 220 nucleotides. While we observe that the median cut divides a graph into two similar-sized subgraphs, the sign and gap cuts partition a graph into two topologically-distinct subgraphs. We find that the gap cut produces the best biologically-relevant partitioning for RNA because it divides RNAs at less stable connections while maintaining junctions intact. The iterative gap cuts suggest basic modules and assembly protocols to design large RNA structures. Our graph substructuring thus suggests a systematic approach to explore the modularity of biological networks. In our applications to RNA structures, subgraphs

A generalization of total graphs

Indian Academy of Sciences (India)

M Afkhami

2018-04-12

Apr 12, 2018 ... product of any lower triangular matrix with the transpose of any element of U belongs to U. The ... total graph of R, which is denoted by T( (R)), is a simple graph with all elements of R as vertices, and ...... [9] Badawi A, On dot-product graph of a commutative ring, Communications in Algebra 43 (2015). 43–50.

Decomposing a planar graph into an independent set and a 3-degenerate graph

DEFF Research Database (Denmark)

Thomassen, Carsten

2001-01-01

We prove the conjecture made by O. V. Borodin in 1976 that the vertex set of every planar graph can be decomposed into an independent set and a set inducing a 3-degenerate graph. (C) 2001 Academic Press....

Commuting graphs of matrix algebras

International Nuclear Information System (INIS)

Akbari, S.; Bidkhori, H.; Mohammadian, A.

2006-08-01

The commuting graph of a ring R, denoted by Γ(R), is a graph whose vertices are all non- central elements of R and two distinct vertices x and y are adjacent if and only if xy = yx. The commuting graph of a group G, denoted by Γ(G), is similarly defined. In this paper we investigate some graph theoretic properties of Γ(M n (F)), where F is a field and n ≥ 2. Also we study the commuting graphs of some classical groups such as GL n (F) and SL n (F). We show that Γ(M n (F)) is a connected graph if and only if every field extension of F of degree n contains a proper intermediate field. We prove that apart from finitely many fields, a similar result is true for Γ(GL n (F)) and Γ(SL n (F)). Also we show that for two fields E and F and integers m, n ≥> 2, if Γ(M m (E)) ≅ Γ(M n (F)), then m = n and vertical bar E vertical bar = vertical bar F vertical bar. (author)

Spectral stability of shifted states on star graphs

Science.gov (United States)

Kairzhan, Adilbek; Pelinovsky, Dmitry E.

2018-03-01

We consider the nonlinear Schrödinger (NLS) equation with the subcritical power nonlinearity on a star graph consisting of N edges and a single vertex under generalized Kirchhoff boundary conditions. The stationary NLS equation may admit a family of solitary waves parameterized by a translational parameter, which we call the shifted states. The two main examples include (i) the star graph with even N under the classical Kirchhoff boundary conditions and (ii) the star graph with one incoming edge and N  -  1 outgoing edges under a single constraint on coefficients of the generalized Kirchhoff boundary conditions. We obtain the general counting results on the Morse index of the shifted states and apply them to the two examples. In the case of (i), we prove that the shifted states with even N ≥slant 4 are saddle points of the action functional which are spectrally unstable under the NLS flow. In the case of (ii), we prove that the shifted states with the monotone profiles in the N  -  1 edges are spectrally stable, whereas the shifted states with non-monotone profiles in the N  -  1 edges are spectrally unstable, the two families intersect at the half-soliton states which are spectrally stable but nonlinearly unstable under the NLS flow. Since the NLS equation on a star graph with shifted states can be reduced to the homogeneous NLS equation on an infinite line, the spectral instability of shifted states is due to the perturbations breaking this reduction. We give a simple argument suggesting that the spectrally stable shifted states in the case of (ii) are nonlinearly unstable under the NLS flow due to the perturbations breaking the reduction to the homogeneous NLS equation.

Graph-theoretical concepts and physicochemical data

Directory of Open Access Journals (Sweden)

Lionello Pogliani

2003-02-01

Full Text Available Graph theoretical concepts have been used to model the molecular polarizabilities of fifty-four organic derivatives, and the induced dipole moment of a set of fifty-seven organic compounds divided into three subsets. The starting point of these modeling strategies is the hydrogen-suppressed chemical graph and pseudograph of a molecule, which works very well for second row atoms. From these types of graphs a set of graph-theoretical basis indices, the molecular connectivity indices, can be derived and used to model properties and activities of molecules. With the aid of the molecular connectivity basis indices it is then possible to build higher-order descriptors. The problem of 'graph' encoding the contribution of the inner-core electrons of heteroatoms can here be solved with the aid of odd complete graphs, Kp-(p-odd. The use of these graph tools allow to draw an optimal modeling of the molecular polarizabilities and a satisfactory modeling of the induced dipole moment of a wide set of organic derivatives.

Graphs whose complement and square are isomorphic

DEFF Research Database (Denmark)

Pedersen, Anders Sune

2014-01-01

We study square-complementary graphs, that is, graphs whose complement and square are isomorphic. We prove several necessary conditions for a graph to be square-complementary, describe ways of building new square-complementary graphs from existing ones, construct infinite families of square-compl...

Graphs & digraphs

CERN Document Server

Chartrand, Gary; Zhang, Ping

2010-01-01

Gary Chartrand has influenced the world of Graph Theory for almost half a century. He has supervised more than a score of Ph.D. dissertations and written several books on the subject. The most widely known of these texts, Graphs and Digraphs, … has much to recommend it, with clear exposition, and numerous challenging examples [that] make it an ideal textbook for the advanced undergraduate or beginning graduate course. The authors have updated their notation to reflect the current practice in this still-growing area of study. By the authors' estimation, the 5th edition is approximately 50% longer than the 4th edition. … the legendary Frank Harary, author of the second graph theory text ever produced, is one of the figures profiled. His book was the standard in the discipline for several decades. Chartrand, Lesniak and Zhang have produced a worthy successor.-John T. Saccoman, MAA Reviews, June 2012 (This book is in the MAA's basic library list.)As with the earlier editions, the current text emphasizes clear...

Packing Degenerate Graphs Greedily

Czech Academy of Sciences Publication Activity Database

Allen, P.; Böttcher, J.; Hladký, J.; Piguet, Diana

2017-01-01

Roč. 61, August (2017), s. 45-51 ISSN 1571-0653 R&D Projects: GA ČR GJ16-07822Y Institutional support: RVO:67985807 Keywords : tree packing conjecture * graph packing * graph processes Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics

Continuous-time quantum walks on star graphs

International Nuclear Information System (INIS)

Salimi, S.

2009-01-01

In this paper, we investigate continuous-time quantum walk on star graphs. It is shown that quantum central limit theorem for a continuous-time quantum walk on star graphs for N-fold star power graph, which are invariant under the quantum component of adjacency matrix, converges to continuous-time quantum walk on K 2 graphs (complete graph with two vertices) and the probability of observing walk tends to the uniform distribution.

Tailored Random Graph Ensembles

International Nuclear Information System (INIS)

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

2013-01-01

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

The Smallest Valid Extension-Based Efficient, Rare Graph Pattern Mining, Considering Length-Decreasing Support Constraints and Symmetry Characteristics of Graphs

Directory of Open Access Journals (Sweden)

Unil Yun

2016-05-01

Full Text Available Frequent graph mining has been proposed to find interesting patterns (i.e., frequent sub-graphs from databases composed of graph transaction data, which can effectively express complex and large data in the real world. In addition, various applications for graph mining have been suggested. Traditional graph pattern mining methods use a single minimum support threshold factor in order to check whether or not mined patterns are interesting. However, it is not a sufficient factor that can consider valuable characteristics of graphs such as graph sizes and features of graph elements. That is, previous methods cannot consider such important characteristics in their mining operations since they only use a fixed minimum support threshold in the mining process. For this reason, in this paper, we propose a novel graph mining algorithm that can consider various multiple, minimum support constraints according to the types of graph elements and changeable minimum support conditions, depending on lengths of graph patterns. In addition, the proposed algorithm performs in mining operations more efficiently because it can minimize duplicated operations and computational overheads by considering symmetry features of graphs. Experimental results provided in this paper demonstrate that the proposed algorithm outperforms previous mining approaches in terms of pattern generation, runtime and memory usage.

Moving beyond the Bar Plot and the Line Graph to Create Informative and Attractive Graphics

Science.gov (United States)

Larson-Hall, Jenifer

2017-01-01

Graphics are often mistaken for a mere frill in the methodological arsenal of data analysis when in fact they can be one of the simplest and at the same time most powerful methods of communicating statistical information (Tufte, 2001). The first section of the article argues for the statistical necessity of graphs, echoing and amplifying similar…

Relating zeta functions of discrete and quantum graphs

Science.gov (United States)

Harrison, Jonathan; Weyand, Tracy

2018-02-01

We write the spectral zeta function of the Laplace operator on an equilateral metric graph in terms of the spectral zeta function of the normalized Laplace operator on the corresponding discrete graph. To do this, we apply a relation between the spectrum of the Laplacian on a discrete graph and that of the Laplacian on an equilateral metric graph. As a by-product, we determine how the multiplicity of eigenvalues of the quantum graph, that are also in the spectrum of the graph with Dirichlet conditions at the vertices, depends on the graph geometry. Finally we apply the result to calculate the vacuum energy and spectral determinant of a complete bipartite graph and compare our results with those for a star graph, a graph in which all vertices are connected to a central vertex by a single edge.

Recognition of fractal graphs

NARCIS (Netherlands)

Perepelitsa, VA; Sergienko, [No Value; Kochkarov, AM

1999-01-01

Definitions of prefractal and fractal graphs are introduced, and they are used to formulate mathematical models in different fields of knowledge. The topicality of fractal-graph recognition from the point of view, of fundamental improvement in the efficiency of the solution of algorithmic problems

Interactive Graph Layout of a Million Nodes

OpenAIRE

Peng Mi; Maoyuan Sun; Moeti Masiane; Yong Cao; Chris North

2016-01-01

Sensemaking of large graphs, specifically those with millions of nodes, is a crucial task in many fields. Automatic graph layout algorithms, augmented with real-time human-in-the-loop interaction, can potentially support sensemaking of large graphs. However, designing interactive algorithms to achieve this is challenging. In this paper, we tackle the scalability problem of interactive layout of large graphs, and contribute a new GPU-based force-directed layout algorithm that exploits graph to...

RATGRAPH: Computer Graphing of Rational Functions.

Science.gov (United States)

Minch, Bradley A.

1987-01-01

Presents an easy-to-use Applesoft BASIC program that graphs rational functions and any asymptotes that the functions might have. Discusses the nature of rational functions, graphing them manually, employing a computer to graph rational functions, and describes how the program works. (TW)

Graph algorithms in the titan toolkit.

Energy Technology Data Exchange (ETDEWEB)

McLendon, William Clarence, III; Wylie, Brian Neil

2009-10-01

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

A Graph Calculus for Predicate Logic

Directory of Open Access Journals (Sweden)

Paulo A. S. Veloso

2013-03-01

Full Text Available We introduce a refutation graph calculus for classical first-order predicate logic, which is an extension of previous ones for binary relations. One reduces logical consequence to establishing that a constructed graph has empty extension, i. e. it represents bottom. Our calculus establishes that a graph has empty extension by converting it to a normal form, which is expanded to other graphs until we can recognize conflicting situations (equivalent to a formula and its negation.

Deep Learning with Dynamic Computation Graphs

OpenAIRE

Looks, Moshe; Herreshoff, Marcello; Hutchins, DeLesley; Norvig, Peter

2017-01-01

Neural networks that compute over graph structures are a natural fit for problems in a variety of domains, including natural language (parse trees) and cheminformatics (molecular graphs). However, since the computation graph has a different shape and size for every input, such networks do not directly support batched training or inference. They are also difficult to implement in popular deep learning libraries, which are based on static data-flow graphs. We introduce a technique called dynami...

Constructs for Programming with Graph Rewrites

OpenAIRE

Rodgers, Peter

2000-01-01

Graph rewriting is becoming increasingly popular as a method for programming with graph based data structures. We present several modifications to a basic serial graph rewriting paradigm and discuss how they improve coding programs in the Grrr graph rewriting programming language. The constructs we present are once only nodes, attractor nodes and single match rewrites. We illustrate the operation of the constructs by example. The advantages of adding these new rewrite modifiers is to reduce t...

Quantum chaos on discrete graphs

International Nuclear Information System (INIS)

Smilansky, Uzy

2007-01-01

Adapting a method developed for the study of quantum chaos on quantum (metric) graphs (Kottos and Smilansky 1997 Phys. Rev. Lett. 79 4794, Kottos and Smilansky 1999 Ann. Phys., NY 274 76), spectral ζ functions and trace formulae for discrete Laplacians on graphs are derived. This is achieved by expressing the spectral secular equation in terms of the periodic orbits of the graph and obtaining functions which belong to the class of ζ functions proposed originally by Ihara (1966 J. Mat. Soc. Japan 18 219) and expanded by subsequent authors (Stark and Terras 1996 Adv. Math. 121 124, Kotani and Sunada 2000 J. Math. Sci. Univ. Tokyo 7 7). Finally, a model of 'classical dynamics' on the discrete graph is proposed. It is analogous to the corresponding classical dynamics derived for quantum graphs (Kottos and Smilansky 1997 Phys. Rev. Lett. 79 4794, Kottos and Smilansky 1999 Ann. Phys., NY 274 76). (fast track communication)

Bipartite separability and nonlocal quantum operations on graphs

Science.gov (United States)

Dutta, Supriyo; Adhikari, Bibhas; Banerjee, Subhashish; Srikanth, R.

2016-07-01

In this paper we consider the separability problem for bipartite quantum states arising from graphs. Earlier it was proved that the degree criterion is the graph-theoretic counterpart of the familiar positive partial transpose criterion for separability, although there are entangled states with positive partial transpose for which the degree criterion fails. Here we introduce the concept of partially symmetric graphs and degree symmetric graphs by using the well-known concept of partial transposition of a graph and degree criteria, respectively. Thus, we provide classes of bipartite separable states of dimension m ×n arising from partially symmetric graphs. We identify partially asymmetric graphs that lack the property of partial symmetry. We develop a combinatorial procedure to create a partially asymmetric graph from a given partially symmetric graph. We show that this combinatorial operation can act as an entanglement generator for mixed states arising from partially symmetric graphs.

Algorithms and Data Structures for Graphs

DEFF Research Database (Denmark)

Rotenberg, Eva

are planar graphs, which are those that can be drawn on a piece of paper without any pair of edges crossing. For planar graphs where each edge can only be traversed in one direction, a fundamental question is whether there is a route from vertex A to vertex B in the graph. We show how such a graph can...... of the form: "Is there an edge such that all paths between A and B go via that edge?" and which can quickly be updated when edges are inserted or deleted. We further show how to represent a planar graph such that we can quickly update our representation when an edge is deleted, and such that questions...

On the nullity number of graphs

Directory of Open Access Journals (Sweden)

Mustapha Aouchiche

2017-10-01

Full Text Available The paper discusses bounds on the nullity number of graphs. It is proved in [B. Cheng and B. Liu, On the nullity of graphs. Electron. J. Linear Algebra 16 (2007 60--67] that $\\eta \\le n - D$, where $\\eta$, n and D denote the nullity number, the order and the diameter of a connected graph, respectively. We first give a necessary condition on the extremal graphs corresponding to that bound, and then we strengthen the bound itself using the maximum clique number. In addition, we prove bounds on the nullity using the number of pendant neighbors in a graph. One of those bounds is an improvement of a known bound involving the domination number.

Graph Transforming Java Data

NARCIS (Netherlands)

de Mol, M.J.; Rensink, Arend; Hunt, James J.

This paper introduces an approach for adding graph transformation-based functionality to existing JAVA programs. The approach relies on a set of annotations to identify the intended graph structure, as well as on user methods to manipulate that structure, within the user’s own JAVA class

Graph processing platforms at scale: practices and experiences

Energy Technology Data Exchange (ETDEWEB)

Lim, Seung-Hwan [ORNL; Lee, Sangkeun (Matt) [ORNL; Brown, Tyler C [ORNL; Sukumar, Sreenivas R [ORNL; Ganesh, Gautam [ORNL

2015-01-01

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

Generalized hypercube graph $\\Q_n(S$, graph products and self-orthogonal codes

Directory of Open Access Journals (Sweden)

Pani Seneviratne

2016-01-01

Full Text Available A generalized hypercube graph $\\Q_n(S$ has $\\F_{2}^{n}=\\{0,1\\}^n$ as the vertex set and two vertices being adjacent whenever their mutual Hamming distance belongs to $S$, where $n \\ge 1$ and $S\\subseteq \\{1,2,\\ldots, n\\}$. The graph $\\Q_n(\\{1\\}$ is the $n$-cube, usually denoted by $\\Q_n$.We study graph boolean products $G_1 = \\Q_n(S\\times \\Q_1, G_2 = \\Q_{n}(S\\wedge \\Q_1$, $G_3 = \\Q_{n}(S[\\Q_1]$ and show that binary codes from neighborhood designs of $G_1, G_2$ and $G_3$ are self-orthogonal for all choices of $n$ and $S$. More over, we show that the class of codes $C_1$ are self-dual. Further we find subgroups of the automorphism group of these graphs and use these subgroups to obtain PD-sets for permutation decoding. As an example we find a full error-correcting PD set for the binary $[32, 16, 8]$ extremal self-dual code.

Survey of Approaches to Generate Realistic Synthetic Graphs

Energy Technology Data Exchange (ETDEWEB)

Lim, Seung-Hwan [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Lee, Sangkeun [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Powers, Sarah S [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Shankar, Mallikarjun [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Imam, Neena [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

2016-10-01

A graph is a flexible data structure that can represent relationships between entities. As with other data analysis tasks, the use of realistic graphs is critical to obtaining valid research results. Unfortunately, using the actual ("real-world") graphs for research and new algorithm development is difficult due to the presence of sensitive information in the data or due to the scale of data. This results in practitioners developing algorithms and systems that employ synthetic graphs instead of real-world graphs. Generating realistic synthetic graphs that provide reliable statistical confidence to algorithmic analysis and system evaluation involves addressing technical hurdles in a broad set of areas. This report surveys the state of the art in approaches to generate realistic graphs that are derived from fitted graph models on real-world graphs.

Constructing Dense Graphs with Unique Hamiltonian Cycles

Science.gov (United States)

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…

Chromatic polynomials of random graphs

International Nuclear Information System (INIS)

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

2010-01-01

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

On some labelings of triangular snake and central graph of triangular snake graph

Science.gov (United States)

Agasthi, P.; Parvathi, N.

2018-04-01

A Triangular snake Tn is obtained from a path u 1 u 2 … u n by joining ui and u i+1 to a new vertex wi for 1≤i≤n‑1. A Central graph of Triangular snake C(T n ) is obtained by subdividing each edge of Tn exactly once and joining all the non adjacent vertices of Tn . In this paper the ways to construct square sum, square difference, Root Mean square, strongly Multiplicative, Even Mean and Odd Mean labeling for Triangular Snake and Central graph of Triangular Snake graphs are reported.

Orientations of infinite graphs with prescribed edge-connectivity

DEFF Research Database (Denmark)

Thomassen, Carsten

2016-01-01

We prove a decomposition result for locally finite graphs which can be used to extend results on edge-connectivity from finite to infinite graphs. It implies that every 4k-edge-connected graph G contains an immersion of some finite 2k-edge-connected Eulerian graph containing any prescribed vertex...... set (while planar graphs show that G need not containa subdivision of a simple finite graph of large edge-connectivity). Also, every 8k-edge connected infinite graph has a k-arc-connected orientation, as conjectured in 1989....

Genus Ranges of 4-Regular Rigid Vertex Graphs.

Science.gov (United States)

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 2 n vertices ( n > 1), we prove that all intervals [ a, b ] for all a genus ranges. For graphs with 2 n - 1 vertices ( n ≥ 1), we prove that all intervals [ a, b ] for all a genus ranges. We also provide constructions of graphs that realize these ranges.

A new cluster algorithm for graphs

NARCIS (Netherlands)

S. van Dongen

1998-01-01

textabstractA new cluster algorithm for graphs called the emph{Markov Cluster algorithm ($MCL$ algorithm) is introduced. The graphs may be both weighted (with nonnegative weight) and directed. Let~$G$~be such a graph. The $MCL$ algorithm simulates flow in $G$ by first identifying $G$ in a

On the structure of critical energy levels for the cubic focusing NLS on star graphs

International Nuclear Information System (INIS)

Adami, Riccardo; Noja, Diego; Cacciapuoti, Claudio; Finco, Domenico

2012-01-01

We provide information on a non-trivial structure of phase space of the cubic nonlinear Schrödinger (NLS) on a three-edge star graph. We prove that, in contrast to the case of the standard NLS on the line, the energy associated with the cubic focusing Schrödinger equation on the three-edge star graph with a free (Kirchhoff) vertex does not attain a minimum value on any sphere of constant L 2 -norm. We moreover show that the only stationary state with prescribed L 2 -norm is indeed a saddle point. (fast track communication)

Chemical Graph Transformation with Stereo-Information

DEFF Research Database (Denmark)

Andersen, Jakob Lykke; Flamm, Christoph; Merkle, Daniel

2017-01-01

Double Pushout graph transformation naturally facilitates the modelling of chemical reactions: labelled undirected graphs model molecules and direct derivations model chemical reactions. However, the most straightforward modelling approach ignores the relative placement of atoms and their neighbo......Double Pushout graph transformation naturally facilitates the modelling of chemical reactions: labelled undirected graphs model molecules and direct derivations model chemical reactions. However, the most straightforward modelling approach ignores the relative placement of atoms...... and their neighbours in space. Stereoisomers of chemical compounds thus cannot be distinguished, even though their chemical activity may differ substantially. In this contribution we propose an extended chemical graph transformation system with attributes that encode information about local geometry. The modelling...... of graph transformation, but we here propose a framework that also allows for partially specified stereoinformation. While there are several stereochemical configurations to be considered, we focus here on the tetrahedral molecular shape, and suggest general principles for how to treat all other chemically...

Large-Scale Graph Processing Using Apache Giraph

KAUST Repository

Sakr, Sherif

2017-01-07

This book takes its reader on a journey through Apache Giraph, a popular distributed graph processing platform designed to bring the power of big data processing to graph data. Designed as a step-by-step self-study guide for everyone interested in large-scale graph processing, it describes the fundamental abstractions of the system, its programming models and various techniques for using the system to process graph data at scale, including the implementation of several popular and advanced graph analytics algorithms.

Large-Scale Graph Processing Using Apache Giraph

KAUST Repository

Sakr, Sherif; Orakzai, Faisal Moeen; Abdelaziz, Ibrahim; Khayyat, Zuhair

2017-01-01

This book takes its reader on a journey through Apache Giraph, a popular distributed graph processing platform designed to bring the power of big data processing to graph data. Designed as a step-by-step self-study guide for everyone interested in large-scale graph processing, it describes the fundamental abstractions of the system, its programming models and various techniques for using the system to process graph data at scale, including the implementation of several popular and advanced graph analytics algorithms.

Graph Algorithm Animation with Grrr

OpenAIRE

Rodgers, Peter; Vidal, Natalia

2000-01-01

We discuss geometric positioning, highlighting of visited nodes and user defined highlighting that form the algorithm animation facilities in the Grrr graph rewriting programming language. The main purpose of animation was initially for the debugging and profiling of Grrr code, but recently it has been extended for the purpose of teaching algorithms to undergraduate students. The animation is restricted to graph based algorithms such as graph drawing, list manipulation or more traditional gra...

Trajectories entropy in dynamical graphs with memory

Directory of Open Access Journals (Sweden)

Francesco eCaravelli

2016-04-01

Full Text Available In this paper we investigate the application of non-local graph entropy to evolving and dynamical graphs. The measure is based upon the notion of Markov diffusion on a graph, and relies on the entropy applied to trajectories originating at a specific node. In particular, we study the model of reinforcement-decay graph dynamics, which leads to scale free graphs. We find that the node entropy characterizes the structure of the network in the two parameter phase-space describing the dynamical evolution of the weighted graph. We then apply an adapted version of the entropy measure to purely memristive circuits. We provide evidence that meanwhile in the case of DC voltage the entropy based on the forward probability is enough to characterize the graph properties, in the case of AC voltage generators one needs to consider both forward and backward based transition probabilities. We provide also evidence that the entropy highlights the self-organizing properties of memristive circuits, which re-organizes itself to satisfy the symmetries of the underlying graph.

On revealing graph cycles via boundary measurements

International Nuclear Information System (INIS)

Belishev, M I; Wada, N

2009-01-01

This paper deals with boundary value inverse problems on a metric graph, the structure of the graph being assumed unknown. The question under consideration is how to detect from the dynamical and/or spectral inverse data whether the graph contains cycles (is not a tree). For any graph Ω, the dynamical as well as spectral boundary inverse data determine the so-called wave diameter d w : H -1 (Ω) → R defined on functionals supported in the graph. The known fact is that if Ω is a tree then d w ≥ 0 holds and, in this case, the inverse data determine Ω up to isometry. A graph Ω is said to be coordinate if the functions {dist Ω (., γ)} γin∂Ω constitute a coordinate system on Ω. For such graphs, we propose a procedure, which reveals the presence/absence of cycles. The hypothesis is that Ω contains cycles if and only if d w takes negative values. We do not justify this hypothesis in the general case but reduce it to a certain special class of graphs (suns)

OPEX: Optimized Eccentricity Computation in Graphs

Energy Technology Data Exchange (ETDEWEB)

Henderson, Keith [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

2011-11-14

Real-world graphs have many properties of interest, but often these properties are expensive to compute. We focus on eccentricity, radius and diameter in this work. These properties are useful measures of the global connectivity patterns in a graph. Unfortunately, computing eccentricity for all nodes is O(n2) for a graph with n nodes. We present OPEX, a novel combination of optimizations which improves computation time of these properties by orders of magnitude in real-world experiments on graphs of many different sizes. We run OPEX on graphs with up to millions of links. OPEX gives either exact results or bounded approximations, unlike its competitors which give probabilistic approximations or sacrifice node-level information (eccentricity) to compute graphlevel information (diameter).

Pixels to Graphs by Associative Embedding

KAUST Repository

Newell, Alejandro

2017-06-22

Graphs are a useful abstraction of image content. Not only can graphs represent details about individual objects in a scene but they can capture the interactions between pairs of objects. We present a method for training a convolutional neural network such that it takes in an input image and produces a full graph. This is done end-to-end in a single stage with the use of associative embeddings. The network learns to simultaneously identify all of the elements that make up a graph and piece them together. We benchmark on the Visual Genome dataset, and report a Recall@50 of 9.7% compared to the prior state-of-the-art at 3.4%, a nearly threefold improvement on the challenging task of scene graph generation.

A faithful functor among algebras and graphs

OpenAIRE

Falcón Ganfornina, Óscar Jesús; Falcón Ganfornina, Raúl Manuel; Núñez Valdés, Juan; Pacheco Martínez, Ana María; Villar Liñán, María Trinidad; Vigo Aguiar, Jesús (Coordinador)

2016-01-01

The problem of identifying a functor between the categories of algebras and graphs is currently open. Based on a known algorithm that identifies isomorphisms of Latin squares with isomorphism of vertex-colored graphs, we describe here a pair of graphs that enable us to find a faithful functor between finite-dimensional algebras over finite fields and these graphs.

Cellular Automata on Graphs: Topological Properties of ER Graphs Evolved towards Low-Entropy Dynamics

Directory of Open Access Journals (Sweden)

Marc-Thorsten Hütt

2012-06-01

Full Text Available Cellular automata (CA are a remarkably  efficient tool for exploring general properties of complex systems and spatiotemporal patterns arising from local rules. Totalistic cellular automata,  where the update  rules depend  only on the density of neighboring states, are at the same time a versatile  tool for exploring  dynamical  processes on graphs. Here we briefly review our previous results on cellular automata on graphs, emphasizing some systematic relationships between network architecture and dynamics identified in this way. We then extend the investigation  towards graphs obtained in a simulated-evolution procedure, starting from Erdő s–Rényi (ER graphs and selecting for low entropies of the CA dynamics. Our key result is a strong association of low Shannon entropies with a broadening of the graph’s degree distribution.

The color space of a graph

DEFF Research Database (Denmark)

Jensen, T.R.; Thomassen, Carsten

2000-01-01

If k is a prime power, and G is a graph with n vertices, then a k-coloring of G may be considered as a vector in GF(k)(n). We prove that the subspace of GF(3)(n) spanned by all 3-colorings of a planar triangle-free graph with n vertices has dimension n. In particular, any such graph has at least n...... - 1 nonequivalent 3-colorings, and the addition of any edge or any vertex of degree 3 results in a 3-colorable graph. (C) 2000 John Wiley & Sons, Inc....

Box graphs and resolutions I

Directory of Open Access Journals (Sweden)

Andreas P. Braun

2016-04-01

Full Text Available Box graphs succinctly and comprehensively characterize singular fibers of elliptic fibrations in codimension two and three, as well as flop transitions connecting these, in terms of representation theoretic data. We develop a framework that provides a systematic map between a box graph and a crepant algebraic resolution of the singular elliptic fibration, thus allowing an explicit construction of the fibers from a singular Weierstrass or Tate model. The key tool is what we call a fiber face diagram, which shows the relevant information of a (partial toric triangulation and allows the inclusion of more general algebraic blowups. We shown that each such diagram defines a sequence of weighted algebraic blowups, thus providing a realization of the fiber defined by the box graph in terms of an explicit resolution. We show this correspondence explicitly for the case of SU(5 by providing a map between box graphs and fiber faces, and thereby a sequence of algebraic resolutions of the Tate model, which realizes each of the box graphs.

Forbidden Structures for Planar Perfect Consecutively Colourable Graphs

Directory of Open Access Journals (Sweden)

Borowiecka-Olszewska Marta

2017-05-01

Full Text Available A consecutive colouring of a graph is a proper edge colouring with posi- tive integers in which the colours of edges incident with each vertex form an interval of integers. The idea of this colouring was introduced in 1987 by Asratian and Kamalian under the name of interval colouring. Sevast- janov showed that the corresponding decision problem is NP-complete even restricted to the class of bipartite graphs. We focus our attention on the class of consecutively colourable graphs whose all induced subgraphs are consecutively colourable, too. We call elements of this class perfect consecutively colourable to emphasise the conceptual similarity to perfect graphs. Obviously, the class of perfect consecutively colourable graphs is induced hereditary, so it can be characterized by the family of induced forbidden graphs. In this work we give a necessary and sufficient conditions that must be satisfied by the generalized Sevastjanov rosette to be an induced forbid- den graph for the class of perfect consecutively colourable graphs. Along the way, we show the exact values of the deficiency of all generalized Sevastjanov rosettes, which improves the earlier known estimating result. It should be mentioned that the deficiency of a graph measures its closeness to the class of consecutively colourable graphs. We motivate the investigation of graphs considered here by showing their connection to the class of planar perfect consecutively colourable graphs.

47 CFR 80.761 - Conversion graphs.

Science.gov (United States)

2010-10-01

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

Building Scalable Knowledge Graphs for Earth Science

Science.gov (United States)

Ramachandran, Rahul; Maskey, Manil; Gatlin, Patrick; Zhang, Jia; Duan, Xiaoyi; Miller, J. J.; Bugbee, Kaylin; Christopher, Sundar; Freitag, Brian

2017-01-01

Knowledge Graphs link key entities in a specific domain with other entities via relationships. From these relationships, researchers can query knowledge graphs for probabilistic recommendations to infer new knowledge. Scientific papers are an untapped resource which knowledge graphs could leverage to accelerate research discovery. Goal: Develop an end-to-end (semi) automated methodology for constructing Knowledge Graphs for Earth Science.

In-line monitoring and interpretation of an indomethacin anti-solvent crystallization process by near-infrared spectroscopy (NIRS).

Science.gov (United States)

Lee, Hea-Eun; Lee, Min-Jeong; Kim, Woo-Sik; Jeong, Myung-Yung; Cho, Young-Sang; Choi, Guang Jin

2011-11-28

PAT (process analytical technology) has been emphasized as one of key elements for the full implementation of QbD (quality-by-design) in the pharmaceutical area. NIRS (near-infrared spectroscopy) has been studied intensively as an in-line/on-line monitoring tool in chemical and biomedical industries. A precise and reliable monitoring of the particle characteristics during crystallization along with a suitable control strategy should be highly encouraged for the conformance to new quality system of pharmaceutical products. In this study, the anti-solvent crystallization process of indomethacin (IMC) was monitored using an in-line NIRS. IMC powders were produced via anti-solvent crystallization using two schemes; 'S-to-A' (solvent-to-antisolvent) and 'A-to-S' (antisolvent-to-solvent). In-line NIR spectra were analyzed by a PCA (principal component analysis) method. Although pure α-form IMC powder was resulted under A-to-S scheme, a mixture of the α-form and γ-form was produced for S-to-A case. By integrating the PCA results with off-line characterization (SEM, XRD, DSC) data, the crystallization process under each scheme was elucidated by three distinct consecutive steps. It was demonstrated that in-line NIRS, combined with PCA, can be very useful to monitor in real time and interpret the anti-solvent crystallization process with respect to the polymorphism and particle size. Copyright © 2011 Elsevier B.V. All rights reserved.

On the diameter of dot-critical graphs

Directory of Open Access Journals (Sweden)

Doost Ali Mojdeh

2009-01-01

Full Text Available A graph G is \\(k\\-dot-critical (totaly \\(k\\-dot-critical if \\(G\\ is dot-critical (totaly dot-critical and the domination number is \\(k\\. In the paper [T. Burtona, D. P. Sumner, Domination dot-critical graphs, Discrete Math, 306 (2006, 11-18] the following question is posed: What are the best bounds for the diameter of a \\(k\\-dot-critical graph and a totally \\(k\\-dot-critical graph \\(G\\ with no critical vertices for \\(k \\geq 4\\? We find the best bound for the diameter of a \\(k\\-dot-critical graph, where \\(k \\in\\{4,5,6\\}\\ and we give a family of \\(k\\-dot-critical graphs (with no critical vertices with sharp diameter \\(2k-3\\ for even \\(k \\geq 4\\.

graphkernels: R and Python packages for graph comparison.

Science.gov (United States)

Sugiyama, Mahito; Ghisu, M Elisabetta; Llinares-López, Felipe; Borgwardt, Karsten

2018-02-01

Measuring the similarity of graphs is a fundamental step in the analysis of graph-structured data, which is omnipresent in computational biology. Graph kernels have been proposed as a powerful and efficient approach to this problem of graph comparison. Here we provide graphkernels, the first R and Python graph kernel libraries including baseline kernels such as label histogram based kernels, classic graph kernels such as random walk based kernels, and the state-of-the-art Weisfeiler-Lehman graph kernel. The core of all graph kernels is implemented in C ++ for efficiency. Using the kernel matrices computed by the package, we can easily perform tasks such as classification, regression and clustering on graph-structured samples. The R and Python packages including source code are available at https://CRAN.R-project.org/package=graphkernels and https://pypi.python.org/pypi/graphkernels. mahito@nii.ac.jp or elisabetta.ghisu@bsse.ethz.ch. Supplementary data are available online at Bioinformatics. © The Author(s) 2017. Published by Oxford University Press.

Graph anomalies in cyber communications

Energy Technology Data Exchange (ETDEWEB)

Vander Wiel, Scott A [Los Alamos National Laboratory; Storlie, Curtis B [Los Alamos National Laboratory; Sandine, Gary [Los Alamos National Laboratory; Hagberg, Aric A [Los Alamos National Laboratory; Fisk, Michael [Los Alamos National Laboratory

2011-01-11

Enterprises monitor cyber traffic for viruses, intruders and stolen information. Detection methods look for known signatures of malicious traffic or search for anomalies with respect to a nominal reference model. Traditional anomaly detection focuses on aggregate traffic at central nodes or on user-level monitoring. More recently, however, traffic is being viewed more holistically as a dynamic communication graph. Attention to the graph nature of the traffic has expanded the types of anomalies that are being sought. We give an overview of several cyber data streams collected at Los Alamos National Laboratory and discuss current work in modeling the graph dynamics of traffic over the network. We consider global properties and local properties within the communication graph. A method for monitoring relative entropy on multiple correlated properties is discussed in detail.

Graphs, groups and surfaces

CERN Document Server

White, AT

1985-01-01

The field of topological graph theory has expanded greatly in the ten years since the first edition of this book appeared. The original nine chapters of this classic work have therefore been revised and updated. Six new chapters have been added, dealing with: voltage graphs, non-orientable imbeddings, block designs associated with graph imbeddings, hypergraph imbeddings, map automorphism groups and change ringing.Thirty-two new problems have been added to this new edition, so that there are now 181 in all; 22 of these have been designated as ``difficult'''' and 9 as ``unsolved''''. Three of the four unsolved problems from the first edition have been solved in the ten years between editions; they are now marked as ``difficult''''.

Subdominant pseudoultrametric on graphs

Energy Technology Data Exchange (ETDEWEB)

Dovgoshei, A A; Petrov, E A [Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, Donetsk (Ukraine)

2013-08-31

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

Equitable Colorings Of Corona Multiproducts Of Graphs

Directory of Open Access Journals (Sweden)

Furmánczyk Hanna

2017-11-01

Full Text Available A graph is equitably k-colorable if its vertices can be partitioned into k independent sets in such a way that the numbers of vertices in any two sets differ by at most one. The smallest k for which such a coloring exists is known as the equitable chromatic number of G and denoted by =(G. It is known that the problem of computation of =(G is NP-hard in general and remains so for corona graphs. In this paper we consider the same model of coloring in the case of corona multiproducts of graphs. In particular, we obtain some results regarding the equitable chromatic number for the l-corona product G ◦l H, where G is an equitably 3- or 4-colorable graph and H is an r-partite graph, a cycle or a complete graph. Our proofs are mostly constructive in that they lead to polynomial algorithms for equitable coloring of such graph products provided that there is given an equitable coloring of G. Moreover, we confirm the Equitable Coloring Conjecture for corona products of such graphs. This paper extends the results from [H. Furmánczyk, K. Kaliraj, M. Kubale and V.J. Vivin, Equitable coloring of corona products of graphs, Adv. Appl. Discrete Math. 11 (2013 103–120].

Sphere and dot product representations of graphs

NARCIS (Netherlands)

R.J. Kang (Ross); T. Müller (Tobias)

2012-01-01

textabstractA graph $G$ is a $k$-sphere graph if there are $k$-dimensional real vectors $v_1,\\dots,v_n$ such that $ij\\in E(G)$ if and only if the distance between $v_i$ and $v_j$ is at most $1$. A graph $G$ is a $k$-dot product graph if there are $k$-dimensional real vectors $v_1,\\dots,v_n$ such

Unsupervised active learning based on hierarchical graph-theoretic clustering.

Science.gov (United States)

Hu, Weiming; Hu, Wei; Xie, Nianhua; Maybank, Steve

2009-10-01

Most existing active learning approaches are supervised. Supervised active learning has the following problems: inefficiency in dealing with the semantic gap between the distribution of samples in the feature space and their labels, lack of ability in selecting new samples that belong to new categories that have not yet appeared in the training samples, and lack of adaptability to changes in the semantic interpretation of sample categories. To tackle these problems, we propose an unsupervised active learning framework based on hierarchical graph-theoretic clustering. In the framework, two promising graph-theoretic clustering algorithms, namely, dominant-set clustering and spectral clustering, are combined in a hierarchical fashion. Our framework has some advantages, such as ease of implementation, flexibility in architecture, and adaptability to changes in the labeling. Evaluations on data sets for network intrusion detection, image classification, and video classification have demonstrated that our active learning framework can effectively reduce the workload of manual classification while maintaining a high accuracy of automatic classification. It is shown that, overall, our framework outperforms the support-vector-machine-based supervised active learning, particularly in terms of dealing much more efficiently with new samples whose categories have not yet appeared in the training samples.

Graph Query Portal

OpenAIRE

Dayal, Amit; Brock, David

2018-01-01

Prashant Chandrasekar, a lead developer for the Social Interactome project, has tasked the team with creating a graph representation of the data collected from the social networks involved in that project. The data is currently stored in a MySQL database. The client requested that the graph database be Cayley, but after a literature review, Neo4j was chosen. The reasons for this shift will be explained in the design section. Secondarily, the team was tasked with coming up with three scena...

An Association-Oriented Partitioning Approach for Streaming Graph Query

Directory of Open Access Journals (Sweden)

Yun Hao

2017-01-01

Full Text Available The volumes of real-world graphs like knowledge graph are increasing rapidly, which makes streaming graph processing a hot research area. Processing graphs in streaming setting poses significant challenges from different perspectives, among which graph partitioning method plays a key role. Regarding graph query, a well-designed partitioning method is essential for achieving better performance. Existing offline graph partitioning methods often require full knowledge of the graph, which is not possible during streaming graph processing. In order to handle this problem, we propose an association-oriented streaming graph partitioning method named Assc. This approach first computes the rank values of vertices with a hybrid approximate PageRank algorithm. After splitting these vertices with an adapted variant affinity propagation algorithm, the process order on vertices in the sliding window can be determined. Finally, according to the level of these vertices and their association, the partition where the vertices should be distributed is decided. We compare its performance with a set of streaming graph partition methods and METIS, a widely adopted offline approach. The results show that our solution can partition graphs with hundreds of millions of vertices in streaming setting on a large collection of graph datasets and our approach outperforms other graph partitioning methods.

A comparative study of applying Mason’s Rule in the case of flow-graphs and bond-graphs

Directory of Open Access Journals (Sweden)

Adriana Grava

2009-05-01

Full Text Available The paper presents two methods to analyzethe electric circuits using the flow-graphs and thebond-graphs studying the differences between thesemethods.As it can be noticed, the two methods are totallydifferent; their common point being Mason’s rule thatis applied in both cases but it is applied differently foreach type of graphs.

An algebraic approach to graph codes

DEFF Research Database (Denmark)

Pinero, Fernando

This thesis consists of six chapters. The first chapter, contains a short introduction to coding theory in which we explain the coding theory concepts we use. In the second chapter, we present the required theory for evaluation codes and also give an example of some fundamental codes in coding...... theory as evaluation codes. Chapter three consists of the introduction to graph based codes, such as Tanner codes and graph codes. In Chapter four, we compute the dimension of some graph based codes with a result combining graph based codes and subfield subcodes. Moreover, some codes in chapter four...

Replica methods for loopy sparse random graphs

International Nuclear Information System (INIS)

Coolen, ACC

2016-01-01

I report on the development of a novel statistical mechanical formalism for the analysis of random graphs with many short loops, and processes on such graphs. The graphs are defined via maximum entropy ensembles, in which both the degrees (via hard constraints) and the adjacency matrix spectrum (via a soft constraint) are prescribed. The sum over graphs can be done analytically, using a replica formalism with complex replica dimensions. All known results for tree-like graphs are recovered in a suitable limit. For loopy graphs, the emerging theory has an appealing and intuitive structure, suggests how message passing algorithms should be adapted, and what is the structure of theories describing spin systems on loopy architectures. However, the formalism is still largely untested, and may require further adjustment and refinement. (paper)

The STAPL Parallel Graph Library

KAUST Repository

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

2013-01-01

This paper describes the stapl Parallel Graph Library, a high-level framework that abstracts the user from data-distribution and parallelism details and allows them to concentrate on parallel graph algorithm development. It includes a customizable

Coloring and The Lonely Graph

OpenAIRE

Rabern, Landon

2007-01-01

We improve upper bounds on the chromatic number proven independently in \\cite{reedNote} and \\cite{ingo}. Our main lemma gives a sufficient condition for two paths in graph to be completely joined. Using this, we prove that if a graph has an optimal coloring with more than $\\frac{\\omega}{2}$ singleton color classes, then it satisfies $\\chi \\leq \\frac{\\omega + \\Delta + 1}{2}$. It follows that a graph satisfying $n - \\Delta < \\alpha + \\frac{\\omega - 1}{2}$ must also satisfy $\\chi \\leq \\frac{\\ome...

Graph Mining Meets the Semantic Web

Energy Technology Data Exchange (ETDEWEB)

Lee, Sangkeun (Matt) [ORNL; Sukumar, Sreenivas R [ORNL; Lim, Seung-Hwan [ORNL

2015-01-01

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

A model of language inflection graphs

Science.gov (United States)

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.

Incremental Frequent Subgraph Mining on Large Evolving Graphs

KAUST Repository

Abdelhamid, Ehab

2017-08-22

Frequent subgraph mining is a core graph operation used in many domains, such as graph data management and knowledge exploration, bioinformatics and security. Most existing techniques target static graphs. However, modern applications, such as social networks, utilize large evolving graphs. Mining these graphs using existing techniques is infeasible, due to the high computational cost. In this paper, we propose IncGM+, a fast incremental approach for continuous frequent subgraph mining problem on a single large evolving graph. We adapt the notion of “fringe” to the graph context, that is the set of subgraphs on the border between frequent and infrequent subgraphs. IncGM+ maintains fringe subgraphs and exploits them to prune the search space. To boost the efficiency, we propose an efficient index structure to maintain selected embeddings with minimal memory overhead. These embeddings are utilized to avoid redundant expensive subgraph isomorphism operations. Moreover, the proposed system supports batch updates. Using large real-world graphs, we experimentally verify that IncGM+ outperforms existing methods by up to three orders of magnitude, scales to much larger graphs and consumes less memory.

Smooth Bundling of Large Streaming and Sequence Graphs

NARCIS (Netherlands)

Hurter, C.; Ersoy, O.; Telea, A.

2013-01-01

Dynamic graphs are increasingly pervasive in modern information systems. However, understanding how a graph changes in time is difficult. We present here two techniques for simplified visualization of dynamic graphs using edge bundles. The first technique uses a recent image-based graph bundling

The groupies of random multipartite graphs

OpenAIRE

Portmann, Marius; Wang, Hongyun

2012-01-01

If a vertex $v$ in a graph $G$ has degree larger than the average of the degrees of its neighbors, we call it a groupie in $G$. In the current work, we study the behavior of groupie in random multipartite graphs with the link probability between sets of nodes fixed. Our results extend the previous ones on random (bipartite) graphs.

Open Graphs and Computational Reasoning

Directory of Open Access Journals (Sweden)

Lucas Dixon

2010-06-01

Full Text Available We present a form of algebraic reasoning for computational objects which are expressed as graphs. Edges describe the flow of data between primitive operations which are represented by vertices. These graphs have an interface made of half-edges (edges which are drawn with an unconnected end and enjoy rich compositional principles by connecting graphs along these half-edges. In particular, this allows equations and rewrite rules to be specified between graphs. Particular computational models can then be encoded as an axiomatic set of such rules. Further rules can be derived graphically and rewriting can be used to simulate the dynamics of a computational system, e.g. evaluating a program on an input. Examples of models which can be formalised in this way include traditional electronic circuits as well as recent categorical accounts of quantum information.

Properly colored connectivity of graphs

CERN Document Server

Li, Xueliang; Qin, Zhongmei

2018-01-01

A comprehensive survey of proper connection of graphs is discussed in this book with real world applications in computer science and network security. Beginning with a brief introduction, comprising relevant definitions and preliminary results, this book moves on to consider a variety of properties of graphs that imply bounds on the proper connection number. Detailed proofs of significant advancements toward open problems and conjectures are presented with complete references. Researchers and graduate students with an interest in graph connectivity and colorings will find this book useful as it builds upon fundamental definitions towards modern innovations, strategies, and techniques. The detailed presentation lends to use as an introduction to proper connection of graphs for new and advanced researchers, a solid book for a graduate level topics course, or as a reference for those interested in expanding and further developing research in the area.

Inferring ontology graph structures using OWL reasoning

KAUST Repository

Rodriguez-Garcia, Miguel Angel

2018-01-05

Ontologies are representations of a conceptualization of a domain. Traditionally, ontologies in biology were represented as directed acyclic graphs (DAG) which represent the backbone taxonomy and additional relations between classes. These graphs are widely exploited for data analysis in the form of ontology enrichment or computation of semantic similarity. More recently, ontologies are developed in a formal language such as the Web Ontology Language (OWL) and consist of a set of axioms through which classes are defined or constrained. While the taxonomy of an ontology can be inferred directly from the axioms of an ontology as one of the standard OWL reasoning tasks, creating general graph structures from OWL ontologies that exploit the ontologies\\' semantic content remains a challenge.We developed a method to transform ontologies into graphs using an automated reasoner while taking into account all relations between classes. Searching for (existential) patterns in the deductive closure of ontologies, we can identify relations between classes that are implied but not asserted and generate graph structures that encode for a large part of the ontologies\\' semantic content. We demonstrate the advantages of our method by applying it to inference of protein-protein interactions through semantic similarity over the Gene Ontology and demonstrate that performance is increased when graph structures are inferred using deductive inference according to our method. Our software and experiment results are available at http://github.com/bio-ontology-research-group/Onto2Graph .Onto2Graph is a method to generate graph structures from OWL ontologies using automated reasoning. The resulting graphs can be used for improved ontology visualization and ontology-based data analysis.

Inferring ontology graph structures using OWL reasoning.

Science.gov (United States)

Rodríguez-García, Miguel Ángel; Hoehndorf, Robert

2018-01-05

Ontologies are representations of a conceptualization of a domain. Traditionally, ontologies in biology were represented as directed acyclic graphs (DAG) which represent the backbone taxonomy and additional relations between classes. These graphs are widely exploited for data analysis in the form of ontology enrichment or computation of semantic similarity. More recently, ontologies are developed in a formal language such as the Web Ontology Language (OWL) and consist of a set of axioms through which classes are defined or constrained. While the taxonomy of an ontology can be inferred directly from the axioms of an ontology as one of the standard OWL reasoning tasks, creating general graph structures from OWL ontologies that exploit the ontologies' semantic content remains a challenge. We developed a method to transform ontologies into graphs using an automated reasoner while taking into account all relations between classes. Searching for (existential) patterns in the deductive closure of ontologies, we can identify relations between classes that are implied but not asserted and generate graph structures that encode for a large part of the ontologies' semantic content. We demonstrate the advantages of our method by applying it to inference of protein-protein interactions through semantic similarity over the Gene Ontology and demonstrate that performance is increased when graph structures are inferred using deductive inference according to our method. Our software and experiment results are available at http://github.com/bio-ontology-research-group/Onto2Graph . Onto2Graph is a method to generate graph structures from OWL ontologies using automated reasoning. The resulting graphs can be used for improved ontology visualization and ontology-based data analysis.

Optical generation of matter qubit graph states

International Nuclear Information System (INIS)

Benjamin, S C; Eisert, J; Stace, T M

2005-01-01

We present a scheme for rapidly entangling matter qubits in order to create graph states for one-way quantum computing. The qubits can be simple three-level systems in separate cavities. Coupling involves only local fields and a static (unswitched) linear optics network. Fusion of graph-state sections occurs with, in principle, zero probability of damaging the nascent graph state. We avoid the finite thresholds of other schemes by operating on two entangled pairs, so that each generates exactly one photon. We do not require the relatively slow single qubit local flips to be applied during the growth phase: growth of the graph state can then become a purely optical process. The scheme naturally generates graph states with vertices of high degree and so is easily able to construct minimal graph states, with consequent resource savings. The most efficient approach will be to create new graph-state edges even as qubits elsewhere are measured, in a 'just in time' approach. An error analysis indicates that the scheme is relatively robust against imperfections in the apparatus

XML Graphs in Program Analysis

DEFF Research Database (Denmark)

Møller, Anders; Schwartzbach, Michael I.

2011-01-01

of XML graphs against different XML schema languages, and provide a software package that enables others to make use of these ideas. We also survey the use of XML graphs for program analysis with four very different languages: XACT (XML in Java), Java Servlets (Web application programming), XSugar......XML graphs have shown to be a simple and effective formalism for representing sets of XML documents in program analysis. It has evolved through a six year period with variants tailored for a range of applications. We present a unified definition, outline the key properties including validation...

Graphs with Eulerian unit spheres

OpenAIRE

Knill, Oliver

2015-01-01

d-spheres in graph theory are inductively defined as graphs for which all unit spheres S(x) are (d-1)-spheres and that the removal of one vertex renders the graph contractible. Eulerian d-spheres are geometric d-spheres which are d+1 colorable. We prove here that G is an Eulerian sphere if and only if the degrees of all the (d-2)-dimensional sub-simplices in G are even. This generalizes a Kempe-Heawood result for d=2 and is work related to the conjecture that all d-spheres have chromatic numb...

The Container Problem in Bubble-Sort Graphs

Science.gov (United States)

Suzuki, Yasuto; Kaneko, Keiichi

Bubble-sort graphs are variants of Cayley graphs. A bubble-sort graph is suitable as a topology for massively parallel systems because of its simple and regular structure. Therefore, in this study, we focus on n-bubble-sort graphs and propose an algorithm to obtain n-1 disjoint paths between two arbitrary nodes in time bounded by a polynomial in n, the degree of the graph plus one. We estimate the time complexity of the algorithm and the sum of the path lengths after proving the correctness of the algorithm. In addition, we report the results of computer experiments evaluating the average performance of the algorithm.

The many faces of graph dynamics

Science.gov (United States)

Pignolet, Yvonne Anne; Roy, Matthieu; Schmid, Stefan; Tredan, Gilles

2017-06-01

The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is known today about the network dynamics: indeed, complex networks in reality are not static, but rather dynamically evolve over time. Our paper is motivated by the empirical observation that network evolution patterns seem far from random, but exhibit structure. Moreover, the specific patterns appear to depend on the network type, contradicting the existence of a ‘one fits it all’ model. However, we still lack observables to quantify these intuitions, as well as metrics to compare graph evolutions. Such observables and metrics are needed for extrapolating or predicting evolutions, as well as for interpolating graph evolutions. To explore the many faces of graph dynamics and to quantify temporal changes, this paper suggests to build upon the concept of centrality, a measure of node importance in a network. In particular, we introduce the notion of centrality distance, a natural similarity measure for two graphs which depends on a given centrality, characterizing the graph type. Intuitively, centrality distances reflect the extent to which (non-anonymous) node roles are different or, in case of dynamic graphs, have changed over time, between two graphs. We evaluate the centrality distance approach for five evolutionary models and seven real-world social and physical networks. Our results empirically show the usefulness of centrality distances for characterizing graph dynamics compared to a null-model of random evolution, and highlight the differences between the considered scenarios. Interestingly, our approach allows us to compare the dynamics of very different networks, in terms of scale and evolution speed.

Low-algorithmic-complexity entropy-deceiving graphs

KAUST Repository

Zenil, Hector

2017-07-08

In estimating the complexity of objects, in particular, of graphs, it is common practice to rely on graphand 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.

Multiple graph regularized nonnegative matrix factorization

KAUST Repository

Wang, Jim Jing-Yan

2013-10-01

Non-negative matrix factorization (NMF) has been widely used as a data representation method based on components. To overcome the disadvantage of NMF in failing to consider the manifold structure of a data set, graph regularized NMF (GrNMF) has been proposed by Cai et al. by constructing an affinity graph and searching for a matrix factorization that respects graph structure. Selecting a graph model and its corresponding parameters is critical for this strategy. This process is usually carried out by cross-validation or discrete grid search, which are time consuming and prone to overfitting. In this paper, we propose a GrNMF, called MultiGrNMF, in which the intrinsic manifold is approximated by a linear combination of several graphs with different models and parameters inspired by ensemble manifold regularization. Factorization metrics and linear combination coefficients of graphs are determined simultaneously within a unified object function. They are alternately optimized in an iterative algorithm, thus resulting in a novel data representation algorithm. Extensive experiments on a protein subcellular localization task and an Alzheimer\\'s disease diagnosis task demonstrate the effectiveness of the proposed algorithm. © 2013 Elsevier Ltd. All rights reserved.

Low-algorithmic-complexity entropy-deceiving graphs

KAUST Repository

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

2017-01-01

In estimating the complexity of objects, in particular, of graphs, it is common practice to rely on graphand 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.

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

Directory of Open Access Journals (Sweden)

Karolina Taczanowska

2017-12-01

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

Graph Sampling for Covariance Estimation

KAUST Repository

Chepuri, Sundeep Prabhakar; Leus, Geert

2017-01-01

specialize for undirected circulant graphs in that the graph nodes leading to the best compression rates are given by the so-called minimal sparse rulers. A near-optimal greedy algorithm is developed to design the subsampling scheme for the non

New method of interpretation of the solar spectrum lines

International Nuclear Information System (INIS)

Sitnik, G.F.

1975-01-01

Close triplet lines, which appear from a common low level or from low sublevels with small energy difference are used. It is supposed that for such lines both the function of the source in line and the frequency dependence of the selective coefficient of absorption are the same over any depth of the region of line production in the atmosphere and change with the depth equally. The residual intensities of some lines of the triplet, which are measured for every line at a number of profile points (at the same distance from its center and at different distances from the solar limb center), serve as initial material. The intensities are expressed in terms of the intensity of the continuous spectrum in the center of the solar limb for the average wave length of the triplet interval. Such observations avoid the usual assumption about the source function constancy in line inside the line. On the contrary, the frequency dependence of this function is clarified by the use of this method. Calculations make it possible to determine the source function in line and its long-wave dependence inside the line; to derive a solar atmosphere model and to determine the source function in the continuous spectrum in accordance with observations at profile points in its middle part and in the wing; to find the relation between the selective and continuous absorption coefficients in the dependence on the optical depth in the continuous spectrum; and to find the long-wave dependences of coefficients for both the selective absorption and the selective emission at different optical depths

Particle transport in breathing quantum graph

International Nuclear Information System (INIS)

Matrasulov, D.U.; Yusupov, J.R.; Sabirov, K.K.; Sobirov, Z.A.

2012-01-01

Full text: Particle transport in nanoscale networks and discrete structures is of fundamental and practical importance. Usually such systems are modeled by so-called quantum graphs, the systems attracting much attention in physics and mathematics during past two decades [1-5]. During last two decades quantum graphs found numerous applications in modeling different discrete structures and networks in nanoscale and mesoscopic physics (e.g., see reviews [1-3]). Despite considerable progress made in the study of particle dynamics most of the problems deal with unperturbed case and the case of time-dependent perturbation has not yet be explored. In this work we treat particle dynamics for quantum star graph with time-dependent bonds. In particular, we consider harmonically breathing quantum star graphs, the cases of monotonically contracting and expanding graphs. The latter can be solved exactly analytically. Edge boundaries are considered to be time-dependent, while branching point is assumed to be fixed. Quantum dynamics of a particle in such graphs is studied by solving Schrodinger equation with time-dependent boundary conditions given on a star graph. Time-dependence of the average kinetic energy is analyzed. Space-time evolution of the Gaussian wave packet is treated for harmonically breathing star graph. It is found that for certain frequencies energy is a periodic function of time, while for others it can be non-monotonically growing function of time. Such a feature can be caused by possible synchronization of the particles motion and the motions of the moving edges of graph bonds. (authors) References: [1] Tsampikos Kottos and Uzy Smilansky, Ann. Phys., 76, 274 (1999). [2] Sven Gnutzmann and Uzy Smilansky, Adv. Phys. 55, 527 (2006). [3] S. GnutzmannJ.P. Keating, F. Piotet, Ann. Phys., 325, 2595 (2010). [4] P.Exner, P.Seba, P.Stovicek, J. Phys. A: Math. Gen. 21, 4009 (1988). [5] J. Boman, P. Kurasov, Adv. Appl. Math., 35, 58 (2005)

Interacting particle systems on graphs

Science.gov (United States)

Sood, Vishal

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

Transduction on Directed Graphs via Absorbing Random Walks.

Science.gov (United States)

De, Jaydeep; Zhang, Xiaowei; Lin, Feng; Cheng, Li

2017-08-11

In this paper we consider the problem of graph-based transductive classification, and we are particularly interested in the directed graph scenario which is a natural form for many real world applications.Different from existing research efforts that either only deal with undirected graphs or circumvent directionality by means of symmetrization, we propose a novel random walk approach on directed graphs using absorbing Markov chains, which can be regarded as maximizing the accumulated expected number of visits from the unlabeled transient states. Our algorithm is simple, easy to implement, and works with large-scale graphs on binary, multiclass, and multi-label prediction problems. Moreover, it is capable of preserving the graph structure even when the input graph is sparse and changes over time, as well as retaining weak signals presented in the directed edges. We present its intimate connections to a number of existing methods, including graph kernels, graph Laplacian based methods, and interestingly, spanning forest of graphs. Its computational complexity and the generalization error are also studied. Empirically our algorithm is systematically evaluated on a wide range of applications, where it has shown to perform competitively comparing to a suite of state-of-the-art methods. In particular, our algorithm is shown to work exceptionally well with large sparse directed graphs with e.g. millions of nodes and tens of millions of edges, where it significantly outperforms other state-of-the-art methods. In the dynamic graph setting involving insertion or deletion of nodes and edge-weight changes over time, it also allows efficient online updates that produce the same results as of the batch update counterparts.

High-performance analysis of filtered semantic graphs

OpenAIRE

Buluç, A; Fox, A; Gilbert, JR; Kamil, S; Lugowski, A; Oliker, L; Williams, S

2012-01-01

High performance is a crucial consideration when executing a complex analytic query on a massive semantic graph. In a semantic graph, vertices and edges carry \\attributes" of various types. Analytic queries on semantic graphs typically depend on the values of these attributes; thus, the computation must either view the graph through a filter that passes only those individual vertices and edges of interest, or else must first materialize a subgraph or subgraphs consisting of only the vertices ...

Bond graph modeling of centrifugal compression systems

OpenAIRE

Uddin, Nur; Gravdahl, Jan Tommy

2015-01-01

A novel approach to model unsteady fluid dynamics in a compressor network by using a bond graph is presented. The model is intended in particular for compressor control system development. First, we develop a bond graph model of a single compression system. Bond graph modeling offers a different perspective to previous work by modeling the compression system based on energy flow instead of fluid dynamics. Analyzing the bond graph model explains the energy flow during compressor surge. Two pri...

On the local edge antimagicness of m-splitting graphs

Science.gov (United States)

Albirri, E. R.; Dafik; Slamin; Agustin, I. H.; Alfarisi, R.

2018-04-01

Let G be a connected and simple graph. A split graph is a graph derived by adding new vertex v‧ in every vertex v‧ such that v‧ adjacent to v in graph G. An m-splitting graph is a graph which has m v‧-vertices, denoted by mSpl(G). A local edge antimagic coloring in G = (V, E) graph is a bijection f:V (G)\\to \\{1,2,3,\\ldots,|V(G)|\\} in which for any two adjacent edges e 1 and e 2 satisfies w({e}1)\

Augmented marked graphs

CERN Document Server

Cheung, King Sing

2014-01-01

Petri nets are a formal and theoretically rich model for the modelling and analysis of systems. A subclass of Petri nets, augmented marked graphs possess a structure that is especially desirable for the modelling and analysis of systems with concurrent processes and shared resources.This monograph consists of three parts: Part I provides the conceptual background for readers who have no prior knowledge on Petri nets; Part II elaborates the theory of augmented marked graphs; finally, Part III discusses the application to system integration. The book is suitable as a first self-contained volume

Co-Roman domination in graphs

Indian Academy of Sciences (India)

1National Centre for Advanced Research in Discrete Mathematics ... 3Department of Computer Science, Ball State University, Muncie, IN, USA .... The corona of two disjoint graphs G1 and G2 is defined to be the graph G = G1 ◦ G2,.

Nested Dynamic Condition Response Graphs

DEFF Research Database (Denmark)

Hildebrandt, Thomas; Mukkamala, Raghava Rao; Slaats, Tijs

2012-01-01

We present an extension of the recently introduced declarative process model Dynamic Condition Response Graphs ( DCR Graphs) to allow nested subgraphs and a new milestone relation between events. The extension was developed during a case study carried out jointly with our industrial partner...

A cluster algorithm for graphs

NARCIS (Netherlands)

S. van Dongen

2000-01-01

textabstractA cluster algorithm for graphs called the emph{Markov Cluster algorithm (MCL~algorithm) is introduced. The algorithm provides basically an interface to an algebraic process defined on stochastic matrices, called the MCL~process. The graphs may be both weighted (with nonnegative weight)

Generating random networks and graphs

CERN Document Server

Coolen, Ton; Roberts, Ekaterina

2017-01-01

This book supports researchers who need to generate random networks, or who are interested in the theoretical study of random graphs. The coverage includes exponential random graphs (where the targeted probability of each network appearing in the ensemble is specified), growth algorithms (i.e. preferential attachment and the stub-joining configuration model), special constructions (e.g. geometric graphs and Watts Strogatz models) and graphs on structured spaces (e.g. multiplex networks). The presentation aims to be a complete starting point, including details of both theory and implementation, as well as discussions of the main strengths and weaknesses of each approach. It includes extensive references for readers wishing to go further. The material is carefully structured to be accessible to researchers from all disciplines while also containing rigorous mathematical analysis (largely based on the techniques of statistical mechanics) to support those wishing to further develop or implement the theory of rand...

The analytic value of a 3-loop sunrise graph in a particular kinematical configuration

International Nuclear Information System (INIS)

Mastrolia, P.; Remiddi, E.

2003-01-01

We consider the scalar integral associated to the 3-loop sunrise graph with a massless line, two massive lines of equal mass M, a fourth line of mass equal to Mx, and the external invariant timelike and equal to the square of the fourth mass. We write the differential equation in x satisfied by the integral, expand it in the continuous dimension d around d=4 and solve the system of the resulting chained differential equations in closed analytic form, expressing the solutions in terms of harmonic polylogarithms. As a byproduct, we give the limiting values of the coefficients of the (d-4) expansion at x=1 and x=0

On the Recognition of Fuzzy Circular Interval Graphs

OpenAIRE

Oriolo, Gianpaolo; Pietropaoli, Ugo; Stauffer, Gautier

2011-01-01

Fuzzy circular interval graphs are a generalization of proper circular arc graphs and have been recently introduced by Chudnovsky and Seymour as a fundamental subclass of claw-free graphs. In this paper, we provide a polynomial-time algorithm for recognizing such graphs, and more importantly for building a suitable representation.

The Thickness of Amalgamations and Cartesian Product of Graphs

Directory of Open Access Journals (Sweden)

Yang Yan

2017-08-01

Full Text Available The thickness of a graph is the minimum number of planar spanning subgraphs into which the graph can be decomposed. It is a measurement of the closeness to the planarity of a graph, and it also has important applications to VLSI design, but it has been known for only few graphs. We obtain the thickness of vertex-amalgamation and bar-amalgamation of graphs, the lower and upper bounds for the thickness of edge-amalgamation and 2-vertex-amalgamation of graphs, respectively. We also study the thickness of Cartesian product of graphs, and by using operations on graphs, we derive the thickness of the Cartesian product Kn □ Pm for most values of m and n.

Generating Realistic Labelled, Weighted Random Graphs

Directory of Open Access Journals (Sweden)

Michael Charles Davis

2015-12-01

Full Text Available Generative algorithms for random graphs have yielded insights into the structure and evolution of real-world networks. Most networks exhibit a well-known set of properties, such as heavy-tailed degree distributions, clustering and community formation. Usually, random graph models consider only structural information, but many real-world networks also have labelled vertices and weighted edges. In this paper, we present a generative model for random graphs with discrete vertex labels and numeric edge weights. The weights are represented as a set of Beta Mixture Models (BMMs with an arbitrary number of mixtures, which are learned from real-world networks. We propose a Bayesian Variational Inference (VI approach, which yields an accurate estimation while keeping computation times tractable. We compare our approach to state-of-the-art random labelled graph generators and an earlier approach based on Gaussian Mixture Models (GMMs. Our results allow us to draw conclusions about the contribution of vertex labels and edge weights to graph structure.

On The Roman Domination Stable Graphs

Directory of Open Access Journals (Sweden)

Hajian Majid

2017-11-01

Full Text Available A Roman dominating function (or just RDF on a graph G = (V,E is a function f : V → {0, 1, 2} satisfying the condition that every vertex u for which f(u = 0 is adjacent to at least one vertex v for which f(v = 2. The weight of an RDF f is the value f(V (G = Pu2V (G f(u. The Roman domination number of a graph G, denoted by R(G, is the minimum weight of a Roman dominating function on G. A graph G is Roman domination stable if the Roman domination number of G remains unchanged under removal of any vertex. In this paper we present upper bounds for the Roman domination number in the class of Roman domination stable graphs, improving bounds posed in [V. Samodivkin, Roman domination in graphs: the class RUV R, Discrete Math. Algorithms Appl. 8 (2016 1650049].

Disease management research using event graphs.

Science.gov (United States)

Allore, H G; Schruben, L W

2000-08-01

Event Graphs, conditional representations of stochastic relationships between discrete events, simulate disease dynamics. In this paper, we demonstrate how Event Graphs, at an appropriate abstraction level, also extend and organize scientific knowledge about diseases. They can identify promising treatment strategies and directions for further research and provide enough detail for testing combinations of new medicines and interventions. Event Graphs can be enriched to incorporate and validate data and test new theories to reflect an expanding dynamic scientific knowledge base and establish performance criteria for the economic viability of new treatments. To illustrate, an Event Graph is developed for mastitis, a costly dairy cattle disease, for which extensive scientific literature exists. With only a modest amount of imagination, the methodology presented here can be seen to apply modeling to any disease, human, plant, or animal. The Event Graph simulation presented here is currently being used in research and in a new veterinary epidemiology course. Copyright 2000 Academic Press.

Measuring Two-Event Structural Correlations on Graphs

Science.gov (United States)

2012-08-01

2012 to 00-00-2012 4. TITLE AND SUBTITLE Measuring Two-Event Structural Correlations on Graphs 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ...by event simulation on the DBLP graph. Then we examine the efficiency and scala - bility of the framework with a Twitter network. The third part of...correlation pattern mining for large graphs. In Proc. of the 8th Workshop on Mining and Learning with Graphs, pages 119–126, 2010. [23] T. Smith. A

Reconstructing Nearly Simple Polytopes from their Graph

OpenAIRE

Doolittle, Joseph

2017-01-01

We present a partial description of which polytopes are reconstructible from their graphs. This is an extension of work by Blind and Mani (1987) and Kalai (1988), which showed that simple polytopes can be reconstructed from their graphs. In particular, we introduce a notion of $h$-nearly simple and prove that 1-nearly simple and 2-nearly simple polytopes are reconstructible from their graphs. We also give an example of a 3-nearly simple polytope which is not reconstructible from its graph. Fu...

Hierarchical organisation of causal graphs

International Nuclear Information System (INIS)

Dziopa, P.

1993-01-01

This paper deals with the design of a supervision system using a hierarchy of models formed by graphs, in which the variables are the nodes and the causal relations between the variables of the arcs. To obtain a representation of the variables evolutions which contains only the relevant features of their real evolutions, the causal relations are completed with qualitative transfer functions (QTFs) which produce roughly the behaviour of the classical transfer functions. Major improvements have been made in the building of the hierarchical organization. First, the basic variables of the uppermost level and the causal relations between them are chosen. The next graph is built by adding intermediary variables to the upper graph. When the undermost graph has been built, the transfer functions parameters corresponding to its causal relations are identified. The second task consists in the upwelling of the information from the undermost graph to the uppermost one. A fusion procedure of the causal relations has been designed to compute the QFTs relevant for each level. This procedure aims to reduce the number of parameters needed to represent an evolution at a high level of abstraction. These techniques have been applied to the hierarchical modelling of nuclear process. (authors). 8 refs., 12 figs

STABILITY OF LINEAR MULTIAGENT SCALAR SYSTEMS AND ITS DEPENDENCE ON CONNECTIVITY GRAPH

Directory of Open Access Journals (Sweden)

S. I. Tomashevich

2014-03-01

Full Text Available Multiagent systems are now finding increasingly wide applications in various engineering fields such as energy, transportation, robotics, aviation and others. There are two main aspects to be focused on when organizing multiagent systems: the dynamics of the agents themselves and the ways of their interaction. This interaction is determined by the structure of information connections between agents. Thus, there are several key points of multiagent systems study: the dynamics of individual agents and shape of the information graph. Formation dynamics, in general, is determined by a set of properties of agents and connectivity graph. The paper deals with the relationship between dynamics of agents and Laplace matrix, which is used to set the graph connections. The present research is based on the results given in the known paper by A. Fax and R. Murray (IEEE Trans. AC, 2004. An illustrative example is given, and the application problem of studying the formation dynamics consisting of the group of quadrocopters is presented. Information exchange between agents is determined in the paper by means of the conventional set of graphs. The paper presents an interpretation of the stability conditions and the method of system performance improvement based on these conditions. Motion of quadrocopters group along the flight height is used as an example for methodology application. The simulation results demonstrate the basic dependencies between the information graph shape (and, consequently, the eigenvalues of the Laplacian, which describes this graph and formation stability. Simulation and consideration of Nyquist diagram connection with the key points give an indication of the system stability and take steps to change the control laws. Necessary conditions for the formation stability are obtained on the basis of this research method. Research result makes it possible to create local control laws for agents to ensure the stability of motion in the selected

Graph Transformation Semantics for a QVT Language

NARCIS (Netherlands)

Rensink, Arend; Nederpel, Ronald; Bruni, Roberto; Varró, Dániel

It has been claimed by many in the graph transformation community that model transformation, as understood in the context of Model Driven Architecture, can be seen as an application of graph transformation. In this paper we substantiate this claim by giving a graph transformation-based semantics to

Modeling Software Evolution using Algebraic Graph Rewriting

NARCIS (Netherlands)

Ciraci, Selim; van den Broek, Pim

We show how evolution requests can be formalized using algebraic graph rewriting. In particular, we present a way to convert the UML class diagrams to colored graphs. Since changes in software may effect the relation between the methods of classes, our colored graph representation also employs the

Cycles in weighted graphs and related topics

NARCIS (Netherlands)

Zhang, Shenggui

2002-01-01

This thesis contains results on paths andcycles in graphs andon a more or less relatedtopic, the vulnerability of graphs. In the first part of the thesis, Chapters 2 through 5, we concentrate on paths andcycles in weightedgraphs. A number of sufficient conditions are presentedfor graphs to contain

Engineering Object-Oriented Semantics Using Graph Transformations

NARCIS (Netherlands)

Kastenberg, H.; Kleppe, A.G.; Rensink, Arend

In this paper we describe the application of the theory of graph transformations to the practise of language design. We have defined the semantics of a small but realistic object-oriented language (called TAAL) by mapping the language constructs to graphs and their operational semantics to graph

Probabilistic Graph Layout for Uncertain Network Visualization.

Science.gov (United States)

Schulz, Christoph; Nocaj, Arlind; Goertler, Jochen; Deussen, Oliver; Brandes, Ulrik; Weiskopf, Daniel

2017-01-01

We present a novel uncertain network visualization technique based on node-link diagrams. Nodes expand spatially in our probabilistic graph layout, depending on the underlying probability distributions of edges. The visualization is created by computing a two-dimensional graph embedding that combines samples from the probabilistic graph. A Monte Carlo process is used to decompose a probabilistic graph into its possible instances and to continue with our graph layout technique. Splatting and edge bundling are used to visualize point clouds and network topology. The results provide insights into probability distributions for the entire network-not only for individual nodes and edges. We validate our approach using three data sets that represent a wide range of network types: synthetic data, protein-protein interactions from the STRING database, and travel times extracted from Google Maps. Our approach reveals general limitations of the force-directed layout and allows the user to recognize that some nodes of the graph are at a specific position just by chance.

Optimizing graph algorithms on pregel-like systems

KAUST Repository

Salihoglu, Semih

2014-03-01

We study the problem of implementing graph algorithms efficiently on Pregel-like systems, which can be surprisingly challenging. Standard graph algorithms in this setting can incur unnecessary inefficiencies such as slow convergence or high communication or computation cost, typically due to structural properties of the input graphs such as large diameters or skew in component sizes. We describe several optimization techniques to address these inefficiencies. Our most general technique is based on the idea of performing some serial computation on a tiny fraction of the input graph, complementing Pregel\\'s vertex-centric parallelism. We base our study on thorough implementations of several fundamental graph algorithms, some of which have, to the best of our knowledge, not been implemented on Pregel-like systems before. The algorithms and optimizations we describe are fully implemented in our open-source Pregel implementation. We present detailed experiments showing that our optimization techniques improve runtime significantly on a variety of very large graph datasets.

Automorphism group of the modified bubble-sort graph

OpenAIRE

Ganesan, Ashwin

2014-01-01

The modified bubble-sort graph of dimension $n$ is the Cayley graph of $S_n$ generated by $n$ cyclically adjacent transpositions. In the present paper, it is shown that the automorphism group of the modified bubble sort graph of dimension $n$ is $S_n \\times D_{2n}$, for all $n \\ge 5$. Thus, a complete structural description of the automorphism group of the modified bubble-sort graph is obtained. A similar direct product decomposition is seen to hold for arbitrary normal Cayley graphs generate...

Total dominator chromatic number of a graph

Directory of Open Access Journals (Sweden)

Adel P. Kazemi

2015-06-01

Full Text Available Given a graph $G$, the total dominator coloring problem seeks a proper coloring of $G$ with the additional property that every vertex in the graph is adjacent to all vertices of a color class. We seek to minimize the number of color classes. We initiate to study this problem on several classes of graphs, as well as finding general bounds and characterizations. We also compare the total dominator chromatic number of a graph with the chromatic number and the total domination number of it.

Khovanov-Rozansky Graph Homology and Composition Product

DEFF Research Database (Denmark)

Wagner, Emmanuel

2008-01-01

In analogy with a recursive formula for the HOMFLY-PT polynomial of links given by Jaeger, we give a recursive formula for the graph polynomial introduced by Kauffman and Vogel. We show how this formula extends to the Khovanov–Rozansky graph homology.......In analogy with a recursive formula for the HOMFLY-PT polynomial of links given by Jaeger, we give a recursive formula for the graph polynomial introduced by Kauffman and Vogel. We show how this formula extends to the Khovanov–Rozansky graph homology....

Graph-based clustering and data visualization algorithms

CERN Document Server

Vathy-Fogarassy, Ágnes

2013-01-01

This work presents a data visualization technique that combines graph-based topology representation and dimensionality reduction methods to visualize the intrinsic data structure in a low-dimensional vector space. The application of graphs in clustering and visualization has several advantages. A graph of important edges (where edges characterize relations and weights represent similarities or distances) provides a compact representation of the entire complex data set. This text describes clustering and visualization methods that are able to utilize information hidden in these graphs, based on

Incremental View Maintenance for Deductive Graph Databases Using Generalized Discrimination Networks

Directory of Open Access Journals (Sweden)

Thomas Beyhl

2016-12-01

Full Text Available Nowadays, graph databases are employed when relationships between entities are in the scope of database queries to avoid performance-critical join operations of relational databases. Graph queries are used to query and modify graphs stored in graph databases. Graph queries employ graph pattern matching that is NP-complete for subgraph isomorphism. Graph database views can be employed that keep ready answers in terms of precalculated graph pattern matches for often stated and complex graph queries to increase query performance. However, such graph database views must be kept consistent with the graphs stored in the graph database. In this paper, we describe how to use incremental graph pattern matching as technique for maintaining graph database views. We present an incremental maintenance algorithm for graph database views, which works for imperatively and declaratively specified graph queries. The evaluation shows that our maintenance algorithm scales when the number of nodes and edges stored in the graph database increases. Furthermore, our evaluation shows that our approach can outperform existing approaches for the incremental maintenance of graph query results.

Multi-organ segmentation from multi-phase abdominal CT via 4D graphs using enhancement, shape and location optimization.

Science.gov (United States)

Linguraru, Marius George; Pura, John A; Chowdhury, Ananda S; Summers, Ronald M

2010-01-01

The interpretation of medical images benefits from anatomical and physiological priors to optimize computer-aided diagnosis (CAD) applications. Diagnosis also relies on the comprehensive analysis of multiple organs and quantitative measures of soft tissue. An automated method optimized for medical image data is presented for the simultaneous segmentation of four abdominal organs from 4D CT data using graph cuts. Contrast-enhanced CT scans were obtained at two phases: non-contrast and portal venous. Intra-patient data were spatially normalized by non-linear registration. Then 4D erosion using population historic information of contrast-enhanced liver, spleen, and kidneys was applied to multi-phase data to initialize the 4D graph and adapt to patient specific data. CT enhancement information and constraints on shape, from Parzen windows, and location, from a probabilistic atlas, were input into a new formulation of a 4D graph. Comparative results demonstrate the effects of appearance and enhancement, and shape and location on organ segmentation.

On a Fuzzy Algebra for Querying Graph Databases

OpenAIRE

Pivert , Olivier; Thion , Virginie; Jaudoin , Hélène; Smits , Grégory

2014-01-01

International audience; This paper proposes a notion of fuzzy graph database and describes a fuzzy query algebra that makes it possible to handle such database, which may be fuzzy or not, in a flexible way. The algebra, based on fuzzy set theory and the concept of a fuzzy graph, is composed of a set of operators that can be used to express preference queries on fuzzy graph databases. The preferences concern i) the content of the vertices of the graph and ii) the structure of the graph. In a s...

Graphs of groups on surfaces interactions and models

CERN Document Server

White, AT

2001-01-01

The book, suitable as both an introductory reference and as a text book in the rapidly growing field of topological graph theory, models both maps (as in map-coloring problems) and groups by means of graph imbeddings on sufaces. Automorphism groups of both graphs and maps are studied. In addition connections are made to other areas of mathematics, such as hypergraphs, block designs, finite geometries, and finite fields. There are chapters on the emerging subfields of enumerative topological graph theory and random topological graph theory, as well as a chapter on the composition of English

A Type Graph Model for Java Programs

NARCIS (Netherlands)

Rensink, Arend; Zambon, Eduardo

2009-01-01

In this report we present a type graph that models all executable constructs of the Java programming language. Such a model is useful for any graph-based technique that relies on a representation of Java programs as graphs. The model can be regarded as a common representation to which all Java

Mutual proximity graphs for improved reachability in music recommendation.

Science.gov (United States)

Flexer, Arthur; Stevens, Jeff

2018-01-01

This paper is concerned with the impact of hubness, a general problem of machine learning in high-dimensional spaces, on a real-world music recommendation system based on visualisation of a k-nearest neighbour (knn) graph. Due to a problem of measuring distances in high dimensions, hub objects are recommended over and over again while anti-hubs are nonexistent in recommendation lists, resulting in poor reachability of the music catalogue. We present mutual proximity graphs, which are an alternative to knn and mutual knn graphs, and are able to avoid hub vertices having abnormally high connectivity. We show that mutual proximity graphs yield much better graph connectivity resulting in improved reachability compared to knn graphs, mutual knn graphs and mutual knn graphs enhanced with minimum spanning trees, while simultaneously reducing the negative effects of hubness.

Efficient dynamic graph construction for inductive semi-supervised learning.

Science.gov (United States)

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.

Coloring geographical threshold graphs

Energy Technology Data Exchange (ETDEWEB)

Bradonjic, Milan [Los Alamos National Laboratory; Percus, Allon [Los Alamos National Laboratory; Muller, Tobias [EINDHOVEN UNIV. OF TECH

2008-01-01

We propose a coloring algorithm for sparse random graphs generated by the geographical threshold graph (GTG) model, a generalization of random geometric graphs (RGG). In a GTG, nodes are distributed in a Euclidean space, and edges are assigned according to a threshold function involving the distance between nodes as well as randomly chosen node weights. The motivation for analyzing this model is that many real networks (e.g., wireless networks, the Internet, etc.) need to be studied by using a 'richer' stochastic model (which in this case includes both a distance between nodes and weights on the nodes). Here, we analyze the GTG coloring algorithm together with the graph's clique number, showing formally that in spite of the differences in structure between GTG and RGG, the asymptotic behavior of the chromatic number is identical: {chi}1n 1n n / 1n n (1 + {omicron}(1)). Finally, we consider the leading corrections to this expression, again using the coloring algorithm and clique number to provide bounds on the chromatic number. We show that the gap between the lower and upper bound is within C 1n n / (1n 1n n){sup 2}, and specify the constant C.

A Reduction of the Graph Reconstruction Conjecture

Directory of Open Access Journals (Sweden)

Monikandan S.

2014-08-01

Full Text Available A graph is said to be reconstructible if it is determined up to isomor- phism from the collection of all its one-vertex deleted unlabeled subgraphs. Reconstruction Conjecture (RC asserts that all graphs on at least three vertices are reconstructible. In this paper, we prove that interval-regular graphs and some new classes of graphs are reconstructible and show that RC is true if and only if all non-geodetic and non-interval-regular blocks G with diam(G = 2 or diam(Ḡ = diam(G = 3 are reconstructible

Quantum Graphs And Their Resonance Properties

International Nuclear Information System (INIS)

Lipovsky, J.

2016-01-01

In the current review, we study the model of quantum graphs. We focus mainly on the resonance properties of quantum graphs. We define resolvent and scattering resonances and show their equivalence. We present various results on the asymptotics of the number of resolvent resonances in both non-magnetic and magnetic quantum graphs and find bounds on the coefficient by the leading term of the asymptotics. We explain methods how to find the spectral and resonance condition. Most of the notions and theorems are illustrated in examples. We show how to find resonances numerically and, in a simple example, we find trajectories of resonances in the complex plane. We discuss Fermi’s golden rule for quantum graphs and distribution of the mean intensity for the topological resonances. (author)

Determining X-chains in graph states

International Nuclear Information System (INIS)

Wu, Jun-Yi; Kampermann, Hermann; Bruß, Dagmar

2016-01-01

The representation of graph states in the X-basis as well as the calculation of graph state overlaps can efficiently be performed by using the concept of X-chains (Wu et al 2015 Phys. Rev. A 92 012322). We present a necessary and sufficient criterion for X-chains and show that they can efficiently be determined by the Bareiss algorithm. An analytical approach for searching X-chain groups of a graph state is proposed. Furthermore we generalize the concept of X-chains to so-called Euler chains, whose induced subgraphs are Eulerian. This approach helps to determine if a given vertex set is an X-chain and we show how Euler chains can be used in the construction of multipartite Bell inequalities for graph states. (paper)

Fixation probability on clique-based graphs

Science.gov (United States)

Choi, Jeong-Ok; Yu, Unjong

2018-02-01

The fixation probability of a mutant in the evolutionary dynamics of Moran process is calculated by the Monte-Carlo method on a few families of clique-based graphs. It is shown that the complete suppression of fixation can be realized with the generalized clique-wheel graph in the limit of small wheel-clique ratio and infinite size. The family of clique-star is an amplifier, and clique-arms graph changes from amplifier to suppressor as the fitness of the mutant increases. We demonstrate that the overall structure of a graph can be more important to determine the fixation probability than the degree or the heat heterogeneity. The dependence of the fixation probability on the position of the first mutant is discussed.

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

Science.gov (United States)

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

2018-04-01

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

Steiner Distance in Graphs--A Survey

OpenAIRE

Mao, Yaping

2017-01-01

For a connected graph $G$ of order at least $2$ and $S\\subseteq V(G)$, the \\emph{Steiner distance} $d_G(S)$ among the vertices of $S$ is the minimum size among all connected subgraphs whose vertex sets contain $S$. In this paper, we summarize the known results on the Steiner distance parameters, including Steiner distance, Steiner diameter, Steiner center, Steiner median, Steiner interval, Steiner distance hereditary graph, Steiner distance stable graph, average Steiner distance, and Steiner ...

Girth 5 graphs from relative difference sets

DEFF Research Database (Denmark)

Jørgensen, Leif Kjær

2005-01-01

We consider the problem of construction of graphs with given degree $k$ and girth 5 and as few vertices as possible. We give a construction of a family of girth 5 graphs based on relative difference sets. This family contains the smallest known graph of degree 8 and girth 5 which was constructed ...

A Type Graph Model for Java Programs

NARCIS (Netherlands)

Rensink, Arend; Zambon, Eduardo; Lee, D.; Lopes, A.; Poetzsch-Heffter, A.

2009-01-01

In this work we present a type graph that models all executable constructs of the Java programming language. Such a model is useful for any graph-based technique that relies on a representation of Java programs as graphs. The model can be regarded as a common representation to which all Java syntax

Analyzing locomotion synthesis with feature-based motion graphs.

Science.gov (United States)

Mahmudi, Mentar; Kallmann, Marcelo

2013-05-01

We propose feature-based motion graphs for realistic locomotion synthesis among obstacles. Among several advantages, feature-based motion graphs achieve improved results in search queries, eliminate the need of postprocessing for foot skating removal, and reduce the computational requirements in comparison to traditional motion graphs. Our contributions are threefold. First, we show that choosing transitions based on relevant features significantly reduces graph construction time and leads to improved search performances. Second, we employ a fast channel search method that confines the motion graph search to a free channel with guaranteed clearance among obstacles, achieving faster and improved results that avoid expensive collision checking. Lastly, we present a motion deformation model based on Inverse Kinematics applied over the transitions of a solution branch. Each transition is assigned a continuous deformation range that does not exceed the original transition cost threshold specified by the user for the graph construction. The obtained deformation improves the reachability of the feature-based motion graph and in turn also reduces the time spent during search. The results obtained by the proposed methods are evaluated and quantified, and they demonstrate significant improvements in comparison to traditional motion graph techniques.

Torsional rigidity, isospectrality and quantum graphs

International Nuclear Information System (INIS)

Colladay, Don; McDonald, Patrick; Kaganovskiy, Leon

2017-01-01

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

Joint Graph Layouts for Visualizing Collections of Segmented Meshes

KAUST Repository

Ren, Jing

2017-09-12

We present a novel and efficient approach for computing joint graph layouts and then use it to visualize collections of segmented meshes. Our joint graph layout algorithm takes as input the adjacency matrices for a set of graphs along with partial, possibly soft, correspondences between nodes of different graphs. We then use a two stage procedure, where in the first step, we extend spectral graph drawing to include a consistency term so that a collection of graphs can be handled jointly. Our second step extends metric multi-dimensional scaling with stress majorization to the joint layout setting, while using the output of the spectral approach as initialization. Further, we discuss a user interface for exploring a collection of graphs. Finally, we show multiple example visualizations of graphs stemming from collections of segmented meshes and we present qualitative and quantitative comparisons with previous work.

Joint Graph Layouts for Visualizing Collections of Segmented Meshes

KAUST Repository

Ren, Jing; Schneider, Jens; Ovsjanikov, Maks; Wonka, Peter

2017-01-01

We present a novel and efficient approach for computing joint graph layouts and then use it to visualize collections of segmented meshes. Our joint graph layout algorithm takes as input the adjacency matrices for a set of graphs along with partial, possibly soft, correspondences between nodes of different graphs. We then use a two stage procedure, where in the first step, we extend spectral graph drawing to include a consistency term so that a collection of graphs can be handled jointly. Our second step extends metric multi-dimensional scaling with stress majorization to the joint layout setting, while using the output of the spectral approach as initialization. Further, we discuss a user interface for exploring a collection of graphs. Finally, we show multiple example visualizations of graphs stemming from collections of segmented meshes and we present qualitative and quantitative comparisons with previous work.

Learning a Nonnegative Sparse Graph for Linear Regression.

Science.gov (United States)

Fang, Xiaozhao; Xu, Yong; Li, Xuelong; Lai, Zhihui; Wong, Wai Keung

2015-09-01

Previous graph-based semisupervised learning (G-SSL) methods have the following drawbacks: 1) they usually predefine the graph structure and then use it to perform label prediction, which cannot guarantee an overall optimum and 2) they only focus on the label prediction or the graph structure construction but are not competent in handling new samples. To this end, a novel nonnegative sparse graph (NNSG) learning method was first proposed. Then, both the label prediction and projection learning were integrated into linear regression. Finally, the linear regression and graph structure learning were unified within the same framework to overcome these two drawbacks. Therefore, a novel method, named learning a NNSG for linear regression was presented, in which the linear regression and graph learning were simultaneously performed to guarantee an overall optimum. In the learning process, the label information can be accurately propagated via the graph structure so that the linear regression can learn a discriminative projection to better fit sample labels and accurately classify new samples. An effective algorithm was designed to solve the corresponding optimization problem with fast convergence. Furthermore, NNSG provides a unified perceptiveness for a number of graph-based learning methods and linear regression methods. The experimental results showed that NNSG can obtain very high classification accuracy and greatly outperforms conventional G-SSL methods, especially some conventional graph construction methods.

GRAMI: Generalized Frequent Subgraph Mining in Large Graphs

KAUST Repository

El Saeedy, Mohammed El Sayed

2011-07-24

Mining frequent subgraphs is an important operation on graphs. Most existing work assumes a database of many small graphs, but modern applications, such as social networks, citation graphs or protein-protein interaction in bioinformatics, are modeled as a single large graph. Interesting interactions in such applications may be transitive (e.g., friend of a friend). Existing methods, however, search for frequent isomorphic (i.e., exact match) subgraphs and cannot discover many useful patterns. In this paper we propose GRAMI, a framework that generalizes frequent subgraph mining in a large single graph. GRAMI discovers frequent patterns. A pattern is a graph where edges are generalized to distance-constrained paths. Depending on the definition of the distance function, many instantiations of the framework are possible. Both directed and undirected graphs, as well as multiple labels per vertex, are supported. We developed an efficient implementation of the framework that models the frequency resolution phase as a constraint satisfaction problem, in order to avoid the costly enumeration of all instances of each pattern in the graph. We also implemented CGRAMI, a version that supports structural and semantic constraints; and AGRAMI, an approximate version that supports very large graphs. Our experiments on real data demonstrate that our framework is up to 3 orders of magnitude faster and discovers more interesting patterns than existing approaches.

Girth 5 graphs from relative difference sets

DEFF Research Database (Denmark)

Jørgensen, Leif Kjær

We consider the problem of construction of graphs with given degree and girth 5 and as few vertices as possible. We give a construction of a family of girth 5 graphs based on relative difference sets. This family contains the smallest known graph of degree 8 and girth 5 which was constructed by G...

Identification of Voxels Confounded by Venous Signals Using Resting-State fMRI Functional Connectivity Graph Clustering

Directory of Open Access Journals (Sweden)

Klaudius eKalcher

2015-12-01

Full Text Available Identifying venous voxels in fMRI datasets is important to increase the specificity of fMRI analyses to microvasculature in the vicinity of the neural processes triggering the BOLD response. This is, however, difficult to achieve in particular in typical studies where magnitude images of BOLD EPI are the only data available. In this study, voxelwise functional connectivity graphs were computed on minimally preprocessed low TR (333 ms multiband resting-state fMRI data, using both high positive and negative correlations to define edges between nodes (voxels. A high correlation threshold for binarization ensures that most edges in the resulting sparse graph reflect the high coherence of signals in medium to large veins. Graph clustering based on the optimization of modularity was then employed to identify clusters of coherent voxels in this graph, and all clusters of 50 or more voxels were then interpreted as corresponding to medium to large veins. Indeed, a comparison with SWI reveals that 75.6 ± 5.9% of voxels within these large clusters overlap with veins visible in the SWI image or lie outside the brain parenchyma. Some of the remainingdifferences between the two modalities can be explained by imperfect alignment or geometric distortions between the two images. Overall, the graph clustering based method for identifying venous voxels has a high specificity as well as the additional advantages of being computed in the same voxel grid as the fMRI dataset itself and not needingany additional data beyond what is usually acquired (and exported in standard fMRI experiments.

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

International Nuclear Information System (INIS)

Lange, Alexander

2005-01-01

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

A distributed query execution engine of big attributed graphs.

Science.gov (United States)

Batarfi, Omar; Elshawi, Radwa; Fayoumi, Ayman; Barnawi, Ahmed; Sakr, Sherif

2016-01-01

A graph is a popular data model that has become pervasively used for modeling structural relationships between objects. In practice, in many real-world graphs, the graph vertices and edges need to be associated with descriptive attributes. Such type of graphs are referred to as attributed graphs. G-SPARQL has been proposed as an expressive language, with a centralized execution engine, for querying attributed graphs. G-SPARQL supports various types of graph querying operations including reachability, pattern matching and shortest path where any G-SPARQL query may include value-based predicates on the descriptive information (attributes) of the graph edges/vertices in addition to the structural predicates. In general, a main limitation of centralized systems is that their vertical scalability is always restricted by the physical limits of computer systems. This article describes the design, implementation in addition to the performance evaluation of DG-SPARQL, a distributed, hybrid and adaptive parallel execution engine of G-SPARQL queries. In this engine, the topology of the graph is distributed over the main memory of the underlying nodes while the graph data are maintained in a relational store which is replicated on the disk of each of the underlying nodes. DG-SPARQL evaluates parts of the query plan via SQL queries which are pushed to the underlying relational stores while other parts of the query plan, as necessary, are evaluated via indexless memory-based graph traversal algorithms. Our experimental evaluation shows the efficiency and the scalability of DG-SPARQL on querying massive attributed graph datasets in addition to its ability to outperform the performance of Apache Giraph, a popular distributed graph processing system, by orders of magnitudes.

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

Science.gov (United States)

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

2017-11-01

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

Interval Routing and Minor-Monotone Graph Parameters

NARCIS (Netherlands)

Bakker, E.M.; Bodlaender, H.L.; Tan, R.B.; Leeuwen, J. van

2006-01-01

We survey a number of minor-monotone graph parameters and their relationship to the complexity of routing on graphs. In particular we compare the interval routing parameters κslir(G) and κsir(G) with Colin de Verdi`ere’s graph invariant μ(G) and its variants λ(G) and κ(G). We show that for all the

Alliances and Bisection Width for Planar Graphs

DEFF Research Database (Denmark)

Olsen, Martin; Revsbæk, Morten

2013-01-01

An alliance in a graph is a set of vertices (allies) such that each vertex in the alliance has at least as many allies (counting the vertex itself) as non-allies in its neighborhood of the graph. We show that any planar graph with minimum degree at least 4 can be split into two alliances in polyn...

A new characterization of trivially perfect graphs

Directory of Open Access Journals (Sweden)

Christian Rubio Montiel

2015-03-01

Full Text Available A graph $G$ is \\emph{trivially perfect} if for every induced subgraph the cardinality of the largest set of pairwise nonadjacent vertices (the stability number $\\alpha(G$ equals the number of (maximal cliques $m(G$. We characterize the trivially perfect graphs in terms of vertex-coloring and we extend some definitions to infinite graphs.

Improper colouring of (random) unit disk graphs

NARCIS (Netherlands)

Kang, R.J.; Müller, T.; Sereni, J.S.

2008-01-01

For any graph G, the k-improper chromatic number ¿k(G) is the smallest number of colours used in a colouring of G such that each colour class induces a subgraph of maximum degree k. We investigate ¿k for unit disk graphs and random unit disk graphs to generalise results of McDiarmid and Reed

Color normalization of histology slides using graph regularized sparse NMF

Science.gov (United States)

Sha, Lingdao; Schonfeld, Dan; Sethi, Amit

2017-03-01

Computer based automatic medical image processing and quantification are becoming popular in digital pathology. However, preparation of histology slides can vary widely due to differences in staining equipment, procedures and reagents, which can reduce the accuracy of algorithms that analyze their color and texture information. To re- duce the unwanted color variations, various supervised and unsupervised color normalization methods have been proposed. Compared with supervised color normalization methods, unsupervised color normalization methods have advantages of time and cost efficient and universal applicability. Most of the unsupervised color normaliza- tion methods for histology are based on stain separation. Based on the fact that stain concentration cannot be negative and different parts of the tissue absorb different stains, nonnegative matrix factorization (NMF), and particular its sparse version (SNMF), are good candidates for stain separation. However, most of the existing unsupervised color normalization method like PCA, ICA, NMF and SNMF fail to consider important information about sparse manifolds that its pixels occupy, which could potentially result in loss of texture information during color normalization. Manifold learning methods like Graph Laplacian have proven to be very effective in interpreting high-dimensional data. In this paper, we propose a novel unsupervised stain separation method called graph regularized sparse nonnegative matrix factorization (GSNMF). By considering the sparse prior of stain concentration together with manifold information from high-dimensional image data, our method shows better performance in stain color deconvolution than existing unsupervised color deconvolution methods, especially in keeping connected texture information. To utilized the texture information, we construct a nearest neighbor graph between pixels within a spatial area of an image based on their distances using heat kernal in lαβ space. The

Three Syntactic Theories for Combinatory Graph Reduction

DEFF Research Database (Denmark)

Danvy, Olivier; Zerny, Ian

2011-01-01

in a third syntactic theory. The structure of the store-based abstract machine corresponding to this third syntactic theory oincides with that of Turner's original reduction machine. The three syntactic theories presented here The three syntactic heories presented here therefore have the following......We present a purely syntactic theory of graph reduction for the canonical combinators S, K, and I, where graph vertices are represented with evaluation contexts and let expressions. We express this syntactic theory as a reduction semantics, which we refocus into the first storeless abstract machine...... for combinatory graph reduction, which we refunctionalize into the first storeless natural semantics for combinatory graph reduction.We then factor out the introduction of let expressions to denote as many graph vertices as possible upfront instead of on demand, resulting in a second syntactic theory, this one...

Approximate Computing Techniques for Iterative Graph Algorithms

Energy Technology Data Exchange (ETDEWEB)

Panyala, Ajay R.; Subasi, Omer; Halappanavar, Mahantesh; Kalyanaraman, Anantharaman; Chavarria Miranda, Daniel G.; Krishnamoorthy, Sriram

2017-12-18

Approximate computing enables processing of large-scale graphs by trading off quality for performance. Approximate computing techniques have become critical not only due to the emergence of parallel architectures but also the availability of large scale datasets enabling data-driven discovery. Using two prototypical graph algorithms, PageRank and community detection, we present several approximate computing heuristics to scale the performance with minimal loss of accuracy. We present several heuristics including loop perforation, data caching, incomplete graph coloring and synchronization, and evaluate their efficiency. We demonstrate performance improvements of up to 83% for PageRank and up to 450x for community detection, with low impact of accuracy for both the algorithms. We expect the proposed approximate techniques will enable scalable graph analytics on data of importance to several applications in science and their subsequent adoption to scale similar graph algorithms.

Parallel Algorithm for Incremental Betweenness Centrality on Large Graphs

KAUST Repository

Jamour, Fuad Tarek

2017-10-17

Betweenness centrality quantifies the importance of nodes in a graph in many applications, including network analysis, community detection and identification of influential users. Typically, graphs in such applications evolve over time. Thus, the computation of betweenness centrality should be performed incrementally. This is challenging because updating even a single edge may trigger the computation of all-pairs shortest paths in the entire graph. Existing approaches cannot scale to large graphs: they either require excessive memory (i.e., quadratic to the size of the input graph) or perform unnecessary computations rendering them prohibitively slow. We propose iCentral; a novel incremental algorithm for computing betweenness centrality in evolving graphs. We decompose the graph into biconnected components and prove that processing can be localized within the affected components. iCentral is the first algorithm to support incremental betweeness centrality computation within a graph component. This is done efficiently, in linear space; consequently, iCentral scales to large graphs. We demonstrate with real datasets that the serial implementation of iCentral is up to 3.7 times faster than existing serial methods. Our parallel implementation that scales to large graphs, is an order of magnitude faster than the state-of-the-art parallel algorithm, while using an order of magnitude less computational resources.

Mathematical Minute: Rotating a Function Graph

Science.gov (United States)

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.

Mizan: Optimizing Graph Mining in Large Parallel Systems

KAUST Repository

Kalnis, Panos

2012-03-01

Extracting information from graphs, from nding shortest paths to complex graph mining, is essential for many ap- plications. Due to the shear size of modern graphs (e.g., social networks), processing must be done on large paral- lel computing infrastructures (e.g., the cloud). Earlier ap- proaches relied on the MapReduce framework, which was proved inadequate for graph algorithms. More recently, the message passing model (e.g., Pregel) has emerged. Although the Pregel model has many advantages, it is agnostic to the graph properties and the architecture of the underlying com- puting infrastructure, leading to suboptimal performance. In this paper, we propose Mizan, a layer between the users\\' code and the computing infrastructure. Mizan considers the structure of the input graph and the architecture of the in- frastructure in order to: (i) decide whether it is bene cial to generate a near-optimal partitioning of the graph in a pre- processing step, and (ii) choose between typical point-to- point message passing and a novel approach that puts com- puting nodes in a virtual overlay ring. We deployed Mizan on a small local Linux cluster, on the cloud (256 virtual machines in Amazon EC2), and on an IBM Blue Gene/P supercomputer (1024 CPUs). We show that Mizan executes common algorithms on very large graphs 1-2 orders of mag- nitude faster than MapReduce-based implementations and up to one order of magnitude faster than implementations relying on Pregel-like hash-based graph partitioning.

A first course in graph theory

CERN Document Server

Chartrand, Gary

2012-01-01

This comprehensive text offers undergraduates a remarkably student-friendly introduction to graph theory. Written by two of the field's most prominent experts, it takes an engaging approach that emphasizes graph theory's history. Unique examples and lucid proofs provide a sound yet accessible treatment that stimulates interest in an evolving subject and its many applications.Optional sections designated as ""excursion"" and ""exploration"" present interesting sidelights of graph theory and touch upon topics that allow students the opportunity to experiment and use their imaginations. Three app

System dynamics and control with bond graph modeling

CERN Document Server

Kypuros, Javier

2013-01-01

Part I Dynamic System ModelingIntroduction to System DynamicsIntroductionSystem Decomposition and Model ComplexityMathematical Modeling of Dynamic SystemsAnalysis and Design of Dynamic SystemsControl of Dynamic SystemsDiagrams of Dynamic SystemsA Graph-Centered Approach to ModelingSummaryPracticeExercisesBasic Bond Graph ElementsIntroductionPower and Energy VariablesBasic 1-Port ElementsBasic 2-Ports ElementsJunction ElementsSimple Bond Graph ExamplesSummaryPracticeExercisesBond Graph Synthesis and Equation DerivationIntroductionGeneral GuidelinesMechanical TranslationMechanical RotationElectrical CircuitsHydraulic CircuitsMixed SystemsState Equation DerivationState-Space RepresentationsAlgebraic Loops and Derivative CausalitySummaryPracticeExercisesImpedance Bond GraphsIntroductionLaplace Transform of the State-Space EquationBasic 1-Port ImpedancesImpedance Bond Graph SynthesisJunctions, Transformers, and GyratorsEffort and Flow DividersSign ChangesTransfer Function DerivationAlternative Derivation of Transf...

GO Explorer: A gene-ontology tool to aid in the interpretation of shotgun proteomics data.

Science.gov (United States)

Carvalho, Paulo C; Fischer, Juliana Sg; Chen, Emily I; Domont, Gilberto B; Carvalho, Maria Gc; Degrave, Wim M; Yates, John R; Barbosa, Valmir C

2009-02-24

Spectral counting is a shotgun proteomics approach comprising the identification and relative quantitation of thousands of proteins in complex mixtures. However, this strategy generates bewildering amounts of data whose biological interpretation is a challenge. Here we present a new algorithm, termed GO Explorer (GOEx), that leverages the gene ontology (GO) to aid in the interpretation of proteomic data. GOEx stands out because it combines data from protein fold changes with GO over-representation statistics to help draw conclusions. Moreover, it is tightly integrated within the PatternLab for Proteomics project and, thus, lies within a complete computational environment that provides parsers and pattern recognition tools designed for spectral counting. GOEx offers three independent methods to query data: an interactive directed acyclic graph, a specialist mode where key words can be searched, and an automatic search. Its usefulness is demonstrated by applying it to help interpret the effects of perillyl alcohol, a natural chemotherapeutic agent, on glioblastoma multiform cell lines (A172). We used a new multi-surfactant shotgun proteomic strategy and identified more than 2600 proteins; GOEx pinpointed key sets of differentially expressed proteins related to cell cycle, alcohol catabolism, the Ras pathway, apoptosis, and stress response, to name a few. GOEx facilitates organism-specific studies by leveraging GO and providing a rich graphical user interface. It is a simple to use tool, specialized for biologists who wish to analyze spectral counting data from shotgun proteomics. GOEx is available at http://pcarvalho.com/patternlab.

Stability notions in synthetic graph generation: a preliminary study

NARCIS (Netherlands)

van Leeuwen, W.; Fletcher, G.H.L.; Yakovets, N.; Bonifati, A.; Markl, Volker; Orlando, Salvatore; Mitschang, Bernhard

2017-01-01

With the rise in adoption of massive graph data, it be- comes increasingly important to design graph processing algorithms which have predictable behavior as the graph scales. This work presents an initial study of stability in the context of a schema-driven synthetic graph generation. Specifically,

Optimal Embeddings of Distance Regular Graphs into Euclidean Spaces

NARCIS (Netherlands)

F. Vallentin (Frank)

2008-01-01

htmlabstractIn this paper we give a lower bound for the least distortion embedding of a distance regular graph into Euclidean space. We use the lower bound for finding the least distortion for Hamming graphs, Johnson graphs, and all strongly regular graphs. Our technique involves semidefinite

Application of Bipolar Fuzzy Sets in Graph Structures