Science.gov

Sample records for graph interpretation skills

  1. Improving Graphing Interpretation Skills and Understanding of Motion Using Microcomputer Based Laboratories.

    ERIC Educational Resources Information Center

    Svec, Michael

    1999-01-01

    Examines the relative effectiveness of the traditional lab method and the microcomputer-based laboratory (MBL) for improving student understanding. Examines three areas of achievement: graphing interpretation skills, and interpreting motion graphs and understanding of motion. Results indicate that MBL laboratories are more effective than…

  2. Measuring Primary Students' Graph Interpretation Skills via a Performance Assessment: A Case Study in Instrument Development

    ERIC Educational Resources Information Center

    Peterman, Karen; Cranston, Kayla A.; Pryor, Marie; Kermish-Allen, Ruth

    2015-01-01

    This case study was conducted within the context of a place-based education project that was implemented with primary school students in the USA. The authors and participating teachers created a performance assessment of standards-aligned tasks to examine 6-10-year-old students' graph interpretation skills as part of an exploratory research…

  3. Measuring Primary Students' Graph Interpretation Skills Via a Performance Assessment: A case study in instrument development

    NASA Astrophysics Data System (ADS)

    Peterman, Karen; Cranston, Kayla A.; Pryor, Marie; Kermish-Allen, Ruth

    2015-11-01

    This case study was conducted within the context of a place-based education project that was implemented with primary school students in the USA. The authors and participating teachers created a performance assessment of standards-aligned tasks to examine 6-10-year-old students' graph interpretation skills as part of an exploratory research project. Fifty-five students participated in a performance assessment interview at the beginning and end of a place-based investigation. Two forms of the assessment were created and counterbalanced within class at pre and post. In situ scoring was conducted such that responses were scored as correct versus incorrect during the assessment's administration. Criterion validity analysis demonstrated an age-level progression in student scores. Tests of discriminant validity showed that the instrument detected variability in interpretation skills across each of three graph types (line, bar, dot plot). Convergent validity was established by correlating in situ scores with those from the Graph Interpretation Scoring Rubric. Students' proficiency with interpreting different types of graphs matched expectations based on age and the standards-based progression of graphs across primary school grades. The assessment tasks were also effective at detecting pre-post gains in students' interpretation of line graphs and dot plots after the place-based project. The results of the case study are discussed in relation to the common challenges associated with performance assessment. Implications are presented in relation to the need for authentic and performance-based instructional and assessment tasks to respond to the Common Core State Standards and the Next Generation Science Standards.

  4. The Development of Fundamental Skills in Tactile Graph Interpretation: A Program for Braille Readers. Final Report.

    ERIC Educational Resources Information Center

    Barth, John L.

    The report describes the development and evaluation of an instructional program in tangible graph interpretation for braille readers. Because graphs frequently appear in textbooks and in other printed sources, lack of appropriate translation for blind persons can be a significant educational obstacle. Based on anlyses of typical graph reading…

  5. The relationships between spatial ability, logical thinking, mathematics performance and kinematics graph interpretation skills of 12th grade physics students

    NASA Astrophysics Data System (ADS)

    Bektasli, Behzat

    Graphs have a broad use in science classrooms, especially in physics. In physics, kinematics is probably the topic for which graphs are most widely used. The participants in this study were from two different grade-12 physics classrooms, advanced placement and calculus-based physics. The main purpose of this study was to search for the relationships between student spatial ability, logical thinking, mathematical achievement, and kinematics graphs interpretation skills. The Purdue Spatial Visualization Test, the Middle Grades Integrated Process Skills Test (MIPT), and the Test of Understanding Graphs in Kinematics (TUG-K) were used for quantitative data collection. Classroom observations were made to acquire ideas about classroom environment and instructional techniques. Factor analysis, simple linear correlation, multiple linear regression, and descriptive statistics were used to analyze the quantitative data. Each instrument has two principal components. The selection and calculation of the slope and of the area were the two principal components of TUG-K. MIPT was composed of a component based upon processing text and a second component based upon processing symbolic information. The Purdue Spatial Visualization Test was composed of a component based upon one-step processing and a second component based upon two-step processing of information. Student ability to determine the slope in a kinematics graph was significantly correlated with spatial ability, logical thinking, and mathematics aptitude and achievement. However, student ability to determine the area in a kinematics graph was only significantly correlated with student pre-calculus semester 2 grades. Male students performed significantly better than female students on the slope items of TUG-K. Also, male students performed significantly better than female students on the PSAT mathematics assessment and spatial ability. This study found that students have different levels of spatial ability, logical thinking

  6. The Relationships between Logical Thinking, Gender, and Kinematics Graph Interpretation Skills

    ERIC Educational Resources Information Center

    Bektasli, Behzat; White, Arthur L.

    2012-01-01

    Problem Statement: Kinematics is one of the topics in physics where graphs are used broadly. Kinematics includes many abstract formulas, and students usually try to solve problems with those formulas. However, using a kinematics graph instead of formulas might be a better option for problem solving in kinematics. Graphs are abstract…

  7. The effects of microcomputer-based laboratory exercises on the acquisition of line graph construction and interpretation skills by high school biology students

    NASA Astrophysics Data System (ADS)

    Adams, D. Daryl; Shrum, John W.

    Effects of microcomputer-based laboratories and level of cognitive development on tenth-grade biology students' ability to construct and interpret line graphs was investigated. Fortysix students enrolled in general biology classes at a rural high school volunteered to participate in the study. These students were administered instruments to assess level of cognitive development and line-graphing ability. Ten students that scored between zero and three and ten students that scored between six and ten on the graphing assessment were chosen to participate in the study. The 20 students were then assigned to either experimental or conventional groups to achieve a matched design with relation to gender and line-graphing ability. Statistical analysis of the data indicated no effect due to instructional method on graph-interpretation abilities. An instructional effect was demonstrated for graph-construction tasks (p < 0.10) with the conventional group outperforming the microcomputer-based laboratory group. Effect sizes of -1.01 and 0.48 were found for graph-construction and -interpretation skills, respectively. Effects related to cognitive development were indicated with those students classified as high cognitive development outscoring those classified as low (p < 0.10) This was true for both graph-construction and graph-interpretation tasks. No two-way interactions were found.

  8. Challenges with Graph Interpretation: A Review of the Literature

    ERIC Educational Resources Information Center

    Glazer, Nirit

    2011-01-01

    With the growing emphasis on the development of scientific inquiry skills, the display and interpretation of data are becoming increasingly important. Graph interpretation competence is, in fact, essential to understanding today's world and to be scientifically literate. However, graph interpretation is a complex and challenging activity. Graph…

  9. Integrating concepts and skills: Slope and kinematics graphs

    NASA Astrophysics Data System (ADS)

    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.

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

    NASA Astrophysics Data System (ADS)

    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

  11. Correlational Analysis and Interpretation: Graphs Prevent Gaffes. Faculty Forum.

    ERIC Educational Resources Information Center

    Peden, Blaine F.

    2001-01-01

    Describes an activity that enables students to exercise their data entry, computational, graphical, and writing skills to learn the importance of graphs in good statistical analysis. Students use four data sets to enter data, compute Pearson correlation values, plot scatter graphs, and write results paragraphs. (CMK)

  12. Interpreting Motion Graphs through Metaphorical Projection of Embodied Experience

    ERIC Educational Resources Information Center

    Botzer, Galit; Yerushalmy, Michal

    2006-01-01

    This paper focuses on the cognitive processes that occur while students are exploring motion graphs. In a classroom experiment, we examine how high-school students (aged 17), with backgrounds in calculus and physics, interpret the graphs they create through drawing the path of the movement of their hand with a computer mouse. Based on recent, and…

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

    ERIC Educational Resources Information Center

    Ubuz, Behiye

    2007-01-01

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

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

    ERIC Educational Resources Information Center

    Deniz, Hasan; Dulger, Mehmet F.

    2012-01-01

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

  15. Adolescents' Graphing Skills: A Descriptive Analysis.

    ERIC Educational Resources Information Center

    Clement, John; And Others

    Clinical interviews were conducted with 25 seventh- and eighth-grade students to determine: (1) the extent to which they could produce correct graphical representations of familiar situations; (2) to what extent they could infer relationships from graphs; (3) what are the most commonly held graphing misconceptions and how stable they are; and (4)…

  16. Neural complexity: A graph theoretic interpretation

    NASA Astrophysics Data System (ADS)

    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.

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

    PubMed Central

    Peebles, David; Ali, Nadia

    2015-01-01

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

  18. Infusing Counseling Skills in Test Interpretation.

    ERIC Educational Resources Information Center

    Rawlins, Melanie E.; And Others

    1991-01-01

    Presents an instructional model based on Neurolinguistic Programming that links counseling student course work in measurement and test interpretation with counseling techniques and theory. A process incorporating Neurolinguistic Programming patterns is outlined for teaching graduate students the counseling skills helpful in test interpretation.…

  19. Pre-Service Science Teachers' Interpretations of Graphs: A Cross-Sectional Study

    ERIC Educational Resources Information Center

    Çil, Emine; Kar, Hazel

    2015-01-01

    This study focuses on pre-service science teachers' interpretations of graphs. First, the paper presents data about the freshman and senior pre-service teachers' interpretations of graphs. Then it discusses the effects of pre-service science teacher training program on student teachers' interpretations of graphs. The participants in the study were…

  20. Assessing and Understanding Line Graph Interpretations Using a Scoring Rubric of Organized Cited Factors

    ERIC Educational Resources Information Center

    Boote, Stacy K.

    2014-01-01

    This study examined how 12- and 13-year-old students' mathematics and science background knowledge affected line graph interpretations and how interpretations were affected by graph question levels. A purposive sample of 14 students engaged in think aloud interviews while completing an excerpted Test of Graphing in Science. Data were…

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

    NASA Astrophysics Data System (ADS)

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

    2016-06-01

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

  2. Assessing and Understanding Line Graph Interpretations Using a Scoring Rubric of Organized Cited Factors

    NASA Astrophysics Data System (ADS)

    Boote, Stacy K.

    2014-04-01

    This study examined how 12- and 13-year-old students' mathematics and science background knowledge affected line graph interpretations and how interpretations were affected by graph question levels. A purposive sample of 14 students engaged in think aloud interviews while completing an excerpted Test of Graphing in Science. Data were collected and coded using a rubric of previously cited factors, categorized by Bertin's (Semiology of graphics: Diagrams, networks, maps. The University of Wisconsin Press, Ltd., Madison, 1983) theory of graph interpretation. Data analysis revealed responses varied by graph question level. Across levels, students interpreted graphs in one or more of the three ways: mathematical word problems (focusing on an algorithm), science data to be analyzed (incorporating science knowledge), or no strategy. Although consistently used across levels, the frequency and usefulness of approaches varied by question level.

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

    ERIC Educational Resources Information Center

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

    2016-01-01

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

  4. Interpreting Unfamiliar Graphs: A Generative, Activity Theoretic Model

    ERIC Educational Resources Information Center

    Roth, Wolff-Michael; Lee, Yew Jin

    2004-01-01

    Research on graphing presents its results as if knowing and understanding were something stored in peoples' minds independent of the situation that they find themselves in. Thus, there are no models that situate interview responses to graphing tasks. How, then, we question, are the interview texts produced? How do respondents begin and end…

  5. Students' Interpretation of a Function Associated with a Real-Life Problem from Its Graph

    ERIC Educational Resources Information Center

    Mahir, Nevin

    2010-01-01

    The properties of a function such as limit, continuity, derivative, growth, or concavity can be determined more easily from its graph than by doing any algebraic operation. For this reason, it is important for students of mathematics to interpret some of the properties of a function from its graph. In this study, we investigated the competence of…

  6. Generalizing a categorization of students' interpretations of linear kinematics graphs

    NASA Astrophysics Data System (ADS)

    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.

  7. Generalizing a Categorization of Students' Interpretations of Linear Kinematics Graphs

    ERIC Educational Resources Information Center

    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…

  8. Improving Graduate Students' Graphing Skills of Multiple Baseline Designs with Microsoft[R] Excel 2007

    ERIC Educational Resources Information Center

    Lo, Ya-yu; Starling, A. Leyf Peirce

    2009-01-01

    This study examined the effects of a graphing task analysis using the Microsoft[R] Office Excel 2007 program on the single-subject multiple baseline graphing skills of three university graduate students. Using a multiple probe across participants design, the study demonstrated a functional relationship between the number of correct graphing…

  9. Bars, Lines, & Pies: A Graphing Skills Program. Expect the Unexpected with Math[R

    ERIC Educational Resources Information Center

    Actuarial Foundation, 2013

    2013-01-01

    "Bars, Lines, & Pies" is a dynamic math program designed to build graphing skills in students, while also showing them the relevance of math in their lives. Developed by The Actuarial Foundation along with Scholastic, the graphing lessons and activities involve engaging, real-world examples about the environment and recycling. In these lessons,…

  10. Effects of Graphing Conventions and Response Options on Interpretation of Small n Graphs

    ERIC Educational Resources Information Center

    Carter, Mark

    2009-01-01

    The present study examined the effects of manipulation of two graphing conventions on judgements of time-series data by novice raters. These conventions involved the presence of phase change lines between baseline and intervention data and whether data points across phase changes were connected. The 1990 study of Matyas and Greenwood was also…

  11. Evaluating Interpreter's Skill by Measurement of Prosody Recognition

    NASA Astrophysics Data System (ADS)

    Tanaka, Saori; Nakazono, Kaoru; Nishida, Masafumi; Horiuchi, Yasuo; Ichikawa, Akira

    Sign language is a visual language in which main articulators are hands, torso, head, and face. For simultaneous interpreters of Japanese sign language (JSL) and spoken Japanese, it is very important to recognize not only the hands movement but also prosody such like head, eye, posture and facial expression. This is because prosody has grammatical rules for representing the case and modification relations in JSL. The goal of this study is to introduce an examination called MPR (Measurement of Prosody Recognition) and to demonstrate that it can be an indicator for the other general skills of interpreters. For this purpose, we conducted two experiments: the first studies the relationship between the interpreter's experience and the performance score on MPR (Experiment-1), and the second investigates the specific skill that can be estimated by MPR (Experiment-2). The data in Experiment-1 came from four interpreters who had more than 1-year experience as interpreters, and more four interpreters who had less than 1-year experience. The mean accuracy of MPR in the more experienced group was higher than that in the less experienced group. The data in Experiment-2 came from three high MPR interpreters and three low MPR interpreters. Two hearing subjects and three deaf subjects evaluated their skill in terms of the speech or sign interpretation skill, the reliability of interpretation, the expeditiousness, and the subjective sense of accomplishment for the ordering pizza task. The two experiments indicated a possibility that MPR could be useful for estimating if the interpreter is sufficiently experienced to interpret from sign language to spoken Japanese, and if they can work on the interpretation expeditiously without making the deaf or the hearing clients anxious. Finally we end this paper with suggestions for conclusions and future work.

  12. Using professional interpreters in undergraduate medical consultation skills teaching

    PubMed Central

    Bansal, Aarti; Swann, Jennifer; Smithson, William Henry

    2014-01-01

    The ability to work with interpreters is a core skill for UK medical graduates. At the University of Sheffield Medical School, this teaching was identified as a gap in the curriculum. Teaching was developed to use professional interpreters in role-play, based on evidence that professional interpreters improve health outcomes for patients with limited English proficiency. Other principles guiding the development of the teaching were an experiential learning format, integration to the core consultation skills curriculum, and sustainable delivery. The session was aligned with existing consultation skills teaching to retain the small-group experiential format and general practitioner (GP) tutor. Core curricular time was found through conversion of an existing consultation skills session. Language pairs of professional interpreters worked with each small group, with one playing patient and the other playing interpreter. These professional interpreters attended training in the scenarios so that they could learn to act as patient and family interpreter. GP tutors attended training sessions to help them facilitate the session. This enhanced the sustainability of the session by providing a cohort of tutors able to pass on their expertise to new staff through the existing shadowing process. Tutors felt that the involvement of professional interpreters improved student engagement. Student evaluation of the teaching suggests that the learning objectives were achieved. Faculty evaluation by GP tutors suggests that they perceived the teaching to be worthwhile and that the training they received had helped improve their own clinical practice in consulting through interpreters. We offer the following recommendations to others who may be interested in developing teaching on interpreted consultations within their core curriculum: 1) consider recruiting professional interpreters as a teaching resource; 2) align the teaching to existing consultation skills sessions to aid integration

  13. Using professional interpreters in undergraduate medical consultation skills teaching.

    PubMed

    Bansal, Aarti; Swann, Jennifer; Smithson, William Henry

    2014-01-01

    The ability to work with interpreters is a core skill for UK medical graduates. At the University of Sheffield Medical School, this teaching was identified as a gap in the curriculum. Teaching was developed to use professional interpreters in role-play, based on evidence that professional interpreters improve health outcomes for patients with limited English proficiency. Other principles guiding the development of the teaching were an experiential learning format, integration to the core consultation skills curriculum, and sustainable delivery. The session was aligned with existing consultation skills teaching to retain the small-group experiential format and general practitioner (GP) tutor. Core curricular time was found through conversion of an existing consultation skills session. Language pairs of professional interpreters worked with each small group, with one playing patient and the other playing interpreter. These professional interpreters attended training in the scenarios so that they could learn to act as patient and family interpreter. GP tutors attended training sessions to help them facilitate the session. This enhanced the sustainability of the session by providing a cohort of tutors able to pass on their expertise to new staff through the existing shadowing process. Tutors felt that the involvement of professional interpreters improved student engagement. Student evaluation of the teaching suggests that the learning objectives were achieved. Faculty evaluation by GP tutors suggests that they perceived the teaching to be worthwhile and that the training they received had helped improve their own clinical practice in consulting through interpreters. We offer the following recommendations to others who may be interested in developing teaching on interpreted consultations within their core curriculum: 1) consider recruiting professional interpreters as a teaching resource; 2) align the teaching to existing consultation skills sessions to aid integration

  14. Graph-based interpretation of the molecular interstellar medium segmentation

    NASA Astrophysics Data System (ADS)

    Colombo, D.; Rosolowsky, E.; Ginsburg, A.; Duarte-Cabral, A.; Hughes, A.

    2015-12-01

    We present a generalization of the giant molecular cloud identification problem based on cluster analysis. The method we designed, SCIMES (Spectral Clustering for Interstellar Molecular Emission Segmentation) considers the dendrogram of emission in the broader framework of graph theory and utilizes spectral clustering to find discrete regions with similar emission properties. For Galactic molecular cloud structures, we show that the characteristic volume and/or integrated CO luminosity are useful criteria to define the clustering, yielding emission structures that closely reproduce `by-eye' identification results. SCIMES performs best on well-resolved, high-resolution data, making it complementary to other available algorithms. Using 12CO(1-0) data for the Orion-Monoceros complex, we demonstrate that SCIMES provides robust results against changes of the dendrogram-construction parameters, noise realizations and degraded resolution. By comparing SCIMES with other cloud decomposition approaches, we show that our method is able to identify all canonical clouds of the Orion-Monoceros region, avoiding the overdivision within high-resolution survey data that represents a common limitation of several decomposition algorithms. The Orion-Monoceros objects exhibit hierarchies and size-line width relationships typical to the turbulent gas in molecular clouds, although `the Scissors' region deviates from this common description. SCIMES represents a significant step forward in moving away from pixel-based cloud segmentation towards a more physical-oriented approach, where virtually all properties of the ISM can be used for the segmentation of discrete objects.

  15. Fragmentation network of doubly charged methionine: Interpretation using graph theory.

    PubMed

    Ha, D T; Yamazaki, K; Wang, Y; Alcamí, M; Maeda, S; Kono, H; Martín, F; Kukk, E

    2016-09-01

    The fragmentation of doubly charged gas-phase methionine (HO2CCH(NH2)CH2CH2SCH3) is systematically studied using the self-consistent charge density functional tight-binding molecular dynamics (MD) simulation method. We applied graph theory to analyze the large number of the calculated MD trajectories, which appears to be a highly effective and convenient means of extracting versatile information from the large data. The present theoretical results strongly concur with the earlier studied experimental ones. Essentially, the dication dissociates into acidic group CO2H and basic group C4NSH10. The former may carry a single or no charge and stays intact in most cases, whereas the latter may hold either a single or a double charge and tends to dissociate into smaller fragments. The decay of the basic group is observed to follow the Arrhenius law. The dissociation pathways to CO2H and C4NSH10 and subsequent fragmentations are also supported by ab initio calculations. PMID:27608997

  16. So Many Graphs, So Little Time

    ERIC Educational Resources Information Center

    Wall, Jennifer J.; Benson, Christine C.

    2009-01-01

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

  17. My Bar Graph Tells a Story

    ERIC Educational Resources Information Center

    McMillen, Sue; McMillen, Beth

    2010-01-01

    Connecting stories to qualitative coordinate graphs has been suggested as an effective instructional strategy. Even students who are able to "create" bar graphs may struggle to correctly "interpret" them. Giving children opportunities to work with qualitative graphs can help them develop the skills to interpret, describe, and compare information…

  18. Hands-on Materials for Teaching about Global Climate Change through Graph Interpretation

    ERIC Educational Resources Information Center

    Rule, Audrey C.; Hallagan, Jean E.; Shaffer, Barbara

    2008-01-01

    Teachers need to address global climate change with students in their classrooms as evidence for consequences from these environmental changes mounts. One way to approach global climate change is through examination of authentic data. Mathematics and science may be integrated by interpreting graphs from the professional literature. This study…

  19. Physics Students' Performance Using Computational Modelling Activities to Improve Kinematics Graphs Interpretation

    ERIC Educational Resources Information Center

    Araujo, Ives Solano; Veit, Eliane Angela; Moreira, Marco Antonio

    2008-01-01

    The purpose of this study was to investigate undergraduate students' performance while exposed to complementary computational modelling activities to improve physics learning, using the software "Modellus." Interpretation of kinematics graphs was the physics topic chosen for investigation. The theoretical framework adopted was based on Halloun's…

  20. On the Relation of Abstract and Concrete in Scientists' Graph Interpretations: A Case Study

    ERIC Educational Resources Information Center

    Roth, Wolff-Michael; Hwang, SungWon

    2006-01-01

    The notions of "abstract" and "concrete" are central to the conceptualization of mathematical knowing and learning. Much of the literature takes a dualist approach, leading to the privileging of the former term at the expense of the latter. In this article, we provide a concrete analysis of a scientist interpreting an unfamiliar graph to show how…

  1. Collaborative Robotic Instruction: A Graph Teaching Experience

    ERIC Educational Resources Information Center

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

    2009-01-01

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

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

    NASA Astrophysics Data System (ADS)

    Berg, Craig A.; Smith, Philip

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

  3. The Relation between the Working Memory Skills of Sign Language Interpreters and the Quality of Their Interpretations

    ERIC Educational Resources Information Center

    Van Dijk, Rick; Christoffels, Ingrid; Postma, Albert; Hermans, Daan

    2012-01-01

    In two experiments we investigated the relationship between the working memory skills of sign language interpreters and the quality of their interpretations. In Experiment 1, we found that scores on 3-back tasks with signs and words were not related to the quality of interpreted narratives. In Experiment 2, we found that memory span scores for…

  4. Line Graph Learning

    ERIC Educational Resources Information Center

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

    2007-01-01

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

  5. Interpretation of Radiological Images: Towards a Framework of Knowledge and Skills

    ERIC Educational Resources Information Center

    van der Gijp, A.; van der Schaaf, M. F.; van der Schaaf, I. C.; Huige, J. C. B. M.; Ravesloot, C. J.; van Schaik, J. P. J.; ten Cate, Th. J.

    2014-01-01

    The knowledge and skills that are required for radiological image interpretation are not well documented, even though medical imaging is gaining importance. This study aims to develop a comprehensive framework of knowledge and skills, required for two-dimensional and multiplanar image interpretation in radiology. A mixed-method study approach was…

  6. The Effect of a Graph-Oriented Computer-Assisted Project-Based Learning Environment on Argumentation Skills

    ERIC Educational Resources Information Center

    Hsu, P. -S.; Van Dyke, M.; Chen, Y.; Smith, T. J.

    2015-01-01

    The purpose of this quasi-experimental study was to explore how seventh graders in a suburban school in the United States developed argumentation skills and science knowledge in a project-based learning environment that incorporated a graph-oriented, computer-assisted application. A total of 54 students (three classes) comprised this treatment…

  7. The Graphing Skills of Students in Mathematics and Science Education. ERIC Digest.

    ERIC Educational Resources Information Center

    Ozgun-Koca, S. Asli

    Graphical representations play an important role in both science and mathematics education. Graphs can summarize very complex information or relationships very effectively. Although graphs are explicitly taught in mathematics classrooms as an end in themselves, many subject areas such as science or social studies utilize graphs to represent and…

  8. Enhancing Table Interpretation Skills via Training in Table Creation

    ERIC Educational Resources Information Center

    Karazsia, Bryan T.

    2013-01-01

    Quantitative and statistical literacy are core domains in the undergraduate psychology curriculum. An important component of such literacy includes interpretation of visual aids, such as tables containing results from statistical analyses. This article presents a new technique for enhancing student interpretation of American Psychological…

  9. Categorization of first-year university students' interpretations of numerical linear distance-time graphs

    NASA Astrophysics Data System (ADS)

    Wemyss, Thomas; van Kampen, Paul

    2013-06-01

    We have investigated the various approaches taken by first-year university students (n≈550) when asked to determine the direction of motion, the constancy of speed, and a numerical value of the speed of an object at a point on a numerical linear distance-time graph. We investigated the prevalence of various well-known general graphing difficulties, such as graph-as-picture errors and slope-height confusion. We established that two-thirds of our students could determine the direction of motion with respect to a reference point, just under 80% could determine that the speed is constant, and just under 20% of our students could correctly determine the value of the speed; in the latter case, about half of the students divided the two coordinates. Three stable categories of correctly explaining the constancy of speed emerged from the data. We found that the reason given for determining that the speed of the object was constant did not correlate with successfully determining a value for the speed. We have established that technical difficulties such as determining the slope of any linear graph did not explain the poor performance. By comparing the answers to similar questions on water level versus time graphs, we were able to establish that context dependence and incorrect prior learning are likely to play a role. Post-test data are used to confirm the validity of the categorization and support the conclusion that being able to determine the slope of a y,x graph and having a correct qualitative understanding of a distance-time graph is not sufficient to correctly determine a value for the speed.

  10. Effects of Training in Dream Recall and Dream Interpretation Skills on Dream Recall, Attitudes, and Dream Interpretation Outcome.

    ERIC Educational Resources Information Center

    Rochlen, Aaron B.; Ligiero, Daniela P.; Hill, Clara E.; Heaton, Kristin J.

    1999-01-01

    Volunteer clients (N=44) with below-average dream recall and attitudes toward dreams participated in training sessions focusing on either improving dream recall and attitudes toward dreams, building dream-interpretation skills, or educating about counseling. No significant differences were found within the three groups. Results suggest that…

  11. Beyond Behavioral Skills to Human-Involved Processes: Relational Nursing Practice and Interpretive Pedagogy.

    ERIC Educational Resources Information Center

    Doane, Gweneth A. Hartrick

    2002-01-01

    Behaviorist teaching of communication skills can interfere with learning of humanistic nursing. Interpretive inquiry can help students experience the transformative power for relationships and develop confidence and trust in their capacity for relational nursing practice. (Contains 20 references.) (SK)

  12. Categorization of First-Year University Students' Interpretations of Numerical Linear Distance-Time Graphs

    ERIC Educational Resources Information Center

    Wemyss, Thomas; van Kampen, Paul

    2013-01-01

    We have investigated the various approaches taken by first-year university students (n[image omitted]550) when asked to determine the direction of motion, the constancy of speed, and a numerical value of the speed of an object at a point on a numerical linear distance-time graph. We investigated the prevalence of various well-known general…

  13. Graphing Reality

    NASA Astrophysics Data System (ADS)

    Beeken, Paul

    2014-11-01

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

  14. Skill Assessment in the Interpretation of 3D Fracture Patterns from Radiographs

    PubMed Central

    Rojas-Murillo, Salvador; Hanley, Jessica M; Kreiter, Clarence D; Karam, Matthew D; Anderson, Donald D

    2016-01-01

    Abstract Background Interpreting two-dimensional radiographs to ascertain the three-dimensional (3D) position and orientation of fracture planes and bone fragments is an important component of orthopedic diagnosis and clinical management. This skill, however, has not been thoroughly explored and measured. Our primary research question is to determine if 3D radiographic image interpretation can be reliably assessed, and whether this assessment varies by level of training. A test designed to measure this skill among orthopedic surgeons would provide a quantitative benchmark for skill assessment and training research. Methods Two tests consisting of a series of online exercises were developed to measure this skill. Each exercise displayed a pair of musculoskeletal radiographs. Participants selected one of three CT slices of the same or similar fracture patterns that best matched the radiographs. In experiment 1, 10 orthopedic residents and staff responded to nine questions. In experiment 2, 52 residents from both orthopedics and radiology responded to 12 questions. Results Experiment 1 yielded a Cronbach alpha of 0.47. Performance correlated with experience; r(8) = 0.87, p<0.01, suggesting that the test could be both valid and reliable with a slight increase in test length. In experiment 2, after removing three non-discriminating items, the Cronbach coefficient alpha was 0.28 and performance correlated with experience; r(50) = 0.25, p<0.10. Conclusions Although evidence for reliability and validity was more compelling with the first experiment, the analyses suggest motivation and test duration are important determinants of test efficacy. The interpretation of radiographs to discern 3D information is a promising and a relatively unexplored area for surgical skill education and assessment. The online test was useful and reliable. Further test development is likely to increase test effectiveness. Clinical Relevance Accurately interpreting radiographic images is an

  15. Graphing Reality

    ERIC Educational Resources Information Center

    Beeken, Paul

    2014-01-01

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

  16. Levels of line graph question interpretation with intermediate elementary students of varying scientific and mathematical knowledge and ability: A think aloud study

    NASA Astrophysics Data System (ADS)

    Keller, Stacy Kathryn

    This study examined how intermediate elementary students' mathematics and science background knowledge affected their interpretation of line graphs and how their interpretations were affected by graph question levels. A purposive sample of 14 6th-grade students engaged in think aloud interviews (Ericsson & Simon, 1993) while completing an excerpted Test of Graphing in Science (TOGS) (McKenzie & Padilla, 1986). Hand gestures were video recorded. Student performance on the TOGS was assessed using an assessment rubric created from previously cited factors affecting students' graphing ability. Factors were categorized using Bertin's (1983) three graph question levels. The assessment rubric was validated by Padilla and a veteran mathematics and science teacher. Observational notes were also collected. Data were analyzed using Roth and Bowen's semiotic process of reading graphs (2001). Key findings from this analysis included differences in the use of heuristics, self-generated questions, science knowledge, and self-motivation. Students with higher prior achievement used a greater number and variety of heuristics and more often chose appropriate heuristics. They also monitored their understanding of the question and the adequacy of their strategy and answer by asking themselves questions. Most used their science knowledge spontaneously to check their understanding of the question and the adequacy of their answers. Students with lower and moderate prior achievement favored one heuristic even when it was not useful for answering the question and rarely asked their own questions. In some cases, if students with lower prior achievement had thought about their answers in the context of their science knowledge, they would have been able to recognize their errors. One student with lower prior achievement motivated herself when she thought the questions were too difficult. In addition, students answered the TOGS in one of three ways: as if they were mathematics word problems

  17. Teacher-Designed Software for Interactive Linear Equations: Concepts, Interpretive Skills, Applications & Word-Problem Solving.

    ERIC Educational Resources Information Center

    Lawrence, Virginia

    No longer just a user of commercial software, the 21st century teacher is a designer of interactive software based on theories of learning. This software, a comprehensive study of straightline equations, enhances conceptual understanding, sketching, graphic interpretive and word problem solving skills as well as making connections to real-life and…

  18. Using the Computer to Teach Methods and Interpretative Skills in the Humanities: Implementing a Project.

    ERIC Educational Resources Information Center

    Jones, Bruce William

    The results of implementing computer-assisted instruction (CAI) in two religion courses and a logic course at California State College, Bakersfield, are examined along with student responses. The main purpose of the CAI project was to teach interpretive skills. The most positive results came in the logic course. The programs in the New Testament…

  19. Determination and Interpretation of the Norm Values of Preschool Social Skills Rating Scale Teacher Form

    ERIC Educational Resources Information Center

    Omeroglu, Esra; Buyukozturk, Sener; Aydogan, Yasemin; Cakan, Mehtap; Cakmak, Ebru Kilic; Ozyurek, Arzu; Akduman, Gulumser Gultekin; Gunindi, Yunus; Kutlu, Omer; Coban, Aysel; Yurt, Ozlem; Kogar, Hakan; Karayol, Seda

    2015-01-01

    This study aimed to determine and interpret norms of the Preschool Social Skills Rating Scale (PSSRS) teacher form. The sample included 224 independent preschools and 169 primary schools. The schools are distributed among 48 provinces and 3324 children were included. Data were obtained from the PSSRS teacher form. The validity and reliability…

  20. An Interpretative Phenomenological Analysis of How Professional Dance Teachers Implement Psychological Skills Training in Practice

    ERIC Educational Resources Information Center

    Klockare, Ellinor; Gustafsson, Henrik; Nordin-Bates, Sanna M.

    2011-01-01

    The aim of this study was to examine how dance teachers work with psychological skills with their students in class. Semi-structured interviews were conducted with six female professional teachers in jazz, ballet and contemporary dance. The interview transcripts were analyzed using interpretative phenomenological analysis (Smith 1996). Results…

  1. Re-Examining the Power of Video Motion Analysis to Promote the Reading and Creating of Kinematic Graphs

    ERIC Educational Resources Information Center

    Eshach, Haim

    2010-01-01

    One essential skill that students who learn physics should possess is the ability to create and interpret kinematic graphs. However, it is well documented in the literature that students show lack of competence in these abilities. They have problems in connecting graphs and physics concepts, as well as graphs and the real world. The present paper…

  2. The Impact of Microcomputer-Based Science Labs on Children's Graphing Skills.

    ERIC Educational Resources Information Center

    Mokros, Janice R.

    Microcomputer-based laboratories (MBL), the use of microcomputers for student-directed data acquisition and analysis, represents a promising new development in science laboratory instruction. This descriptive study determined the impact of MBLs on middle school students' understanding of graphs of distance and velocity. The study was based on the…

  3. Graph/Chart Interpretation and Reading Comprehension as Critical Thinking Skills

    ERIC Educational Resources Information Center

    Malamitsa, Katerina; Kokkotas, Panagiotis; Kasoutas, Michael

    2008-01-01

    In contemporary academic literature and in many national curricula, there is a widespread acceptance that critical thinking should be an important dimension of Education. Teachers and researchers recognize the importance of developing students critical thinking, but there are still great difficulties in defining and assessing critical-thinking…

  4. Understanding of Idiomatic Expressions in Context in Skilled and Less Skilled Comprehenders: Online Processing and Interpretation

    ERIC Educational Resources Information Center

    Oakhill, Jane; Cain, Kate; Nesi, Barbara

    2016-01-01

    This article reports a study in which good and poor comprehenders (in 2 age groups: 8- and 10-year-olds) read short passages containing phrases that could be interpreted as idiomatic or not, depending on the context. Familiarity was manipulated by including real (English) idioms and novel (translations of Italian) idioms. Reading times for the…

  5. Offline signature verification and skilled forgery detection using HMM and sum graph features with ANN and knowledge based classifier

    NASA Astrophysics Data System (ADS)

    Mehta, Mohit; Choudhary, Vijay; Das, Rupam; Khan, Ilyas

    2010-02-01

    Signature verification is one of the most widely researched areas in document analysis and signature biometric. Various methodologies have been proposed in this area for accurate signature verification and forgery detection. In this paper we propose a unique two stage model of detecting skilled forgery in the signature by combining two feature types namely Sum graph and HMM model for signature generation and classify them with knowledge based classifier and probability neural network. We proposed a unique technique of using HMM as feature rather than a classifier as being widely proposed by most of the authors in signature recognition. Results show a higher false rejection than false acceptance rate. The system detects forgeries with an accuracy of 80% and can detect the signatures with 91% accuracy. The two stage model can be used in realistic signature biometric applications like the banking applications where there is a need to detect the authenticity of the signature before processing documents like checks.

  6. Chemical Understanding and Graphing Skills in an Honors Case-Based Computerized Chemistry Laboratory Environment: The Value of Bidirectional Visual and Textual Representations

    ERIC Educational Resources Information Center

    Dori, Yehudit J.; Sasson, Irit

    2008-01-01

    The case-based computerized laboratory (CCL) is a chemistry learning environment that integrates computerized experiments with emphasis on scientific inquiry and comprehension of case studies. The research objective was to investigate chemical understanding and graphing skills of high school honors students via bidirectional visual and textual…

  7. Measures of Fine Motor Skills in People with Tremor Disorders: Appraisal and Interpretation

    PubMed Central

    Norman, Kathleen E.; Héroux, Martin E.

    2013-01-01

    People with Parkinson’s disease, essential tremor, or other movement disorders involving tremor have changes in fine motor skills that are among the hallmarks of these diseases. Numerous measurement tools have been created and other methods devised to measure such changes in fine motor skills. Measurement tools may focus on specific features – e.g., motor skills or dexterity, slowness in movement execution associated with parkinsonian bradykinesia, or magnitude of tremor. Less obviously, some tools may be better suited than others for specific goals such as detecting subtle dysfunction early in disease, revealing aspects of brain function affected by disease, or tracking changes expected from treatment or disease progression. The purpose of this review is to describe and appraise selected measurement tools of fine motor skills appropriate for people with tremor disorders. In this context, we consider the tools’ content – i.e., what movement features they focus on. In addition, we consider how measurement tools of fine motor skills relate to measures of a person’s disease state or a person’s function. These considerations affect how one should select and interpret the results of these tools in laboratory and clinical contexts. PMID:23717299

  8. Teaching and Learning about Graphing through Computer-Assisted Problem Solving: Issues in the Design and Interpretation of Graphs, the Design and Use of Educational Software, and Classroom Research Methodology.

    ERIC Educational Resources Information Center

    Jackson, David F.; And Others

    Recent research has demonstrated the promise of graphing software as an aid to teaching graphs in two content areas: line graphs of aspects of motion and graphs of algebraic functions. This study attempted to generalize the idea of computer-assisted graphing to include the use of several kinds of graphs to solve a wider range of problems. A unit…

  9. When There isn't a Right Answer: Interpretation and reasoning, key skills for twenty-first century geoscience

    NASA Astrophysics Data System (ADS)

    Bond, Clare Elizabeth; Philo, Chris; Shipton, Zoe Kai

    2011-03-01

    A key challenge in university geoscience teaching is to give students the skills to cope with uncertainty. Professional geoscientists can rarely be certain of the 'right answer' to problems posed by most geological datasets, and reasoning through this uncertainty, being intelligently flexible in interpreting data which are limited in resolution and spatial distribution, is an important skill for students to learn. Understanding how interpretative and reasoning skills are, or might better be, developed alongside foundational geological concepts and techniques is crucial for the effective training of our future geoscientists. In the study presented here, a seismic interpretation exercise was undertaken by 36 geoscientists ranging in experience from novice to expert. During the exercise, observations were made of the approaches taken by the participants, what we term the interpretational process, and an evaluation was made of what they actually accomplished, what we term the final interpretational outcomes. From a comparison of the different experience cohorts, we show that even as a novice it is important to develop geological reasoning skills to enhance the interpretation of datasets where there is indeed no 'right answer'.

  10. When There Isn't a Right Answer: Interpretation and Reasoning, Key Skills for Twenty-First Century Geoscience

    ERIC Educational Resources Information Center

    Bond, Clare Elizabeth; Philo, Chris; Shipton, Zoe Kai

    2011-01-01

    A key challenge in university geoscience teaching is to give students the skills to cope with uncertainty. Professional geoscientists can rarely be certain of the "right answer" to problems posed by most geological datasets, and reasoning through this uncertainty, being intelligently flexible in interpreting data which are limited in resolution…

  11. A matter of interpretation: developing primary pupils' enquiry skills using position-linked datalogging

    NASA Astrophysics Data System (ADS)

    Davies, Daniel John; Collier, Christopher; Howe, Alan

    2012-11-01

    not been sustained. While there is evidence of pupils developing a range of scientific enquiry skills through the project, the extent to which their interpretation of data improved is unclear. All participating schools made greater use of scientific data than before the project to develop their environmental education. Conclusions: The project has demonstrated the potential of combining datalogging with GPS technology to support challenging, motivating and relevant scientific enquiry. Primary teachers require targeted technical and pedagogical support to maximise learning benefits for pupils.

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

    NASA Astrophysics Data System (ADS)

    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

  13. Understanding graphs with two independent variables

    NASA Astrophysics Data System (ADS)

    Cooper, Jennifer L.

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

  14. Impossible Graphs.

    ERIC Educational Resources Information Center

    Noble, Tracy; And Others

    Graphs without a time axis, such as velocity-versus-position graphs, offer interesting possibilities for exploring graphing and motion. Relations depicted by these graphs are not limited to functions. Interviews with a high school student named Olivia, who uses a motion detector to create such graphs, indicate that she uses thought experiments as…

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

    NASA Astrophysics Data System (ADS)

    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.

  16. A Cross-Cultural Study of the Effect of a Graph-Oriented Computer-Assisted Project-Based Learning Environment on Middle School Students' Science Knowledge and Argumentation Skills

    ERIC Educational Resources Information Center

    Hsu, P.-S.; Van Dyke, M.; Chen, Y.; Smith, T. J.

    2016-01-01

    The purpose of this mixed-methods study was to explore how seventh graders in a suburban school in the United States and sixth graders in an urban school in Taiwan developed argumentation skills and science knowledge in a project-based learning environment that incorporated a graph-oriented, computer-assisted application (GOCAA). A total of 42…

  17. Interpretive Structural Modeling of MLearning Curriculum Implementation Model of English Language Communication Skills for Undergraduates

    ERIC Educational Resources Information Center

    Abdullah, Muhammad Ridhuan Tony Lim; Siraj, Saedah; Asra; Hussin, Zaharah

    2014-01-01

    In the field of distance education, learning mediated through mobile technology or mobile learning (mLearning) has rapidly building a repertoire of influence in distance education research. This paper aims to propose an mLearning curriculum implementation model for English Language and Communication skills course among undergraduates using…

  18. Acquisition of Visual Perceptual Skills from Worked Examples: Learning to Interpret Electrocardiograms (ECGs)

    ERIC Educational Resources Information Center

    van den Berge, Kees; van Gog, Tamara; Mamede, Silvia; Schmidt, Henk G.; van Saase, Jan L. C. M.; Rikers, Remy M. J. P.

    2013-01-01

    Research has shown that for acquiring problem-solving skills, instruction consisting of studying worked examples is more effective and efficient for novice learners than instruction consisting of problem-solving. This study investigated whether worked examples would also be a useful instructional format for the acquisition of visual perceptual…

  19. Effect of Scientific Argumentation on the Development of Scientific Process Skills in the Context of Teaching Chemistry

    ERIC Educational Resources Information Center

    Gultepe, Nejla; Kilic, Ziya

    2015-01-01

    This study was conducted in order to determine the differences in integrated scientific process skills (designing experiments, forming data tables, drawing graphs, graph interpretation, determining the variables and hypothesizing, changing and controlling variables) of students (n = 17) who were taught with an approach based on scientific…

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

    NASA Astrophysics Data System (ADS)

    Laverty, James T.

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

  1. Evolutionary stability on graphs

    PubMed Central

    Ohtsuki, Hisashi; Nowak, Martin A.

    2008-01-01

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

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

    ERIC Educational Resources Information Center

    Stuessy, Carol L.; Rowland, Paul M.

    1989-01-01

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

  3. Total Quality & Basic Skills. The TQ Castle--Using Basic Skills Development to Evade Alligators in the Moat.

    ERIC Educational Resources Information Center

    Lewe, Glenda

    1994-01-01

    Key skills required in the total quality workplace are cross-functional teaming, interpreting charts/graphs, oral communication, brainstorming, understanding cause/effect, categorizing ideas, critical pathing, formulating suggestions, analyzing the needs of internal and external customers, and writing status reports. (SK)

  4. Cookies and Graphs

    ERIC Educational Resources Information Center

    Cooper, Carol

    1975-01-01

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

  5. A Study of the Competency of Third Year Medical Students to Interpret Biochemically Based Clinical Scenarios Using Knowledge and Skills Gained in Year 1 and 2

    ERIC Educational Resources Information Center

    Gowda, Veena Bhaskar S.; Nagaiah, Bhaskar Hebbani; Sengodan, Bharathi

    2016-01-01

    Medical students build clinical knowledge on the grounds of previously obtained basic knowledge. The study aimed to evaluate the competency of third year medical students to interpret biochemically based clinical scenarios using knowledge and skills gained during year 1 and 2 of undergraduate medical training. Study was conducted on year 3 MBBS…

  6. Using the Dreyfus Model of Skill Acquisition to Describe and Interpret Skill Acquisition and Clinical Judgment in Nursing Practice and Education

    ERIC Educational Resources Information Center

    Benner, Patricia

    2004-01-01

    Three studies using the Dreyfus model of skill acquisition were conducted over a period of 21 years. Nurses with a range of experience and reported skillfulness were interviewed. Each study used nurses' narrative accounts of actual clinical situations. A subsample of participants were observed and interviewed at work. These studies extend the…

  7. Graphing Predictions

    ERIC Educational Resources Information Center

    Connery, Keely Flynn

    2007-01-01

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

  8. Graph Theory

    SciTech Connect

    Sanfilippo, Antonio P.

    2005-12-27

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

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

    ERIC Educational Resources Information Center

    Zucker, Andrew; Kay, Rachel; Staudt, Carolyn

    2014-01-01

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

  10. The Effect of Calculator-Based Ranger Activities on Students' Graphing Ability.

    ERIC Educational Resources Information Center

    Kwon, Oh Nam

    2002-01-01

    Addresses three issues of Calculator-based Ranger (CBR) activities on graphing abilities: (a) the effect of CBR activities on graphing abilities; (b) the extent to which prior knowledge about graphing skills affects graphing ability; and (c) the influence of instructional styles on students' graphing abilities. Indicates that CBR activities are…

  11. Graphing Calculators: The Newest Revolution in Mathematics.

    ERIC Educational Resources Information Center

    Clutter, Martha

    1999-01-01

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

  12. Insight into earthquake sequencing: analysis and interpretation of time-series constructed from the directed graph of the Markov chain model

    NASA Astrophysics Data System (ADS)

    Cavers, M. S.; Vasudevan, K.

    2015-02-01

    Directed graph representation of a Markov chain model to study global earthquake sequencing leads to a time-series of state-to-state transition probabilities that includes the spatio-temporally linked recurrent events in the record-breaking sense. A state refers to a configuration comprised of zones with either the occurrence or non-occurrence of an earthquake in each zone in a pre-determined time interval. Since the time-series is derived from non-linear and non-stationary earthquake sequencing, we use known analysis methods to glean new information. We apply decomposition procedures such as ensemble empirical mode decomposition (EEMD) to study the state-to-state fluctuations in each of the intrinsic mode functions. We subject the intrinsic mode functions, the orthogonal basis set derived from the time-series using the EEMD, to a detailed analysis to draw information-content of the time-series. Also, we investigate the influence of random-noise on the data-driven state-to-state transition probabilities. We consider a second aspect of earthquake sequencing that is closely tied to its time-correlative behavior. Here, we extend the Fano factor and Allan factor analysis to the time-series of state-to state transition frequencies of a Markov chain. Our results support not only the usefulness the intrinsic mode functions in understanding the time-series but also the presence of power-law behaviour exemplified by the Fano factor and the Allan factor.

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

    NASA Astrophysics Data System (ADS)

    Zucker, Andrew; Kay, Rachel; Staudt, Carolyn

    2014-06-01

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

  14. Prospective Middle School Mathematics Teachers' Reflective Thinking Skills: Descriptions of Their Students' Thinking and Interpretations of Their Teaching

    ERIC Educational Resources Information Center

    Jansen, Amanda; Spitzer, Sandy M.

    2009-01-01

    In this study, we examined prospective middle school mathematics teachers' reflective thinking skills to understand how they learned from their own teaching practice when engaging in a modified lesson study experience. Our goal was to identify variations among prospective teachers' descriptions of students' thinking and frequency of their…

  15. The Feynman Identity for Planar Graphs

    NASA Astrophysics Data System (ADS)

    da Costa, G. A. T. F.

    2016-08-01

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

  16. Student Reasoning about Graphs in Different Contexts

    ERIC Educational Resources Information Center

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

    2016-01-01

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

  17. Body Motion and Graphing. Working Paper.

    ERIC Educational Resources Information Center

    Nemirovsky, Ricardo; Tierney, Cornelia; Wright, Tracey

    This paper explores children's efforts to make sense of graphs by analyzing two students' use of a computer-based motion detector. The analysis focuses on the students' growing understanding of the motion detector which enables them to plan their movements in order to create graphs and interpret them in terms of kinesthetic actions. Students…

  18. The Awareness of Knowledge and Skill of Self-Defined Instructional Technologists in the Corporate Environment: An Interpretive Study

    ERIC Educational Resources Information Center

    Hutson, Patricia Evonne

    2013-01-01

    The description of the self-defined expert instructional technologist is unclear. Technologists in the field are identified in various ways. To determine the characteristics and competencies of self-defined expert instructional technologists, an interpretive field study consisting of interviews was conducted. The results revealed three core…

  19. The Graph Choice Chart

    ERIC Educational Resources Information Center

    Webber, Hannah; Nelson, Sarah J.; Weatherbee, Ryan; Zoellick, Bill; Schauffler, Molly

    2014-01-01

    Data literacy is complex. When students investigate the natural world, they must be able to gather data, organize it in tables and spreadsheets, analyze it in context, and describe and interpret it--usually as evidence to support a scientific argument. These skills are echoed in the science and engineering practices of the "Next Generation…

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

    ERIC Educational Resources Information Center

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

    2016-01-01

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

  1. Can Comparison of Contrastive Examples Facilitate Graph Understanding?

    ERIC Educational Resources Information Center

    Smith, Linsey A.; Gentner, Dedre

    2011-01-01

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

  2. Motion, Technology, Gestures in Interpreting Graphs

    ERIC Educational Resources Information Center

    Robutti, Ornella

    2006-01-01

    This report is part of a long-term research on the construction of mathematical meanings through the interaction with various technologies. The research involved a set of teaching experiments based on body motion with sensors and calculators at different school levels, from kindergarten to secondary school. Here I refer to the one developed in a…

  3. Graphing Polar Curves

    ERIC Educational Resources Information Center

    Lawes, Jonathan F.

    2013-01-01

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

  4. Path Separability of Graphs

    NASA Astrophysics Data System (ADS)

    Diot, Emilie; Gavoille, Cyril

    In this paper we investigate the structural properties of k-path separable graphs, that are the graphs that can be separated by a set of k shortest paths. We identify several graph families having such path separability, and we show that this property is closed under minor taking. In particular we establish a list of forbidden minors for 1-path separable graphs.

  5. Graphing for Any Grade.

    ERIC Educational Resources Information Center

    Nibbelink, William

    1982-01-01

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

  6. Student reasoning about graphs in different contexts

    NASA Astrophysics Data System (ADS)

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

    2016-06-01

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

  7. Capacitated max -Batching with Interval Graph Compatibilities

    NASA Astrophysics Data System (ADS)

    Nonner, Tim

    We consider the problem of partitioning interval graphs into cliques of bounded size. Each interval has a weight, and the weight of a clique is the maximum weight of any interval in the clique. This natural graph problem can be interpreted as a batch scheduling problem. Solving a long-standing open problem, we show NP-hardness, even if the bound on the clique sizes is constant. Moreover, we give a PTAS based on a novel dynamic programming technique for this case.

  8. Statistical Literacy in Action: Should All Graphs Start at Zero?

    ERIC Educational Resources Information Center

    Watson, Jane

    2015-01-01

    Using statistical literacy skills to determine appropriate scales to be used on graphs is an essential part of numeracy. Using several meaningful contexts, this article explains very clearly when it is appropriate and inappropriate to begin the scale of a graph at zero.

  9. Are Graphs Finally Surfacing?

    ERIC Educational Resources Information Center

    Beineke, Lowell W.

    1989-01-01

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

  10. Graph-Plotting Routine

    NASA Technical Reports Server (NTRS)

    Kantak, Anil V.

    1987-01-01

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

  11. Graphing Important People

    ERIC Educational Resources Information Center

    Reading Teacher, 2012

    2012-01-01

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

  12. Graphing Inequalities, Connecting Meaning

    ERIC Educational Resources Information Center

    Switzer, J. Matt

    2014-01-01

    Students often have difficulty with graphing inequalities (see Filloy, Rojano, and Rubio 2002; Drijvers 2002), and J. Matt Switzer's students were no exception. Although students can produce graphs for simple inequalities, they often struggle when the format of the inequality is unfamiliar. Even when producing a correct graph of an…

  13. TIGRE: Combinator graph reduction on the RTX 2000

    NASA Technical Reports Server (NTRS)

    Koopman, Philip, Jr.

    1990-01-01

    An efficient evaluation technique is examined for lazy functional programs based on combinator graph reduction. Graph reduction is widely believed to be slow and inefficient, but an abstract machine called the Threaded Interpretive Graph Reduction Engine (TIGRE) achieves a substantial speedup over previous reduction techniques. The runtime system of TIGRE is a threaded system that permits self-modifying program execution with compiler-guaranteed safety. This paper describes an implementation of TIGRE in Forth for the Harris RTX 2000 stack processor.

  14. Structural differentiation of graphs using Hosoya-based indices.

    PubMed

    Dehmer, Matthias; Mowshowitz, Abbe; Shi, Yongtang

    2014-01-01

    In this paper, we introduce the Hosoya-Spectral indices and the Hosoya information content of a graph. The first measure combines structural information captured by partial Hosoya polynomials and graph spectra. The latter is a graph entropy measure which is based on blocks consisting of vertices with the same partial Hosoya polynomial. We evaluate the discrimination power of these quantities by interpreting numerical results. PMID:25019933

  15. Methods of visualizing graphs

    DOEpatents

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

    2008-12-23

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

  16. Hyperbolic graph generator

    NASA Astrophysics Data System (ADS)

    Aldecoa, Rodrigo; Orsini, Chiara; Krioukov, Dmitri

    2015-11-01

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

  17. Signals on graphs: Transforms and tomograms

    NASA Astrophysics Data System (ADS)

    Vilela Mendes, R.; Mendes, Hugo C.; Araújo, Tanya

    2016-05-01

    Development of efficient tools for the representation of large datasets is a precondition for the study of dynamics on networks. Generalizations of the Fourier transform on graphs have been constructed through projections on the eigenvectors of graph matrices. By exploring mappings of the spectrum of these matrices we show how to construct more general transforms, in particular wavelet-like transforms on graphs. For time-series, tomograms, a generalization of the Radon transforms to arbitrary pairs of non-commuting operators, are positive bilinear transforms with a rigorous probabilistic interpretation which provide a full characterization of the signals and are robust in the presence of noise. Here the notion of tomogram is also extended to signals on arbitrary graphs.

  18. Development of a Framework for Graph Choice and Construction

    ERIC Educational Resources Information Center

    Angra, Aakanksha; Gardner, Stephanie M.

    2016-01-01

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

  19. Speed of evolution on graphs

    NASA Astrophysics Data System (ADS)

    Sui, Xiukai; Wu, Bin; Wang, Long

    2015-12-01

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

  20. Activities. Mathematics as Communication: Graphing Information Collected Over Time.

    ERIC Educational Resources Information Center

    Moody, Marian

    1990-01-01

    Described is a learning activity that requires students to observe, read, and interpret graphs and organize and describe data. Included are the grade level, materials, objectives, prerequisites, directions, answers to questions, and copies of handouts. (KR)

  1. Graph theory in structure-property correlations

    NASA Astrophysics Data System (ADS)

    Vinogradova, M. G.; Fedina, Yu. A.; Papulov, Yu. G.

    2016-02-01

    The possibilities of the theoretical graph approach to the construction and interpretation of additive schemes for calculation and prediction are discussed. Working formulas are derived for calculating the thermodynamic properties of alkanes and their substitutes. The obtained algorithms are used to calculate thermodynamic properties of chloroalkanes that correspond to experimental values.

  2. An algorithm for automatic reduction of complex signal flow graphs

    NASA Technical Reports Server (NTRS)

    Young, K. R.; Hoberock, L. L.; Thompson, J. G.

    1976-01-01

    A computer algorithm is developed that provides efficient means to compute transmittances directly from a signal flow graph or a block diagram. Signal flow graphs are cast as directed graphs described by adjacency matrices. Nonsearch computation, designed for compilers without symbolic capability, is used to identify all arcs that are members of simple cycles for use with Mason's gain formula. The routine does not require the visual acumen of an interpreter to reduce the topology of the graph, and it is particularly useful for analyzing control systems described for computer analyses by means of interactive graphics.

  3. Topologies on directed graphs

    NASA Technical Reports Server (NTRS)

    Lieberman, R. N.

    1972-01-01

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

  4. Graph Generator Survey

    SciTech Connect

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

    2013-12-01

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

  5. mpiGraph

    Energy Science and Technology Software Center (ESTSC)

    2007-05-22

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

  6. Coloring random graphs.

    PubMed

    Mulet, R; Pagnani, A; Weigt, M; Zecchina, R

    2002-12-23

    We study the graph coloring problem over random graphs of finite average connectivity c. Given a number q of available colors, we find that graphs with low connectivity admit almost always a proper coloring, whereas graphs with high connectivity are uncolorable. Depending on q, we find the precise value of the critical average connectivity c(q). Moreover, we show that below c(q) there exists a clustering phase c in [c(d),c(q)] in which ground states spontaneously divide into an exponential number of clusters and where the proliferation of metastable states is responsible for the onset of complexity in local search algorithms. PMID:12484862

  7. mpiGraph

    SciTech Connect

    Moody, Adam

    2007-05-22

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

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

    ERIC Educational Resources Information Center

    Patterson, Thomas F.; Leonard, Jonathan G.

    2005-01-01

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

  9. Beyond Slopes and Points: Teaching Students How Graphs Describe the Relationships between Scientific Pheomena

    ERIC Educational Resources Information Center

    Harris, David; Gomez Zwiep, Susan

    2013-01-01

    Graphs represent complex information. They show relationships and help students see patterns and compare data. Students often do not appreciate the illuminating power of graphs, interpreting them literally rather than as symbolic representations (Leinhardt, Zaslavsky, and Stein 1990). Students often read graphs point by point instead of seeing…

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

    SciTech Connect

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

    2015-01-01

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

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

    DOE PAGESBeta

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

    2015-01-01

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

  12. Representing clusters using a maximum common edge substructure algorithm applied to reduced graphs and molecular graphs.

    PubMed

    Gardiner, Eleanor J; Gillet, Valerie J; Willett, Peter; Cosgrove, David A

    2007-01-01

    Chemical databases are routinely clustered, with the aim of grouping molecules which share similar structural features. Ideally, medicinal chemists are then able to browse a few representatives of the cluster in order to interpret the shared activity of the cluster members. However, when molecules are clustered using fingerprints, it may be difficult to decipher the structural commonalities which are present. Here, we seek to represent a cluster by means of a maximum common substructure based on the shared functionality of the cluster members. Previously, we have used reduced graphs, where each node corresponds to a generalized functional group, as topological molecular descriptors for virtual screening. In this work, we precluster a database using any clustering method. We then represent the molecules in a cluster as reduced graphs. By repeated application of a maximum common edge substructure (MCES) algorithm, we obtain one or more reduced graph cluster representatives. The sparsity of the reduced graphs means that the MCES calculations can be performed in real time. The reduced graph cluster representatives are readily interpretable in terms of functional activity and can be mapped directly back to the molecules to which they correspond, giving the chemist a rapid means of assessing potential activities contained within the cluster. Clusters of interest are then subject to a detailed R-group analysis using the same iterated MCES algorithm applied to the molecular graphs. PMID:17309248

  13. Making "Photo" Graphs

    ERIC Educational Resources Information Center

    Doto, Julianne; Golbeck, Susan

    2007-01-01

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

  14. Reflections on "The Graph"

    ERIC Educational Resources Information Center

    Petrosino, Anthony

    2012-01-01

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

  15. Exploring Graphs: WYSIWYG.

    ERIC Educational Resources Information Center

    Johnson, Millie

    1997-01-01

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

  16. Walking Out Graphs

    ERIC Educational Resources Information Center

    Shen, Ji

    2009-01-01

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

  17. Real World Graph Connectivity

    ERIC Educational Resources Information Center

    Lind, Joy; Narayan, Darren

    2009-01-01

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

  18. Graphing Electric Potential.

    ERIC Educational Resources Information Center

    De Jong, Marvin L.

    1993-01-01

    Describes the powerful graphing ability of computer algebra systems (CAS) to create three-dimensional graphs or surface graphics of electric potentials. Provides equations along with examples of the printouts. Lists the programs Mathematica, Maple, Derive, Theorist, MathCad, and MATLAB as promising CAS systems. (MVL)

  19. ACTIVITIES: Graphs and Games

    ERIC Educational Resources Information Center

    Hirsch, Christian R.

    1975-01-01

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

  20. Let's Do It: Making Graphs.

    ERIC Educational Resources Information Center

    Shaw, Jean M.

    1984-01-01

    Reasons for having students make graphs are noted. Then specific graphing topics and materials appropriate for young learners are presented, including life-sized, floor, clothespin, felt-face, block, and magnetic graphs, and polls of pupils. (MNS)

  1. Random graph coloring: statistical physics approach.

    PubMed

    van Mourik, J; Saad, D

    2002-11-01

    The problem of vertex coloring in random graphs is studied using methods of statistical physics and probability. Our analytical results are compared to those obtained by exact enumeration and Monte Carlo simulations. We critically discuss the merits and shortcomings of the various methods, and interpret the results obtained. We present an exact analytical expression for the two-coloring problem as well as general replica symmetric approximated solutions for the thermodynamics of the graph coloring problem with p colors and K-body edges. PMID:12513569

  2. Using Sorting Networks for Skill Building and Reasoning

    ERIC Educational Resources Information Center

    Andre, Robert; Wiest, Lynda R.

    2007-01-01

    Sorting networks, used in graph theory, have instructional value as a skill- building tool as well as an interesting exploration in discrete mathematics. Students can practice mathematics facts and develop reasoning and logic skills with this topic. (Contains 4 figures.)

  3. Knowing a Lot for One's Age: Vocabulary Skill and Not Age Is Associated with Anticipatory Incremental Sentence Interpretation in Children and Adults

    ERIC Educational Resources Information Center

    Borovsky, Arielle; Elman, Jeffrey L.; Fernald, Anne

    2012-01-01

    Adults can incrementally combine information from speech with astonishing speed to anticipate future words. Concurrently, a growing body of work suggests that vocabulary ability is crucially related to lexical processing skills in children. However, little is known about this relationship with predictive sentence processing in children or adults.…

  4. A Comparison of Video Modeling, Text-Based Instruction, and No Instruction for Creating Multiple Baseline Graphs in Microsoft Excel

    ERIC Educational Resources Information Center

    Tyner, Bryan C.; Fienup, Daniel M.

    2015-01-01

    Graphing is socially significant for behavior analysts; however, graphing can be difficult to learn. Video modeling (VM) may be a useful instructional method but lacks evidence for effective teaching of computer skills. A between-groups design compared the effects of VM, text-based instruction, and no instruction on graphing performance.…

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

    ERIC Educational Resources Information Center

    Ocak, Mehmet Akif

    2008-01-01

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

  6. Graph ranking for exploratory gene data analysis

    PubMed Central

    2009-01-01

    Background Microarray technology has made it possible to simultaneously monitor the expression levels of thousands of genes in a single experiment. However, the large number of genes greatly increases the challenges of analyzing, comprehending and interpreting the resulting mass of data. Selecting a subset of important genes is inevitable to address the challenge. Gene selection has been investigated extensively over the last decade. Most selection procedures, however, are not sufficient for accurate inference of underlying biology, because biological significance does not necessarily have to be statistically significant. Additional biological knowledge needs to be integrated into the gene selection procedure. Results We propose a general framework for gene ranking. We construct a bipartite graph from the Gene Ontology (GO) and gene expression data. The graph describes the relationship between genes and their associated molecular functions. Under a species condition, edge weights of the graph are assigned to be gene expression level. Such a graph provides a mathematical means to represent both species-independent and species-dependent biological information. We also develop a new ranking algorithm to analyze the weighted graph via a kernelized spatial depth (KSD) approach. Consequently, the importance of gene and molecular function can be simultaneously ranked by a real-valued measure, KSD, which incorporates the global and local structure of the graph. Over-expressed and under-regulated genes also can be separately ranked. Conclusion The gene-function bigraph integrates molecular function annotations into gene expression data. The relevance of genes is described in the graph (through a common function). The proposed method provides an exploratory framework for gene data analysis. PMID:19811684

  7. A study on vague graphs.

    PubMed

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

    2016-01-01

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

  8. A Semantic Graph Query Language

    SciTech Connect

    Kaplan, I L

    2006-10-16

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

  9. Ellenore Flood's Skills Confidence Inventory.

    ERIC Educational Resources Information Center

    Subich, Linda Mezydlo

    1998-01-01

    Presents background information on the Skills Confidence Inventory (SCI) and the construct it assesses. Interprets the skills confidence and interest profiles of a 29-year-old female high school teacher using the SCI and the Strong Interest Inventory. (MKA)

  10. Direct reciprocity on graphs

    PubMed Central

    Ohtsuki, Hisashi; Nowak, Martin A.

    2008-01-01

    Direct reciprocity is a mechanism for the evolution of cooperation based on the idea of repeated encounters between the same two individuals. Here we examine direct reciprocity in structured populations, where individuals occupy the vertices of a graph. The edges denote who interacts with whom. The graph represents spatial structure or a social network. For birth-death or pairwise comparison updating, we find that evolutionary stability of direct reciprocity is more restrictive on a graph than in a well-mixed population, but the condition for reciprocators to be advantageous is less restrictive on a graph. For death-birth and imitation updating, in contrast, both conditions are easier to fulfill on a graph. Moreover, for all four update mechanisms, reciprocators can dominate defectors on a graph, which is never possible in a well-mixed population. We also study the effect of an error rate, which increases with the number of links per individual; interacting with more people simultaneously enhances the probability of making mistakes. We provide analytic derivations for all results. PMID:17466339

  11. Commuting projections on graphs

    SciTech Connect

    Vassilevski, Panayot S.; Zikatanov, Ludmil T.

    2013-02-19

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

  12. Clique graphs and overlapping communities

    NASA Astrophysics Data System (ADS)

    Evans, T. S.

    2010-12-01

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

  13. "What Does This Graph Mean?" Formative Assessment With Science Inquiry to Improve Data Analysis

    NASA Astrophysics Data System (ADS)

    Leech, Andrea Dawn

    This study investigated the use of formative assessment to improve three specific data analysis skills within the context of a high school chemistry class: graph interpretation, pattern recognition, and making conclusions based on data. Students need to be able to collect data, analyze that data, and produce accurate scientific explanations (NRC, 2011) if they want to be ready for college and careers after high school. This mixed methods study, performed in a high school chemistry classroom, investigated the impact of the formative assessment process on data analysis skills that require higher order thinking. We hypothesized that the use of evaluative feedback within the formative assessment process would improve specific data analysis skills. The evaluative feedback was given to the one group and withheld from the other for the first part of the study. The treatment group had statistically better data analysis skills after evaluative feedback over the control. While these results are promising, they must be considered preliminary due to a number of limitations involved in this study.

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

    NASA Astrophysics Data System (ADS)

    Kotzagiannidis, Madeleine S.; Dragotti, Pier Luigi

    2015-08-01

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

  15. Selected Social Studies Skills: 88 Reinforcement Lessons for Secondary Students.

    ERIC Educational Resources Information Center

    Stockhaus, Stuart, Ed.

    Presented is a series of 88 lessons designed by classroom teachers to help junior high school students reinforce social studies skills. Lessons are categorized into four main skill areas: (1) using reference aids; (2) understanding tables, graphs, and cartoons; (3) developing graphic skills; and (4) evaluating information. For each skill area,…

  16. The Study Skills Component of the Wisconsin Design.

    ERIC Educational Resources Information Center

    Kamm, Karlyn

    Initial development of the list of skills and related behavioral objectives in the study skills area of The Wisconsin Design for Reading Skill Development began with an extensive search. As an organizational framework, the area was divided into three subareas: maps, graphs and tables, and reference skills. The professional literature,…

  17. ASK-GraphView: A large scale graph visualization system.

    PubMed

    Abello, James; van Ham, Frank; Krishnan, Neeraj

    2006-01-01

    We describe ASK-GraphView, a node-link-based graph visualization system that allows clustering and interactive navigation of large graphs, ranging in size up to 16 million edges. The system uses a scalable architecture and a series of increasingly sophisticated clustering algorithms to construct a hierarchy on an arbitrary, weighted undirected input graph. By lowering the interactivity requirements we can scale to substantially bigger graphs. The user is allowed to navigate this hierarchy in a top down manner by interactively expanding individual clusters. ASK-GraphView also provides facilities for filtering and coloring, annotation and cluster labeling. PMID:17080786

  18. New Graph Calculi for Planar Non-3-Colorable Graphs

    NASA Astrophysics Data System (ADS)

    Hanatani, Yoichi; Horiyama, Takashi; Iwama, Kazuo; Tamaki, Suguru

    The Hajós calculus is a nondeterministic procedure which generates the class of non-3-colorable graphs. If all non-3-colorable graphs can be constructed in polynomial steps by the calculus, then NP=co-NP holds. Up to date, however, it remains open whether there exists a family of graphs that cannot be generated in polynomial steps. To attack this problem, we propose two graph calculi PHC and PHC* that generate non-3-colorable planar graphs, where intermediate graphs in the calculi are also restricted to be planar. Then we prove that PHC and PHC* are sound and complete. We also show that PHC* can polynomially simulate PHC.

  19. Graphing. USMES Beginning "How To" Set.

    ERIC Educational Resources Information Center

    Agro, Sally; And Others

    In this set of eight booklets on graphing, primary grade students learn how to choose which graph to make and how to make a bar graph, bar graph histogram, conversion graph, line chart, line graph, scatter graph, and slope diagram. The major emphasis in all Unified Sciences and Mathematics for Elementary Schools (USMES) units is on open-ended,…

  20. Movement Forms: A Graph-Dynamic Perspective

    PubMed Central

    Saltzman, Elliot; Holt, Ken

    2014-01-01

    The focus of this paper is on characterizing the physical movement forms (e.g., walk, crawl, roll, etc.) that can be used to actualize abstract, functionally-specified behavioral goals (e.g., locomotion). Emphasis is placed on how such forms are distinguished from one another, in part, by the set of topological patterns of physical contact between agent and environment (i.e., the set of physical graphs associated with each form) and the transitions among these patterns displayed over the course of performance (i.e., the form’s physical graph dynamics). Crucial in this regard is the creation and dissolution of loops in these graphs, which can be related to the distinction between open and closed kinematic chains. Formal similarities are described within the theoretical framework of task-dynamics between physically-closed kinematic chains (physical loops) that are created during various movement forms and functionally-closed kinematic chains (functional loops) that are associated with task-space control of end-effectors; it is argued that both types of loop must be flexibly incorporated into the coordinative structures that govern skilled action. Final speculation is focused on the role of graphs and their dynamics, not only in processes of coordination and control for individual agents, but also in processes of inter-agent coordination and the coupling of agents with (non-sentient) environmental objects. PMID:24910507

  1. Applied and computational harmonic analysis on graphs and networks

    NASA Astrophysics Data System (ADS)

    Irion, Jeff; Saito, Naoki

    2015-09-01

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

  2. Flexibility in data interpretation: effects of representational format

    PubMed Central

    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. PMID:24427145

  3. Guide to graphing data and taking action.

    PubMed

    1992-01-01

    3 kinds of graphs are presented as instructional examples of how to display data collected on family planning (FP) programs. The first is a trend analysis of new acceptors and requires monthly summaries of new acceptors serviced by the clinic. The objective is to gauge declines or increases over time in new acceptors for each contraceptive method offered. The second graph requires a monthly summary of new acceptors by method mix. The third graph needs data on the reason for attending the particular FP clinic. IEC activities can be enhanced with this information. In the example for graph 1, new acceptors over an 18-month-period are plotted on one axis by monthly units, and the other axis by number of new acceptors. The connection of dots reflects the trend over time. There is a specific example with data from Yena clinic over a 12-month-period; the interpretations and possible actions are indicated. Instructions for presenting a pie chart are also given for new acceptors by method mix; the example is given for data from Yena Clinic and possible interpretations and actions are indicated. A visual presentation of the data worksheet needed for a pie chart is provided. Calculations must be made for the fraction of new acceptors out of total acceptors and the percent of total new acceptors for each method. An explanation is given for constructing a bar chart; again an example is given of a completed bar chart with data and the accompanying data sheet. A checklist identifies important guidelines for developing and using line graphs, bar charts, and pie charts. PMID:12318345

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

    NASA Astrophysics Data System (ADS)

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

    2016-08-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2016-04-01

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

  6. Algebraic distance on graphs.

    SciTech Connect

    Chen, J.; Safro, I.

    2011-01-01

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

  7. Quantum Ergodicity on Graphs

    NASA Astrophysics Data System (ADS)

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

    2008-12-01

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

  8. Subdominant pseudoultrametric on graphs

    SciTech Connect

    Dovgoshei, A A; Petrov, E A

    2013-08-31

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

  9. Graphing Calculator Mini Course

    NASA Technical Reports Server (NTRS)

    Karnawat, Sunil R.

    1996-01-01

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

  10. Interpretations of Literacy

    ERIC Educational Resources Information Center

    Layton, Lyn; Miller, Carol

    2004-01-01

    The National Literacy Strategy (NLS) was introduced into schools in England in 1998 with the aim of raising the literacy attainments of primary-aged children. The Framework for Teaching the Literacy Hour, a key component of the NLS, proposes an interpretation of literacy that emphasises reading, writing and spelling skills. An investigation of the…

  11. Living Skills as a Core Curriculum Component.

    ERIC Educational Resources Information Center

    Dufty, David

    Schools should help students develop daily living skills in addition to basic cognitive skills such as reading, writing, and figuring. Living skills are interpreted to include those skills which help students cope with rapid social change. Skills need to be taught on health and nutrition, safety and first aid, interpersonal relationships, family…

  12. Knowing a lot for one's age: Vocabulary skill and not age is associated with anticipatory incremental sentence interpretation in children and adults.

    PubMed

    Borovsky, Arielle; Elman, Jeffrey L; Fernald, Anne

    2012-08-01

    Adults can incrementally combine information from speech with astonishing speed to anticipate future words. Concurrently, a growing body of work suggests that vocabulary ability is crucially related to lexical processing skills in children. However, little is known about this relationship with predictive sentence processing in children or adults. We explore this question by comparing the degree to which an upcoming sentential theme is anticipated by combining information from a prior agent and action. 48 children, aged of 3 to 10, and 48 college-aged adults' eye-movements were recorded as they heard a sentence (e.g., The pirate hides the treasure) in which the object referred to one of four images that included an agent-related, action-related and unrelated distractor image. Pictures were rotated so that, across all versions of the study, each picture appeared in all conditions, yielding a completely balanced within-subjects design. Adults and children quickly made use of combinatory information available at the action to generate anticipatory looks to the target object. Speed of anticipatory fixations did not vary with age. When controlling for age, individuals with higher vocabularies were faster to look to the target than those with lower vocabulary scores. Together, these results support and extend current views of incremental processing in which adults and children make use of linguistic information to continuously update their mental representation of ongoing language. PMID:22632758

  13. Using graph approach for managing connectivity in integrative landscape modelling

    NASA Astrophysics Data System (ADS)

    Rabotin, Michael; Fabre, Jean-Christophe; Libres, Aline; Lagacherie, Philippe; Crevoisier, David; Moussa, Roger

    2013-04-01

    FLUID-landr library has been developed in order i) to be used with no GIS expert skills needed (common gis formats can be read and simplified spatial management is provided), ii) to easily develop adapted rules of landscape discretization and graph creation to follow spatialized model requirements and iii) to allow model developers to manage dynamic and complex spatial topology. Graph management in OpenFLUID are shown with i) examples of hydrological modelizations on complex farmed landscapes and ii) the new implementation of Geo-MHYDAS tool based on the OpenFLUID-landr library, which allows to discretize a landscape and create graph structure for the MHYDAS model requirements.

  14. Graph for locked rotor current

    NASA Technical Reports Server (NTRS)

    Peck, R. R.

    1972-01-01

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

  15. Coloring geographical threshold graphs

    SciTech Connect

    Bradonjic, Milan; Percus, Allon; Muller, Tobias

    2008-01-01

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

  16. Body Motion and Graphing.

    ERIC Educational Resources Information Center

    Nemirovsky, Ricardo; Tierney, Cornelia; Wright, Tracy

    1998-01-01

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

  17. Graphs in Real Time.

    ERIC Educational Resources Information Center

    Beckmann, Charlene E.; Rozanski, Kara

    1999-01-01

    Presents a lesson that uses a motion detector in order for students to experience the interplay between motion and its graphical representation of the slope. Focuses on the change in the appearance of the graph with regard to changing speed. (ASK)

  18. Straight Line Graphs

    ERIC Educational Resources Information Center

    Krueger, Tom

    2010-01-01

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

  19. GraphLib

    Energy Science and Technology Software Center (ESTSC)

    2013-02-19

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

  20. Graph-theoretical exorcism

    SciTech Connect

    Simmons, G.J.

    1985-01-01

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

  1. Physics on Graphs

    NASA Astrophysics Data System (ADS)

    Schrader, Robert

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

  2. Temporal Representation in Semantic Graphs

    SciTech Connect

    Levandoski, J J; Abdulla, G M

    2007-08-07

    A wide range of knowledge discovery and analysis applications, ranging from business to biological, make use of semantic graphs when modeling relationships and concepts. Most of the semantic graphs used in these applications are assumed to be static pieces of information, meaning temporal evolution of concepts and relationships are not taken into account. Guided by the need for more advanced semantic graph queries involving temporal concepts, this paper surveys the existing work involving temporal representations in semantic graphs.

  3. Quantum walks on quotient graphs

    SciTech Connect

    Krovi, Hari; Brun, Todd A.

    2007-06-15

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

  4. A Clustering Graph Generator

    SciTech Connect

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

    2015-10-26

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

  5. Topic Model for Graph Mining.

    PubMed

    Xuan, Junyu; Lu, Jie; Zhang, Guangquan; Luo, Xiangfeng

    2015-12-01

    Graph mining has been a popular research area because of its numerous application scenarios. Many unstructured and structured data can be represented as graphs, such as, documents, chemical molecular structures, and images. However, an issue in relation to current research on graphs is that they cannot adequately discover the topics hidden in graph-structured data which can be beneficial for both the unsupervised learning and supervised learning of the graphs. Although topic models have proved to be very successful in discovering latent topics, the standard topic models cannot be directly applied to graph-structured data due to the "bag-of-word" assumption. In this paper, an innovative graph topic model (GTM) is proposed to address this issue, which uses Bernoulli distributions to model the edges between nodes in a graph. It can, therefore, make the edges in a graph contribute to latent topic discovery and further improve the accuracy of the supervised and unsupervised learning of graphs. The experimental results on two different types of graph datasets show that the proposed GTM outperforms the latent Dirichlet allocation on classification by using the unveiled topics of these two models to represent graphs. PMID:25616091

  6. Random Walks on Random Graphs

    NASA Astrophysics Data System (ADS)

    Cooper, Colin; Frieze, Alan

    The aim of this article is to discuss some of the notions and applications of random walks on finite graphs, especially as they apply to random graphs. In this section we give some basic definitions, in Section 2 we review applications of random walks in computer science, and in Section 3 we focus on walks in random graphs.

  7. Editing graphs for maximum effect

    SciTech Connect

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

    1991-01-08

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

  8. Mining and Indexing Graph Databases

    ERIC Educational Resources Information Center

    Yuan, Dayu

    2013-01-01

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

  9. Kevin Bacon and Graph Theory

    ERIC Educational Resources Information Center

    Hopkins, Brian

    2004-01-01

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

  10. Recursive Feature Extraction in Graphs

    Energy Science and Technology Software Center (ESTSC)

    2014-08-14

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

  11. A Note on Hamiltonian Graphs

    ERIC Educational Resources Information Center

    Skurnick, Ronald; Davi, Charles; Skurnick, Mia

    2005-01-01

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

  12. Quantitative Literacy: Working with Log Graphs

    NASA Astrophysics Data System (ADS)

    Shawl, S.

    2013-04-01

    The need for working with and understanding different types of graphs is a common occurrence in everyday life. Examples include anything having to do investments, being an educated juror in a case that involves evidence presented graphically, and understanding many aspect of our current political discourse. Within a science class graphs play a crucial role in presenting and interpreting data. In astronomy, where the range of graphed values is many orders of magnitude, log-axes must be used and understood. Experience shows that students do not understand how to read and interpret log-axes or how they differ from linear. Alters (1996), in a study of college students in an algebra-based physics class, found little understanding of log plotting. The purpose of this poster is to show the method and progression I have developed for use in my “ASTRO 101” class, with the goal being to help students better understand the H-R diagram, mass-luminosity relationship, and digital spectra.

  13. What is a complex graph?

    NASA Astrophysics Data System (ADS)

    Kim, Jongkwang; Wilhelm, Thomas

    2008-04-01

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

  14. Graphing. USMES Intermediate "How To" Set.

    ERIC Educational Resources Information Center

    Agro, Sally; And Others

    In this set of six booklets on graphing, intermediate grade students learn how to choose which kind of graph to make; make bar graphs, histograms, line graphs, and conversion graphs; and use graphs to compare two sets of data. The major emphasis in all Unified Sciences and Mathematics for Elementary Schools (USMES) units is on open-ended,…

  15. Random graphs with hidden color.

    PubMed

    Söderberg, Bo

    2003-07-01

    We propose and investigate a unifying class of sparse random graph models, based on a hidden coloring of edge-vertex incidences, extending an existing approach, random graphs with a given degree distribution, in a way that admits a nontrivial correlation structure in the resulting graphs. The approach unifies a number of existing random graph ensembles within a common general formalism, and allows for the analytic calculation of observable graph characteristics. In particular, generating function techniques are used to derive the size distribution of connected components (clusters) as well as the location of the percolation threshold where a giant component appears. PMID:12935185

  16. Spectral fluctuations of quantum graphs

    SciTech Connect

    Pluhař, Z.; Weidenmüller, H. A.

    2014-10-15

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

  17. Component Evolution in General Random Intersection Graphs

    NASA Astrophysics Data System (ADS)

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

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

  18. Project on Teaching Charts and Graphs to ABE Students. Part I: Teacher's Guide [and] Part II: Transparency Assembly Package.

    ERIC Educational Resources Information Center

    Renton Vocational Inst., WA.

    The teacher's guide and collection of transparency masters are designed for use in teaching adult basic education (ABE) students how to read and interpret graphs and charts. Covered in the individual lessons of the instructional unit are the reading and interpretation of charts as well as picture, line, bar, and circle graphs. Each unit contains a…

  19. SimGraph: A Flight Simulation Data Visualization Workstation

    NASA Technical Reports Server (NTRS)

    Kaplan, Joseph A.; Kenney, Patrick S.

    1997-01-01

    Today's modern flight simulation research produces vast amounts of time sensitive data, making a qualitative analysis of the data difficult while it remains in a numerical representation. Therefore, a method of merging related data together and presenting it to the user in a more comprehensible format is necessary. Simulation Graphics (SimGraph) is an object-oriented data visualization software package that presents simulation data in animated graphical displays for easy interpretation. Data produced from a flight simulation is presented by SimGraph in several different formats, including: 3-Dimensional Views, Cockpit Control Views, Heads-Up Displays, Strip Charts, and Status Indicators. SimGraph can accommodate the addition of new graphical displays to allow the software to be customized to each user s particular environment. A new display can be developed and added to SimGraph without having to design a new application, allowing the graphics programmer to focus on the development of the graphical display. The SimGraph framework can be reused for a wide variety of visualization tasks. Although it was created for the flight simulation facilities at NASA Langley Research Center, SimGraph can be reconfigured to almost any data visualization environment. This paper describes the capabilities and operations of SimGraph.

  20. Novice Interpretations of Visual Representations of Geosciences Data

    NASA Astrophysics Data System (ADS)

    Burkemper, L. K.; Arthurs, L.

    2013-12-01

    Past cognition research of individual's perception and comprehension of bar and line graphs are substantive enough that they have resulted in the generation of graph design principles and graph comprehension theories; however, gaps remain in our understanding of how people process visual representations of data, especially of geologic and atmospheric data. This pilot project serves to build on others' prior research and begin filling the existing gaps. The primary objectives of this pilot project include: (i) design a novel data collection protocol based on a combination of paper-based surveys, think-aloud interviews, and eye-tracking tasks to investigate student data handling skills of simple to complex visual representations of geologic and atmospheric data, (ii) demonstrate that the protocol yields results that shed light on student data handling skills, and (iii) generate preliminary findings upon which tentative but perhaps helpful recommendations on how to more effectively present these data to the non-scientist community and teach essential data handling skills. An effective protocol for the combined use of paper-based surveys, think-aloud interviews, and computer-based eye-tracking tasks for investigating cognitive processes involved in perceiving, comprehending, and interpreting visual representations of geologic and atmospheric data is instrumental to future research in this area. The outcomes of this pilot study provide the foundation upon which future more in depth and scaled up investigations can build. Furthermore, findings of this pilot project are sufficient for making, at least, tentative recommendations that can help inform (i) the design of physical attributes of visual representations of data, especially more complex representations, that may aid in improving students' data handling skills and (ii) instructional approaches that have the potential to aid students in more effectively handling visual representations of geologic and atmospheric data

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

    PubMed

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

    2013-08-01

    The interrelationships between pathological processes and emerging clinical phenotypes in Alzheimer's disease (AD) are important yet complicated to study, because the brain is a complex network where local disruptions can have widespread effects. Recently, properties in brain networks obtained with neuroimaging techniques have been studied in AD with tools from graph theory. However, the interpretation of graph alterations remains unclear, because the definition of connectivity depends on the imaging modality used. Here we examined which graph properties have been consistently reported to be disturbed in AD studies, using a heuristically defined "graph space" to investigate which theoretical models can best explain graph alterations in AD. Findings from structural and functional graphs point to a loss of highly connected areas in AD. However, studies showed considerable variability in reported group differences of most graph properties. This suggests that brain graphs might not be isometric, which complicates the interpretation of graph measurements. We highlight confounding factors such as differences in graph construction methods and provide recommendations for future research. PMID:23541878

  2. An Unusual Exponential Graph

    ERIC Educational Resources Information Center

    Syed, M. Qasim; Lovatt, Ian

    2014-01-01

    This paper is an addition to the series of papers on the exponential function begun by Albert Bartlett. In particular, we ask how the graph of the exponential function y = e[superscript -t/t] would appear if y were plotted versus ln t rather than the normal practice of plotting ln y versus t. In answering this question, we find a new way to…

  3. Graphs in molecular biology

    PubMed Central

    Huber, Wolfgang; Carey, Vincent J; Long, Li; Falcon, Seth; Gentleman, Robert

    2007-01-01

    Graph theoretical concepts are useful for the description and analysis of interactions and relationships in biological systems. We give a brief introduction into some of the concepts and their areas of application in molecular biology. We discuss software that is available through the Bioconductor project and present a simple example application to the integration of a protein-protein interaction and a co-expression network. PMID:17903289

  4. Community detection in graphs

    NASA Astrophysics Data System (ADS)

    Fortunato, Santo

    2010-02-01

    The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i.e. the organization of vertices in clusters, with many edges joining vertices of the same cluster and comparatively few edges joining vertices of different clusters. Such clusters, or communities, can be considered as fairly independent compartments of a graph, playing a similar role like, e.g., the tissues or the organs in the human body. Detecting communities is of great importance in sociology, biology and computer science, disciplines where systems are often represented as graphs. This problem is very hard and not yet satisfactorily solved, despite the huge effort of a large interdisciplinary community of scientists working on it over the past few years. We will attempt a thorough exposition of the topic, from the definition of the main elements of the problem, to the presentation of most methods developed, with a special focus on techniques designed by statistical physicists, from the discussion of crucial issues like the significance of clustering and how methods should be tested and compared against each other, to the description of applications to real networks.

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

    ERIC Educational Resources Information Center

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

    2012-01-01

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

  6. The Effects of Data and Graph Type on Concepts and Visualizations of Variability

    ERIC Educational Resources Information Center

    Cooper, Linda L.; Shore, Felice S.

    2010-01-01

    Recognizing and interpreting variability in data lies at the heart of statistical reasoning. Since graphical displays should facilitate communication about data, statistical literacy should include an understanding of how variability in data can be gleaned from a graph. This paper identifies several types of graphs that students typically…

  7. Fostering the Development of Quantitative Life Skills through Introductory Astronomy: Can it be Done?

    NASA Astrophysics Data System (ADS)

    Follette, Katherine B.; McCarthy, D. W.

    2012-01-01

    We present preliminary results from a student survey designed to test whether the all-important life skill of numeracy/quantitative literacy can be fostered and improved upon in college students through the vehicle of non-major introductory courses in Astronomy. Many instructors of introductory science courses for non-majors would state that a major goal of our classes is to teach our students to distinguish between science and pseudoscience, truth and fiction, in their everyday lives. It is difficult to believe that such a skill can truly be mastered without a fair amount of mathematical sophistication in the form of arithmetic, statistical and graph reading skills that many American college students unfortunately lack when they enter our classrooms. In teaching what is frequently their "terminal science course in life” can we instill in our students the numerical skills that they need to be savvy consumers, educated citizens and discerning interpreters of the ever-present polls, studies and surveys in which our society is awash? In what may well be their final opportunity to see applied mathematics in the classroom, can we impress upon them the importance of mathematical sophistication in interpreting the statistics that they are bombarded with by the media? Our study is in its second semester, and is designed to investigate to what extent it is possible to improve important quantitative skills in college students through a single semester introductory Astronomy course.

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

    SciTech Connect

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

    2016-01-01

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

  9. Graph Coarsening for Path Finding in Cybersecurity Graphs

    SciTech Connect

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

    2013-01-01

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

  10. Cactus Graphs for Genome Comparisons

    NASA Astrophysics Data System (ADS)

    Paten, Benedict; Diekhans, Mark; Earl, Dent; St. John, John; Ma, Jian; Suh, Bernard; Haussler, David

    We introduce a data structure, analysis and visualization scheme called a cactus graph for comparing sets of related genomes. Cactus graphs capture some of the advantages of de Bruijn and breakpoint graphs in one unified framework. They naturally decompose the common substructures in a set of related genomes into a hierarchy of chains that can be visualized as multiple alignments and nets that can be visualized in circular genome plots.

  11. Abstract Interpreters for Free

    NASA Astrophysics Data System (ADS)

    Might, Matthew

    In small-step abstract interpretations, the concrete and abstract semantics bear an uncanny resemblance. In this work, we present an analysis-design methodology that both explains and exploits that resemblance. Specifically, we present a two-step method to convert a small-step concrete semantics into a family of sound, computable abstract interpretations. The first step re-factors the concrete state-space to eliminate recursive structure; this refactoring of the state-space simultaneously determines a store-passing-style transformation on the underlying concrete semantics. The second step uses inference rules to generate an abstract state-space and a Galois connection simultaneously. The Galois connection allows the calculation of the "optimal" abstract interpretation. The two-step process is unambiguous, but nondeterministic: at each step, analysis designers face choices. Some of these choices ultimately influence properties such as flow-, field- and context-sensitivity. Thus, under the method, we can give the emergence of these properties a graph-theoretic characterization. To illustrate the method, we systematically abstract the continuation-passing style lambda calculus to arrive at two distinct families of analyses. The first is the well-known k-CFA family of analyses. The second consists of novel "environment-centric" abstract interpretations, none of which appear in the literature on static analysis of higher-order programs.

  12. Contact Graph Routing

    NASA Technical Reports Server (NTRS)

    Burleigh, Scott C.

    2011-01-01

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

  13. Graphing the Past

    ERIC Educational Resources Information Center

    Clary, Renee; Wandersee, James

    2014-01-01

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

  14. Hyperspectral Data Classification Using Factor Graphs

    NASA Astrophysics Data System (ADS)

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

    2012-07-01

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

  15. Graph Visualization for RDF Graphs with SPARQL-EndPoints

    Energy Science and Technology Software Center (ESTSC)

    2014-07-11

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

  16. [Quantitative interpretation of graphs from Stuart pantography. II. Geometrical bases].

    PubMed

    Ott, K

    1977-05-01

    In an experimental investigation, Stuart pantographic records are geometrically analyzed. The influence of the parameters' inclination and curving of condylar guidance, intercondylar distance, Bennett angle, distance of the plate, and position of the recording pencil are studied. Further quanitative analysis was not performed, as Stuart pantography is only meant for transmission to the respective articulator and is nto suitable for metric recording. PMID:266456

  17. Quantum Graph Analysis

    SciTech Connect

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

    2016-01-01

    In recent years, advanced network analytics have become increasingly important to na- tional security with applications ranging from cyber security to detection and disruption of ter- rorist networks. While classical computing solutions have received considerable investment, the development of quantum algorithms to address problems, such as data mining of attributed relational graphs, is a largely unexplored space. Recent theoretical work has shown that quan- tum algorithms for graph analysis can be more efficient than their classical counterparts. Here, we have implemented a trapped-ion-based two-qubit quantum information proces- sor to address these goals. Building on Sandia's microfabricated silicon surface ion traps, we have designed, realized and characterized a quantum information processor using the hyperfine qubits encoded in two 171 Yb + ions. We have implemented single qubit gates using resonant microwave radiation and have employed Gate set tomography (GST) to characterize the quan- tum process. For the first time, we were able to prove that the quantum process surpasses the fault tolerance thresholds of some quantum codes by demonstrating a diamond norm distance of less than 1 . 9 x 10 [?] 4 . We used Raman transitions in order to manipulate the trapped ions' motion and realize two-qubit gates. We characterized the implemented motion sensitive and insensitive single qubit processes and achieved a maximal process infidelity of 6 . 5 x 10 [?] 5 . We implemented the two-qubit gate proposed by Molmer and Sorensen and achieved a fidelity of more than 97 . 7%.

  18. Detecting alternative graph clusterings.

    PubMed

    Mandala, Supreet; Kumara, Soundar; Yao, Tao

    2012-07-01

    The problem of graph clustering or community detection has enjoyed a lot of attention in complex networks literature. A quality function, modularity, quantifies the strength of clustering and on maximization yields sensible partitions. However, in most real world networks, there are an exponentially large number of near-optimal partitions with some being very different from each other. Therefore, picking an optimal clustering among the alternatives does not provide complete information about network topology. To tackle this problem, we propose a graph perturbation scheme which can be used to identify an ensemble of near-optimal and diverse clusterings. We establish analytical properties of modularity function under the perturbation which ensures diversity. Our approach is algorithm independent and therefore can leverage any of the existing modularity maximizing algorithms. We numerically show that our methodology can systematically identify very different partitions on several existing data sets. The knowledge of diverse partitions sheds more light into the topological organization and helps gain a more complete understanding of the underlying complex network. PMID:23005495

  19. Detecting alternative graph clusterings

    NASA Astrophysics Data System (ADS)

    Mandala, Supreet; Kumara, Soundar; Yao, Tao

    2012-07-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2014-11-01

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

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

    SciTech Connect

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

    2013-09-15

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

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

    NASA Astrophysics Data System (ADS)

    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.

  3. CANCER MORTALITY MAPS AND GRAPHS

    EPA Science Inventory

    The Cancer Mortality Maps & Graph Web Site provides interactive maps, graphs (which are accessible to the blind and visually-impaired), text, tables and figures showing geographic patterns and time trends of cancer death rates for the time period 1950-1994 for more than 40 cancer...

  4. Graphs as Statements of Belief.

    ERIC Educational Resources Information Center

    Lake, David

    2002-01-01

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

  5. A PVS Graph Theory Library

    NASA Technical Reports Server (NTRS)

    Butler, Ricky W.; Sjogren, Jon A.

    1998-01-01

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

  6. Graph models of habitat mosaics.

    PubMed

    Urban, Dean L; Minor, Emily S; Treml, Eric A; Schick, Robert S

    2009-03-01

    Graph theory is a body of mathematics dealing with problems of connectivity, flow, and routing in networks ranging from social groups to computer networks. Recently, network applications have erupted in many fields, and graph models are now being applied in landscape ecology and conservation biology, particularly for applications couched in metapopulation theory. In these applications, graph nodes represent habitat patches or local populations and links indicate functional connections among populations (i.e. via dispersal). Graphs are models of more complicated real systems, and so it is appropriate to review these applications from the perspective of modelling in general. Here we review recent applications of network theory to habitat patches in landscape mosaics. We consider (1) the conceptual model underlying these applications; (2) formalization and implementation of the graph model; (3) model parameterization; (4) model testing, insights, and predictions available through graph analyses; and (5) potential implications for conservation biology and related applications. In general, and for a variety of ecological systems, we find the graph model a remarkably robust framework for applications concerned with habitat connectivity. We close with suggestions for further work on the parameterization and validation of graph models, and point to some promising analytic insights. PMID:19161432

  7. Graphs and Zero-Divisors

    ERIC Educational Resources Information Center

    Axtell, M.; Stickles, J.

    2010-01-01

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

  8. Improving teaching skills: from interactive classroom to applicable knowledge.

    PubMed

    Vujovic, Predrag

    2016-03-01

    Making the transition from more traditional to more interactive lecturing can be successfully achieved by applying numerous teaching techniques. To use lecture time in the most efficient way, a lecturer should first instruct students to acquire basic knowledge before coming to class. Various in-class activities then can be used to help students develop higher thinking skills and gain better understanding of the studied material. These in-class activities can take many forms (multiple-choice questions of various complexities, compare-and-contrast tasks, quantitative and problem-solving tasks, questions dealing with interpretations of tables, graphs, and charts, etc.) and should be designed to help student integrate their knowledge, to facilitate communication among students, and at the same time to allow the lecturer to closely monitor the learning process as it happens in the classroom. PMID:26847251

  9. A Collection of Features for Semantic Graphs

    SciTech Connect

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

    2007-05-02

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

  10. A parallel graph coloring heuristic

    SciTech Connect

    Jones, M.T.; Plassmann, P.E. )

    1993-05-01

    The problem of computing good graph colorings arises in many diverse applications, such as in the estimation of sparse Jacobians and in the development of efficient, parallel iterative methods for solving sparse linear systems. This paper presents an asynchronous graph coloring heuristic well suited to distributed memory parallel computers. Experimental results obtained on an Intel iPSC/860 are presented, which demonstrate that, for graphs arising from finite element applications, the heuristic exhibits scalable performance and generates colorings usually within three or four colors of the best-known linear time sequential heuristics. For bounded degree graphs, it is shown that the expected running time of the heuristic under the P-Ram computation model is bounded by EO(log(n)/log log(n)). This bound is an improvement over the previously known best upper bound for the expected running time of a random heuristic for the graph coloring problem.

  11. Semi-Markov Graph Dynamics

    PubMed Central

    Raberto, Marco; Rapallo, Fabio; Scalas, Enrico

    2011-01-01

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

  12. Graph Partitioning and Sequencing Software

    Energy Science and Technology Software Center (ESTSC)

    1995-09-19

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

  13. Multiple directed graph large-class multi-spectral processor

    NASA Technical Reports Server (NTRS)

    Casasent, David; Liu, Shiaw-Dong; Yoneyama, Hideyuki

    1988-01-01

    Numerical analysis techniques for the interpretation of high-resolution imaging-spectrometer data are described and demonstrated. The method proposed involves the use of (1) a hierarchical classifier with a tree structure generated automatically by a Fisher linear-discriminant-function algorithm and (2) a novel multiple-directed-graph scheme which reduces the local maxima and the number of perturbations required. Results for a 500-class test problem involving simulated imaging-spectrometer data are presented in tables and graphs; 100-percent-correct classification is achieved with an improvement factor of 5.

  14. Graph hierarchies for phylogeography.

    PubMed

    Cybis, Gabriela B; Sinsheimer, Janet S; Lemey, Philippe; Suchard, Marc A

    2013-03-19

    Bayesian phylogeographic methods simultaneously integrate geographical and evolutionary modelling, and have demonstrated value in assessing spatial spread patterns of measurably evolving organisms. We improve on existing phylogeographic methods by combining information from multiple phylogeographic datasets in a hierarchical setting. Consider N exchangeable datasets or strata consisting of viral sequences and locations, each evolving along its own phylogenetic tree and according to a conditionally independent geographical process. At the hierarchical level, a random graph summarizes the overall dispersion process by informing which migration rates between sampling locations are likely to be relevant in the strata. This approach provides an efficient and improved framework for analysing inherently hierarchical datasets. We first examine the evolutionary history of multiple serotypes of dengue virus in the Americas to showcase our method. Additionally, we explore an application to intrahost HIV evolution across multiple patients. PMID:23382428

  15. Gaining a Better Understanding of Estuarine Circulation and Improving Data Visualization Skills Through a Hands-on Contouring Exercise

    NASA Astrophysics Data System (ADS)

    Mailloux, B. J.; Kenna, T. C.

    2008-12-01

    The creation and accurate interpretation of graphs is becoming a lost art among students. The availability of numerous graphing software programs makes the act of graphing data easy but does not necessarily aide students in interpreting complex visual data. This is especially true for contour maps; which have become a critical skill in the earth sciences and everyday life. In multiple classes, we have incorporated a large-scale, hands-on, contouring exercise of temperature, salinity, and density data collected in the Hudson River Estuary. The exercise allows students to learn first-hand how to plot, analyze, and present three dimensional data. As part of a day-long sampling expedition aboard an 80' research vessel, students deploy a water profiling instrument (Seabird CTD). Data are collected along a transect between the Verrazano and George Washington Bridges. The data are then processed and binned at 0.5 meter intervals. The processed data is then used during a later laboratory period for the contouring exercise. In class, students work in groups of 2 to 4 people and are provided with the data, a set of contouring instructions, a piece of large (3' x 3') graph paper, a ruler, and a set of colored markers. We then let the groups work together to determine the details of the graphs. Important steps along the way are talking to the students about X and Y scales, interpolation, and choices of contour intervals and colors. Frustration and bottlenecks are common at the beginning when students are unsure how to even begin with the raw data. At some point during the exercise, students start to understand the contour concept and each group usually produces a finished contour map in an hour or so. Interestingly, the groups take pride in the coloring portion of the contouring as it indicates successful interpretation of the data. The exercise concludes with each group presenting and discussing their contour plot. In almost every case, the hands-on graphing has improved the

  16. "Communication Skills for the Gifted"

    ERIC Educational Resources Information Center

    Sisk, Dorothy A.

    1975-01-01

    A teacher training coordinator stresses the importance of developing gifted children's communication abilities and briefly describes two group dynamics activities ("Circle Partners" and "Think Pink") for building listening, interpretation and discussion skills. (LH)

  17. Interpreting functions of one-dimensional kinematics

    NASA Astrophysics Data System (ADS)

    Canty, Reality S.

    The present work examined several factors related to interpreting graphical representations of motion concepts. Since the seminal work of Larkin and Simon (1987), cognitive research has investigated informational equivalence and computational efficiency by contrasting performance across different representations systems such as line versus bar graph (Ali & Peebles, 2012; Shah & Freedman, 2009; Zacks & Tversky, 1999), table versus graph (Speier, 2006; Vessey, 1991) or table versus map (Smelcer & Carmel, 1997). Physics education research has focused on difficulties related to interpreting motion concepts in graphs, accounting for them in terms of misconceptions. Kinematics, the branch of physics concerned with the motion of objects, makes an interesting study of informational equivalence and computational efficiency because its three primary representations -- position-time, velocity-time, and acceleration-time graphs -- can reflect the same information in the same representational system which provides a different type of contrast than has usually been used in this area of cognitive research. In the present work, four experiments were used to test several hypotheses concerned with whether information about the motion of objects can be directly read-off the graph or whether it needed additional processing beyond what was directly visible; Palmer (1987) referred to this as the derivational structure of representations. The main findings across the four experiments were that (a) graph type was not a reliable factor of graph interpretation difficulty, (b) derivational structure was useful for analyzing tasks but there was no evidence supporting it as a process account, (c) graph-based judgment is susceptible to visual features in the graph that trigger powerful spatial-conceptual correspondences particularly height (e.g., higher means more, lower means less), direction of slope (e.g., zero, positive, negative), and curvature (e.g., increasing rate of change, decreasing

  18. Interpretive Experiments

    ERIC Educational Resources Information Center

    DeHaan, Frank, Ed.

    1977-01-01

    Describes an interpretative experiment involving the application of symmetry and temperature-dependent proton and fluorine nmr spectroscopy to the solution of structural and kinetic problems in coordination chemistry. (MLH)

  19. Graph duality as an instrument of Gauge-String correspondence

    NASA Astrophysics Data System (ADS)

    Diaz, Pablo; Lin, Hai; Veliz-Osorio, Alvaro

    2016-05-01

    We explore an identity between two branching graphs and propose a physical meaning in the context of the gauge-gravity correspondence. From the mathematical point of view, the identity equates probabilities associated with GT, the branching graph of the unitary groups, with probabilities associated with 𝕐, the branching graph of the symmetric groups. In order to furnish the identity with physical meaning, we exactly reproduce these probabilities as the square of three point functions involving certain hook-shaped backgrounds. We study these backgrounds in the context of LLM geometries and discover that they are domain walls interpolating two AdS spaces with different radii. We also find that, in certain cases, the probabilities match the eigenvalues of some observables, the embedding chain charges. We finally discuss a holographic interpretation of the mathematical identity through our results.

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

    ERIC Educational Resources Information Center

    McDuffie, Amy Roth

    2001-01-01

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

  1. Multigraph: Reusable Interactive Data Graphs

    NASA Astrophysics Data System (ADS)

    Phillips, M. B.

    2010-12-01

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

  2. The Nature of Employability Skills: Empirical Evidence from Singapore

    ERIC Educational Resources Information Center

    Sung, Johnny; Ng, Michael Chi Man; Loke, Fiona; Ramos, Catherine

    2013-01-01

    This paper concerns the changing nature of employability skills, moving from the original life skills or basic skills concepts to the increasingly work-oriented interpretation. The early concept of employability skills linked employability skills to job readiness and holding down employment. However, the work-oriented focus is increasingly linking…

  3. Evolutionary games on graphs

    NASA Astrophysics Data System (ADS)

    Szabó, György; Fáth, Gábor

    2007-07-01

    Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to those applied in non-equilibrium statistical physics. This review gives a tutorial-type overview of the field for physicists. The first four sections introduce the necessary background in classical and evolutionary game theory from the basic definitions to the most important results. The fifth section surveys the topological complications implied by non-mean-field-type social network structures in general. The next three sections discuss in detail the dynamic behavior of three prominent classes of models: the Prisoner's Dilemma, the Rock-Scissors-Paper game, and Competing Associations. The major theme of the review is in what sense and how the graph structure of interactions can modify and enrich the picture of long term behavioral patterns emerging in evolutionary games.

  4. Stacked graphs--geometry & aesthetics.

    PubMed

    Byron, Lee; Wattenberg, Martin

    2008-01-01

    In February 2008, the New York Times published an unusual chart of box office revenues for 7500 movies over 21 years. The chart was based on a similar visualization, developed by the first author, that displayed trends in music listening. This paper describes the design decisions and algorithms behind these graphics, and discusses the reaction on the Web. We suggest that this type of complex layered graph is effective for displaying large data sets to a mass audience. We provide a mathematical analysis of how this layered graph relates to traditional stacked graphs and to techniques such as ThemeRiver, showing how each method is optimizing a different "energy function". Finally, we discuss techniques for coloring and ordering the layers of such graphs. Throughout the paper, we emphasize the interplay between considerations of aesthetics and legibility. PMID:18988970

  5. Graph anomalies in cyber communications

    SciTech Connect

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

    2011-01-11

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

  6. Constructing Dense Graphs with Unique Hamiltonian Cycles

    ERIC Educational Resources Information Center

    Lynch, Mark A. M.

    2012-01-01

    It is not difficult to construct dense graphs containing Hamiltonian cycles, but it is difficult to generate dense graphs that are guaranteed to contain a unique Hamiltonian cycle. This article presents an algorithm for generating arbitrarily large simple graphs containing "unique" Hamiltonian cycles. These graphs can be turned into dense graphs…

  7. Finding long cycles in graphs

    NASA Astrophysics Data System (ADS)

    Marinari, Enzo; Semerjian, Guilhem; van Kerrebroeck, Valery

    2007-06-01

    We analyze the problem of discovering long cycles inside a graph. We propose and test two algorithms for this task. The first one is based on recent advances in statistical mechanics and relies on a message passing procedure. The second follows a more standard Monte Carlo Markov chain strategy. Special attention is devoted to Hamiltonian cycles of (nonregular) random graphs of minimal connectivity equal to 3.

  8. Mathematical Inscriptions and the Reflexive Elaboration of Understanding: An Ethnography of Graphing and Numeracy in a Fish Hatchery

    ERIC Educational Resources Information Center

    Roth, Wolff-Michael

    2005-01-01

    The power of mathematical inscriptions, such as graphs, is often attributed to the fact that they summarize a lot of information independent of their contextual particulars. There is evidence, however, that even quintessential experts and scientists have difficulties interpreting graphs when they are unfamiliar with the entities represented and…

  9. Zeta functions of quantum graphs

    NASA Astrophysics Data System (ADS)

    Harrison, J. M.; Kirsten, K.

    2011-06-01

    In this paper, we construct zeta functions of quantum graphs using a contour integral technique based on the argument principle. We start by considering the special case of the star graph with Neumann matching conditions at the center of the star. We then extend the technique to allow any matching conditions at the center for which the Laplace operator is self-adjoint and finally obtain an expression for the zeta function of any graph with general vertex matching conditions. In the process, it is convenient to work with new forms for the secular equation of a quantum graph that extend the well-known secular equation of the Neumann star graph. In the second half of this paper, we apply the zeta function to obtain new results for the spectral determinant, vacuum energy and heat kernel coefficients of quantum graphs. These have all been topics of current research in their own right and in each case this unified approach significantly expands results in the literature.

  10. Khovanov homology of graph-links

    SciTech Connect

    Nikonov, Igor M

    2012-08-31

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

  11. Design Document. EKG Interpretation Program.

    ERIC Educational Resources Information Center

    Webb, Sandra M.

    This teaching plan is designed to assist nursing instructors assigned to advanced medical surgical nursing courses in acquainting students with the basic skills needed to perform electrocardiographic (ECG or EKG) interpretations. The first part of the teaching plan contains a statement of purpose; audience recommendations; a flow chart detailing…

  12. Performing Interpretation

    ERIC Educational Resources Information Center

    Kothe, Elsa Lenz; Berard, Marie-France

    2013-01-01

    Utilizing a/r/tographic methodology to interrogate interpretive acts in museums, multiple areas of inquiry are raised in this paper, including: which knowledge is assigned the greatest value when preparing a gallery talk; what lies outside of disciplinary knowledge; how invitations to participate invite and disinvite in the same gesture; and what…

  13. Interpreting Evidence.

    ERIC Educational Resources Information Center

    Munsart, Craig A.

    1993-01-01

    Presents an activity that allows students to experience the type of discovery process that paleontologists necessarily followed during the early dinosaur explorations. Students are read parts of a story taken from the "American Journal of Science" and interpret the evidence leading to the discovery of Triceratops and Stegosaurus. (PR)

  14. Interpreting Metonymy.

    ERIC Educational Resources Information Center

    Pankhurst, Anne

    1994-01-01

    This paper examines some of the problems associated with interpreting metonymy, a figure of speech in which an attribute or commonly associated feature is used to name or designate something. After defining metonymy and outlining the principles of metonymy, the paper explains the differences between metonymy, synecdoche, and metaphor. It is…

  15. Component evolution in general random intersection graphs

    SciTech Connect

    Bradonjic, Milan; Hagberg, Aric; Hengartner, Nick; Percus, Allon G

    2010-01-01

    We analyze component evolution in general random intersection graphs (RIGs) and give conditions on existence and uniqueness of the giant component. Our techniques generalize the existing methods for analysis on component evolution in RIGs. That is, we analyze survival and extinction properties of a dependent, inhomogeneous Galton-Watson branching process on general RIGs. Our analysis relies on bounding the branching processes and inherits the fundamental concepts from the study on component evolution in Erdos-Renyi graphs. The main challenge becomes from the underlying structure of RIGs, when the number of offsprings follows a binomial distribution with a different number of nodes and different rate at each step during the evolution. RIGs can be interpreted as a model for large randomly formed non-metric data sets. Besides the mathematical analysis on component evolution, which we provide in this work, we perceive RIGs as an important random structure which has already found applications in social networks, epidemic networks, blog readership, or wireless sensor networks.

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

    NASA Astrophysics Data System (ADS)

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

    2016-06-01

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

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

    PubMed

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

    2014-01-01

    Graph search is attractive for the quantitative analysis of volumetric medical images, and especially for layered tissues, because it allows globally optimal solutions in low-order polynomial time. However, because nodes of graphs typically encode evenly distributed voxels of the volume with arcs connecting orthogonally sampled voxels in Euclidean space, segmentation cannot achieve greater precision than a single unit, i.e. the distance between two adjoining nodes, and partial volume effects are ignored. We generalize the graph to non-Euclidean space by allowing non-equidistant spacing between nodes, so that subvoxel accurate segmentation is achievable. Because the number of nodes and edges in the graph remains the same, running time and memory use are similar, while all the advantages of graph search, including global optimality and computational efficiency, are retained. A deformation field calculated from the volume data adaptively changes regional node density so that node density varies with the inverse of the expected cost. We validated our approach using optical coherence tomography (OCT) images of the retina and 3-D MR of the arterial wall, and achieved statistically significant increased accuracy. Our approach allows improved accuracy in volume data acquired with the same hardware, and also, preserved accuracy with lower resolution, more cost-effective, image acquisition equipment. The method is not limited to any specific imaging modality and readily extensible to higher dimensions. PMID:25314272

  18. Digital video, learning styles, and student understanding of kinematics graphs

    NASA Astrophysics Data System (ADS)

    Hein, Teresa Lee

    1997-12-01

    Student ability to analyze and interpret motion graphs following laboratory instruction that utilized interactive digital video as well as traditional instructional techniques was investigated. Research presented suggested that digital video tools serve to motivate students and may be an effective mechanism to enhance student understanding of motion concepts. Two laboratory exercises involving motion concepts were developed for this study. Students were divided into two instructional groups. The treatment group used digital video techniques and the control group used traditional techniques to perform the laboratory exercises. Student understanding of motion concepts were assessed, in part, using the Test of Understanding Graphs-Kinematics. Other assessment measures included student responses to a set of written graphical analysis questions and two post-lab activities. Possible relationships between individual learning style preferences and student understanding of motion concepts were also addressed. Learning style preferences were assessed using the Productivity Environmental Preference Survey prior to the instructional treatments. Students were asked to comment in writing about their learning styles before and after they were given the learning style assessment. Student comments revealed that the results they received from Productivity Environmental Preference Survey accurately reflected their learning styles. Results presented in this study showed that no significant relationship exists between students' learning style preferences and their ability to interpret motion graphs as measured by scores on the Test of Understanding Graphs-Kinematics. In addition, the results showed no significant difference between instructional treatment and mean scores on the Test of Understanding Graphs-Kinematics. Analysis of writing activities revealed that students in the treatment group responded more effectively than students in the control group to graphical interpretation

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

    ERIC Educational Resources Information Center

    Kukla, David

    2007-01-01

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

  20. Library Skills.

    ERIC Educational Resources Information Center

    Paul, Karin; Kuhlthau, Carol C.; Branch, Jennifer L.; Solowan, Diane Galloway; Case, Roland; Abilock, Debbie; Eisenberg, Michael B.; Koechlin, Carol; Zwaan, Sandi; Hughes, Sandra; Low, Ann; Litch, Margaret; Lowry, Cindy; Irvine, Linda; Stimson, Margaret; Schlarb, Irene; Wilson, Janet; Warriner, Emily; Parsons, Les; Luongo-Orlando, Katherine; Hamilton, Donald

    2003-01-01

    Includes 19 articles that address issues related to library skills and Canadian school libraries. Topics include information literacy; inquiry learning; critical thinking and electronic research; collaborative inquiry; information skills and the Big 6 approach to problem solving; student use of online databases; library skills; Internet accuracy;…

  1. Basic Skills.

    ERIC Educational Resources Information Center

    Luparelli, Augustus N.; And Others

    1981-01-01

    These four articles focus on developing basic reading, science, and job search skills: "Reading Program for Vocational Classes" by Augustus Luparelli; "Why Teach Employability Skills?" by Larry Siefferman; "Improving Vocabulary and Reading Skills" by Edythe Conway; and "Science in Everyday Life" by Virginia Eleazer and George Carney. (SK)

  2. Skill Set

    ERIC Educational Resources Information Center

    Holdsworth, Tom

    2007-01-01

    With competition to attract quality students into career and technical education programs and many entrants to the workforce inadequately prepared with employability skills, some community colleges have found a way to answer industry's call--they are launching SkillsUSA chapters on campus. In this article, the author features SkillsUSA, a…

  3. Graph transformation expert system (GTES)

    NASA Astrophysics Data System (ADS)

    Li, Guiquing; Ge, Qihong; Zhong, Luo; Xie, Weiping

    1996-03-01

    The design of many industrial and engineering systems can often be accomplished using flow graphs of various types. Examples include manufacturing processes and data processing applications, Graph Transformation Expert System, is an expert system which has been developed by WUT for applying techniques of artificial intelligence to the architectural design of data and signal processing systems. Software and hardware architectures may be defined for such systems using data flow graphs, in which nodes represent data processing steps and directed areas represent the `flow' of data between the processing steps. Starting with a user- defined generic processing graphic, this expert will transform the graph by applying transformation rules in order to specialize the processing graph to satisfy specified design goals and/or hardware constraints. Although the particular application for which this expert is designed is that of data and signal processing systems, it can provide an expert system framework for other problems specified graphically; for example, manufacturing systems, information systems, and product distribution systems.

  4. Eigenfunction statistics on quantum graphs

    SciTech Connect

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

    2010-12-15

    We investigate the spatial statistics of the energy eigenfunctions on large quantum graphs. It has previously been conjectured that these should be described by a Gaussian Random Wave Model, by analogy with quantum chaotic systems, for which such a model was proposed by Berry in 1977. The autocorrelation functions we calculate for an individual quantum graph exhibit a universal component, which completely determines a Gaussian Random Wave Model, and a system-dependent deviation. This deviation depends on the graph only through its underlying classical dynamics. Classical criteria for quantum universality to be met asymptotically in the large graph limit (i.e. for the non-universal deviation to vanish) are then extracted. We use an exact field theoretic expression in terms of a variant of a supersymmetric {sigma} model. A saddle-point analysis of this expression leads to the estimates. In particular, intensity correlations are used to discuss the possible equidistribution of the energy eigenfunctions in the large graph limit. When equidistribution is asymptotically realized, our theory predicts a rate of convergence that is a significant refinement of previous estimates. The universal and system-dependent components of intensity correlation functions are recovered by means of an exact trace formula which we analyse in the diagonal approximation, drawing in this way a parallel between the field theory and semiclassics. Our results provide the first instance where an asymptotic Gaussian Random Wave Model has been established microscopically for eigenfunctions in a system with no disorder.

  5. Box graphs and resolutions I

    NASA Astrophysics Data System (ADS)

    Braun, Andreas P.; Schäfer-Nameki, Sakura

    2016-04-01

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

  6. Discrete Signal Processing on Graphs: Sampling Theory

    NASA Astrophysics Data System (ADS)

    Chen, Siheng; Varma, Rohan; Sandryhaila, Aliaksei; Kovacevic, Jelena

    2015-12-01

    We propose a sampling theory for signals that are supported on either directed or undirected graphs. The theory follows the same paradigm as classical sampling theory. We show that perfect recovery is possible for graph signals bandlimited under the graph Fourier transform. The sampled signal coefficients form a new graph signal, whose corresponding graph structure preserves the first-order difference of the original graph signal. For general graphs, an optimal sampling operator based on experimentally designed sampling is proposed to guarantee perfect recovery and robustness to noise; for graphs whose graph Fourier transforms are frames with maximal robustness to erasures as well as for Erd\\H{o}s-R\\'enyi graphs, random sampling leads to perfect recovery with high probability. We further establish the connection to the sampling theory of finite discrete-time signal processing and previous work on signal recovery on graphs. To handle full-band graph signals, we propose a graph filter bank based on sampling theory on graphs. Finally, we apply the proposed sampling theory to semi-supervised classification on online blogs and digit images, where we achieve similar or better performance with fewer labeled samples compared to previous work.

  7. Interpretive Medicine

    PubMed Central

    Reeve, Joanne

    2010-01-01

    Patient-centredness is a core value of general practice; it is defined as the interpersonal processes that support the holistic care of individuals. To date, efforts to demonstrate their relationship to patient outcomes have been disappointing, whilst some studies suggest values may be more rhetoric than reality. Contextual issues influence the quality of patient-centred consultations, impacting on outcomes. The legitimate use of knowledge, or evidence, is a defining aspect of modern practice, and has implications for patient-centredness. Based on a critical review of the literature, on my own empirical research, and on reflections from my clinical practice, I critique current models of the use of knowledge in supporting individualised care. Evidence-Based Medicine (EBM), and its implementation within health policy as Scientific Bureaucratic Medicine (SBM), define best evidence in terms of an epistemological emphasis on scientific knowledge over clinical experience. It provides objective knowledge of disease, including quantitative estimates of the certainty of that knowledge. Whilst arguably appropriate for secondary care, involving episodic care of selected populations referred in for specialist diagnosis and treatment of disease, application to general practice can be questioned given the complex, dynamic and uncertain nature of much of the illness that is treated. I propose that general practice is better described by a model of Interpretive Medicine (IM): the critical, thoughtful, professional use of an appropriate range of knowledges in the dynamic, shared exploration and interpretation of individual illness experience, in order to support the creative capacity of individuals in maintaining their daily lives. Whilst the generation of interpreted knowledge is an essential part of daily general practice, the profession does not have an adequate framework by which this activity can be externally judged to have been done well. Drawing on theory related to the

  8. Algebraic connectivity and graph robustness.

    SciTech Connect

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

    2009-07-01

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

  9. Quantum snake walk on graphs

    SciTech Connect

    Rosmanis, Ansis

    2011-02-15

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

  10. Graph Analytics for Signature Discovery

    SciTech Connect

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

    2013-06-01

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

  11. Optimal preparation of graph states

    SciTech Connect

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

    2011-04-15

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

  12. Graph modeling systems and methods

    DOEpatents

    Neergaard, Mike

    2015-10-13

    An apparatus and a method for vulnerability and reliability modeling are provided. The method generally includes constructing a graph model of a physical network using a computer, the graph model including a plurality of terminating vertices to represent nodes in the physical network, a plurality of edges to represent transmission paths in the physical network, and a non-terminating vertex to represent a non-nodal vulnerability along a transmission path in the physical network. The method additionally includes evaluating the vulnerability and reliability of the physical network using the constructed graph model, wherein the vulnerability and reliability evaluation includes a determination of whether each terminating and non-terminating vertex represents a critical point of failure. The method can be utilized to evaluate wide variety of networks, including power grid infrastructures, communication network topologies, and fluid distribution systems.

  13. Sequential visibility-graph motifs

    NASA Astrophysics Data System (ADS)

    Iacovacci, Jacopo; Lacasa, Lucas

    2016-04-01

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

  14. Elicited Speech from Graph Items on the Test of Spoken English[TM]. Research Reports. Report 74. RR-04-06

    ERIC Educational Resources Information Center

    Katz, Irvin R.; Xi, Xiaoming; Kim, Hyun-Joo; Cheng, Peter C. H.

    2004-01-01

    This research applied a cognitive model to identify item features that lead to irrelevant variance on the Test of Spoken English[TM] (TSE[R]). The TSE is an assessment of English oral proficiency and includes an item that elicits a description of a statistical graph. This item type sometimes appears to tap graph-reading skills--an irrelevant…

  15. Interacting particle systems on graphs

    NASA Astrophysics Data System (ADS)

    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

  16. Synchronizability of random rectangular graphs

    SciTech Connect

    Estrada, Ernesto Chen, Guanrong

    2015-08-15

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

  17. Graphs for Early Elementary Social Studies.

    ERIC Educational Resources Information Center

    Freeland, Kent; Brewer, Samrie

    1989-01-01

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

  18. Comparison Graph of Sea Ice Minimum - 2010

    NASA Video Gallery

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

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

    Energy Science and Technology Software Center (ESTSC)

    2007-11-19

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

  20. Graphing and Social Studies: An Interdisciplinary Activity.

    ERIC Educational Resources Information Center

    Brehm, Julia L.

    1996-01-01

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

  1. Mathematical Minute: Rotating a Function Graph

    ERIC Educational Resources Information Center

    Bravo, Daniel; Fera, Joseph

    2013-01-01

    Using calculus only, we find the angles you can rotate the graph of a differentiable function about the origin and still obtain a function graph. We then apply the solution to odd and even degree polynomials.

  2. Standard Distributions: One Graph Fits All

    ERIC Educational Resources Information Center

    Wagner, Clifford H.

    2007-01-01

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

  3. Graph theory findings in the pathophysiology of temporal lobe epilepsy

    PubMed Central

    Chiang, Sharon; Haneef, Zulfi

    2014-01-01

    Temporal lobe epilepsy (TLE) is the most common form of adult epilepsy. Accumulating evidence has shown that TLE is a disorder of abnormal epileptogenic networks, rather than focal sources. Graph theory allows for a network-based representation of TLE brain networks, and has potential to illuminate characteristics of brain topology conducive to TLE pathophysiology, including seizure initiation and spread. We review basic concepts which we believe will prove helpful in interpreting results rapidly emerging from graph theory research in TLE. In addition, we summarize the current state of graph theory findings in TLE as they pertain its pathophysiology. Several common findings have emerged from the many modalities which have been used to study TLE using graph theory, including structural MRI, diffusion tensor imaging, surface EEG, intracranial EEG, magnetoencephalography, functional MRI, cell cultures, simulated models, and mouse models, involving increased regularity of the interictal network configuration, altered local segregation and global integration of the TLE network, and network reorganization of temporal lobe and limbic structures. As different modalities provide different views of the same phenomenon, future studies integrating data from multiple modalities are needed to clarify findings and contribute to the formation of a coherent theory on the pathophysiology of TLE. PMID:24831083

  4. Graph theory findings in the pathophysiology of temporal lobe epilepsy.

    PubMed

    Chiang, Sharon; Haneef, Zulfi

    2014-07-01

    Temporal lobe epilepsy (TLE) is the most common form of adult epilepsy. Accumulating evidence has shown that TLE is a disorder of abnormal epileptogenic networks, rather than focal sources. Graph theory allows for a network-based representation of TLE brain networks, and has potential to illuminate characteristics of brain topology conducive to TLE pathophysiology, including seizure initiation and spread. We review basic concepts which we believe will prove helpful in interpreting results rapidly emerging from graph theory research in TLE. In addition, we summarize the current state of graph theory findings in TLE as they pertain its pathophysiology. Several common findings have emerged from the many modalities which have been used to study TLE using graph theory, including structural MRI, diffusion tensor imaging, surface EEG, intracranial EEG, magnetoencephalography, functional MRI, cell cultures, simulated models, and mouse models, involving increased regularity of the interictal network configuration, altered local segregation and global integration of the TLE network, and network reorganization of temporal lobe and limbic structures. As different modalities provide different views of the same phenomenon, future studies integrating data from multiple modalities are needed to clarify findings and contribute to the formation of a coherent theory on the pathophysiology of TLE. PMID:24831083

  5. Effects of Graphing, Goal Setting, and Conferencing on Reading and Math Achievement

    ERIC Educational Resources Information Center

    Snyder, Amy T.

    2016-01-01

    Improving foundational academic skills for elementary level students continues to be a challenge for classroom teachers. This study implemented weekly progress monitoring procedures using curriculum-based measurement assessments in conjunction with weekly individual student-teacher graphing and goal-setting conferences to determine the effect the…

  6. A Comparison of Two Approaches to Training Visual Analysis of AB Graphs

    ERIC Educational Resources Information Center

    Wolfe, Katie; Slocum, Timothy A.

    2015-01-01

    Visual analysis is the primary method of evaluating data in single-subject research. Few studies have evaluated interventions to teach visual analysis skills. The purpose of this study was to evaluate systematic instruction, delivered using computer-based intervention or a recorded lecture, on identifying changes in slope and level in AB graphs.…

  7. The Role of Microcomputer-Based Laboratories in Learning To Make Graphs of Distance and Velocity.

    ERIC Educational Resources Information Center

    Brasell, Heather

    Two questions about the effects of microcomputer-based laboratory (MBL) activities on graphing skills were addressed in this study: (1) the extent to which activities help students link their concrete experiences with motion with graphic representations of these experiences; and (2) the degree of importance of the real-time aspect of the MBL in…

  8. Writing, Tables, and Graphs: Experience with Group Discussions in Microbiology Practical Work.

    ERIC Educational Resources Information Center

    Wyatt, H. V.

    1984-01-01

    Suggests that microbiology activities/experiments are suitable for teaching skills in designing experiments, manipulating tables/graphs, and the rewriting of work. Shows how students design an experiment using a table and how another experiment provides material for a group discussion on writing and rewriting. (DH)

  9. Fibonacci Identities, Matrices, and Graphs

    ERIC Educational Resources Information Center

    Huang, Danrun

    2005-01-01

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

  10. Two-Player Graph Pebbling

    NASA Astrophysics Data System (ADS)

    Prudente, Matthew James

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

  11. Graphs and Enhancing Maple Multiplication.

    ERIC Educational Resources Information Center

    Cecil, David R.; Wang, Rongdong

    2002-01-01

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

  12. Situating Graphs as Workplace Knowledge

    ERIC Educational Resources Information Center

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

    2007-01-01

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

  13. Affect and Graphing Calculator Use

    ERIC Educational Resources Information Center

    McCulloch, Allison W.

    2011-01-01

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

  14. Humidity Graphs for All Seasons.

    ERIC Educational Resources Information Center

    Esmael, F.

    1982-01-01

    In a previous article in this journal (Vol. 17, p358, 1979), a wet-bulb depression table was recommended for two simple experiments to determine relative humidity. However, the use of a graph is suggested because it gives the relative humidity directly from the wet and dry bulb readings. (JN)

  15. Ancestral Genres of Mathematical Graphs

    ERIC Educational Resources Information Center

    Gerofsky, Susan

    2011-01-01

    Drawing from sources in gesture studies, cognitive science, the anthropology of religion and art/architecture history, this article explores cultural, bodily and cosmological resonances carried (unintentionally) by mathematical graphs on Cartesian coordinates. Concepts of asymmetric bodily spaces, grids, orthogonality, mapping and sacred spaces…

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

    ERIC Educational Resources Information Center

    Hansen, Peter J.; Jurs, Peter C.

    1988-01-01

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

  17. Around the Sun in a Graphing Calculator.

    ERIC Educational Resources Information Center

    Demana, Franklin; Waits, Bert K.

    1989-01-01

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

  18. 47 CFR 80.761 - Conversion graphs.

    Code of Federal Regulations, 2010 CFR

    2010-10-01

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

  19. 47 CFR 80.761 - Conversion graphs.

    Code of Federal Regulations, 2014 CFR

    2014-10-01

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

  20. 47 CFR 80.761 - Conversion graphs.

    Code of Federal Regulations, 2011 CFR

    2011-10-01

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

  1. 47 CFR 80.761 - Conversion graphs.

    Code of Federal Regulations, 2012 CFR

    2012-10-01

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

  2. 47 CFR 80.761 - Conversion graphs.

    Code of Federal Regulations, 2013 CFR

    2013-10-01

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

  3. Some Applications of Graph Theory to Clustering

    ERIC Educational Resources Information Center

    Hubert, Lawrence J.

    1974-01-01

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

  4. Research and Teaching: Data Visualization Literacy: Investigating Data Interpretation along the Novice-Expert Continuum

    ERIC Educational Resources Information Center

    Maltese, Adam V.; Svetina, Dubravka; Harsh, Joseph A.

    2015-01-01

    In the STEM fields, adequate proficiency in reading and interpreting graphs is widely held as a central element for scientific literacy given the importance of data visualizations to succinctly present complex information. Although prior research espouses methods to improve graphing proficiencies, there is little understanding about when and how…

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

    NASA Astrophysics Data System (ADS)

    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.

  6. Fast graph operations in quantum computation

    NASA Astrophysics Data System (ADS)

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

    2016-03-01

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

  7. Communication Skills.

    ERIC Educational Resources Information Center

    Carlisle, Lynn

    This document presents one module in a set of training resources for trainers to use with parents and/or professionals serving children with disabilities; focus is on communication skills. The modules stress content and activities that build skills and offer resources to promote parent-professional collaboration. Each training module takes about 2…

  8. Study Skills.

    ERIC Educational Resources Information Center

    Thomas, Anne

    1993-01-01

    Three developments lend support to the idea that schools must help teach study skills: (1) advances in cognitive psychology that suggest children are active learners; (2) society's concern for at-risk students; and (3) growing demands for improved student performance. There is evidence that systematic study skills instruction does improve academic…

  9. Sharing Skills.

    ERIC Educational Resources Information Center

    Snoddon, Ruth V.; And Others

    1987-01-01

    Descriptions of activities designed to enhance the learning of library and information skills focus on the location of materials (ready-to-use library skills games); finding materials in the card catalog; and Aesop's fables. Games and puzzles are provided. (CLB)

  10. High Performance Descriptive Semantic Analysis of Semantic Graph Databases

    SciTech Connect

    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.

  11. Measuring geographic segregation: a graph-based approach

    NASA Astrophysics Data System (ADS)

    Hong, Seong-Yun; Sadahiro, Yukio

    2014-04-01

    Residential segregation is a multidimensional phenomenon that encompasses several conceptually distinct aspects of geographical separation between populations. While various indices have been developed as a response to different definitions of segregation, the reliance on such single-figure indices could oversimplify the complex, multidimensional phenomena. In this regard, this paper suggests an alternative graph-based approach that provides more detailed information than simple indices: The concentration profile graphically conveys information about how evenly a population group is distributed over the study region, and the spatial proximity profile depicts the degree of clustering across different threshold levels. These graphs can also be summarized into single numbers for comparative purposes, but the interpretation can be more accurate by inspecting the additional information. To demonstrate the use of these methods, the residential patterns of three major ethnic groups in Auckland, namely Māori, Pacific peoples, and Asians, are examined using the 2006 census data.

  12. Generalized graph states based on Hadamard matrices

    SciTech Connect

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

    2015-07-15

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

  13. Constrained Graph Optimization: Interdiction and Preservation Problems

    SciTech Connect

    Schild, Aaron V

    2012-07-30

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

  14. Fast Approximate Quadratic Programming for Graph Matching

    PubMed Central

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

    2015-01-01

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

  15. Fast approximate quadratic programming for graph matching.

    PubMed

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

    2015-01-01

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

  16. Subgraph-Based Filterbanks for Graph Signals

    NASA Astrophysics Data System (ADS)

    Tremblay, Nicolas; Borgnat, Pierre

    2016-08-01

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

  17. Hierarchical structure of the logical Internet graph

    NASA Astrophysics Data System (ADS)

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

    2001-07-01

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

  18. On a programming language for graph algorithms

    NASA Technical Reports Server (NTRS)

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

    1971-01-01

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

  19. Choosability of P 5-Free Graphs

    NASA Astrophysics Data System (ADS)

    Golovach, Petr A.; Heggernes, Pinar

    A graph is k-choosable if it admits a proper coloring of its vertices for every assignment of k (possibly different) allowed colors to choose from for each vertex. It is NP-hard to decide whether a given graph is k-choosable for k ≥ 3, and this problem is considered strictly harder than the k-coloring problem. Only few positive results are known on input graphs with a given structure. Here, we prove that the problem is fixed parameter tractable on P 5-free graphs when parameterized by k. This graph class contains the well known and widely studied class of cographs. Our result is surprising since the parameterized complexity of k-coloring is still open on P 5-free graphs. To give a complete picture, we show that the problem remains NP-hard on P 5-free graphs when k is a part of the input.

  20. The weighted random graph model

    NASA Astrophysics Data System (ADS)

    Garlaschelli, Diego

    2009-07-01

    We introduce the weighted random graph (WRG) model, which represents the weighted counterpart of the Erdos-Renyi random graph and provides fundamental insights into more complicated weighted networks. We find analytically that the WRG is characterized by a geometric weight distribution, a binomial degree distribution and a negative binomial strength distribution. We also characterize exactly the percolation phase transitions associated with edge removal and with the appearance of weighted subgraphs of any order and intensity. We find that even this completely null model displays a percolation behaviour similar to what is observed in real weighted networks, implying that edge removal cannot be used to detect community structure empirically. By contrast, the analysis of clustering successfully reveals different patterns between the WRG and real networks.

  1. Relativity on Rotated Graph Paper

    NASA Astrophysics Data System (ADS)

    Salgado, Roberto

    2011-11-01

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

  2. Topological structure of dictionary graphs

    NASA Astrophysics Data System (ADS)

    Fukś, Henryk; Krzemiński, Mark

    2009-09-01

    We investigate the topological structure of the subgraphs of dictionary graphs constructed from WordNet and Moby thesaurus data. In the process of learning a foreign language, the learner knows only a subset of all words of the language, corresponding to a subgraph of a dictionary graph. When this subgraph grows with time, its topological properties change. We introduce the notion of the pseudocore and argue that the growth of the vocabulary roughly follows decreasing pseudocore numbers—that is, one first learns words with a high pseudocore number followed by smaller pseudocores. We also propose an alternative strategy for vocabulary growth, involving decreasing core numbers as opposed to pseudocore numbers. We find that as the core or pseudocore grows in size, the clustering coefficient first decreases, then reaches a minimum and starts increasing again. The minimum occurs when the vocabulary reaches a size between 103 and 104. A simple model exhibiting similar behavior is proposed. The model is based on a generalized geometric random graph. Possible implications for language learning are discussed.

  3. Models of random graph hierarchies

    NASA Astrophysics Data System (ADS)

    Paluch, Robert; Suchecki, Krzysztof; Hołyst, Janusz A.

    2015-10-01

    We introduce two models of inclusion hierarchies: random graph hierarchy (RGH) and limited random graph hierarchy (LRGH). In both models a set of nodes at a given hierarchy level is connected randomly, as in the Erdős-Rényi random graph, with a fixed average degree equal to a system parameter c. Clusters of the resulting network are treated as nodes at the next hierarchy level and they are connected again at this level and so on, until the process cannot continue. In the RGH model we use all clusters, including those of size 1, when building the next hierarchy level, while in the LRGH model clusters of size 1 stop participating in further steps. We find that in both models the number of nodes at a given hierarchy level h decreases approximately exponentially with h. The height of the hierarchy H, i.e. the number of all hierarchy levels, increases logarithmically with the system size N, i.e. with the number of nodes at the first level. The height H decreases monotonically with the connectivity parameter c in the RGH model and it reaches a maximum for a certain c max in the LRGH model. The distribution of separate cluster sizes in the LRGH model is a power law with an exponent about - 1.25. The above results follow from approximate analytical calculations and have been confirmed by numerical simulations.

  4. Affinity learning with diffusion on tensor product graph.

    PubMed

    Yang, Xingwei; Prasad, Lakshman; Latecki, Longin Jan

    2013-01-01

    In many applications, we are given a finite set of data points sampled from a data manifold and represented as a graph with edge weights determined by pairwise similarities of the samples. Often the pairwise similarities (which are also called affinities) are unreliable due to noise or due to intrinsic difficulties in estimating similarity values of the samples. As observed in several recent approaches, more reliable similarities can be obtained if the original similarities are diffused in the context of other data points, where the context of each point is a set of points most similar to it. Compared to the existing methods, our approach differs in two main aspects. First, instead of diffusing the similarity information on the original graph, we propose to utilize the tensor product graph (TPG) obtained by the tensor product of the original graph with itself. Since TPG takes into account higher order information, it is not a surprise that we obtain more reliable similarities. However, it comes at the price of higher order computational complexity and storage requirement. The key contribution of the proposed approach is that the information propagation on TPG can be computed with the same computational complexity and the same amount of storage as the propagation on the original graph. We prove that a graph diffusion process on TPG is equivalent to a novel iterative algorithm on the original graph, which is guaranteed to converge. After its convergence we obtain new edge weights that can be interpreted as new, learned affinities. We stress that the affinities are learned in an unsupervised setting. We illustrate the benefits of the proposed approach for data manifolds composed of shapes, images, and image patches on two very different tasks of image retrieval and image segmentation. With learned affinities, we achieve the bull's eye retrieval score of 99.99 percent on the MPEG-7 shape dataset, which is much higher than the state-of-the-art algorithms. When the data

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

    PubMed Central

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

    2015-01-01

    Graph theory is increasingly being used to study brain connectivity across the spectrum of Alzheimer's disease (AD), but prior findings have been inconsistent, likely reflecting methodological differences. We systematically investigated how methods of graph creation (i.e., type of correlation matrix and edge weighting) affect structural network properties and group differences. We estimated the structural connectivity of brain networks based on correlation maps of cortical thickness obtained from MRI. Four groups were compared: 126 cognitively normal older adults, 103 individuals with Mild Cognitive Impairment (MCI) who retained MCI status for at least 3 years (stable MCI), 108 individuals with MCI who progressed to AD-dementia within 3 years (progressive MCI), and 105 individuals with AD-dementia. Small-world measures of connectivity (characteristic path length and clustering coefficient) differed across groups, consistent with prior studies. Groups were best discriminated by the Randić index, which measures the degree to which highly connected nodes connect to other highly connected nodes. The Randić index differentiated the stable and progressive MCI groups, suggesting that it might be useful for tracking and predicting the progression of AD. Notably, however, the magnitude and direction of group differences in all three measures were dependent on the method of graph creation, indicating that it is crucial to take into account how graphs are constructed when interpreting differences across diagnostic groups and studies. The algebraic connectivity measures showed few group differences, independent of the method of graph construction, suggesting that global connectivity as it relates to node degree is not altered in early AD. PMID:25984446

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

    PubMed

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

    2015-01-01

    Graph theory is increasingly being used to study brain connectivity across the spectrum of Alzheimer's disease (AD), but prior findings have been inconsistent, likely reflecting methodological differences. We systematically investigated how methods of graph creation (i.e., type of correlation matrix and edge weighting) affect structural network properties and group differences. We estimated the structural connectivity of brain networks based on correlation maps of cortical thickness obtained from MRI. Four groups were compared: 126 cognitively normal older adults, 103 individuals with Mild Cognitive Impairment (MCI) who retained MCI status for at least 3 years (stable MCI), 108 individuals with MCI who progressed to AD-dementia within 3 years (progressive MCI), and 105 individuals with AD-dementia. Small-world measures of connectivity (characteristic path length and clustering coefficient) differed across groups, consistent with prior studies. Groups were best discriminated by the Randić index, which measures the degree to which highly connected nodes connect to other highly connected nodes. The Randić index differentiated the stable and progressive MCI groups, suggesting that it might be useful for tracking and predicting the progression of AD. Notably, however, the magnitude and direction of group differences in all three measures were dependent on the method of graph creation, indicating that it is crucial to take into account how graphs are constructed when interpreting differences across diagnostic groups and studies. The algebraic connectivity measures showed few group differences, independent of the method of graph construction, suggesting that global connectivity as it relates to node degree is not altered in early AD. PMID:25984446

  7. Using a Problem Solving-Cooperative Learning Approach to Improve Students' Skills for Interpreting [Superscript 1]H NMR Spectra of Unknown Compounds in an Organic Spectroscopy Course

    ERIC Educational Resources Information Center

    Angawi, Rihab F.

    2014-01-01

    To address third- and fourth-year chemistry students' difficulties with the challenge of interpreting [superscript 1]H NMR spectra, a problem solving-cooperative learning technique was incorporated in a Spectra of Organic Compounds course. Using this approach helped students deepen their understanding of the basics of [superscript 1]H NMR…

  8. Graph theoretical analysis of climate data

    NASA Astrophysics Data System (ADS)

    Zerenner, T.; Hense, A.

    2012-04-01

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

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

    ERIC Educational Resources Information Center

    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…

  10. Computational Genomics Using Graph Theory

    NASA Astrophysics Data System (ADS)

    Schlick, Tamar

    2005-03-01

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

  11. Interpretation Of Biomechanical Data To A Gymnastics Coach

    NASA Astrophysics Data System (ADS)

    Shierman, Gail

    1982-02-01

    Several trials of many different gymnastics skills on various pieces of apparatus were filmed and the results were studied with the coach. The time to accomplish the entire skill as well as the time for each segment of the skill was important to the coach. He was also interested in angle of release or push-off and the path of the center of gravity. Lastly, graphs of velocities and accelerations of limb segments were revealing to the coach. Biomechanical analysis has helped him see why the performances were good; he is more interested in working with the investigator in all the events in gymnastics through the medium of cinematography.

  12. The Optimum Text in Simultaneous Interpreting: A Cognitive Approach to Interpreters' Training.

    ERIC Educational Resources Information Center

    Alexieva, Bistra

    A discussion of text translatability in simultaneous interpreting (SI) looks at semantic redundancy, the repetition of semantic components essential to creating an utterance, and offers some classroom techniques for teaching interpreting skills. It is proposed that the translatability of a text in SI should be studied in terms of the experiential…

  13. Computing Information Value from RDF Graph Properties

    SciTech Connect

    al-Saffar, Sinan; Heileman, Gregory

    2010-11-08

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

  14. Inferring Pedigree Graphs from Genetic Distances

    NASA Astrophysics Data System (ADS)

    Tamura, Takeyuki; Ito, Hiro

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

  15. Components in time-varying graphs.

    PubMed

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

    2012-06-01

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

  16. Components in time-varying graphs

    NASA Astrophysics Data System (ADS)

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

    2012-06-01

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

  17. JavaGenes: Evolving Graphs with Crossover

    NASA Technical Reports Server (NTRS)

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

    2000-01-01

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

  18. A New SAS program for behavioral analysis of electrical penetration graph data

    Technology Transfer Automated Retrieval System (TEKTRAN)

    Monitoring feeding behaviors of insects whose piercing-sucking mouthparts are inserted into plant tissue is done by making the insect part of an electronic circuit, using electropenetrography (EPG). Fluctuating voltage signals in the circuit are graphed, and resulting waveforms are interpreted as sp...

  19. Supporting Generative Thinking about Number Lines, the Cartesian Plane, and Graphs of Linear Functions

    ERIC Educational Resources Information Center

    Earnest, Darrell Steven

    2012-01-01

    This dissertation explores fifth and eighth grade students' interpretations of three kinds of mathematical representations: number lines, the Cartesian plane, and graphs of linear functions. Two studies were conducted. In Study 1, I administered the paper-and-pencil Linear Representations Assessment (LRA) to examine students'…

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

    ERIC Educational Resources Information Center

    Botzer, Galit; Yerushalmy, Michal

    2008-01-01

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

  1. API Requirements for Dynamic Graph Prediction

    SciTech Connect

    Gallagher, B; Eliassi-Rad, T

    2006-10-13

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

  2. Fast generation of sparse random kernel graphs

    DOE PAGESBeta

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

    2015-09-10

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

  3. Fast generation of sparse random kernel graphs

    SciTech Connect

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

    2015-09-10

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

  4. Fast Generation of Sparse Random Kernel Graphs

    PubMed Central

    2015-01-01

    The development of kernel-based inhomogeneous random graphs has provided models that are flexible enough to capture many observed characteristics of real networks, and that are also mathematically tractable. We specify a class of inhomogeneous random graph models, called random kernel graphs, that produces sparse graphs with tunable graph properties, and we develop an efficient generation algorithm to sample random instances from this model. As real-world networks are usually large, it is essential that the run-time of generation algorithms scales better than quadratically in the number of vertices n. We show that for many practical kernels our algorithm runs in time at most 𝒪(n(logn)2). As a practical example we show how to generate samples of power-law degree distribution graphs with tunable assortativity. PMID:26356296

  5. Weight of quadratic forms and graph states

    NASA Astrophysics Data System (ADS)

    Cosentino, Alessandro; Severini, Simone

    2009-11-01

    We prove a connection between Schmidt rank and weight of quadratic forms. This provides a new tool for the classification of graph states based on entanglement. Our main tool arises from a reformulation of previously known results concerning the weight of quadratic forms in terms of graph states properties. As a byproduct, we obtain a straightforward characterization of the weight of functions associated with pivot-minor of bipartite graphs.

  6. Graph-matching based CTA.

    PubMed

    Maksimov, Dmitry; Hesser, Jürgen; Brockmann, Carolin; Jochum, Susanne; Dietz, Tiina; Schnitzer, Andreas; Düber, Christoph; Schoenberg, Stefan O; Diehl, Steffen

    2009-12-01

    Separating bone, calcification, and vessels in computer tomography angiography (CTA) allows for a detailed diagnosis of vessel stenosis. This paper presents a new, graph-based technique that solves this difficult problem with high accuracy. The approach requires one native data set and one that is contrast enhanced. On each data set, an attributed level-graph is derived and both graphs are matched by dynamic programming to differentiate between bone, on one hand side, and vessel/calcification on the other hand side. Lumen and calcified regions are then separated by a profile technique. Evaluation is based on data from vessels of pelvis and lower extremities of elderly patients. Due to substantial calcification and motion of patients between and during the acquisitions, the underlying approach is tested on a class of difficult cases. Analysis requires 3-5 min on a Pentium IV 3 GHz for a 700 MByte data set. Among 37 patients, our approach correctly identifies all three components in 80% of cases correctly compared to visual control. Critical inconsistencies with visual inspection were found in 6% of all cases; 70% of these inconsistencies are due to small vessels that have 1) a diameter near the resolution of the CT and 2) are passing next to bony structures. All other remaining deviations are found in an incorrect handling of the iliac artery since the slice thickness is near the diameter of this vessel and since the orientation is not in cranio-caudal direction. Increasing resolution is thus expected to solve many the aforementioned difficulties. PMID:19574161

  7. Breddin's graph for tectonic regimes

    NASA Astrophysics Data System (ADS)

    Célérier, Bernard; Séranne, Michel

    2001-05-01

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

  8. Naming on a Directed Graph

    NASA Astrophysics Data System (ADS)

    Gosti, Giorgio; Batchelder, William H.

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

  9. The alignment-distribution graph

    NASA Technical Reports Server (NTRS)

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

    1993-01-01

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

  10. The alignment-distribution graph

    NASA Technical Reports Server (NTRS)

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

    1993-01-01

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

  11. On designing heteroclinic networks from graphs

    NASA Astrophysics Data System (ADS)

    Ashwin, Peter; Postlethwaite, Claire

    2013-12-01

    Robust heteroclinic networks are invariant sets that can appear as attractors in symmetrically coupled or otherwise constrained dynamical systems. These networks may have a complicated structure determined to a large extent by the constraints and dimension of the system. As these networks are of great interest as dynamical models of biological and cognitive processes, it is useful to understand how particular directed graphs can be realised as attracting robust heteroclinic networks between states in phase space. This paper presents two methods of realising arbitrarily complex directed graphs as robust heteroclinic networks for flows generated by ODEs-we say the ODEs realise the graphs as heteroclinic networks between equilibria that represent the vertices. Suppose we have a directed graph on nv vertices with ne edges. The “simplex realisation” embeds the graph as an invariant set of a flow on an (nv-1)-simplex. This method realises the graph as long as it is one- and two-cycle free. The “cylinder realisation” embeds a graph as an invariant set of a flow on a (ne+1)-dimensional space. This method realises the graph as long as it is one-cycle free. In both cases we realise the graph as an invariant set within an attractor, and discuss some illustrative examples, including the influence of noise and parameters on the dynamics. In particular we show that the resulting heteroclinic network may or may not display “memory” of the vertices visited.

  12. Evolutionary Games of Multiplayer Cooperation on Graphs

    PubMed Central

    Arranz, Jordi; Traulsen, Arne

    2016-01-01

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

  13. Evolutionary Games of Multiplayer Cooperation on Graphs.

    PubMed

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

    2016-08-01

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

  14. Generation of graph-state streams

    SciTech Connect

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

    2011-01-15

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

  15. Graph algorithms in the titan toolkit.

    SciTech Connect

    McLendon, William Clarence, III; Wylie, Brian Neil

    2009-10-01

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

  16. Simple scale interpolator facilitates reading of graphs

    NASA Technical Reports Server (NTRS)

    Fetterman, D. E., Jr.

    1965-01-01

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

  17. Acyclic colorings of graphs with bounded degree

    NASA Astrophysics Data System (ADS)

    Fiedorowicz, Anna; Sidorowicz, Elżbieta

    2016-07-01

    A $k$-colouring (not necessarily proper) of vertices of a graph is called {\\it acyclic}, if for every pair of distinct colours $i$ and $j$ the subgraph induced by the edges whose endpoints have colours $i$ and $j$ is acyclic. In the paper we consider some generalised acyclic $k$-colourings, namely, we require that each colour class induces an acyclic or bounded degree graph. Mainly we focus on graphs with maximum degree 5. We prove that any such graph has an acyclic $5$-colouring such that each colour class induces an acyclic graph with maximum degree at most 4. We prove that the problem of deciding whether a graph $G$ has an acyclic 2-colouring in which each colour class induces a graph with maximum degree at most 3 is NP-complete, even for graphs with maximum degree 5. We also give a linear-time algorithm for an acyclic $t$-improper colouring of any graph with maximum degree $d$ assuming that the number of colors is large enough.

  18. A Factor Graph Approach to Automated GO Annotation.

    PubMed

    Spetale, Flavio E; Tapia, Elizabeth; Krsticevic, Flavia; Roda, Fernando; Bulacio, Pilar

    2016-01-01

    As volume of genomic data grows, computational methods become essential for providing a first glimpse onto gene annotations. Automated Gene Ontology (GO) annotation methods based on hierarchical ensemble classification techniques are particularly interesting when interpretability of annotation results is a main concern. In these methods, raw GO-term predictions computed by base binary classifiers are leveraged by checking the consistency of predefined GO relationships. Both formal leveraging strategies, with main focus on annotation precision, and heuristic alternatives, with main focus on scalability issues, have been described in literature. In this contribution, a factor graph approach to the hierarchical ensemble formulation of the automated GO annotation problem is presented. In this formal framework, a core factor graph is first built based on the GO structure and then enriched to take into account the noisy nature of GO-term predictions. Hence, starting from raw GO-term predictions, an iterative message passing algorithm between nodes of the factor graph is used to compute marginal probabilities of target GO-terms. Evaluations on Saccharomyces cerevisiae, Arabidopsis thaliana and Drosophila melanogaster protein sequences from the GO Molecular Function domain showed significant improvements over competing approaches, even when protein sequences were naively characterized by their physicochemical and secondary structure properties or when loose noisy annotation datasets were considered. Based on these promising results and using Arabidopsis thaliana annotation data, we extend our approach to the identification of most promising molecular function annotations for a set of proteins of unknown function in Solanum lycopersicum. PMID:26771463

  19. Gap detection in endoscopic video sequences using graphs.

    PubMed

    Behrens, Alexander; Takami, Masato; Gross, Sebastian; Aach, Til

    2011-01-01

    In minimal invasive surgery (MIS) a complete and seamless inspection of organs, e.g. the urinary bladder, using video endoscopes is often required for diagnostics. Since the endoscope is usually guided by free-hand, it is difficult to ensure a sequence of seamless frame transitions. Also 2-D panoramic images showing an extended field of view (FOV) do not provide always reliable results, since their interpretations are limited by potentially strong geometric distortions. To overcome these limitations and provide a direct verification method, we develop a gap detection algorithm using graphs. Exploiting the motion information of the applied zig-zag scan, we construct a graph representation of the video sequence. Without any explicit global image visualization our graph search algorithm identifies reliably frame discontinuities, which would lead to holes and slit artifacts in a panoramic view. The algorithm shows high detection rates and provides a fast method to verify frame discontinuities in the whole video sequence. Missed regions are highlighted by local image compositions which can be displayed during the intervention for assistance and inspection control. PMID:22255860

  20. A Factor Graph Approach to Automated GO Annotation

    PubMed Central

    Spetale, Flavio E.; Tapia, Elizabeth; Krsticevic, Flavia; Roda, Fernando; Bulacio, Pilar

    2016-01-01

    As volume of genomic data grows, computational methods become essential for providing a first glimpse onto gene annotations. Automated Gene Ontology (GO) annotation methods based on hierarchical ensemble classification techniques are particularly interesting when interpretability of annotation results is a main concern. In these methods, raw GO-term predictions computed by base binary classifiers are leveraged by checking the consistency of predefined GO relationships. Both formal leveraging strategies, with main focus on annotation precision, and heuristic alternatives, with main focus on scalability issues, have been described in literature. In this contribution, a factor graph approach to the hierarchical ensemble formulation of the automated GO annotation problem is presented. In this formal framework, a core factor graph is first built based on the GO structure and then enriched to take into account the noisy nature of GO-term predictions. Hence, starting from raw GO-term predictions, an iterative message passing algorithm between nodes of the factor graph is used to compute marginal probabilities of target GO-terms. Evaluations on Saccharomyces cerevisiae, Arabidopsis thaliana and Drosophila melanogaster protein sequences from the GO Molecular Function domain showed significant improvements over competing approaches, even when protein sequences were naively characterized by their physicochemical and secondary structure properties or when loose noisy annotation datasets were considered. Based on these promising results and using Arabidopsis thaliana annotation data, we extend our approach to the identification of most promising molecular function annotations for a set of proteins of unknown function in Solanum lycopersicum. PMID:26771463

  1. Practicing Language Arts Skills Using Drama.

    ERIC Educational Resources Information Center

    Beutler, Suzanne A.

    This paper attempts to show a one-to-one relationship between the various activities involved in dramatic interpretation and specific language arts skills: reading, writing, speaking, and listening. The skills listed in this model reflect both the cognitive and the affective domains and include concentration, perception, factual recall,…

  2. Basic Skills in Asian Studies: India.

    ERIC Educational Resources Information Center

    Hantula, James

    Designed for an Asian studies program at the secondary level and using learning activities centering on India, the guide develops four basic skills: reading, applying critical thinking, interpreting the geography, and understanding history. Five learning activities are provided for each basic skill and each unit is introduced with a description…

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

    NASA Astrophysics Data System (ADS)

    Birrane, Edward; Burleigh, Scott; Kasch, Niels

    2012-06-01

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

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

    PubMed

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

    2010-01-01

    Graph data mining is an active research area. Graphs are general modeling tools to organize information from heterogeneous sources and have been applied in many scientific, engineering, and business fields. With the fast accumulation of graph data, building highly accurate predictive models for graph data emerges as a new challenge that has not been fully explored in the data mining community. In this paper, we demonstrate a novel technique called graph pattern diffusion (GPD) kernel. Our idea is to leverage existing frequent pattern discovery methods and to explore the application of kernel classifier (e.g., support vector machine) in building highly accurate graph classification. In our method, we first identify all frequent patterns from a graph database. We then map subgraphs to graphs in the graph database and use a process we call "pattern diffusion" to label nodes in the graphs. Finally, we designed a graph alignment algorithm to compute the inner product of two graphs. We have tested our algorithm using a number of chemical structure data. The experimental results demonstrate that our method is significantly better than competing methods such as those kernel functions based on paths, cycles, and subgraphs. PMID:20431140

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

    ERIC Educational Resources Information Center

    Xi, Xiaoming

    2010-01-01

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

  6. Feature Tracking Using Reeb Graphs

    SciTech Connect

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

    2010-08-02

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

  7. Phase unwrapping via graph cuts.

    PubMed

    Bioucas-Dias, José M; Valadão, Gonçalo

    2007-03-01

    Phase unwrapping is the inference of absolute phase from modulo-2pi phase. This paper introduces a new energy minimization framework for phase unwrapping. The considered objective functions are first-order Markov random fields. We provide an exact energy minimization algorithm, whenever the corresponding clique potentials are convex, namely for the phase unwrapping classical Lp norm, with p > or = 1. Its complexity is KT (n, 3n), where K is the length of the absolute phase domain measured in 2pi units and T (n, m) is the complexity of a max-flow computation in a graph with n nodes and m edges. For nonconvex clique potentials, often used owing to their discontinuity preserving ability, we face an NP-hard problem for which we devise an approximate solution. Both algorithms solve integer optimization problems by computing a sequence of binary optimizations, each one solved by graph cut techniques. Accordingly, we name the two algorithms PUMA, for phase unwrappping max-flow/min-cut. A set of experimental results illustrates the effectiveness of the proposed approach and its competitiveness in comparison with state-of-the-art phase unwrapping algorithms. PMID:17357730

  8. Clique percolation in random graphs.

    PubMed

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

    2015-10-01

    As a generation of the classical percolation, clique percolation focuses on the connection of cliques in a graph, where the connection of two k cliques means that they share at least lgraphs, which gives not only the exact solutions of the critical point, but also the corresponding order parameter. Based on this, we prove theoretically that the fraction ψ of cliques in the giant clique cluster always makes a continuous phase transition as the classical percolation. However, the fraction ϕ of vertices in the giant clique cluster for l>1 makes a step-function-like discontinuous phase transition in the thermodynamic limit and a continuous phase transition for l=1. More interesting, our analysis shows that at the critical point, the order parameter ϕ(c) for l>1 is neither 0 nor 1, but a constant depending on k and l. All these theoretical findings are in agreement with the simulation results, which give theoretical support and clarification for previous simulation studies of clique percolation. PMID:26565177

  9. Multithreaded Algorithms for Graph Coloring

    SciTech Connect

    Catalyurek, Umit V.; Feo, John T.; Gebremedhin, Assefaw H.; Halappanavar, Mahantesh; Pothen, Alex

    2012-10-21

    Graph algorithms are challenging to parallelize when high performance and scalability are primary goals. Low concurrency, poor data locality, irregular access pattern, and high data access to computation ratio are among the chief reasons for the challenge. The performance implication of these features is exasperated on distributed memory machines. More success is being achieved on shared-memory, multi-core architectures supporting multithreading. We consider a prototypical graph problem, coloring, and show how a greedy algorithm for solving it can be e*ectively parallelized on multithreaded architectures. We present in particular two di*erent parallel algorithms. The first relies on speculation and iteration, and is suitable for any shared-memory, multithreaded system. The second uses data ow principles and is targeted at the massively multithreaded Cray XMT system. We benchmark the algorithms on three di*erent platforms and demonstrate scalable runtime performance. In terms of quality of solution, both algorithms use nearly the same number of colors as the serial algorithm.

  10. Clique percolation in random graphs

    NASA Astrophysics Data System (ADS)

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

    2015-10-01

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

  11. Reproducibility and Robustness of Graph Measures of the Associative-Semantic Network

    PubMed Central

    Wang, Yu; Nelissen, Natalie; Adamczuk, Katarzyna; De Weer, An-Sofie; Vandenbulcke, Mathieu; Sunaert, Stefan; Vandenberghe, Rik; Dupont, Patrick

    2014-01-01

    Graph analysis is a promising tool to quantify brain connectivity. However, an essential requirement is that the graph measures are reproducible and robust. We have studied the reproducibility and robustness of various graph measures in group based and in individual binary and weighted networks derived from a task fMRI experiment during explicit associative-semantic processing of words and pictures. The nodes of the network were defined using an independent study and the connectivity was based on the partial correlation of the time series between any pair of nodes. The results showed that in case of binary networks, global graph measures exhibit a good reproducibility and robustness for networks which are not too sparse and these figures of merit depend on the graph measure and on the density of the network. Furthermore, group based binary networks should be derived from groups of sufficient size and the lower the density the more subjects are required to obtain robust values. Local graph measures are very variable in terms of reproducibility and should be interpreted with care. For weighted networks, we found good reproducibility (average test-retest variability <5% and ICC values >0.4) when using subject specific networks and this will allow us to relate network properties to individual subject information. PMID:25500823

  12. Enabling Graph Appliance for Genome Assembly

    SciTech Connect

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

    2015-01-01

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

  13. Electrocardiography: A Technologist's Guide to Interpretation.

    PubMed

    Tso, Colin; Currie, Geoffrey M; Gilmore, David; Kiat, Hosen

    2015-12-01

    The nuclear medicine technologist works with electrocardiography when performing cardiac stress testing and gated cardiac imaging and when monitoring critical patients. To enhance patient care, basic electrocardiogram interpretation skills and recognition of key arrhythmias are essential for the nuclear medicine technologist. This article provides insight into the anatomy of an electrocardiogram trace, covers basic electrocardiogram interpretation methods, and describes an example case typical in the nuclear medicine environment. PMID:26471331

  14. Strategic leadership: the essential skills.

    PubMed

    Schoemaker, Paul J H; Krupp, Steve; Howland, Samantha

    2013-01-01

    The more uncertain your environment, the greater the opportunity--if you have the leadership skills to capitalize on it. Research at the Wharton school and at the authors' consulting firm, involving more than 20,000 executives to date, has identified six skills that, when mastered and used in concert, allow leaders to think strategically and navigate the unknown effectively. They are the abilities to anticipate, challenge, interpret, decide, align, and learn. This article describes the six skills in detail and includes a self-assessment that will enable you to identify the ones that most need your attention. The authors have found that strength in one skill cannot easily compensate for a deficit in another. An adaptive strategic leader has learned to apply all six at once. PMID:23390746

  15. Feynman graph generation and calculations in the Hopf algebra of Feynman graphs

    NASA Astrophysics Data System (ADS)

    Borinsky, Michael

    2014-12-01

    Two programs for the computation of perturbative expansions of quantum field theory amplitudes are provided. feyngen can be used to generate Feynman graphs for Yang-Mills, QED and φk theories. Using dedicated graph theoretic tools feyngen can generate graphs of comparatively high loop orders. feyncop implements the Hopf algebra of those Feynman graphs which incorporates the renormalization procedure necessary to calculate finite results in perturbation theory of the underlying quantum field theory. feyngen is validated by comparison to explicit calculations of zero dimensional quantum field theories and feyncop is validated using a combinatorial identity on the Hopf algebra of graphs.

  16. Stereo Vision By Pyramidal Bli Graph Matching

    NASA Astrophysics Data System (ADS)

    Shen, Jun; Castan, Serge; Zhao, Jian

    1988-04-01

    We propose the pyramidal BLI (Binary Laplacian Image) graph matching method for stereo vision, which uses the local as well as the global similarities to assure a good precision of matching results and to eliminate the ambiguities. Because the BLI is detected by DRF method which has a fast realization and matching between graphs is fast, a pseudo-real time system is possible.

  17. This Is Us! Great Graphs for Kids.

    ERIC Educational Resources Information Center

    Sullivan, Delia; O'Neil, Mary Ann

    1980-01-01

    Described are graphing activities which can be instrumental in introducing the mathematics concepts of counting, sorting, grouping, and comparing on the primary level. On the intermediate level, these activites can be used to introduce collecting and sorting unorganized data, and creating graphs to represent the data. (Author/TG)

  18. TI-83 Graphing Calculator Keystroke Guide.

    ERIC Educational Resources Information Center

    Panik, Cathy

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

  19. Generative Graph Prototypes from Information Theory.

    PubMed

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

    2015-10-01

    In this paper we present a method for constructing a generative prototype for a set of graphs by adopting a minimum description length approach. The method is posed in terms of learning a generative supergraph model from which the new samples can be obtained by an appropriate sampling mechanism. We commence by constructing a probability distribution for the occurrence of nodes and edges over the supergraph. We encode the complexity of the supergraph using an approximate Von Neumann entropy. A variant of the EM algorithm is developed to minimize the description length criterion in which the structure of the supergraph and the node correspondences between the sample graphs and the supergraph are treated as missing data. To generate new graphs, we assume that the nodes and edges of graphs arise under independent Bernoulli distributions and sample new graphs according to their node and edge occurrence probabilities. Empirical evaluations on real-world databases demonstrate the practical utility of the proposed algorithm and show the effectiveness of the generative model for the tasks of graph classification, graph clustering and generating new sample graphs. PMID:26340255

  20. Multi-A Graph Patrolling and Partitioning

    NASA Astrophysics Data System (ADS)

    Elor, Y.; Bruckstein, A. M.

    2012-12-01

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

  1. Using a Microcomputer for Graphing Practice.

    ERIC Educational Resources Information Center

    Beichner, Robert J.

    1986-01-01

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

  2. Qualitative Graphing: A Construction in Mathematics.

    ERIC Educational Resources Information Center

    Narode, Ronald

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

  3. Graph Coloring Used to Model Traffic Lights.

    ERIC Educational Resources Information Center

    Williams, John

    1992-01-01

    Two scheduling problems, one involving setting up an examination schedule and the other describing traffic light problems, are modeled as colorings of graphs consisting of a set of vertices and edges. The chromatic number, the least number of colors necessary for coloring a graph, is employed in the solutions. (MDH)

  4. Cognitive Aids for Guiding Graph Comprehension

    ERIC Educational Resources Information Center

    Mautone, Patricia D.; Mayer, Richard E.

    2007-01-01

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

  5. A Ring Construction Using Finite Directed Graphs

    ERIC Educational Resources Information Center

    Bardzell, Michael

    2012-01-01

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

  6. Critiquing the Culture of Computer Graphing Practices.

    ERIC Educational Resources Information Center

    Brasseur, Lee

    2001-01-01

    Argues that current approaches to computer graphing practices are ill suited to meet the complex needs of real users. Offers an overview of work in two major areas of graphing theory and research: the sociology of science and the educational research of mathematics and scientific students. Suggests what technical communicators can do to improve…

  7. Developing Data Graph Comprehension. Third Edition

    ERIC Educational Resources Information Center

    Curcio, Frances

    2010-01-01

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

  8. Pattern vectors from algebraic graph theory.

    PubMed

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

    2005-07-01

    Graph structures have proven computationally cumbersome for pattern analysis. The reason for this is that, before graphs can be converted to pattern vectors, correspondences must be established between the nodes of structures which are potentially of different size. To overcome this problem, in this paper, we turn to the spectral decomposition of the Laplacian matrix. We show how the elements of the spectral matrix for the Laplacian can be used to construct symmetric polynomials that are permutation invariants. The coefficients of these polynomials can be used as graph features which can be encoded in a vectorial manner. We extend this representation to graphs in which there are unary attributes on the nodes and binary attributes on the edges by using the spectral decomposition of a Hermitian property matrix that can be viewed as a complex analogue of the Laplacian. To embed the graphs in a pattern space, we explore whether the vectors of invariants can be embedded in a low-dimensional space using a number of alternative strategies, including principal components analysis (PCA), multidimensional scaling (MDS), and locality preserving projection (LPP). Experimentally, we demonstrate that the embeddings result in well-defined graph clusters. Our experiments with the spectral representation involve both synthetic and real-world data. The experiments with synthetic data demonstrate that the distances between spectral feature vectors can be used to discriminate between graphs on the basis of their structure. The real-world experiments show that the method can be used to locate clusters of graphs. PMID:16013758

  9. ON CLUSTERING TECHNIQUES OF CITATION GRAPHS.

    ERIC Educational Resources Information Center

    CHIEN, R.T.; PREPARATA, F.P.

    ONE OF THE PROBLEMS ENCOUNTERED IN CLUSTERING TECHNIQUES AS APPLIED TO DOCUMENT RETRIEVAL SYSTEMS USING BIBLIOGRAPHIC COUPLING DEVICES IS THAT THE COMPUTATIONAL EFFORT REQUIRED GROWS ROUGHLY AS THE SQUARE OF THE COLLECTION SIZE. IN THIS STUDY GRAPH THEORY IS APPLIED TO THIS PROBLEM BY FIRST MAPPING THE CITATION GRAPH OF THE DOCUMENT COLLECTION…

  10. Attitudes towards Graphing Calculators in Developmental Mathematics

    ERIC Educational Resources Information Center

    Rajan, Shaun Thomas

    2013-01-01

    The purpose of this exploratory study was to examine instructor and student attitudes towards the use of the graphing calculator in the developmental mathematics classroom. A focus of the study was to see if instructors or students believed there were changes in the conceptual understanding of mathematics as a result of graphing calculator…

  11. Teaching Discrete Mathematics with Graphing Calculators.

    ERIC Educational Resources Information Center

    Masat, Francis E.

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

  12. Coping Skills.

    ERIC Educational Resources Information Center

    Library of Congress, Washington, DC. National Library Service for the Blind and Physically Handicapped.

    This annotated bibliography lists approximately 150 braille books and 300 audiocassettes of books which address coping skills for people in a variety of situations. All items listed are available in the network library collections provided by the National Library Service for the Blind and Physically Handicapped of the Library of Congress.…

  13. Skill Standards.

    ERIC Educational Resources Information Center

    Glover, Robert W.

    1992-01-01

    Industry-based skill assessment and certification should (1) be independent of training providers; (2) use variety of instruments; (3) recognize multiple levels of mastery; (4) promote broad training and continuous learning; (5) be geared to high-performance work organizations; (6) be voluntary; and (7) be flexible to keep pace with technology.…

  14. Sharing Skills.

    ERIC Educational Resources Information Center

    Thompson, Verna; And Others

    1994-01-01

    Provides three activities that help develop library skills for elementary school students. One describes a riddle card game that reviews research book terms; one explains a book report activity; and one focuses on cooperative problem-solving activities to find titles by favorite authors. (LRW)

  15. Skills Center.

    ERIC Educational Resources Information Center

    Canter, Patricia; And Others

    The services of the Living Skills Center for the Visually Handicapped, a habilitative service for blind young adults, are described. It is explained that the Center houses its participants in their own apartments in a large complex and has served over 70 young people in 4 years. The evaluation section describes such assessment instruments as an…

  16. On linear area embedding of planar graphs

    NASA Astrophysics Data System (ADS)

    Dolev, D.; Trickey, H.

    1981-09-01

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

  17. Quantum graphs and random-matrix theory

    NASA Astrophysics Data System (ADS)

    Pluhař, Z.; Weidenmüller, H. A.

    2015-07-01

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

  18. Vortices and superfields on a graph

    SciTech Connect

    Kan, Nahomi; Kobayashi, Koichiro; Shiraishi, Kiyoshi

    2009-08-15

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

  19. Vortices and superfields on a graph

    NASA Astrophysics Data System (ADS)

    Kan, Nahomi; Kobayashi, Koichiro; Shiraishi, Kiyoshi

    2009-08-01

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

  20. Graph Mining Meets the Semantic Web

    SciTech Connect

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

    2015-01-01

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

  1. Structure and strategy in encoding simplified graphs

    NASA Technical Reports Server (NTRS)

    Schiano, Diane J.; Tversky, Barbara

    1992-01-01

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

  2. Quantum walk search on Johnson graphs

    NASA Astrophysics Data System (ADS)

    Wong, Thomas G.

    2016-05-01

    The Johnson graph J(n,k) is defined by n symbols, where vertices are k-element subsets of the symbols, and vertices are adjacent if they differ in exactly one symbol. In particular, J(n,1) is the complete graph K n , and J(n,2) is the strongly regular triangular graph T n , both of which are known to support fast spatial search by continuous-time quantum walk. In this paper, we prove that J(n,3), which is the n-tetrahedral graph, also supports fast search. In the process, we show that a change of basis is needed for degenerate perturbation theory to accurately describe the dynamics. This method can also be applied to general Johnson graphs J(n,k) with fixed k.

  3. Weibull probability graph paper: a call for standardization

    NASA Astrophysics Data System (ADS)

    Kane, Martin D.

    2001-04-01

    Weibull analysis of tensile strength data is routinely performed to determine the quality of optical fiber. A typical Weibull analysis includes setting up an experiment, testing the samples, plotting and interpreting the data, and performing a statistical analysis. One typical plot that is often included in the analysis is the Weibull probability plot in which the data are plotted as points on a special type of graph paper known as Weibull probability paper. If the data belong to a Weibull probability density function, they will fall approximately on a straight line. A search of the literature reveals that many Weibull analyses have been performed on optical fiber, but the associated Weibull probability plots have been drawn incorrectly. In some instances the plots have been shown with the ordinate (Probability) starting from 0% and ending at 100%. This has no physical meaning because the Weibull probability density function is a continuous distribution and is inherently not bounded. This paper will discuss the Weibull probability density function, the proper construction of Weibull probability graph paper, and interpretation of data through analysis of the associated probability plot.

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

    SciTech Connect

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

    2015-09-30

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

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

    SciTech Connect

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

    2015-11-15

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

  6. What's It All About? A Manual for Basic Skills Workshop.

    ERIC Educational Resources Information Center

    Johnson, Willis N.; And Others

    Presented is a collection of materials developed and used with teachers in western Kentucky in workshops on the teaching of basic skills. The material is particularly concerned with methods teachers can use to provide motivation for students to learn and enjoy mathematics. Included are activities for problem solving, graphing, addition,…

  7. Developing Science Process Skills in Special Schools in South Africa.

    ERIC Educational Resources Information Center

    Johnson, Sally; Sadeck, Melanie; Hodges, Merle

    2002-01-01

    Teachers were taught "Translation Activities" (TA) to teach science process skills in three special education schools in South Africa. In TA, information and data are provided as text, diagrams, tables, or graphs, and cooperative learning takes place. Teachers indicated the use of TA enabled them to deliver Outcomes Based Education. (Contains…

  8. A First-Year Course That Teaches Research Skills

    ERIC Educational Resources Information Center

    Czarneski, Debra

    2013-01-01

    In the Fall semester of 2009, I taught a first-year course that focused on skills required to successfully complete undergraduate research. This paper will discuss the Simpson College first-year course requirements, my course goals, the graph theory topics covered, student feedback, and instructor reflection.

  9. The Effect of Graphing Calculators on Student Achievement in College Algebra and Pre-Calculus Mathematics Courses

    ERIC Educational Resources Information Center

    Hatem, Neil

    2010-01-01

    This study investigates the relationship between the use of graphing calculators employed as Type II technology and student achievement, as determined by assessing students' problem solving skills associated with the concept of function, at the college algebra and pre-calculus level. In addition, this study explores the integration of graphing…

  10. Fieldcrest Cannon, Inc. Advanced Technical Preparation. Statistical Process Control (SPC). PRE-SPC 11: SPC & Graphs. Instructor Book.

    ERIC Educational Resources Information Center

    Averitt, Sallie D.

    This instructor guide, which was developed for use in a manufacturing firm's advanced technical preparation program, contains the materials required to present a learning module that is designed to prepare trainees for the program's statistical process control module by improving their basic math skills in working with line graphs and teaching…

  11. Join-Graph Propagation Algorithms

    PubMed Central

    Mateescu, Robert; Kask, Kalev; Gogate, Vibhav; Dechter, Rina

    2010-01-01

    The paper investigates parameterized approximate message-passing schemes that are based on bounded inference and are inspired by Pearl's belief propagation algorithm (BP). We start with the bounded inference mini-clustering algorithm and then move to the iterative scheme called Iterative Join-Graph Propagation (IJGP), that combines both iteration and bounded inference. Algorithm IJGP belongs to the class of Generalized Belief Propagation algorithms, a framework that allowed connections with approximate algorithms from statistical physics and is shown empirically to surpass the performance of mini-clustering and belief propagation, as well as a number of other state-of-the-art algorithms on several classes of networks. We also provide insight into the accuracy of iterative BP and IJGP by relating these algorithms to well known classes of constraint propagation schemes. PMID:20740057

  12. Balanced Paths in Colored Graphs

    NASA Astrophysics Data System (ADS)

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

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

  13. Relativity on rotated graph paper

    NASA Astrophysics Data System (ADS)

    Salgado, Roberto B.

    2016-05-01

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

  14. Degree distribution and assortativity in line graphs of complex networks

    NASA Astrophysics Data System (ADS)

    Wang, Xiangrong; Trajanovski, Stojan; Kooij, Robert E.; Van Mieghem, Piet

    2016-03-01

    Topological characteristics of links of complex networks influence the dynamical processes executed on networks triggered by links, such as cascading failures triggered by links in power grids and epidemic spread due to link infection. The line graph transforms links in the original graph into nodes. In this paper, we investigate how graph metrics in the original graph are mapped into those for its line graph. In particular, we study the degree distribution and the assortativity of a graph and its line graph. Specifically, we show, both analytically and numerically, the degree distribution of the line graph of an Erdős-Rényi graph follows the same distribution as its original graph. We derive a formula for the assortativity of line graphs and indicate that the assortativity of a line graph is not linearly related to its original graph. Additionally, line graphs of various graphs, e.g. Erdős-Rényi graphs, scale-free graphs, show positive assortativity. In contrast, we find certain types of trees and non-trees whose line graphs have negative assortativity.

  15. Infants Interpret Ambiguous Requests for Absent Objects

    ERIC Educational Resources Information Center

    Saylor, Megan M.; Ganea, Patricia

    2007-01-01

    The current studies investigated 2 skills involved in 14- to 20-month-olds' ability to interpret ambiguous requests for absent objects: tracking others' experiences (Study 1) and representing links between speakers and object features across present and absent reference episodes (Study 2). In the basic task, 2 experimenters played separately with…

  16. Interpretive Management: What General Managers Can Learn from Design.

    ERIC Educational Resources Information Center

    Lester, Richard K.; Piore, Michael J.; Malek, Kamal M.

    1998-01-01

    An analytical management approach reflects a traditional perspective and an interpretive approach involves a perspective suited to rapidly changing, unpredictable markets. Both approaches are valid, but each serves different purposes and calls for different strategies and skills. (JOW)

  17. Approximate von Neumann entropy for directed graphs.

    PubMed

    Ye, Cheng; Wilson, Richard C; Comin, César H; Costa, Luciano da F; Hancock, Edwin R

    2014-05-01

    In this paper, we develop an entropy measure for assessing the structural complexity of directed graphs. Although there are many existing alternative measures for quantifying the structural properties of undirected graphs, there are relatively few corresponding measures for directed graphs. To fill this gap in the literature, we explore an alternative technique that is applicable to directed graphs. We commence by using Chung's generalization of the Laplacian of a directed graph to extend the computation of von Neumann entropy from undirected to directed graphs. We provide a simplified form of the entropy which can be expressed in terms of simple node in-degree and out-degree statistics. Moreover, we find approximate forms of the von Neumann entropy that apply to both weakly and strongly directed graphs, and that can be used to characterize network structure. We illustrate the usefulness of these simplified entropy forms defined in this paper on both artificial and real-world data sets, including structures from protein databases and high energy physics theory citation networks. PMID:25353841

  18. Graph isomorphism and adiabatic quantum computing

    NASA Astrophysics Data System (ADS)

    Gaitan, Frank; Clark, Lane

    2014-03-01

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

  19. Object Discovery: Soft Attributed Graph Mining.

    PubMed

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

    2016-03-01

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

  20. Partitioning sparse matrices with eigenvectors of graphs

    NASA Technical Reports Server (NTRS)

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

    1990-01-01

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

  1. Massive graph visualization : LDRD final report.

    SciTech Connect

    Wylie, Brian Neil; Moreland, Kenneth D.

    2007-10-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2016-05-01

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

  3. BioGraphE: High-performance bionetwork analysis using the Biological Graph Environment

    SciTech Connect

    Chin, George; Chavarría-Miranda, Daniel; Nakamura, Grant C.; Sofia, Heidi J.

    2008-05-28

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

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

    DOE PAGESBeta

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

    2016-01-01

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

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

    SciTech Connect

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

    2016-01-01

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

  6. Encoding the core electrons with graph concepts.

    PubMed

    Pogliani, Lionello

    2004-01-01

    The core electron problem of atoms in chemical graph studies has always been considered as a minor problem. Usually, chemical graphs had to encode just a small set of second row atoms, i.e., C, N, O, and F, thus, graph and, in some cases, pseudograph concepts were enough to "graph" encode the molecules at hand. Molecular connectivity theory, together with its side-branch the electrotopological state, introduced two "ad hoc" algorithms for the core electrons of higher-row atoms based, mainly, on quantum concepts alike. Recently, complete graphs, and, especially, odd complete graphs have been introduced to encode the core electrons of higher-row atoms. By the aid of these types of graphs a double-valued algorithm has been proposed for the valence delta, deltav, of any type of atoms of the periodic table with a principal quantum number n > or =2. The new algorithm is centered on an invariant suggested by the hand-shaking theorem, and the values it gives rise to parallel in some way the values derived by the aid of the two old "quantum" algorithms. A thorough comparative analysis of the newly proposed algorithms has been undertaken for atoms of the group 1A-7A of the periodic table. This comparative study includes the electronegativity, the size of the atoms, the first ionization energy, and the electron affinity. The given algorithm has also been tested with sequential complete graphs, while the even complete graphs give rise to conceptual difficulties. QSAR/QSPR studies do not show a clear-cut preference for any of the two values the algorithm gives rise to, even if recent results seem to prefer one of the two values. PMID:14741009

  7. The Turc-Budyko adimensional graphs as a tool for consistency assessment

    NASA Astrophysics Data System (ADS)

    Andréassian, Vazken; Perrin, Charles; Coron, Laurent; Le Moine, Nicolas

    2015-04-01

    This poster discusses the Turc-Budyko nondimensional graph, a widely used nondimensional representation relating long-term actual evaporation to precipitation and potential evaporation as a tool for assessing the consistency of catchment water balance. We present examples showing both the classical use of the graph (based on long-term averages, see Andréassian and Perrin, 2012) but also a newer use involving dated annual values, which allows to check the consistency of individual years (see Coron et al., 2015). References Andréassian, V., and C. Perrin (2012), On the ambiguous interpretation of the Turc-Budyko nondimensional graph, Water Resour. Res., 48, W10601, doi:10.1029/2012WR012532. Coron, L., V. Andréassian, C. Perrin & N. Le Moine. 2015. Graphical tools based on Turc-Budyko plots to detect changes in catchment behaviour. Hydrological Sciences Journal, doi: 10.1080/02626667.2014.964245

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

    NASA Astrophysics Data System (ADS)

    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

  9. Scale-invariant geometric random graphs

    NASA Astrophysics Data System (ADS)

    Xie, Zheng; Rogers, Tim

    2016-03-01

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

  10. Line graphs for a multiplex network.

    PubMed

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

    2016-06-01

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

  11. A heterogeneous graph-based recommendation simulator

    SciTech Connect

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

    2013-01-01

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

  12. Intelligent Graph Layout Using Many Users' Input.

    PubMed

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

    2012-12-01

    In this paper, we propose a new strategy for graph drawing utilizing layouts of many sub-graphs supplied by a large group of people in a crowd sourcing manner. We developed an algorithm based on Laplacian constrained distance embedding to merge subgraphs submitted by different users, while attempting to maintain the topological information of the individual input layouts. To facilitate collection of layouts from many people, a light-weight interactive system has been designed to enable convenient dynamic viewing, modification and traversing between layouts. Compared with other existing graph layout algorithms, our approach can achieve more aesthetic and meaningful layouts with high user preference. PMID:26357179

  13. Spectral statistics of nearly unidirectional quantum graphs

    NASA Astrophysics Data System (ADS)

    Akila, Maram; Gutkin, Boris

    2015-08-01

    The energy levels of a quantum graph with time reversal symmetry and unidirectional classical dynamics are doubly degenerate and obey the spectral statistics of the Gaussian unitary ensemble. These degeneracies, however, are lifted when the unidirectionality is broken in one of the graph’s vertices by a singular perturbation. Based on a random matrix model we derive an analytic expression for the nearest neighbour distribution between energy levels of such systems. As we demonstrate the result agrees excellently with the actual statistics for graphs with a uniform distribution of eigenfunctions. Yet, it exhibits quite substantial deviations for classes of graphs which show strong scarring.

  14. The MultiThreaded Graph Library (MTGL)

    SciTech Connect

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

    2008-07-17

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

  15. Coloring random graphs and maximizing local diversity.

    PubMed

    Bounkong, S; van Mourik, J; Saad, D

    2006-11-01

    We study a variation of the graph coloring problem on random graphs of finite average connectivity. Given the number of colors, we aim to maximize the number of different colors at neighboring vertices (i.e., one edge distance) of any vertex. Two efficient algorithms, belief propagation and Walksat, are adapted to carry out this task. We present experimental results based on two types of random graphs for different system sizes and identify the critical value of the connectivity for the algorithms to find a perfect solution. The problem and the suggested algorithms have practical relevance since various applications, such as distributed storage, can be mapped onto this problem. PMID:17280022

  16. Loops in Reeb Graphs of 2-Manifolds

    SciTech Connect

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

    2004-12-16

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

  17. Loops in Reeb Graphs of 2-Manifolds

    SciTech Connect

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

    2003-02-11

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

  18. Finite Frames and Graph Theoretic Uncertainty Principles

    NASA Astrophysics Data System (ADS)

    Koprowski, Paul J.

    The subject of analytical uncertainty principles is an important field within harmonic analysis, quantum physics, and electrical engineering. We explore uncertainty principles in the context of the graph Fourier transform, and we prove additive results analogous to the multiplicative version of the classical uncertainty principle. We establish additive uncertainty principles for finite Parseval frames. Lastly, we examine the feasibility region of simultaneous values of the norms of a graph differential operator acting on a function f ∈ l2(G) and its graph Fourier transform.

  19. Line graphs for a multiplex network

    NASA Astrophysics Data System (ADS)

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

    2016-06-01

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

  20. Speculation and Historical Interpretation for Fifth and Sixth Graders.

    ERIC Educational Resources Information Center

    Schneider, Elizabeth; Gregory, Leslie A.

    2000-01-01

    Describes a unit for fifth- and sixth-grade students that helps develop critical thinking skills. Explains that students read the book, "Leonardo da Vinci" (Diane Stanley), to develop their historical interpretation skills and demonstrate that there is not just one right answer in history. (CMK)

  1. Practical skills of the future innovator

    NASA Astrophysics Data System (ADS)

    Kaurov, Vitaliy

    2015-03-01

    Physics graduates face and often are disoriented by the complex and turbulent world of startups, incubators, emergent technologies, big data, social network engineering, and so on. In order to build the curricula that foster the skills necessary to navigate this world, we will look at the experiences at the Wolfram Science Summer School that gathers annually international students for already more than a decade. We will look at the examples of projects and see the development of such skills as innovative thinking, data mining, machine learning, cloud technologies, device connectivity and the Internet of things, network analytics, geo-information systems, formalized computable knowledge, and the adjacent applied research skills from graph theory to image processing and beyond. This should give solid ideas to educators who will build standard curricula adapted for innovation and entrepreneurship education.

  2. Library Technician Skill Standards.

    ERIC Educational Resources Information Center

    Highline Community Coll., Des Moines, WA.

    This document presents skill standards for library technicians. Introductory sections describe the industry and the job, what skill standards are, how the library technician skill standards were developed, employability skills and critical competencies, and the SCANS (Secretary's Commission on Achieving Necessary Skills) foundation skills profile.…

  3. Basic visual observation skills training course: Appendix A. Final report

    SciTech Connect

    Toquam, J.L.; Morris, F.A.; Griggs, J.R.

    1995-06-01

    The purpose of the basic visual observation skills course is to help safeguards inspectors evaluate and improve their skills in making observations during inspections and in evaluating and interpreting this information. The first 12 hours of the course provide training in five skill areas: perception and recognition; attention to detail; memory; mental imaging, mapping, and modeling skills; and judgment and decision making. Following this training is an integrating exercise involving a simulated safeguards inspection. This report contains the course manual and materials.

  4. Data graphs and mechanistic explanation.

    PubMed

    Burnston, Daniel C

    2016-06-01

    It is a widespread assumption in philosophy of science that representations of data are not explanatory-that they are mere stepping stones towards an explanation, such as a representation of a mechanism. I draw on instances of representational and explanatory practice from mammalian chronobiology to suggest that this assumption is unsustainable. In many instances, biologists employ representations of data in explanatory ways that are not reducible to constraints on or evidence for representations of mechanisms. Data graphs are used to represent relationships between quantities across conditions, and often these representations are necessary for explaining particular aspects of the phenomena under study. The benefit of the analysis is two-fold. First, it provides a more accurate account of explanatory practice in broadly mechanistic investigation in biology. Second, it suggests that there is not an explanatorily "fundamental" type of representation in biology. Rather, the practice of explanation consists in the construction of different types of representations and their employment for distinct explanatory purposes. PMID:26871740

  5. Fast Robust PCA on Graphs

    NASA Astrophysics Data System (ADS)

    Shahid, Nauman; Perraudin, Nathanael; Kalofolias, Vassilis; Puy, Gilles; Vandergheynst, Pierre

    2016-06-01

    Mining useful clusters from high dimensional data has received significant attention of the computer vision and pattern recognition community in the recent years. Linear and non-linear dimensionality reduction has played an important role to overcome the curse of dimensionality. However, often such methods are accompanied with three different problems: high computational complexity (usually associated with the nuclear norm minimization), non-convexity (for matrix factorization methods) and susceptibility to gross corruptions in the data. In this paper we propose a principal component analysis (PCA) based solution that overcomes these three issues and approximates a low-rank recovery method for high dimensional datasets. We target the low-rank recovery by enforcing two types of graph smoothness assumptions, one on the data samples and the other on the features by designing a convex optimization problem. The resulting algorithm is fast, efficient and scalable for huge datasets with O(nlog(n)) computational complexity in the number of data samples. It is also robust to gross corruptions in the dataset as well as to the model parameters. Clustering experiments on 7 benchmark datasets with different types of corruptions and background separation experiments on 3 video datasets show that our proposed model outperforms 10 state-of-the-art dimensionality reduction models. Our theoretical analysis proves that the proposed model is able to recover approximate low-rank representations with a bounded error for clusterable data.

  6. Leadership skills?

    PubMed

    2016-09-01

    Senior executive leaders might be interested in applying for the NHS Leadership Academy's director programme, which is designed to 'stretch and challenge' those with an 'existing level of complex leadership skills'. The programme also offers an opportunity for participants to work with other leaders and other parts of the system to enhance inclusiveness. There are three cohorts a year, and the programme runs for a 12 months. Closing dates for applicants are 4 September 2016, 22 January 2017 and 21 May 2017. PMID:27581902

  7. Trivalent Graphs, Volume Conjectures and Character Varieties

    NASA Astrophysics Data System (ADS)

    Nawata, Satoshi; Pichai, Ramadevi; Zodinmawia

    2014-10-01

    The generalized volume conjecture and the AJ conjecture (a.k.a. the quantum volume conjecture) are extended to colored quantum invariants of the theta and tetrahedron graph. The character variety of the fundamental group of the complement of a trivalent graph with E edges in S 3 is a Lagrangian subvariety of the Hitchin moduli space over the Riemann surface of genus g = E/3 + 1. For the theta and tetrahedron graph, we conjecture that the configuration of the character variety is locally determined by large color asymptotics of the quantum invariants of the trivalent graph in terms of complex Fenchel-Nielsen coordinates. Moreover, the q-holonomic difference equation of the quantum invariants provides the quantization of the character variety.

  8. Bipartite graph partitioning and data clustering

    SciTech Connect

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

    2001-05-07

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

  9. Experiments on parallel graph coloring and applications

    SciTech Connect

    Lewandowski, G.; Condon, A.

    1994-12-31

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

  10. An Investigation of the Coauthor Graph.

    ERIC Educational Resources Information Center

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

    1987-01-01

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

  11. Bipartite Graphs of Large Clique-Width

    NASA Astrophysics Data System (ADS)

    Korpelainen, Nicholas; Lozin, Vadim V.

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

  12. Graph Theory and the High School Student.

    ERIC Educational Resources Information Center

    Chartrand, Gary; Wall, Curtiss E.

    1980-01-01

    Graph theory is presented as a tool to instruct high school mathematics students. A variety of real world problems can be modeled which help students recognize the importance and difficulty of applying mathematics. (MP)

  13. Graph500 in OpenSHMEM

    SciTech Connect

    D'Azevedo, Ed F; Imam, Neena

    2015-01-01

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

  14. Fault-tolerant dynamic task graph scheduling

    SciTech Connect

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

    2014-11-16

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

  15. Exploring Hill Ciphers with Graphing Calculators.

    ERIC Educational Resources Information Center

    St. John, Dennis

    1998-01-01

    Explains how to code and decode messages using Hill ciphers which combine matrix multiplication and modular arithmetic. Discusses how a graphing calculator can facilitate the matrix and modular arithmetic used in the coding and decoding procedures. (ASK)

  16. Note on resolution, connection graphs, and subsumption

    SciTech Connect

    De Champeaux, D.

    1982-07-01

    Completeness is endangered by the combination in connection graph of subsumption deletion rules and the run time pure literal rule. With some care completeness can be restored. How this can be achieved is briefly discussed. 3 references.

  17. Unimodular lattice triangulations as small-world and scale-free random graphs

    NASA Astrophysics Data System (ADS)

    Krüger, B.; Schmidt, E. M.; Mecke, K.

    2015-02-01

    Real-world networks, e.g., the social relations or world-wide-web graphs, exhibit both small-world and scale-free behaviour. We interpret lattice triangulations as planar graphs by identifying triangulation vertices with graph nodes and one-dimensional simplices with edges. Since these triangulations are ergodic with respect to a certain Pachner flip, applying different Monte Carlo simulations enables us to calculate average properties of random triangulations, as well as canonical ensemble averages, using an energy functional that is approximately the variance of the degree distribution. All considered triangulations have clustering coefficients comparable with real-world graphs; for the canonical ensemble there are inverse temperatures with small shortest path length independent of system size. Tuning the inverse temperature to a quasi-critical value leads to an indication of scale-free behaviour for degrees k≥slant 5. Using triangulations as a random graph model can improve the understanding of real-world networks, especially if the actual distance of the embedded nodes becomes important.

  18. Pre-Service Elementary Teachers' Understandings of Graphs

    ERIC Educational Resources Information Center

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

    2011-01-01

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

  19. Continuous Time Group Discovery in Dynamic Graphs

    SciTech Connect

    Miller, K; Eliassi-Rad, T

    2010-11-04

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

  20. Illinois Occupational Skill Standards: Machining Skills Cluster.

    ERIC Educational Resources Information Center

    Illinois Occupational Skill Standards and Credentialing Council, Carbondale.

    This document of skill standards for the machining skills cluster serves as a guide to workforce preparation program providers in defining content for their programs and to employers to establish the skills and standards necessary for job acquisition. These 67 occupational skill standards describe what people should know and be able to do in an…

  1. Accelerating semantic graph databases on commodity clusters

    SciTech Connect

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

    2013-10-06

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

  2. On the Kirchhoff Index of Graphs

    NASA Astrophysics Data System (ADS)

    Das, Kinkar C.

    2013-09-01

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

  3. Inverse scattering problem for quantum graph vertices

    SciTech Connect

    Cheon, Taksu; Turek, Ondrej; Exner, Pavel

    2011-06-15

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

  4. A software tool for dataflow graph scheduling

    NASA Technical Reports Server (NTRS)

    Jones, Robert L., III

    1994-01-01

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

  5. Program for Generating Graphs and Charts

    NASA Technical Reports Server (NTRS)

    Ackerson, C. T.

    1986-01-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2016-02-01

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

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

    NASA Technical Reports Server (NTRS)

    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.

  8. Graph representation of protein free energy landscape

    SciTech Connect

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

    2013-11-14

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

  9. Identifying student difficulties with basic scientific reasoning skills: An example from control of variables

    NASA Astrophysics Data System (ADS)

    Boudreaux, Andrew

    2006-05-01

    Current national and local standards for the science learning of K-12 students emphasize both basic concepts (such as density) and fundamental reasoning skills (such as proportional reasoning, the interpretation of graphs, and the use of control of variables). At Western Washington University (WWU) and the University of Washington (UW), an effort is underway to examine the ability of university students to apply these same concepts and skills. Populations include students in liberal arts physics courses, introductory calculus-based physics courses, and special courses for the preparation of teachers. One focus of the research has been on the idea of control of variables. This topic is studied by students at all levels, from the primary grades, in which the notion of a ``fair test,'' is sometimes used, to university courses. This talk will discuss research tasks in which students are expected to infer from experimental data whether a particular variable influences (i.e., affects) or by itself determines (i.e., predicts) a given result. Student responses will be presented to identify specific difficulties.

  10. Bipartite separability and nonlocal quantum operations on graphs

    NASA Astrophysics Data System (ADS)

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

    2016-07-01

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

  11. A Graph Based Methodology for Temporal Signature Identification from EHR

    PubMed Central

    Wang, Fei; Liu, Chuanren; Wang, Yajuan; Hu, Jianying; Yu, Guoqiang

    2015-01-01

    Data driven technology is believed to be a promising technique for transforming the current status of healthcare. Electronic Health Records (EHR) is one of the main carriers for conducting the data driven healthcare research, where the goal is to derive insights from healthcare data and utilize such insights to improve the quality of care delivery. Due to the progression nature of human disease, one important aspect for analyzing healthcare data is temporality, which suggests the temporal relationships among different healthcare events and how their values evolve over time. Sequential pattern mining is a popular tool to extract time-invariant patterns from discrete sequences and has been applied in analyzing EHR before. However, due to the complexity of EHR, those approaches usually suffers from the pattern explosion problem, which means that a huge number of patterns will be detected with improper setting of the support threshold. To address this challenge, in this paper, we develop a novel representation, namely the temporal graph, for event sequences like EHR, wherein the nodes are medical events and the edges indicate the temporal relationships among those events in patient EHRs. Based on the temporal graph representation, we further develop an approach for temporal signature identification to identify the most significant and interpretable graph bases as temporal signatures, and the expressing coefficients can be treated as the embeddings of the patients in such temporal signature space. Our temporal signature identification framework is also flexible to incorporate semi-supervised/supervised information. We validate our framework on two real-world tasks. One is predicting the onset risk of heart failure. The other is predicting the risk of heart failure related hospitalization for patients with COPD pre-condition. Our results show that the prediction performance in both tasks can be improved by the proposed approaches. PMID:26958267

  12. Continuous-time quantum walks on star graphs

    SciTech Connect

    Salimi, S.

    2009-06-15

    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{sub 2} graphs (complete graph with two vertices) and the probability of observing walk tends to the uniform distribution.

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

    PubMed Central

    Wang, Yue; Wu, Xintao

    2014-01-01

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

  14. Labeled Graph Kernel for Behavior Analysis.

    PubMed

    Zhao, Ruiqi; Martinez, Aleix M

    2016-08-01

    Automatic behavior analysis from video is a major topic in many areas of research, including computer vision, multimedia, robotics, biology, cognitive science, social psychology, psychiatry, and linguistics. Two major problems are of interest when analyzing behavior. First, we wish to automatically categorize observed behaviors into a discrete set of classes (i.e., classification). For example, to determine word production from video sequences in sign language. Second, we wish to understand the relevance of each behavioral feature in achieving this classification (i.e., decoding). For instance, to know which behavior variables are used to discriminate between the words apple and onion in American Sign Language (ASL). The present paper proposes to model behavior using a labeled graph, where the nodes define behavioral features and the edges are labels specifying their order (e.g., before, overlaps, start). In this approach, classification reduces to a simple labeled graph matching. Unfortunately, the complexity of labeled graph matching grows exponentially with the number of categories we wish to represent. Here, we derive a graph kernel to quickly and accurately compute this graph similarity. This approach is very general and can be plugged into any kernel-based classifier. Specifically, we derive a Labeled Graph Support Vector Machine (LGSVM) and a Labeled Graph Logistic Regressor (LGLR) that can be readily employed to discriminate between many actions (e.g., sign language concepts). The derived approach can be readily used for decoding too, yielding invaluable information for the understanding of a problem (e.g., to know how to teach a sign language). The derived algorithms allow us to achieve higher accuracy results than those of state-of-the-art algorithms in a fraction of the time. We show experimental results on a variety of problems and datasets, including multimodal data. PMID:26415154

  15. Graph theory and the Virasoro master equation

    SciTech Connect

    Obers, N.A.J.

    1991-01-01

    A brief history of affine Lie algebra, the Virasoro algebra and its culmination in the Virasoro master equation is given. By studying ansaetze of the master equation, the author obtains exact solutions and gains insight in the structure of large slices of affine-Virasoro space. He finds an isomorphism between the constructions in the ansatz SO(n){sub diag}, which is a set of unitary, generically irrational affine-Virasoro constructions on SO(n), and the unlabeled graphs of order n. On the one hand, the conformal constructions, are classified by the graphs, while, conversely, a group-theoretic and conformal field-theoretic identification is obtained for every graph of graph theory. He also defines a class of magic Lie group bases in which the Virasoro master equation admits a simple metric ansatz {l brace}g{sub metric}{r brace}, whose structure is visible in the high-level expansion. When a magic basis is real on compact g, the corresponding g{sub metric} is a large system of unitary, generically irrational conformal field theories. Examples in this class include the graph-theory ansatz SO(n){sub diag} in the Cartesian basis of SO(n), and the ansatz SU(n){sub metric} in the Pauli-like basis of SU(n). Finally, he defines the sine-area graphs' of SU(n), which label the conformal field theories of SU(n){sub metric}, and he notes that, in similar fashion, each magic basis of g defines a generalized graph theory on g which labels the conformal field theories of g{sub metric}.

  16. A graph theoretic approach to scene matching

    NASA Technical Reports Server (NTRS)

    Ranganath, Heggere S.; Chipman, Laure J.

    1991-01-01

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

  17. Graph optimized Laplacian eigenmaps for face recognition

    NASA Astrophysics Data System (ADS)

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

    2015-01-01

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

  18. A graph theoretic approach to scene matching

    NASA Astrophysics Data System (ADS)

    Ranganath, Heggere S.; Chipman, Laure J.

    1991-08-01

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

  19. Efficient Sampling Set Selection for Bandlimited Graph Signals Using Graph Spectral Proxies

    NASA Astrophysics Data System (ADS)

    Anis, Aamir; Gadde, Akshay; Ortega, Antonio

    2016-07-01

    We study the problem of selecting the best sampling set for bandlimited reconstruction of signals on graphs. A frequency domain representation for graph signals can be defined using the eigenvectors and eigenvalues of variation operators that take into account the underlying graph connectivity. Smoothly varying signals defined on the nodes are of particular interest in various applications, and tend to be approximately bandlimited in the frequency basis. Sampling theory for graph signals deals with the problem of choosing the best subset of nodes for reconstructing a bandlimited signal from its samples. Most approaches to this problem require a computation of the frequency basis (i.e., the eigenvectors of the variation operator), followed by a search procedure using the basis elements. This can be impractical, in terms of storage and time complexity, for real datasets involving very large graphs. We circumvent this issue in our formulation by introducing quantities called graph spectral proxies, defined using the powers of the variation operator, in order to approximate the spectral content of graph signals. This allows us to formulate a direct sampling set selection approach that does not require the computation and storage of the basis elements. We show that our approach also provides stable reconstruction when the samples are noisy or when the original signal is only approximately bandlimited. Furthermore, the proposed approach is valid for any choice of the variation operator, thereby covering a wide range of graphs and applications. We demonstrate its effectiveness through various numerical experiments.

  20. Comprehensive Interpretive Planning.

    ERIC Educational Resources Information Center

    Kohen, Richard; Sikoryak, Kim

    1999-01-01

    Discusses interpretive planning and provides information on how to maximize a sense of ownership shared by managers, staff, and other organizational shareholders. Presents practical and effective plans for providing interpretive services. (CCM)

  1. Ground photography for improvved image interpretation training

    NASA Technical Reports Server (NTRS)

    Lougeay, R.

    1981-01-01

    Systematic sets of ground based color and color infrared photography were presented to students in remote sensing classes to enhance their ability to interpret satellite images. Features readily apparent on computer enhanced LANDSAT images were presented simultaneously with ground based photography in the format of slide triplicates. It was hypothesized that this instructional approach would improve the students' abilities to recognize, understand and interpret ground phenomena present on remotely sensed imagery. Tests conducted in undergraduate remote sensing classes substantially upheld this hypothesis. Student image interpretive abilities were tested before and after being exposed to the ground level photography. In general, image interpretive skills of the class improved by 25%. Also, the performance of students having different academic majors varied greatly for differing types of image subjects.

  2. Journalists as Interpretive Communities.

    ERIC Educational Resources Information Center

    Zelizer, Barbie

    1993-01-01

    Proposes viewing journalists as members of an interpretive community (not a profession) united by its shared discourse and collective interpretations of key public events. Applies the frame of the interpretive community to journalistic discourse about two events central for American journalists--Watergate and McCarthyism. (SR)

  3. Interpreting. NETAC Teacher Tipsheet.

    ERIC Educational Resources Information Center

    Darroch, Kathy; Marshall, Liza

    This tipsheet explains that an interpreter's role is to facilitate communication and convey all auditory and signed information so that individuals with and without hearing may fully interact. It outlines the common types of services provided by interpreters, and discusses principles guiding the professional behaviors of interpreters. When working…

  4. Using medical interpreters.

    PubMed

    Hart, Dionne; Bowen, Juan; DeJesus, Ramona; Maldonado, Alejandro; Jiwa, Fatima

    2010-04-01

    Research has demonstrated that appropriate use of interpreters in clinical encounters improves outcomes and decreases adverse events. This article reviews both the medical reasons for working with trained medical interpreters and the related laws, and offers practical tips for working effectively with interpreters. PMID:20481167

  5. Interpreting. PEPNet Tipsheet

    ERIC Educational Resources Information Center

    Darroch, Kathleen

    2010-01-01

    An interpreter's role is to facilitate communication and convey all auditory and signed information so that both hearing and deaf individuals may fully interact. The common types of services provided by interpreters are: (1) American Sign Language (ASL) Interpretation--a visual-gestural language with its own linguistic features; (2) Sign Language…

  6. Better dual-task processing in simultaneous interpreters

    PubMed Central

    Strobach, Tilo; Becker, Maxi; Schubert, Torsten; Kühn, Simone

    2015-01-01

    Simultaneous interpreting (SI) is a highly complex activity and requires the performance and coordination of multiple, simultaneous tasks: analysis and understanding of the discourse in a first language, reformulating linguistic material, storing of intermediate processing steps, and language production in a second language among others. It is, however, an open issue whether persons with experience in SI possess superior skills in coordination of multiple tasks and whether they are able to transfer these skills to lab-based dual-task situations. Within the present study, we set out to explore whether interpreting experience is associated with related higher-order executive functioning in the context of dual-task situations of the Psychological Refractory Period (PRP) type. In this PRP situation, we found faster reactions times in participants with experience in simultaneous interpretation in contrast to control participants without such experience. Thus, simultaneous interpreters possess superior skills in coordination of multiple tasks in lab-based dual-task situations. PMID:26528232

  7. Better dual-task processing in simultaneous interpreters.

    PubMed

    Strobach, Tilo; Becker, Maxi; Schubert, Torsten; Kühn, Simone

    2015-01-01

    Simultaneous interpreting (SI) is a highly complex activity and requires the performance and coordination of multiple, simultaneous tasks: analysis and understanding of the discourse in a first language, reformulating linguistic material, storing of intermediate processing steps, and language production in a second language among others. It is, however, an open issue whether persons with experience in SI possess superior skills in coordination of multiple tasks and whether they are able to transfer these skills to lab-based dual-task situations. Within the present study, we set out to explore whether interpreting experience is associated with related higher-order executive functioning in the context of dual-task situations of the Psychological Refractory Period (PRP) type. In this PRP situation, we found faster reactions times in participants with experience in simultaneous interpretation in contrast to control participants without such experience. Thus, simultaneous interpreters possess superior skills in coordination of multiple tasks in lab-based dual-task situations. PMID:26528232

  8. Data handling in the primary classroom: Children's perception of the purpose of graphs

    NASA Astrophysics Data System (ADS)

    Rodrigues, Susan

    1994-12-01

    The National Curriculum programme of study for Science 1 in England and Wales states that pupils should be encouraged to develop investigative skills and understanding of science through activities which “promote the search for patterns in data and the ability to make simple predictions based on findings” (Department of Education and Science, 1991, p. 14). In order to search for patterns children have to first understand the purpose of graphs and the relationship of variables. This paper describes some of the preliminary findings of the Data Handling in Primary Science Project. The majority of primary school children, involved in a data handling project (Rodrigues, 1994), see graphs in science as an end product to be displayed. In addition the children appeared to have a very limited understanding for the type of graph employed being determined by the variable involved. Furthermore whilst some of the children were able to read information from a graph, the language used had a marked effect on cueing the response.

  9. Field Geology Reasoning Skills in the Classroom

    NASA Astrophysics Data System (ADS)

    Richardson, Alan

    2013-04-01

    develop essential reasoning skills before going into the field; they could form the basis of follow-up work after a field day, or could be used as a substitute for field work if severe weather prevented an excursion. Each Outcrop Exercise consists of an A3 data sheet, a question sheet, specimen cards and, if appropriate, topographic and geologic maps. The most important dimension of each exercise is the nature and structure of the questions, which begin by requiring the student to make simple observations and lead to a comprehensive interpretation of the exposure. The materials are intended to be used in a variety of ways: for example, if the resources are available it is preferable to replace the specimen cards with real specimens; if time is short, data processing can be omitted by supplying students with prepared graphs. With future developments, it will be possible to link exercises together to generate a geological history for a whole area from primary data. These exercises must not be seen as a substitute for real fieldwork, but it is hoped that they will enhance students' appreciation of the data that they must collect in the field.

  10. Competency in ECG Interpretation Among Medical Students

    PubMed Central

    Kopeć, Grzegorz; Magoń, Wojciech; Hołda, Mateusz; Podolec, Piotr

    2015-01-01

    Background Electrocardiogram (ECG) is commonly used in diagnosis of heart diseases, including many life-threatening disorders. We aimed to assess skills in ECG interpretation among Polish medical students and to analyze the determinants of these skills. Material/Methods Undergraduates from all Polish medical schools were asked to complete a web-based survey containing 18 ECG strips. Questions concerned primary ECG parameters (rate, rhythm, and axis), emergencies, and common ECG abnormalities. Analysis was restricted to students in their clinical years (4th–6th), and students in their preclinical years (1st–3rd) were used as controls. Results We enrolled 536 medical students (females: n=299; 55.8%), aged 19 to 31 (23±1.6) years from all Polish medical schools. Most (72%) were in their clinical years. The overall rate of good response was better in students in years 4th–5th than those in years 1st–3rd (66% vs. 56%; p<0.0001). Competency in ECG interpretation was higher in students who reported ECG self-learning (69% vs. 62%; p<0.0001) but no difference was found between students who attended or did not attend regular ECG classes (66% vs. 66%; p=0.99). On multivariable analysis (p<0.0001), being in clinical years (OR: 2.45 [1.35–4.46] and self-learning (OR: 2.44 [1.46–4.08]) determined competency in ECG interpretation. Conclusions Polish medical students in their clinical years have a good level of competency in interpreting the primary ECG parameters, but their ability to recognize ECG signs of emergencies and common heart abnormalities is low. ECG interpretation skills are determined by self-education but not by attendance at regular ECG classes. Our results indicate qualitative and quantitative deficiencies in teaching ECG interpretation at medical schools. PMID:26541993

  11. GrouseFlocks: steerable exploration of graph hierarchy space.

    PubMed

    Archambault, Daniel; Munzner, Tamara; Auber, David

    2008-01-01

    Several previous systems allow users to interactively explore a large input graph through cuts of a superimposed hierarchy. This hierarchy is often created using clustering algorithms or topological features present in the graph. However, many graphs have domain-specific attributes associated with the nodes and edges, which could be used to create many possible hierarchies providing unique views of the input graph. GrouseFlocks is a system for the exploration of this graph hierarchy space. By allowing users to see several different possible hierarchies on the same graph, the system helps users investigate graph hierarchy space instead of a single fixed hierarchy. GrouseFlocks provides a simple set of operations so that users can create and modify their graph hierarchies based on selections. These selections can be made manually or based on patterns in the attribute data provided with the graph. It provides feedback to the user within seconds, allowing interactive exploration of this space. PMID:18467763

  12. Application of graph colouring to biological networks.

    PubMed

    Khor, S

    2010-05-01

    The author explores the application of graph colouring to biological networks, specifically protein-protein interaction (PPI) networks. First, the author finds that given similar conditions (i.e. graph size, degree distribution and clustering), fewer colours are needed to colour disassortative than assortative networks. Fewer colours create fewer independent sets which in turn imply higher concurrency potential for a network. Since PPI networks tend to be disassortative, the author suggests that in addition to functional specificity and stability proposed previously by Maslov and Sneppen (Science, 296, 2002), the disassortative nature of PPI networks may promote the ability of cells to perform multiple, crucial and functionally diverse tasks concurrently. Second, because graph colouring is closely related to the presence of cliques in a graph, the significance of node colouring information to the problem of identifying protein complexes (dense subgraphs in PPI networks), is investigated. The author finds that for PPI networks where 1-11% of nodes participate in at least one identified protein complex, such as H. sapien, DSATUR (a well-known complete graph colouring algorithm) node colouring information can improve the quality (homogeneity and separation) of initial candidate complexes. This finding may help improve existing protein complex detection methods, and/or suggest new methods. [Includes supplementary material]. PMID:20499999

  13. Modeling Transmission Line Networks Using Quantum Graphs

    NASA Astrophysics Data System (ADS)

    Koch, Trystan; Antonsen, Thomas

    Quantum graphs--one dimensional edges, connecting nodes, that support propagating Schrödinger wavefunctions--have been studied extensively as tractable models of wave chaotic behavior (Smilansky and Gnutzmann 2006, Berkolaiko and Kuchment 2013). Here we consider the electrical analog, in which the graph represents an electrical network where the edges are transmission lines (Hul et. al. 2004) and the nodes contain either discrete circuit elements or intricate circuit elements best represented by arbitrary scattering matrices. Including these extra degrees of freedom at the nodes leads to phenomena that do not arise in simpler graph models. We investigate the properties of eigenfrequencies and eigenfunctions on these graphs, and relate these to the statistical description of voltages on the transmission lines when driving the network externally. The study of electromagnetic compatibility, the effect of external radiation on complicated systems with numerous interconnected cables, motivates our research into this extension of the graph model. Work supported by the Office of Naval Research (N0014130474) and the Air Force Office of Scientific Research.

  14. DT-MRI segmentation using graph cuts

    NASA Astrophysics Data System (ADS)

    Weldeselassie, Yonas T.; Hamarneh, Ghassan

    2007-03-01

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

  15. Linear Time Vertex Partitioning on Massive Graphs

    PubMed Central

    Mell, Peter; Harang, Richard; Gueye, Assane

    2016-01-01

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

  16. Visualizing intelligence information using correlation graphs

    NASA Astrophysics Data System (ADS)

    Verma, Vivek; Gagvani, Nikhil

    2005-03-01

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

  17. Exploiting graph properties of game trees

    SciTech Connect

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

    1996-12-31

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

  18. Towards Scalable Graph Computation on Mobile Devices

    PubMed Central

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

    2015-01-01

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

  19. An analysis of spectral transformation techniques on graphs

    NASA Astrophysics Data System (ADS)

    Djurović, Igor; Sejdić, Ervin; Bulatović, Nikola; Simeunović, Marko

    2015-05-01

    Emerging methods for the spectral analysis of graphs are analyzed in this paper, as graphs are currently used to study interactions in many fields from neuroscience to social networks. There are two main approaches related to the spectral transformation of graphs. The first approach is based on the Laplacian matrix. The graph Fourier transform is defined as an expansion of a graph signal in terms of eigenfunctions of the graph Laplacian. The calculated eigenvalues carry the notion of frequency of graph signals. The second approach is based on the graph weighted adjacency matrix, as it expands the graph signal into a basis of eigenvectors of the adjacency matrix instead of the graph Laplacian. Here, the notion of frequency is then obtained from the eigenvalues of the adjacency matrix or its Jordan decomposition. In this paper, advantages and drawbacks of both approaches are examined. Potential challenges and improvements to graph spectral processing methods are considered as well as the generalization of graph processing techniques in the spectral domain. Its generalization to the time-frequency domain and other potential extensions of classical signal processing concepts to graph datasets are also considered. Lastly, it is given an overview of the compressive sensing on graphs concepts.

  20. Polynomial Kernels for Hard Problems on Disk Graphs

    NASA Astrophysics Data System (ADS)

    Jansen, Bart

    Kernelization is a powerful tool to obtain fixed-parameter tractable algorithms. Recent breakthroughs show that many graph problems admit small polynomial kernels when restricted to sparse graph classes such as planar graphs, bounded-genus graphs or H-minor-free graphs. We consider the intersection graphs of (unit) disks in the plane, which can be arbitrarily dense but do exhibit some geometric structure. We give the first kernelization results on these dense graph classes. Connected Vertex Cover has a kernel with 12k vertices on unit-disk graphs and with 3k 2 + 7k vertices on disk graphs with arbitrary radii. Red-Blue Dominating Set parameterized by the size of the smallest color class has a linear-vertex kernel on planar graphs, a quadratic-vertex kernel on unit-disk graphs and a quartic-vertex kernel on disk graphs. Finally we prove that H -Matching on unit-disk graphs has a linear-vertex kernel for every fixed graph H.