The behavioral outcomes of a technology-supported leisure activity in people with dementia
J.E.W.C. Gemert-Pijnen; N. Nijhof; Joost van Hoof; H. van Rijn
2013-01-01
BACKGROUND: This paper presents the results of an evaluation of a technology-supported leisure game for people with dementia in relation to the stimulation of social behavior. OBJECTIVE: In this study we explore the additional impact of technology-supported leisure activities on behavioral outcomes
Bhayee, Sheffy; Tomaszewski, Patricia; Lee, Daniel H; Moffat, Graeme; Pino, Lou; Moreno, Sylvain; Farb, Norman A S
2016-11-29
Mindfulness training (MT) programs represent an approach to attention training with well-validated mental health benefits. However, research supporting MT efficacy is based predominantly on weekly-meeting, facilitator-led, group-intervention formats. It is unknown whether participants might benefit from neurofeedback-assisted, technology-supported MT (N-tsMT), in which meditation is delivered individually, without the need for a facilitator, travel to a training site, or the presence of a supportive group environment. Mirroring the validation of group MT interventions, the first step in addressing this question requires identifying whether N-tsMT promotes measurable benefits. Here, we report on an initial investigation of a commercial N-tsMT system. In a randomized, active control trial, community-dwelling healthy adult participants carried out 6 weeks of daily practice, receiving either N-tsMT (n = 13), or a control condition of daily online math training (n = 13). Training effects were assessed on target measures of attention and well-being. Participants also completed daily post-training surveys assessing effects on mood, body awareness, calm, effort, and stress. Analysis revealed training effects specific to N-tsMT, with attentional improvements in overall reaction time on a Stroop task, and well-being improvements via reduced somatic symptoms on the Brief Symptom Inventory. Attention and well-being improvements were correlated, and effects were greatest for the most neurotic participants. However, secondary, exploratory measures of attention and well-being did not show training-specific effects. N-tsMT was associated with greater body awareness and calm, and initially greater effort that later converged with effort in the control condition. Preliminary findings indicate that N-tsMT promotes modest benefits for attention and subjective well-being in a healthy community sample relative to an active control condition. However, the findings would benefit
Exploration of Tensions in a Mobile-Technology Supported Fieldtrip: An Activity Theory Perspective
Lai, Chih-Hung; Chen, Fei-Ching; Yang, Jie-Chi
2014-01-01
The purpose of this study was to analyze how mobile technologies were incorporated and implemented in an outdoor learning activity. Two classes of primary school students participated in the experiment. Using activity theory as an analytical framework, it is found that underlying tensions provided rich insights into system dynamics and that…
Phillips, Siobhan M; Collins, Linda M; Penedo, Frank J; Courneya, Kerry S; Welch, Whitney; Cottrell, Alison; Lloyd, Gillian R; Gavin, Kara; Cella, David; Ackermann, Ronald T; Siddique, Juned; Spring, Bonnie
2018-03-01
Fit2Thrive is a theory-guided physical activity promotion trial using the Multiphase Optimization Strategy (MOST) to test efficacy for improving physical activity of five technology-supported physical activity promotion intervention components among breast cancer survivors. This trial will recruit 256 inactive breast cancer survivors nationwide. All participants will receive the core intervention which includes a Fitbit and standard self-monitoring Fit2Thrive smartphone application which will be downloaded to their personal phone. Women will be randomized to one of 32 conditions in a factorial design involving five factors with two levels: support calls (No vs. Yes), app type (standard vs. deluxe), text messaging (No vs. Yes), online gym (No vs. Yes) and Fitbit Buddy (No vs. Yes). The proposed trial examines the effects of the components on physical activity at 12 and 24weeks. Results will support the selection of a final package of intervention components that has been optimized to maximize physical activity and is subject to an upper limit of cost. The optimized intervention will be tested in a future trial. Fit2Thrive is the first trial to use the MOST framework to develop and test a physical activity promotion intervention in breast cancer survivors and will lead to an improved understanding of how to effectively change survivors' physical activity. These findings could result in more scalable, effective physical activity interventions for breast cancer survivors, and, ultimately, improve health and disease outcomes. Copyright © 2018 Elsevier Inc. All rights reserved.
Simulating activation propagation in social networks using the graph theory
Directory of Open Access Journals (Sweden)
František Dařena
2010-01-01
Full Text Available The social-network formation and analysis is nowadays one of objects that are in a focus of intensive research. The objective of the paper is to suggest the perspective of representing social networks as graphs, with the application of the graph theory to problems connected with studying the network-like structures and to study spreading activation algorithm for reasons of analyzing these structures. The paper presents the process of modeling multidimensional networks by means of directed graphs with several characteristics. The paper also demonstrates using Spreading Activation algorithm as a good method for analyzing multidimensional network with the main focus on recommender systems. The experiments showed that the choice of parameters of the algorithm is crucial, that some kind of constraint should be included and that the algorithm is able to provide a stable environment for simulations with networks.
Inflammatory aetiology of human myometrial activation tested using directed graphs.
Directory of Open Access Journals (Sweden)
2005-07-01
Full Text Available THERE ARE THREE MAIN HYPOTHESES FOR THE ACTIVATION OF THE HUMAN UTERUS AT LABOUR: functional progesterone withdrawal, inflammatory stimulation, and oxytocin receptor activation. To test these alternatives we have taken information and data from the literature to develop causal pathway models for the activation of human myometrium. The data provided quantitative RT-PCR results on key genes from samples taken before and during labour. Principal component analysis showed that pre-labour samples form a homogenous group compared to those during labour. We therefore modelled the alternative causal pathways in non-labouring samples using directed graphs and statistically compared the likelihood of the different models using structural equations and D-separation approaches. Using the computer program LISREL, inflammatory activation as a primary event was highly consistent with the data (p = 0.925, progesterone withdrawal, as a primary event, is plausible (p = 0.499, yet comparatively unlikely, oxytocin receptor mediated initiation is less compatible with the data (p = 0.091. DGraph, a software program that creates directed graphs, produced similar results (p= 0.684, p= 0.280, and p = 0.04, respectively. This outcome supports an inflammatory aetiology for human labour. Our results demonstrate the value of directed graphs in determining the likelihood of causal relationships in biology in situations where experiments are not possible.
Technology support for participatory budgeting
DEFF Research Database (Denmark)
Rose, Jeremy; Rios, Jesus; Lippa, Barbara
2010-01-01
Participatory budgeting is a reasonably well-established governance practice, particularly in South America. It is information and communication rich - making it well suited for modern technology support; in addition, the widespread participation of many citizens is difficult to achieve without...... this support. Participatory budgeting is associated with eParticipation, where much is already known about the kinds of technologies supporting citizen participation and how they are used. This paper identifies (from the existing literature) basic processes which are common to most participatory budgeting......, is integrated with a purpose-built internet platform; here we use the analysis to understand how the internet-based technologies are used to support the various participatory budgeting processes. We identify a range of these technologies which are currently used to support different eParticipation activities...
Unsupervised active learning based on hierarchical graph-theoretic clustering.
Hu, Weiming; Hu, Wei; Xie, Nianhua; Maybank, Steve
2009-10-01
Most existing active learning approaches are supervised. Supervised active learning has the following problems: inefficiency in dealing with the semantic gap between the distribution of samples in the feature space and their labels, lack of ability in selecting new samples that belong to new categories that have not yet appeared in the training samples, and lack of adaptability to changes in the semantic interpretation of sample categories. To tackle these problems, we propose an unsupervised active learning framework based on hierarchical graph-theoretic clustering. In the framework, two promising graph-theoretic clustering algorithms, namely, dominant-set clustering and spectral clustering, are combined in a hierarchical fashion. Our framework has some advantages, such as ease of implementation, flexibility in architecture, and adaptability to changes in the labeling. Evaluations on data sets for network intrusion detection, image classification, and video classification have demonstrated that our active learning framework can effectively reduce the workload of manual classification while maintaining a high accuracy of automatic classification. It is shown that, overall, our framework outperforms the support-vector-machine-based supervised active learning, particularly in terms of dealing much more efficiently with new samples whose categories have not yet appeared in the training samples.
Sampling frequency affects ActiGraph activity counts
DEFF Research Database (Denmark)
Brønd, Jan Christian; Arvidsson, Daniel
-15 Hz escaped the bandpass filter when sampled at 40, 50, 70, 80 and 100 Hz, while this was not the case when sampled at 30, 60 and 90 Hz. During the ambulatory activities this artifact resultet in different activity count output from the ActiLife software with different sampling frequency....... The difference increased with increasing activity intensity, with up to 1000 counts per minute at fast running.Discussion & conclusions: Activity counts from vigorous physical activity is highly attenuated with the ActiLife software. High frequency movement and noise information escape the bandpass filter...... depending on the sampling frequency of data collection, adding unexplained variation in activity counts. Therefore, the choice of sampling frequency may be an additional source of error with large impact on phsyical activty research as many investigators are using the ActiGraph with the ActiLife software...
Sampling frequency affects ActiGraph activity counts
DEFF Research Database (Denmark)
Brønd, Jan Christian; Arvidsson, Daniel
that is normally performed at frequencies higher than 2.5 Hz. With the ActiGraph model GT3X one has the option to select sample frequency from 30 to 100 Hz. This study investigated the effect of the sampling frequency on the ouput of the bandpass filter.Methods: A synthetic frequency sweep of 0-15 Hz was generated...... in Matlab and sampled at frequencies of 30-100 Hz. Also, acceleration signals during indoor walking and running were sampled at 30 Hz using the ActiGraph GT3X and resampled in Matlab to frequencies of 40-100 Hz. All data was processed with the ActiLife software.Results: Acceleration frequencies between 5......-15 Hz escaped the bandpass filter when sampled at 40, 50, 70, 80 and 100 Hz, while this was not the case when sampled at 30, 60 and 90 Hz. During the ambulatory activities this artifact resultet in different activity count output from the ActiLife software with different sampling frequency...
Undergraduate Student Construction and Interpretation of Graphs in Physics Lab Activities
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…
International Nuclear Information System (INIS)
Deecke, T.A.; Hyde, J.V.; Hylko, J.M.
2006-01-01
The weather is the most significant and unmanageable variable when performing environmental remediation activities. This variable can contribute to the failure of a project in two ways: 1) severe injury to an employee or employees following a cloud-to-ground lightning strike without prior visual or audible warnings; and 2) excessive 'down time' associated with mobilization and demobilization activities after a false alarm (e.g., lightning was seen in the distance but was actually moving away from the site). Therefore, in order for a project to be successful from both safety and financial viewpoints, the uncertainties associated with inclement weather, specifically lightning, need to be understood to eliminate the element of surprise. This paper discusses educational information related to the history and research of lightning, how lightning storms develop, types of lightning, the mechanisms of lightning injuries and fatalities, and follow-up medical treatment. Fortunately, lightning storm monitoring does not have to be either costly or elaborate. WESKEM, LLC selected the Boltek StormTracker Lightning Detection System with the Aninoquisi Lightning 2000 TM software. This fixed system, used in combination with online weather web pages, monitors and alarms WESKEM, LLC field personnel in the event of an approaching lightning storm. This application was expanded to justify the purchase of the hand-held Sky Scan Lightning/Storm Detector Model P5 used by the Heath Youth Athletic Association (HYAA) which is a non-profit, charitable organization offering sports programs for the youth and young adults in the local community. Fortunately, a lightning injury or fatality has never occurred on a WESKEM Paducah project or an HYAA-sponsored event. Using these fixed and hand-held systems will continue to prevent such injuries from occurring in the foreseeable future. (authors)
Directory of Open Access Journals (Sweden)
Wang J
2012-03-01
Full Text Available Jing Wang1, Susan M Sereika2,3, Eileen R Chasens2, Linda J Ewing4, Judith T Matthews2,5, Lora E Burke2,31School of Nursing, University of Texas Health Science Center at Houston, Houston, TX, 2School of Nursing, 3Graduate School of Public Health, 4School of Medicine, 5University Center for Social and Urban Research, University of Pittsburgh, Pittsburgh, PA, USABackground: Examination of mediating behavioral factors could explain how an intervention works and thus provide guidance to optimize behavioral weight-loss programs. This study examined the mediating role of adherence to self-monitoring of diet and physical activity on weight loss in a behavioral weight-loss trial testing the use of personal digital assistants (PDA for self-monitoring.Methods: Mediation analysis was conducted to examine the possible mediating role of adherence to self-monitoring of diet and physical activity between treatments using varying self-monitoring methods (paper record, PDA, and PDA with daily tailored feedback messages and weight loss.Findings: The sample (N = 210 was predominantly white (78% and female (85%. Compared to a paper record, using a PDA for self-monitoring diet (P = 0.027 and physical activity (P = 0.014 had significant direct effects on weight loss at 12 months, as well as a significant indirect effect on outcomes through improved adherence to self-monitoring (PS < 0.001. Receiving an automated daily feedback message via PDA only had a significant indirect effect on weight through self-monitoring adherence to diet (P = 0.004 and physical activity (P = 0.002.Conclusions: Adherence to self-monitoring of diet and physical activity is important as the underlying mechanism in this technology-supported behavioral weight-loss intervention.Keywords: behavioral intervention, self-monitoring, mobile technology, mediation analysis, weight loss, adherence
Staffing Up for Technology Support.
Carter, Kim
2000-01-01
Examines current technology staffing in school districts and compares technology-related roles with a similar study conducted in 1997. Discusses job titles; responsibilities; career paths; lack of technology support in schools; district-level support; teacher training; peer assistance; student roles; collaboration with library media specialists;…
SIMULATION OF DRIVER’S LOCOMOTIVE-HANDLING ACTIVITY USING THE THEORY OF FUZZY GRAPHS
Directory of Open Access Journals (Sweden)
T. V. Butko
2015-03-01
Full Text Available Purpose. The efficiency and safety of locomotive control improving is important and relevant scientific and practical problem. Every driver during the trains-handling bases on his experience and knowledge, that is why the compilation and detection the most efficient ways to control the locomotive-handling is one of the stages of measures development to reduce transportation costs. The purpose of this paper is a formalization process description of locomotive-handling and quality parameters determination of this process. Methodology. In order to achieve this goal the theory of fuzzy probabilistic graphs was used. Vertices of the graph correspond to the events start and end operations at train-handling. The graph arcs describe operations on train-handling. Graph consists of thirteen peaks corresponding to the main control actions of the engine-driver. The weighting factors of transitions between vertices are assigned by fuzzy numbers. Their values were obtained by expert estimates. Fuzzy probabilities and transition time are presented as numbers with trapezoidal membership function. Findings. Using successive merging of parallel arcs, loops and vertices elimination, the equivalent fuzzy graph of train-handling and the corresponding L-matrix were obtained. Equivalent graph takes into account separately activity of the driver during normal operation and during emergency situations. Originality. The theoretical foundations of describing process formalization in driver’s locomotive-handling activity were developed using the fuzzy probabilistic graph. The parameters characterizing the decision-making process of engineer were obtained. Practical value. With the resulting model it is possible to estimate the available reserves for the quality improvement of locomotive-handling. Reduction in the time for decision-making will lead to the approximation the current mode of control to the rational one and decrease costs of hauling operations. And reduction
Comparison of three generations of ActiGraph activity monitors under free-living conditions
DEFF Research Database (Denmark)
Grydeland, May; Hansen, Bjørge Herman; Ried-Larsen, M.
2014-01-01
.7%. The inter-generation differences varied in magnitude and direction across intensity levels, with the largest difference found in the highest intensities. CONCLUSION: We found that the ActiGraph model AM7164 yields higher outputs of mean physical activity intensity (mcpm) than the models GT1M and GT3X...
A Visualization System for Predicting Learning Activities Using State Transition Graphs
Okubo, Fumiya; Shimada, Atsushi; Taniguchi, Yuta
2017-01-01
In this paper, we present a system for visualizing learning logs of a course in progress together with predictions of learning activities of the following week and the final grades of students by state transition graphs. Data are collected from 236 students attending the course in progress and from 209 students attending the past course for…
Seiller, Thomas
2014-01-01
In two previous papers, we exposed a combinatorial approach to the program of Geometry of Interaction, a program initiated by Jean-Yves Girard. The strength of our approach lies in the fact that we interpret proofs by simpler structures - graphs - than Girard's constructions, while generalizing the latter since they can be recovered as special cases of our setting. This third paper extends this approach by considering a generalization of graphs named graphings, which is in some way a geometri...
Gupta-Ostermann, Disha; Hu, Ye; Bajorath, Jürgen
2012-06-14
A graphical method is introduced for compound data mining and structure-activity relationship (SAR) data analysis that is based upon a canonical structural organization scheme and captures a compound-scaffold-skeleton hierarchy. The graph representation has a constant layout, integrates compound activity data, and provides direct access to SAR information. Characteristic SAR patterns that emerge from the graph are easily identified. The molecular hierarchy enables "forward-backward" analysis of compound data and reveals both global and local SAR patterns. For example, in heterogeneous data sets, compound series are immediately identified that convey interpretable SAR information in isolation or in the structural context of related series, which often define SAR pathways through data sets.
Graph-based representation of behavior in detection and prediction of daily living activities.
Augustyniak, Piotr; Ślusarczyk, Grażyna
2018-04-01
Various surveillance systems capture signs of human activities of daily living (ADLs) and store multimodal information as time line behavioral records. In this paper, we present a novel approach to the analysis of a behavioral record used in a surveillance system designed for use in elderly smart homes. The description of a subject's activity is first decomposed into elementary poses - easily detectable by dedicated intelligent sensors - and represented by the share coefficients. Then, the activity is represented in the form of an attributed graph, where nodes correspond to elementary poses. As share coefficients of poses are expressed as attributes assigned to graph nodes, their change corresponding to a subject's action is represented by flow in graph edges. The behavioral record is thus a time series of graphs, which tiny size facilitates storage and management of long-term monitoring results. At the system learning stage, the contribution of elementary poses is accumulated, discretized and probability-ordered leading to a finite list representing the possible transitions between states. Such a list is independently built for each room in the supervised residence, and employed for assessment of the current action in the context of subject's habits and a room purpose. The proposed format of a behavioral record, applied to an adaptive surveillance system, is particularly advantageous for representing new activities not known at the setup stage, for providing a quantitative measure of transitions between poses and for expressing the difference between a predicted and actual action in a numerical way. Copyright © 2017 The Authors. Published by Elsevier Ltd.. All rights reserved.
Subgraph detection using graph signals
Chepuri, Sundeep Prabhakar
2017-03-06
In this paper we develop statistical detection theory for graph signals. In particular, given two graphs, namely, a background graph that represents an usual activity and an alternative graph that represents some unusual activity, we are interested in answering the following question: To which of the two graphs does the observed graph signal fit the best? To begin with, we assume both the graphs are known, and derive an optimal Neyman-Pearson detector. Next, we derive a suboptimal detector for the case when the alternative graph is not known. The developed theory is illustrated with numerical experiments.
Directory of Open Access Journals (Sweden)
Hoi-Chi Woo
Full Text Available Certain hand activities cause deformation and displacement of the median nerve at the carpal tunnel due to the gliding motion of tendons surrounding it. As smartphone usage escalates, this raises the public's concern whether hand activities while using smartphones can lead to median nerve problems.The aims of this study were to 1 develop kinematic graphs and 2 investigate the associated deformation and rotational information of median nerve in the carpal tunnel during hand activities.Dominant wrists of 30 young adults were examined with ultrasonography by placing a transducer transversely on their wrist crease. Ultrasound video clips were recorded when the subject performing 1 thumb opposition with the wrist in neutral position, 2 thumb opposition with the wrist in ulnar deviation and 3 pinch grip with the wrist in neutral position. Six still images that were separated by 0.2-second intervals were then captured from the ultrasound video for the determination of 1 cross-sectional area (CSA, 2 flattening ratio (FR, 3 rotational displacement (RD and 4 translational displacement (TD of median nerve in the carpal tunnel, and these collected information of deformation, rotational and displacement of median nerve were compared between 1 two successive time points during a single hand activity and 2 different hand motions at the same time point. Finally, kinematic graphs were constructed to demonstrate the mobility of median nerve during different hand activities.Performing different hand activities during this study led to a gradual reduction in CSA of the median nerve, with thumb opposition together with the wrist in ulnar deviation causing the greatest extent of deformation of the median nerve. Thumb opposition with the wrist in ulnar deviation also led to the largest extent of TD when compared to the other two hand activities of this study. Kinematic graphs showed that the motion pathways of median nerve during different hand activities were complex
Woo, Hoi-Chi; White, Peter; Ng, Ho-Kwan; Lai, Christopher W K
2016-01-01
Certain hand activities cause deformation and displacement of the median nerve at the carpal tunnel due to the gliding motion of tendons surrounding it. As smartphone usage escalates, this raises the public's concern whether hand activities while using smartphones can lead to median nerve problems. The aims of this study were to 1) develop kinematic graphs and 2) investigate the associated deformation and rotational information of median nerve in the carpal tunnel during hand activities. Dominant wrists of 30 young adults were examined with ultrasonography by placing a transducer transversely on their wrist crease. Ultrasound video clips were recorded when the subject performing 1) thumb opposition with the wrist in neutral position, 2) thumb opposition with the wrist in ulnar deviation and 3) pinch grip with the wrist in neutral position. Six still images that were separated by 0.2-second intervals were then captured from the ultrasound video for the determination of 1) cross-sectional area (CSA), 2) flattening ratio (FR), 3) rotational displacement (RD) and 4) translational displacement (TD) of median nerve in the carpal tunnel, and these collected information of deformation, rotational and displacement of median nerve were compared between 1) two successive time points during a single hand activity and 2) different hand motions at the same time point. Finally, kinematic graphs were constructed to demonstrate the mobility of median nerve during different hand activities. Performing different hand activities during this study led to a gradual reduction in CSA of the median nerve, with thumb opposition together with the wrist in ulnar deviation causing the greatest extent of deformation of the median nerve. Thumb opposition with the wrist in ulnar deviation also led to the largest extent of TD when compared to the other two hand activities of this study. Kinematic graphs showed that the motion pathways of median nerve during different hand activities were complex
Diestel, Reinhard
2017-01-01
This standard textbook of modern graph theory, now in its fifth edition, combines the authority of a classic with the engaging freshness of style that is the hallmark of active mathematics. It covers the core material of the subject with concise yet reliably complete proofs, while offering glimpses of more advanced methods in each field by one or two deeper results, again with proofs given in full detail. The book can be used as a reliable text for an introductory course, as a graduate text, and for self-study. From the reviews: “This outstanding book cannot be substituted with any other book on the present textbook market. It has every chance of becoming the standard textbook for graph theory.”Acta Scientiarum Mathematiciarum “Deep, clear, wonderful. This is a serious book about the heart of graph theory. It has depth and integrity. ”Persi Diaconis & Ron Graham, SIAM Review “The book has received a very enthusiastic reception, which it amply deserves. A masterly elucidation of modern graph theo...
Noble, S D; Welsh, D J A
2000-01-01
We consider the equivalence classes of graphs induced by the unsigned versions of the Reidemeister moves on knot diagrams. Any graph which is reducible by some finite sequence of these moves, to a graph with no edges is called a knot graph. We show that the class of knot graphs strictly contains the set of delta-wye graphs. We prove that the dimension of the intersection of the cycle and cocycle spaces is an effective numerical invariant of these classes.
Effect of ActiGraph's low frequency extension for estimating steps and physical activity intensity.
Directory of Open Access Journals (Sweden)
Yuri Feito
Full Text Available This study examined the effects of the ActiGraph's (AG low-frequency extension (LFE filter on steps and physical activity classification in the free-living environment. Thirty-four African-American women (age, 24.5±5.2 years; BMI, 24.9±4.5 kg/m2 had daily activity measured simultaneously with an AG-GT3X+ accelerometer and a New Lifestyles NL-800 pedometer for seven days. Steps per day (steps/day and time (minutes/day spent in sedentary, light, and moderate-to-vigorous physical activity (MVPA were examined with and without the LFE filter (AG-LFE and AG-N, respectively. The AG-LFE recorded more total steps (13,723±4,983 steps/day compared to AG-N and NL-800 (6,172±2,838 and 5,817±3,037 steps/day, respectively; p<0.001. Compared to the AG-N, the AG-LFE estimated less time in sedentary behaviors (518.7±92.1 vs. 504.2±105.4 min/day, respectively; p<0.001, and more time in light (247.7±70.4 vs. 279.1±74.7 min/day, respectively; p<0.001 and MVPA (18.9±16.9 vs. 21.5±18.2 min/day, respectively; p<0.001, respectively. These data suggest that steps and physical activity classifications will be affected when using the ActiGraph with and without the LFE filter. Future research should investigate the accuracy of these measures using the LFE filter.
Diestel, Reinhard
2012-01-01
HauptbeschreibungThis standard textbook of modern graph theory, now in its fourth edition, combinesthe authority of a classic with the engaging freshness of style that is the hallmarkof active mathematics. It covers the core material of the subject with concise yetreliably complete proofs, while offering glimpses of more advanced methodsin each field by one or two deeper results, again with proofs given in full detail.The book can be used as a reliable text for an introductory course, as a graduatetext, and for self-study. Rezension"Deep, clear, wonderful. This is a serious book about the
DEFF Research Database (Denmark)
Hartnell, B.L.; Vestergaard, Preben Dahl
There are many results dealing with the problem of decomposing a fixed graph into isomorphic subgraphs. There has also been work on characterizing graphs with the property that one can delete the edges of a number of edge disjoint copies of the subgraph and, regardless of how that is done......, the graph that remains can still be decomposed (such graphs are called or ). In this paper we consider the follwing variation. Given a fixed graph H, determine which graphs (call them ) have the property that every edge disjoint packing with H is maximum. In the case that the graph H is isomorphic...... to the path on 3 nodes, we characterize the equipackable graphs of girth 5 or more. randomly packable randomly decomposable equipackable maximal...
DEFF Research Database (Denmark)
Vestergaard, Preben Dahl; Hartnell, Bert L.
2006-01-01
There are many results dealing with the problem of decomposing a fixed graph into isomorphic subgraphs. There has also been work on characterizing graphs with the property that one can delete the edges of a number of edge disjoint copies of the subgraph and, regardless of how that is done......, the graph that remains can still be decomposed (such graphs are called randomly packable or randomly decomposable). In this paper we consider the following variation. Given a fixed graph H, determine which graphs (call them equipackable) have the property that every maximal edge disjoint packing with H...... is maximum. In the case that the graph H is isomorphic to the path on 3 nodes, we characterize the equipackable graphs of girth 5 or more....
Comparison of Sedentary Estimates between activPAL and Hip- and Wrist-Worn ActiGraph
DEFF Research Database (Denmark)
Koster, Annemarie; Shiroma, Eric J; Caserotti, Paolo
2016-01-01
, and nondominant wrist for 7 d in a free-living environment. Using the activPAL as the reference criteria, we compared classification of sedentary time to hip-worn and wrist-worn ActiGraph accelerometers over a range of cutoff points for both 60-s and 15-s epochs. Results The optimal cutoff point for the hip...
Trecia Markes, C.
1998-04-01
This paper will report on the development of an activity-based approach to teaching introductory physics that makes extensive use of the Calculator-Based Laboratory (CBL) system from Texas Instruments to collect and analyze data. Studies have suggested that an activity-based instruction format and computer-implemented data acquisition and analysis are effective in enhancing teaching effectiveness. However, implementation of this kind of class is accompanied by significant financial, spatial, and portability constraints. The TI-85/92 graphing calculators provide sufficient computational capacity and speed to handle most of the data acquisition and analysis requirements found in activity based introductory physics instruction. This paper will show how some physical laws can be derived from data obtained using the calculator/CBL system. Other data that can be easily obtained will also be shown and discussed. Results of pre-test and post-test given to both activity-based sections and lecture/laboratory sectioons of algebra-level introductory physics classes will also be discussed.
Graph passing in graph transformation
Ghamarian, A.H.; Rensink, Arend; Fish, Andrew; Lambers, Leen
Graph transformation works under the whole world assumption. Therefore, in realistic systems, both the individual graphs and the set of all such graphs can grow very large. In reactive formalisms such as process algebra, on the other hand, each system is split into smaller components which
Graph Passing in Graph Transformation
Ghamarian, A.H.; Rensink, Arend
2012-01-01
Graph transformation works under the whole world assumption. Therefore, in realistic systems, both the individual graphs and the set of all such graphs can grow very large. In reactive formalisms such as process algebra, on the other hand, each system is split into smaller components which
DEFF Research Database (Denmark)
Merker, Martin
The topic of this PhD thesis is graph decompositions. While there exist various kinds of decompositions, this thesis focuses on three problems concerning edgedecompositions. Given a family of graphs H we ask the following question: When can the edge-set of a graph be partitioned so that each part...... k(T)-edge-connected graph whose size is divisible by the size of T admits a T-decomposition. This proves a conjecture by Barát and Thomassen from 2006. Moreover, we introduce a new arboricity notion where we restrict the diameter of the trees in a decomposition into forests. We conjecture......-connected planar graph contains two edge-disjoint 18/19 -thin spanning trees. Finally, we make progress on a conjecture by Baudon, Bensmail, Przybyło, and Wozniak stating that if a graph can be decomposed into locally irregular graphs, then there exists such a decomposition with at most 3 parts. We show...
DOF Decoupling Task Graph Model: Reducing the Complexity of Touch-Based Active Sensing
Directory of Open Access Journals (Sweden)
Niccoló Tosi
2015-05-01
Full Text Available This article presents: (i a formal, generic model for active sensing tasks; (ii the insight that active sensing actions can very often be searched on less than six-dimensional configuration spaces (bringing an exponential reduction in the computational costs involved in the search; (iii an algorithm for selecting actions explicitly trading off information gain, execution time and computational cost; and (iv experimental results of touch-based localization in an industrial setting. Generalizing from prior work, the formal model represents an active sensing task by six primitives: configuration space, information space, object model, action space, inference scheme and action-selection scheme; prior work applications conform to the model as illustrated by four concrete examples. On top of the mentioned primitives, the task graph is then introduced as the relationship to represent an active sensing task as a sequence of low-complexity actions defined over different configuration spaces of the object. The presented act-reason algorithm is an action selection scheme to maximize the expected information gain of each action, explicitly constraining the time allocated to compute and execute the actions. The experimental contributions include localization of objects with: (1 a force-controlled robot equipped with a spherical touch probe; (2 a geometric complexity of the to-be-localized objects up to industrial relevance; (3 an initial uncertainty of (0.4 m, 0.4 m, 2Π; and (4 a configuration of act-reason to constrain the allocated time to compute and execute the next action as a function of the current uncertainty. Localization is accomplished when the probability mass within a 5-mm tolerance reaches a specified threshold of 80%. Four objects are localized with final {mean; standard-deviation} error spanning from {0.0043 m; 0.0034 m} to {0.0073 m; 0.0048 m}.
Zippo, Antonio G; Storchi, Riccardo; Nencini, Sara; Caramenti, Gian Carlo; Valente, Maurizio; Biella, Gabriele Eliseo M
2013-01-01
Small-World Networks (SWNs) represent a fundamental model for the comprehension of many complex man-made and biological networks. In the central nervous system, SWN models have been shown to fit well both anatomical and functional maps at the macroscopic level. However, the functional microscopic level, where the nodes of a network are represented by single neurons, is still poorly understood. At this level, although recent evidences suggest that functional connection graphs exhibit small-world organization, it is not known whether and how these maps, potentially distributed in multiple brain regions, change across different conditions, such as spontaneous and stimulus-evoked activities. We addressed these questions by analyzing the data from simultaneous multi-array extracellular recordings in three brain regions of rats, diversely involved in somatosensory information processing: the ventropostero-lateral thalamic nuclei, the primary somatosensory cortex and the centro-median thalamic nuclei. From both spike and Local Field Potential (LFP) recordings, we estimated the functional connection graphs by using the Normalized Compression Similarity for spikes and the Phase Synchrony for LFPs. Then, by using graph-theoretical statistics, we characterized the functional topology both during spontaneous activity and sensory stimulation. Our main results show that: (i) spikes and LFPs show SWN organization during spontaneous activity; (ii) after stimulation onset, while substantial functional graph reconfigurations occur both in spike and LFPs, small-worldness is nonetheless preserved; (iii) the stimulus triggers a significant increase of inter-area LFP connections without modifying the topology of intra-area functional connections. Finally, investigating computationally the functional substrate that supports the observed phenomena, we found that (iv) the fundamental concept of cell assemblies, transient groups of activating neurons, can be described by small
Hoehner, Christine M; Sabounchi, Nasim S; Brennan, Laura K; Hovmand, Peter; Kemner, Allison
2015-01-01
In the evaluation of the Healthy Kids, Healthy Communities initiative, investigators implemented Group Model Building (GMB) to promote systems thinking at the community level. As part of the GMB sessions held in each community partnership, participants created behavior-over-time graphs (BOTGs) to characterize their perceptions of changes over time related to policies, environments, collaborations, and social determinants in their community related to healthy eating, active living, and childhood obesity. To describe the process of coding BOTGs and their trends. Descriptive study of trends among BOTGs from 11 domains (eg, active living environments, social determinants of health, funding) and relevant categories and subcategories based on the graphed variables. In addition, BOTGs were distinguished by whether the variables were positively (eg, access to healthy foods) or negatively (eg, screen time) associated with health. The GMB sessions were held in 49 community partnerships across the United States. Participants in the GMB sessions (n = 590; n = 5-21 per session) included key individuals engaged in or impacted by the policy, system, or environmental changes occurring in the community. Thirty codes were developed to describe the direction (increasing, decreasing, stable) and shape (linear, reinforcing, balancing, or oscillating) of trends from 1660 graphs. The patterns of trends varied by domain. For example, among variables positively associated with health, the prevalence of reinforcing increasing trends was highest for active living and healthy eating environments (37.4% and 29.3%, respectively), partnership and community capacity (38.8%), and policies (30.2%). Examination of trends of specific variables suggested both convergence (eg, for cost of healthy foods) and divergence (eg, for farmers' markets) of trends across partnerships. Behavior-over-time graphs provide a unique data source for understanding community-level trends and, when combined with causal
Agreement between activPAL and ActiGraph for assessing children's sedentary time
Directory of Open Access Journals (Sweden)
Ridgers Nicola D
2012-02-01
Full Text Available Abstract Background Accelerometers have been used to determine the amount of time that children spend sedentary. However, as time spent sitting may be detrimental to health, research is needed to examine whether accelerometer sedentary cut-points reflect the amount of time children spend sitting. The aim of this study was to: a examine agreement between ActiGraph (AG cut-points for sedentary time and objectively-assessed periods of free-living sitting and sitting plus standing time using the activPAL (aP; and b identify cut-points to determine time spent sitting and sitting plus standing. Methods Forty-eight children (54% boys aged 8-12 years wore a waist-mounted AG and thigh-mounted aP for two consecutive school days (9-3:30 pm. AG data were analyzed using 17 cut-points between 50-850 counts·min-1 in 50 counts·min-1 increments to determine sedentary time during class-time, break time and school hours. Sitting and sitting plus standing time were obtained from the aP for these periods. Limits of agreement were computed to evaluate bias between AG50 to AG850 sedentary time and sitting and sitting plus standing time. Receiver Operator Characteristic (ROC analyses identified AG cut-points that maximized sensitivity and specificity for sitting and sitting plus standing time. Results The smallest mean bias between aP sitting time and AG sedentary time was AG150 for class time (3.8 minutes, AG50 for break time (-0.8 minutes, and AG100 for school hours (-5.2 minutes. For sitting plus standing time, the smallest bias was observed for AG850. ROC analyses revealed an optimal cut-point of 96 counts·min-1 (AUC = 0.75 for sitting time, which had acceptable sensitivity (71.7% and specificity (67.8%. No optimal cut-point was obtained for sitting plus standing (AUC = 0.51. Conclusions Estimates of free-living sitting time in children during school hours can be obtained using an AG cut-point of 100 counts·min-1. Higher sedentary cut-points may capture both
Gomersall, Sjaan R; Ng, Norman; Burton, Nicola W; Pavey, Toby G; Gilson, Nicholas D; Brown, Wendy J
2016-09-07
Activity trackers are increasingly popular with both consumers and researchers for monitoring activity and for promoting positive behavior change. However, there is a lack of research investigating the performance of these devices in free-living contexts, for which findings are likely to vary from studies conducted in well-controlled laboratory settings. The aim was to compare Fitbit One and Jawbone UP estimates of steps, moderate-to-vigorous physical activity (MVPA), and sedentary behavior with data from the ActiGraph GT3X+ accelerometer in a free-living context. Thirty-two participants were recruited using convenience sampling; 29 provided valid data for this study (female: 90%, 26/29; age: mean 39.6, SD 11.0 years). On two occasions for 7 days each, participants wore an ActiGraph GT3X+ accelerometer on their right hip and either a hip-worn Fitbit One (n=14) or wrist-worn Jawbone UP (n=15) activity tracker. Daily estimates of steps and very active minutes were derived from the Fitbit One (n=135 days) and steps, active time, and longest idle time from the Jawbone UP (n=154 days). Daily estimates of steps, MVPA, and longest sedentary bout were derived from the corresponding days of ActiGraph data. Correlation coefficients and Bland-Altman plots with examination of systematic bias were used to assess convergent validity and agreement between the devices and the ActiGraph. Cohen's kappa was used to assess the agreement between each device and the ActiGraph for classification of active versus inactive (≥10,000 steps per day and ≥30 min/day of MVPA) comparable with public health guidelines. Correlations with ActiGraph estimates of steps and MVPA ranged between .72 and .90 for Fitbit One and .56 and .75 for Jawbone UP. Compared with ActiGraph estimates, both devices overestimated daily steps by 8% (Fitbit One) and 14% (Jawbone UP). However, mean differences were larger for daily MVPA (Fitbit One: underestimated by 46%; Jawbone UP: overestimated by 50%). There was
Trudeau, Richard J
1994-01-01
Preface1. Pure Mathematics Introduction; Euclidean Geometry as Pure Mathematics; Games; Why Study Pure Mathematics?; What's Coming; Suggested Reading2. Graphs Introduction; Sets; Paradox; Graphs; Graph diagrams; Cautions; Common Graphs; Discovery; Complements and Subgraphs; Isomorphism; Recognizing Isomorphic Graphs; Semantics The Number of Graphs Having a Given nu; Exercises; Suggested Reading3. Planar Graphs Introduction; UG, K subscript 5, and the Jordan Curve Theorem; Are there More Nonplanar Graphs?; Expansions; Kuratowski's Theorem; Determining Whether a Graph is Planar or
DEFF Research Database (Denmark)
Seiller, Thomas
2016-01-01
Interaction graphs were introduced as a general, uniform, construction of dynamic models of linear logic, encompassing all Geometry of Interaction (GoI) constructions introduced so far. This series of work was inspired from Girard's hyperfinite GoI, and develops a quantitative approach that should...... be understood as a dynamic version of weighted relational models. Until now, the interaction graphs framework has been shown to deal with exponentials for the constrained system ELL (Elementary Linear Logic) while keeping its quantitative aspect. Adapting older constructions by Girard, one can clearly define...... "full" exponentials, but at the cost of these quantitative features. We show here that allowing interpretations of proofs to use continuous (yet finite in a measure-theoretic sense) sets of states, as opposed to earlier Interaction Graphs constructions were these sets of states were discrete (and finite...
2015-12-31
An example of an acoustic transceiver that could be used for underwater acoustic communication is the WHO! Micro- Modem. It can operate at 10 kHz...Research Laboratory NUMBER The Pennsylvania State University P. 0 . Box 30 State College, PA 16804-0030 9. SPONSORING I MONITORING AGENCY NAME(S...the areas of continuous active sonar (CAS) and unmanned underwater vehicle signal processing. Closed-form factor graph formulations for detection
Maximal outerplanar graphs as chordal graphs, path-neighborhood graphs, and triangle graphs
R.C. Laskar (R.C.); H.M. Mulder (Martyn); B. Novick (Beth)
2011-01-01
textabstractMaximal outerplanar graphs are characterized using three different classes of graphs. A path-neighborhood graph is a connected graph in which every neighborhood induces a path. The triangle graph $T(G)$ has the triangles of the graph $G$ as its vertices, two of these being adjacent
Gould, Ronald
2012-01-01
This introduction to graph theory focuses on well-established topics, covering primary techniques and including both algorithmic and theoretical problems. The algorithms are presented with a minimum of advanced data structures and programming details. This thoroughly corrected 1988 edition provides insights to computer scientists as well as advanced undergraduates and graduate students of topology, algebra, and matrix theory. Fundamental concepts and notation and elementary properties and operations are the first subjects, followed by examinations of paths and searching, trees, and networks. S
Chartrand, Gary; Zhang, Ping
2010-01-01
Gary Chartrand has influenced the world of Graph Theory for almost half a century. He has supervised more than a score of Ph.D. dissertations and written several books on the subject. The most widely known of these texts, Graphs and Digraphs, … has much to recommend it, with clear exposition, and numerous challenging examples [that] make it an ideal textbook for the advanced undergraduate or beginning graduate course. The authors have updated their notation to reflect the current practice in this still-growing area of study. By the authors' estimation, the 5th edition is approximately 50% longer than the 4th edition. … the legendary Frank Harary, author of the second graph theory text ever produced, is one of the figures profiled. His book was the standard in the discipline for several decades. Chartrand, Lesniak and Zhang have produced a worthy successor.-John T. Saccoman, MAA Reviews, June 2012 (This book is in the MAA's basic library list.)As with the earlier editions, the current text emphasizes clear...
Hillman, Thomas
2014-01-01
This article examines mathematical activity with digital technology by tracing it from its development through its use in classrooms. Drawing on material-semiotic approaches from the field of Science and Technology Studies, it examines the visions of mathematical activity that developers had for an advanced graphing calculator. It then follows the…
CHARACTERISATION OF REGULAR GRAPHS AS LOOP GRAPHS ...
African Journals Online (AJOL)
There have been various generalisations of Cayley graphs, prototypes of transitive graphs. The most generalised is the description of graphs on general groupoids. What has clearly emerged in this exercise is that the philosophy of constructing graphs on groupoids offers a fruitful avenue from which we may understand ...
De Bruijn graphs and DNA graphs
Pendavingh, Rudi; Schuurman, Petra; Woeginger, Gerhard; Brandstädt, Andreas; Le, Van Bang
2001-01-01
In this paper we prove the NP-hardness of various recognition problems for subgraphs of De Bruijn graphs. In particular, the recognition of DNA graphs is shown to be NP-hard; DNA graphs are the vertex induced subgraphs of De Bruijn graphs over a four letter alphabet. As a consequence, two open
Hekler, Eric B; Buman, Matthew P; Grieco, Lauren; Rosenberger, Mary; Winter, Sandra J; Haskell, William; King, Abby C
2015-04-15
There is increasing interest in using smartphones as stand-alone physical activity monitors via their built-in accelerometers, but there is presently limited data on the validity of this approach. The purpose of this work was to determine the validity and reliability of 3 Android smartphones for measuring physical activity among midlife and older adults. A laboratory (study 1) and a free-living (study 2) protocol were conducted. In study 1, individuals engaged in prescribed activities including sedentary (eg, sitting), light (sweeping), moderate (eg, walking 3 mph on a treadmill), and vigorous (eg, jogging 5 mph on a treadmill) activity over a 2-hour period wearing both an ActiGraph and 3 Android smartphones (ie, HTC MyTouch, Google Nexus One, and Motorola Cliq). In the free-living study, individuals engaged in usual daily activities over 7 days while wearing an Android smartphone (Google Nexus One) and an ActiGraph. Study 1 included 15 participants (age: mean 55.5, SD 6.6 years; women: 56%, 8/15). Correlations between the ActiGraph and the 3 phones were strong to very strong (ρ=.77-.82). Further, after excluding bicycling and standing, cut-point derived classifications of activities yielded a high percentage of activities classified correctly according to intensity level (eg, 78%-91% by phone) that were similar to the ActiGraph's percent correctly classified (ie, 91%). Study 2 included 23 participants (age: mean 57.0, SD 6.4 years; women: 74%, 17/23). Within the free-living context, results suggested a moderate correlation (ie, ρ=.59, PAndroid smartphone can provide comparable estimates of physical activity to an ActiGraph in both a laboratory-based and free-living context for estimating sedentary and MVPA and that different Android smartphones may reliably confer similar estimates.
Graph limits and hereditary properties
Janson, Svante
2011-01-01
We collect some general results on graph limits associated to hereditary classes of graphs. As examples, we consider some classes defined by forbidden subgraphs and some classes of intersection graphs, including triangle-free graphs, chordal graphs, cographs, interval graphs, unit interval graphs, threshold graphs, and line graphs.
Chartrand, Gary; Rosen, Kenneth H
2008-01-01
Beginning with the origin of the four color problem in 1852, the field of graph colorings has developed into one of the most popular areas of graph theory. Introducing graph theory with a coloring theme, Chromatic Graph Theory explores connections between major topics in graph theory and graph colorings as well as emerging topics. This self-contained book first presents various fundamentals of graph theory that lie outside of graph colorings, including basic terminology and results, trees and connectivity, Eulerian and Hamiltonian graphs, matchings and factorizations, and graph embeddings. The remainder of the text deals exclusively with graph colorings. It covers vertex colorings and bounds for the chromatic number, vertex colorings of graphs embedded on surfaces, and a variety of restricted vertex colorings. The authors also describe edge colorings, monochromatic and rainbow edge colorings, complete vertex colorings, several distinguishing vertex and edge colorings, and many distance-related vertex coloring...
Akama, Hiroyuki; Miyake, Maki; Jung, Jaeyoung; Murphy, Brian
2015-01-01
In this study, we introduce an original distance definition for graphs, called the Markov-inverse-F measure (MiF). This measure enables the integration of classical graph theory indices with new knowledge pertaining to structural feature extraction from semantic networks. MiF improves the conventional Jaccard and/or Simpson indices, and reconciles both the geodesic information (random walk) and co-occurrence adjustment (degree balance and distribution). We measure the effectiveness of graph-based coefficients through the application of linguistic graph information for a neural activity recorded during conceptual processing in the human brain. Specifically, the MiF distance is computed between each of the nouns used in a previous neural experiment and each of the in-between words in a subgraph derived from the Edinburgh Word Association Thesaurus of English. From the MiF-based information matrix, a machine learning model can accurately obtain a scalar parameter that specifies the degree to which each voxel in (the MRI image of) the brain is activated by each word or each principal component of the intermediate semantic features. Furthermore, correlating the voxel information with the MiF-based principal components, a new computational neurolinguistics model with a network connectivity paradigm is created. This allows two dimensions of context space to be incorporated with both semantic and neural distributional representations.
Directory of Open Access Journals (Sweden)
Hiroyuki Akama
Full Text Available In this study, we introduce an original distance definition for graphs, called the Markov-inverse-F measure (MiF. This measure enables the integration of classical graph theory indices with new knowledge pertaining to structural feature extraction from semantic networks. MiF improves the conventional Jaccard and/or Simpson indices, and reconciles both the geodesic information (random walk and co-occurrence adjustment (degree balance and distribution. We measure the effectiveness of graph-based coefficients through the application of linguistic graph information for a neural activity recorded during conceptual processing in the human brain. Specifically, the MiF distance is computed between each of the nouns used in a previous neural experiment and each of the in-between words in a subgraph derived from the Edinburgh Word Association Thesaurus of English. From the MiF-based information matrix, a machine learning model can accurately obtain a scalar parameter that specifies the degree to which each voxel in (the MRI image of the brain is activated by each word or each principal component of the intermediate semantic features. Furthermore, correlating the voxel information with the MiF-based principal components, a new computational neurolinguistics model with a network connectivity paradigm is created. This allows two dimensions of context space to be incorporated with both semantic and neural distributional representations.
Directory of Open Access Journals (Sweden)
Juan eNunez-Iglesias
2014-04-01
Full Text Available The aim in high-resolution connectomics is to reconstruct complete neuronal connectivity in a tissue. Currently, the only technology capable of resolving the smallest neuronal processes is electron microscopy (EM. Thus, a common approach is to perform automatic segmentation of EM images, followed by manual proofreading by experts to fix errors. We developed an algorithm and software library to not only improve the accuracy of the initial automatic segmentation, but also point out the image coordinates where it is likely to have made errors. Our software, called gala (graph-based active learning of agglomeration, improves the state of the art in agglomerative image segmentation. It is implemented in Python and makes extensive use of the scientific Python stack (numpy, scipy, networkx, scikit-learn, scikit-image, and others. We present here the software architecture of the gala library, and discuss several designs that we consider would be generally useful for other segmentation packages. We also discuss the limitations of the gala library and how we intend to address them.
Nunez-Iglesias, Juan; Kennedy, Ryan; Plaza, Stephen M; Chakraborty, Anirban; Katz, William T
2014-01-01
The aim in high-resolution connectomics is to reconstruct complete neuronal connectivity in a tissue. Currently, the only technology capable of resolving the smallest neuronal processes is electron microscopy (EM). Thus, a common approach to network reconstruction is to perform (error-prone) automatic segmentation of EM images, followed by manual proofreading by experts to fix errors. We have developed an algorithm and software library to not only improve the accuracy of the initial automatic segmentation, but also point out the image coordinates where it is likely to have made errors. Our software, called gala (graph-based active learning of agglomeration), improves the state of the art in agglomerative image segmentation. It is implemented in Python and makes extensive use of the scientific Python stack (numpy, scipy, networkx, scikit-learn, scikit-image, and others). We present here the software architecture of the gala library, and discuss several designs that we consider would be generally useful for other segmentation packages. We also discuss the current limitations of the gala library and how we intend to address them.
Shao, Zheng; Hirayama, Yuya; Yamanishi, Yoshihiro; Saigo, Hiroto
2015-12-28
Graph data are becoming increasingly common in machine learning and data mining, and its application field pervades to bioinformatics and cheminformatics. Accordingly, as a method to extract patterns from graph data, graph mining recently has been studied and developed rapidly. Since the number of patterns in graph data is huge, a central issue is how to efficiently collect informative patterns suitable for subsequent tasks such as classification or regression. In this paper, we consider mining discriminative subgraphs from graph data with multiple labels. The resulting task has important applications in cheminformatics, such as finding common functional groups that trigger multiple drug side effects, or identifying ligand functional groups that hit multiple targets. In computational experiments, we first verify the effectiveness of the proposed approach in synthetic data, then we apply it to drug adverse effect prediction problem. In the latter dataset, we compared the proposed method with L1-norm logistic regression in combination with the PubChem/Open Babel fingerprint, in that the proposed method showed superior performance with a much smaller number of subgraph patterns. Software is available from https://github.com/axot/GLP.
Internationalization at home : Technology-supported multicultural learning in Peru
Olivos Rossini, L.M.
2016-01-01
This research contributes to the disciplines of information systems, management science in particular the field of management education and cross-cultural studies. It further proposes a model to understand technology-supported multicultural learning in Peru. In addition, the model examines
Technology-Supported Learning Environments in Science Classrooms in India
Gupta, Adit; Fisher, Darrell
2012-01-01
The adoption of technology has created a major impact in the field of education at all levels. Technology-supported classroom learning environments, involving modern information and communication technologies, are also entering the Indian educational system in general and the schools in Jammu region (Jammu & Kashmir State, India) in…
Technology Support for Self-Organized Learners (Guest Editorial)
Kalz, Marco; Koper, Rob; Hornung-Prähauser, Veronika
2010-01-01
Kalz, M., Koper, R., & Hornung-Prähauser, V. (2009). Technology Support for Self-Organized Learners (Guest Editorial) [Special issue]. In M. Kalz, R. Koper & V. Hornung-Prähauser (Eds.), Journal of Educational Technology & Society, 12(3), 1-3.
First Reformulated Zagreb Indices of Some Classes of Graphs
Directory of Open Access Journals (Sweden)
V. Kaladevi
2017-12-01
Full Text Available A topological index of a graph is a parameter related to the graph; it does not depend on labeling or pictorial representation of the graph. Graph operations plays a vital role to analyze the structure and properties of a large graph which is derived from the smaller graphs. The Zagreb indices are the important topological indices found to have the applications in Quantitative Structure Property Relationship(QSPR and Quantitative Structure Activity Relationship(QSAR studies as well. There are various study of different versions of Zagreb indices. One of the most important Zagreb indices is the reformulated Zagreb index which is used in QSPR study.In this paper, we obtain the first reformulated Zagreb indices of some derived graphs such as double graph, extended double graph, thorn graph, subdivision vertex corona graph, subdivision graph and triangle parallel graph. In addition, we compute the first reformulated Zagreb indices of two important transformation graphs such as the generalized transformation graph and generalized Mycielskian graph.
Bapat, Ravindra B
2014-01-01
This new edition illustrates the power of linear algebra in the study of graphs. The emphasis on matrix techniques is greater than in other texts on algebraic graph theory. Important matrices associated with graphs (for example, incidence, adjacency and Laplacian matrices) are treated in detail. Presenting a useful overview of selected topics in algebraic graph theory, early chapters of the text focus on regular graphs, algebraic connectivity, the distance matrix of a tree, and its generalized version for arbitrary graphs, known as the resistance matrix. Coverage of later topics include Laplacian eigenvalues of threshold graphs, the positive definite completion problem and matrix games based on a graph. Such an extensive coverage of the subject area provides a welcome prompt for further exploration. The inclusion of exercises enables practical learning throughout the book. In the new edition, a new chapter is added on the line graph of a tree, while some results in Chapter 6 on Perron-Frobenius theory are reo...
Components in time-varying graphs.
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.
Chemical Graph Transformation with Stereo-Information
DEFF Research Database (Denmark)
Andersen, Jakob Lykke; Flamm, Christoph; Merkle, Daniel
2017-01-01
Double Pushout graph transformation naturally facilitates the modelling of chemical reactions: labelled undirected graphs model molecules and direct derivations model chemical reactions. However, the most straightforward modelling approach ignores the relative placement of atoms and their neighbo......Double Pushout graph transformation naturally facilitates the modelling of chemical reactions: labelled undirected graphs model molecules and direct derivations model chemical reactions. However, the most straightforward modelling approach ignores the relative placement of atoms...... and their neighbours in space. Stereoisomers of chemical compounds thus cannot be distinguished, even though their chemical activity may differ substantially. In this contribution we propose an extended chemical graph transformation system with attributes that encode information about local geometry. The modelling...... of graph transformation, but we here propose a framework that also allows for partially specified stereoinformation. While there are several stereochemical configurations to be considered, we focus here on the tetrahedral molecular shape, and suggest general principles for how to treat all other chemically...
Graph algorithms in the titan toolkit.
Energy Technology Data Exchange (ETDEWEB)
McLendon, William Clarence, III; Wylie, Brian Neil
2009-10-01
Graph algorithms are a key component in a wide variety of intelligence analysis activities. The Graph-Based Informatics for Non-Proliferation and Counter-Terrorism project addresses the critical need of making these graph algorithms accessible to Sandia analysts in a manner that is both intuitive and effective. Specifically we describe the design and implementation of an open source toolkit for doing graph analysis, informatics, and visualization that provides Sandia with novel analysis capability for non-proliferation and counter-terrorism.
Integral trees and integral graphs
Wang, Ligong
2005-01-01
This monograph deals with integral graphs, Laplacian integral regular graphs, cospectral graphs and cospectral integral graphs. The organization of this work, which consists of eight chapters, is as follows.
Directory of Open Access Journals (Sweden)
Amine Labriji
2017-07-01
Full Text Available The topic of identifying the similarity of graphs was considered as highly recommended research field in the Web semantic, artificial intelligence, the shape recognition and information research. One of the fundamental problems of graph databases is finding similar graphs to a graph query. Existing approaches dealing with this problem are usually based on the nodes and arcs of the two graphs, regardless of parental semantic links. For instance, a common connection is not identified as being part of the similarity of two graphs in cases like two graphs without common concepts, the measure of similarity based on the union of two graphs, or the one based on the notion of maximum common sub-graph (SCM, or the distance of edition of graphs. This leads to an inadequate situation in the context of information research. To overcome this problem, we suggest a new measure of similarity between graphs, based on the similarity measure of Wu and Palmer. We have shown that this new measure satisfies the properties of a measure of similarities and we applied this new measure on examples. The results show that our measure provides a run time with a gain of time compared to existing approaches. In addition, we compared the relevance of the similarity values obtained, it appears that this new graphs measure is advantageous and offers a contribution to solving the problem mentioned above.
Loukas, A.
2015-01-01
We have recently seen a surge of research focusing on the processing of graph data. The emerging field of signal processing on graphs focuses on the extension of classical discrete signal processing techniques to the graph setting. Arguably, the greatest breakthrough of the field has been the
Indian Academy of Sciences (India)
IAS Admin
graph. We also note before closing this general discus- sion that among the family of regular and connected graphs, the graphs in the family of SRGs are character- ized by having exactly three distinct eigenvalues of the adjacency matrix. The friendship theorem asserts that if friendship in a community is a symmetric relation ...
Brouwer, A.E.; Haemers, W.H.
2012-01-01
This book gives an elementary treatment of the basic material about graph spectra, both for ordinary, and Laplace and Seidel spectra. The text progresses systematically, by covering standard topics before presenting some new material on trees, strongly regular graphs, two-graphs, association
Graphing Inequalities, Connecting Meaning
Switzer, J. Matt
2014-01-01
Students often have difficulty with graphing inequalities (see Filloy, Rojano, and Rubio 2002; Drijvers 2002), and J. Matt Switzer's students were no exception. Although students can produce graphs for simple inequalities, they often struggle when the format of the inequality is unfamiliar. Even when producing a correct graph of an…
Pluhař, Z; Weidenmüller, H A
2014-04-11
For time-reversal invariant graphs we prove the Bohigas-Giannoni-Schmit conjecture in its most general form: For graphs that are mixing in the classical limit, all spectral correlation functions coincide with those of the Gaussian orthogonal ensemble of random matrices. For open graphs, we derive the analogous identities for all S-matrix correlation functions.
Sotirov, Renata
2017-01-01
The graph bisection problem is the problem of partitioning the vertex set of a graph into two sets of given sizes such that the sum of weights of edges joining these two sets is optimized. We present a semidefinite programming relaxation for the graph bisection problem with a matrix variable of
Hyperbolicity in median graphs
Indian Academy of Sciences (India)
If is hyperbolic, we denote by () the sharp hyperbolicity constant of , i.e., ( X ) = inf { ≥ 0 : X is − hyperbolic } . In this paper we study the hyperbolicity of median graphs and we also obtain some results about general hyperbolic graphs. In particular, we prove that a median graph is hyperbolic if and only if its ...
An analysis of facebook's graph search
CSIR Research Space (South Africa)
Khan, ZC
2014-11-01
Full Text Available digital media. With the large number of users active on Facebook, an upgrade to Facebook’s searching capability was made through the launch of graph search. Graph search is a powerful search feature which allows users to search Facebook using queries...
Gross, Jonathan L
2003-01-01
The Handbook of Graph Theory is the most comprehensive single-source guide to graph theory ever published. Best-selling authors Jonathan Gross and Jay Yellen assembled an outstanding team of experts to contribute overviews of more than 50 of the most significant topics in graph theory-including those related to algorithmic and optimization approaches as well as ""pure"" graph theory. They then carefully edited the compilation to produce a unified, authoritative work ideal for ready reference.Designed and edited with non-experts in mind, the Handbook of Graph Theory makes information easy to fi
Hell, Pavol
2004-01-01
This is a book about graph homomorphisms. Graph theory is now an established discipline but the study of graph homomorphisms has only recently begun to gain wide acceptance and interest. The subject gives a useful perspective in areas such as graph reconstruction, products, fractional and circular colourings, and has applications in complexity theory, artificial intelligence, telecommunication, and, most recently, statistical physics.Based on the authors' lecture notes for graduate courses, this book can be used as a textbook for a second course in graph theory at 4th year or master's level an
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.
Simplicial complexes of graphs
Jonsson, Jakob
2008-01-01
A graph complex is a finite family of graphs closed under deletion of edges. Graph complexes show up naturally in many different areas of mathematics, including commutative algebra, geometry, and knot theory. Identifying each graph with its edge set, one may view a graph complex as a simplicial complex and hence interpret it as a geometric object. This volume examines topological properties of graph complexes, focusing on homotopy type and homology. Many of the proofs are based on Robin Forman's discrete version of Morse theory. As a byproduct, this volume also provides a loosely defined toolbox for attacking problems in topological combinatorics via discrete Morse theory. In terms of simplicity and power, arguably the most efficient tool is Forman's divide and conquer approach via decision trees; it is successfully applied to a large number of graph and digraph complexes.
Graphing trillions of triangles.
Burkhardt, Paul
2017-07-01
The increasing size of Big Data is often heralded but how data are transformed and represented is also profoundly important to knowledge discovery, and this is exemplified in Big Graph analytics. Much attention has been placed on the scale of the input graph but the product of a graph algorithm can be many times larger than the input. This is true for many graph problems, such as listing all triangles in a graph. Enabling scalable graph exploration for Big Graphs requires new approaches to algorithms, architectures, and visual analytics. A brief tutorial is given to aid the argument for thoughtful representation of data in the context of graph analysis. Then a new algebraic method to reduce the arithmetic operations in counting and listing triangles in graphs is introduced. Additionally, a scalable triangle listing algorithm in the MapReduce model will be presented followed by a description of the experiments with that algorithm that led to the current largest and fastest triangle listing benchmarks to date. Finally, a method for identifying triangles in new visual graph exploration technologies is proposed.
Directory of Open Access Journals (Sweden)
Kostiantyn S. Khoruzhyi
2014-12-01
Full Text Available In the article, the content and nature of organizational activities in scope of methodological and technological support of the education quality management information system (EQMIS for future economists are described. The content of the organizational activities for the implementation of methodological and technological support of EQMIS for future economists includes four stages (preparatory, instructional/adaptational, methodological/basic, as well as experimental/evaluational and contains a set of methodological and technological measures for each of the stages of the EQMIS implementation. A study of the pedagogical impact of the proposed methodology of using EQMIS in the formation of professional competence of economics students was also conducted. The main stages, methods and sequence of implementation arrangements for the methodological and technological support of EQMIS are defined.
Graphs on Surfaces and the Partition Function of String Theory
Garcia-Islas, J. Manuel
2007-01-01
Graphs on surfaces is an active topic of pure mathematics belonging to graph theory. It has also been applied to physics and relates discrete and continuous mathematics. In this paper we present a formal mathematical description of the relation between graph theory and the mathematical physics of discrete string theory. In this description we present problems of the combinatorial world of real importance for graph theorists. The mathematical details of the paper are as follows: There is a com...
Chartrand, Gary
1984-01-01
Graph theory is used today in the physical sciences, social sciences, computer science, and other areas. Introductory Graph Theory presents a nontechnical introduction to this exciting field in a clear, lively, and informative style. Author Gary Chartrand covers the important elementary topics of graph theory and its applications. In addition, he presents a large variety of proofs designed to strengthen mathematical techniques and offers challenging opportunities to have fun with mathematics. Ten major topics - profusely illustrated - include: Mathematical Models, Elementary Concepts of Grap
Uncertain Graph Sparsification
Parchas, Panos; Papailiou, Nikolaos; Papadias, Dimitris; Bonchi, Francesco
2016-01-01
Uncertain graphs are prevalent in several applications including communications systems, biological databases and social networks. The ever increasing size of the underlying data renders both graph storage and query processing extremely expensive. Sparsification has often been used to reduce the size of deterministic graphs by maintaining only the important edges. However, adaptation of deterministic sparsification methods fails in the uncertain setting. To overcome this problem, we introduce...
Directory of Open Access Journals (Sweden)
Aleks Kissinger
2014-03-01
Full Text Available String diagrams are a powerful tool for reasoning about physical processes, logic circuits, tensor networks, and many other compositional structures. Dixon, Duncan and Kissinger introduced string graphs, which are a combinatoric representations of string diagrams, amenable to automated reasoning about diagrammatic theories via graph rewrite systems. In this extended abstract, we show how the power of such rewrite systems can be greatly extended by introducing pattern graphs, which provide a means of expressing infinite families of rewrite rules where certain marked subgraphs, called !-boxes ("bang boxes", on both sides of a rule can be copied any number of times or removed. After reviewing the string graph formalism, we show how string graphs can be extended to pattern graphs and how pattern graphs and pattern rewrite rules can be instantiated to concrete string graphs and rewrite rules. We then provide examples demonstrating the expressive power of pattern graphs and how they can be applied to study interacting algebraic structures that are central to categorical quantum mechanics.
Creating more effective graphs
Robbins, Naomi B
2012-01-01
A succinct and highly readable guide to creating effective graphs The right graph can be a powerful tool for communicating information, improving a presentation, or conveying your point in print. If your professional endeavors call for you to present data graphically, here's a book that can help you do it more effectively. Creating More Effective Graphs gives you the basic knowledge and techniques required to choose and create appropriate graphs for a broad range of applications. Using real-world examples everyone can relate to, the author draws on her years of experience in gr
DEFF Research Database (Denmark)
Mansutti, Alessio; Miculan, Marino; Peressotti, Marco
2017-01-01
We introduce loose graph simulations (LGS), a new notion about labelled graphs which subsumes in an intuitive and natural way subgraph isomorphism (SGI), regular language pattern matching (RLPM) and graph simulation (GS). Being a unification of all these notions, LGS allows us to express directly...... also problems which are “mixed” instances of previous ones, and hence which would not fit easily in any of them. After the definition and some examples, we show that the problem of finding loose graph simulations is NP-complete, we provide formal translation of SGI, RLPM, and GS into LGSs, and we give...
DEFF Research Database (Denmark)
Thomassen, Carsten
2014-01-01
We prove a general result on graph factors modulo k . A special case says that, for each natural number k , every (12k−7)-edge-connected graph with an even number of vertices contains a spanning subgraph in which each vertex has degree congruent to k modulo 2k.......We prove a general result on graph factors modulo k . A special case says that, for each natural number k , every (12k−7)-edge-connected graph with an even number of vertices contains a spanning subgraph in which each vertex has degree congruent to k modulo 2k....
Gelfand, I M; Shnol, E E
1969-01-01
The second in a series of systematic studies by a celebrated mathematician I. M. Gelfand and colleagues, this volume presents students with a well-illustrated sequence of problems and exercises designed to illuminate the properties of functions and graphs. Since readers do not have the benefit of a blackboard on which a teacher constructs a graph, the authors abandoned the customary use of diagrams in which only the final form of the graph appears; instead, the book's margins feature step-by-step diagrams for the complete construction of each graph. The first part of the book employs simple fu
Energy Technology Data Exchange (ETDEWEB)
Lothian, Joshua [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Powers, Sarah S. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Sullivan, Blair D. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Baker, Matthew B. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Schrock, Jonathan [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Poole, Stephen W. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
2013-10-01
The benchmarking effort within the Extreme Scale Systems Center at Oak Ridge National Laboratory seeks to provide High Performance Computing benchmarks and test suites of interest to the DoD sponsor. The work described in this report is a part of the effort focusing on graph generation. A previously developed benchmark, SystemBurn, allowed the emulation of different application behavior profiles within a single framework. To complement this effort, similar capabilities are desired for graph-centric problems. This report examines existing synthetic graph generator implementations in preparation for further study on the properties of their generated synthetic graphs.
Characterisations of Intersection Graphs by Vertex Orderings
Wood, David R.
2004-01-01
Characterisations of interval graphs, comparability graphs, co-comparability graphs, permutation graphs, and split graphs in terms of linear orderings of the vertex set are presented. As an application, it is proved that interval graphs, co-comparability graphs, AT-free graphs, and split graphs have bandwidth bounded by their maximum degree.
Directory of Open Access Journals (Sweden)
A. Assari
2016-01-01
Full Text Available In this paper, a graph is assigned to any probability measure on the σ-algebra of Borel sets of a topological space. Using this construction, it is proved that given any number n (finite or infinite there exists a nonregular graph such that its clique, chromatic, and dominating number equals n.
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)
de Mol, M.J.; Rensink, Arend; Hunt, James J.
This paper introduces an approach for adding graph transformation-based functionality to existing JAVA programs. The approach relies on a set of annotations to identify the intended graph structure, as well as on user methods to manipulate that structure, within the user’s own JAVA class
Perepelitsa, VA; Sergienko, [No Value; Kochkarov, AM
1999-01-01
Definitions of prefractal and fractal graphs are introduced, and they are used to formulate mathematical models in different fields of knowledge. The topicality of fractal-graph recognition from the point of view, of fundamental improvement in the efficiency of the solution of algorithmic problems
Joyner, W David
2017-01-01
This textbook acts as a pathway to higher mathematics by seeking and illuminating the connections between graph theory and diverse fields of mathematics, such as calculus on manifolds, group theory, algebraic curves, Fourier analysis, cryptography and other areas of combinatorics. An overview of graph theory definitions and polynomial invariants for graphs prepares the reader for the subsequent dive into the applications of graph theory. To pique the reader’s interest in areas of possible exploration, recent results in mathematics appear throughout the book, accompanied with examples of related graphs, how they arise, and what their valuable uses are. The consequences of graph theory covered by the authors are complicated and far-reaching, so topics are always exhibited in a user-friendly manner with copious graphs, exercises, and Sage code for the computation of equations. Samples of the book’s source code can be found at github.com/springer-math/adventures-in-graph-theory. The text is geared towards ad...
Packing Degenerate Graphs Greedily
Czech Academy of Sciences Publication Activity Database
Allen, P.; Böttcher, J.; Hladký, J.; Piguet, Diana
2017-01-01
Roč. 61, August (2017), s. 45-51 ISSN 1571-0653 R&D Projects: GA ČR GJ16-07822Y Institutional support: RVO:67985807 Keywords : tree packing conjecture * graph packing * graph processes Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics
DEFF Research Database (Denmark)
Husfeldt, Thore
2015-01-01
This chapter presents an introduction to graph colouring algorithms. The focus is on vertex-colouring algorithms that work for general classes of graphs with worst-case performance guarantees in a sequential model of computation. The presentation aims to demonstrate the breadth of available...
Moment graphs and representations
DEFF Research Database (Denmark)
Jantzen, Jens Carsten
2012-01-01
Moment graphs and sheaves on moment graphs are basically combinatorial objects that have be used to describe equivariant intersectiion cohomology. In these lectures we are going to show that they can be used to provide a direct link from this cohomology to the representation theory of simple Lie...
Directory of Open Access Journals (Sweden)
Behnaz Tolue
2018-07-01
Full Text Available In this paper we introduce stable subgroup graph associated to the group $G$. It is a graph with vertex set all subgroups of $G$ and two distinct subgroups $H_1$ and $H_2$ are adjacent if $St_{G}(H_1\\cap H_2\
Generalized connectivity of graphs
Li, Xueliang
2016-01-01
Noteworthy results, proof techniques, open problems and conjectures in generalized (edge-) connectivity are discussed in this book. Both theoretical and practical analyses for generalized (edge-) connectivity of graphs are provided. Topics covered in this book include: generalized (edge-) connectivity of graph classes, algorithms, computational complexity, sharp bounds, Nordhaus-Gaddum-type results, maximum generalized local connectivity, extremal problems, random graphs, multigraphs, relations with the Steiner tree packing problem and generalizations of connectivity. This book enables graduate students to understand and master a segment of graph theory and combinatorial optimization. Researchers in graph theory, combinatorics, combinatorial optimization, probability, computer science, discrete algorithms, complexity analysis, network design, and the information transferring models will find this book useful in their studies.
Product of Locally Primitive Graphs
Directory of Open Access Journals (Sweden)
Amir Assari
2014-01-01
Full Text Available Many large graphs can be constructed from existing smaller graphs by using graph operations, such as the product of two graphs. Many properties of such large graphs are closely related to those of the corresponding smaller ones. In this paper we consider the product of two locally primitive graphs and prove that only tensor product of them will also be locally primitive.
Graph Abstraction and Abstract Graph Transformation
Boneva, I.B.; Rensink, Arend; Kurban, M.E.; Bauer, J.
2007-01-01
Many important systems like concurrent heap-manipulating programs, communication networks, or distributed algorithms are hard to verify due to their inherent dynamics and unboundedness. Graphs are an intuitive representation of states of these systems, where transitions can be conveniently described
Chen, Xinjian; Udupa, Jayaram K; Alavi, Abass; Torigian, Drew A
2013-05-01
Image segmentation methods may be classified into two categories: purely image based and model based. Each of these two classes has its own advantages and disadvantages. In this paper, we propose a novel synergistic combination of the image based graph-cut (GC) method with the model based ASM method to arrive at the GC-ASM method for medical image segmentation. A multi-object GC cost function is proposed which effectively integrates the ASM shape information into the GC framework. The proposed method consists of two phases: model building and segmentation. In the model building phase, the ASM model is built and the parameters of the GC are estimated. The segmentation phase consists of two main steps: initialization (recognition) and delineation. For initialization, an automatic method is proposed which estimates the pose (translation, orientation, and scale) of the model, and obtains a rough segmentation result which also provides the shape information for the GC method. For delineation, an iterative GC-ASM algorithm is proposed which performs finer delineation based on the initialization results. The proposed methods are implemented to operate on 2D images and evaluated on clinical chest CT, abdominal CT, and foot MRI data sets. The results show the following: (a) An overall delineation accuracy of TPVF > 96%, FPVF segmentation step compared to GC which requires seed specification and improves on the accuracy of GC. (e) One disadvantage of GC-ASM is its increased computational expense owing to the iterative nature of the algorithm.
Lloyd, Gillian R.; Oza, Sonal; Kozey-Keadle, Sarah; Pellegrini, Christine A.; Conroy, David E.; Penedo, Frank J.; Spring, Bonnie J.; Phillips, Siobhan M.
2017-01-01
Purpose Less time spent in sedentary behaviors is associated with improved health and disease outcomes in breast cancer survivors. However, little is known about survivors’ interest in sedentary behavior reduction interventions and how to effectively reduce this risk behavior. The purpose of this study was to explore breast cancer survivors’ interest in and preferences for technology-supported sedentary behavior reduction interventions. Methods Breast cancer survivors [n=279; Mage=60.7 (SD=9.7)] completed a battery of online questionnaires. Descriptive statistics were calculated for all data. To examine potential relationships between demographic, disease and behavioral factors, and survivors’ interest in a technology-supported sedentary behavior reduction intervention, we conducted logistic regression analyses. These same factors were examined in relation to the perceptions of the effectiveness of such intervention using multiple regression analyses. Results On average, survivors spent 10.1 (SD=4.3) hours/day in sedentary activity. They believed prolonged periods of sedentary behavior were harmful to their health (87.0%) and that reducing sedentary behavior could improve their health (88.4%). Survivors believed they should move around after 30–60 (56.7%) or ≥60 (29.9%) minutes of sedentary behavior and indicated they were most likely to replace sedentary behaviors with walking around (97.1%) or walking in place (73.4%). The majority of survivors (79.9%) was interested in participating in a technology-supported sedentary behavior reduction intervention and indicated they would use a smartphone application (61.3%) 2–3 times/day (48.0%), 6 to 7 days/week (52.0%). Most survivors (73.5%) believed reminders would help them decrease sedentary behavior and preferred they be delivered after sitting for 60 minutes (60.5%) via vibrations on a wrist worn activity tracker (77.3%) or text messages (54.4%). Conclusions Technology-supported sedentary behavior
Graph-theoretical concepts and physicochemical data
Directory of Open Access Journals (Sweden)
Lionello Pogliani
2003-02-01
Full Text Available Graph theoretical concepts have been used to model the molecular polarizabilities of fifty-four organic derivatives, and the induced dipole moment of a set of fifty-seven organic compounds divided into three subsets. The starting point of these modeling strategies is the hydrogen-suppressed chemical graph and pseudograph of a molecule, which works very well for second row atoms. From these types of graphs a set of graph-theoretical basis indices, the molecular connectivity indices, can be derived and used to model properties and activities of molecules. With the aid of the molecular connectivity basis indices it is then possible to build higher-order descriptors. The problem of 'graph' encoding the contribution of the inner-core electrons of heteroatoms can here be solved with the aid of odd complete graphs, Kp-(p-odd. The use of these graph tools allow to draw an optimal modeling of the molecular polarizabilities and a satisfactory modeling of the induced dipole moment of a wide set of organic derivatives.
Bollobas, Bela
2004-01-01
The ever-expanding field of extremal graph theory encompasses a diverse array of problem-solving methods, including applications to economics, computer science, and optimization theory. This volume, based on a series of lectures delivered to graduate students at the University of Cambridge, presents a concise yet comprehensive treatment of extremal graph theory.Unlike most graph theory treatises, this text features complete proofs for almost all of its results. Further insights into theory are provided by the numerous exercises of varying degrees of difficulty that accompany each chapter. A
Decomposing Oriented Graphs into Six Locally Irregular Oriented Graphs
DEFF Research Database (Denmark)
Bensmail, Julien; Renault, Gabriel
2016-01-01
An undirected graph G is locally irregular if every two of its adjacent vertices have distinct degrees. We say that G is decomposable into k locally irregular graphs if there exists a partition E1∪E2∪⋯∪Ek of the edge set E(G) such that each Ei induces a locally irregular graph. It was recently...... conjectured by Baudon et al. that every undirected graph admits a decomposition into at most three locally irregular graphs, except for a well-characterized set of indecomposable graphs. We herein consider an oriented version of this conjecture. Namely, can every oriented graph be decomposed into at most...... three locally irregular oriented graphs, i.e. whose adjacent vertices have distinct outdegrees? We start by supporting this conjecture by verifying it for several classes of oriented graphs. We then prove a weaker version of this conjecture. Namely, we prove that every oriented graph can be decomposed...
Alspach, BR
1985-01-01
This volume deals with a variety of problems involving cycles in graphs and circuits in digraphs. Leading researchers in this area present here 3 survey papers and 42 papers containing new results. There is also a collection of unsolved problems.
Tailored Random Graph Ensembles
International Nuclear Information System (INIS)
Roberts, E S; Annibale, A; Coolen, A C C
2013-01-01
Tailored graph ensembles are a developing bridge between biological networks and statistical mechanics. The aim is to use this concept to generate a suite of rigorous tools that can be used to quantify and compare the topology of cellular signalling networks, such as protein-protein interaction networks and gene regulation networks. We calculate exact and explicit formulae for the leading orders in the system size of the Shannon entropies of random graph ensembles constrained with degree distribution and degree-degree correlation. We also construct an ergodic detailed balance Markov chain with non-trivial acceptance probabilities which converges to a strictly uniform measure and is based on edge swaps that conserve all degrees. The acceptance probabilities can be generalized to define Markov chains that target any alternative desired measure on the space of directed or undirected graphs, in order to generate graphs with more sophisticated topological features.
Learning Probabilistic Decision Graphs
DEFF Research Database (Denmark)
Jaeger, Manfred; Dalgaard, Jens; Silander, Tomi
2004-01-01
Probabilistic decision graphs (PDGs) are a representation language for probability distributions based on binary decision diagrams. PDGs can encode (context-specific) independence relations that cannot be captured in a Bayesian network structure, and can sometimes provide computationally more...
Wilson, Robin J
1985-01-01
Graph Theory has recently emerged as a subject in its own right, as well as being an important mathematical tool in such diverse subjects as operational research, chemistry, sociology and genetics. This book provides a comprehensive introduction to the subject.
Efficiently Controllable Graphs.
Gokler, Can; Lloyd, Seth; Shor, Peter; Thompson, Kevin
2017-06-30
We investigate graphs that can be disconnected into small components by removing a vanishingly small fraction of their vertices. We show that, when a controllable quantum network is described by such a graph and the gaps in eigenfrequencies and in transition frequencies are bounded exponentially in the number of vertices, the network is efficiently controllable, in the sense that universal quantum computation can be performed using a control sequence polynomial in the size of the network while controlling a vanishingly small fraction of subsystems. We show that networks corresponding to finite-dimensional lattices are efficiently controllable and explore generalizations to percolation clusters and random graphs. We show that the classical computational complexity of estimating the ground state of Hamiltonians described by controllable graphs is polynomial in the number of subsystems or qubits.
Graph Embedded Extreme Learning Machine.
Iosifidis, Alexandros; Tefas, Anastasios; Pitas, Ioannis
2016-01-01
In this paper, we propose a novel extension of the extreme learning machine (ELM) algorithm for single-hidden layer feedforward neural network training that is able to incorporate subspace learning (SL) criteria on the optimization process followed for the calculation of the network's output weights. The proposed graph embedded ELM (GEELM) algorithm is able to naturally exploit both intrinsic and penalty SL criteria that have been (or will be) designed under the graph embedding framework. In addition, we extend the proposed GEELM algorithm in order to be able to exploit SL criteria in arbitrary (even infinite) dimensional ELM spaces. We evaluate the proposed approach on eight standard classification problems and nine publicly available datasets designed for three problems related to human behavior analysis, i.e., the recognition of human face, facial expression, and activity. Experimental results denote the effectiveness of the proposed approach, since it outperforms other ELM-based classification schemes in all the cases.
Groups, graphs and random walks
Salvatori, Maura; Sava-Huss, Ecaterina
2017-01-01
An accessible and panoramic account of the theory of random walks on groups and graphs, stressing the strong connections of the theory with other branches of mathematics, including geometric and combinatorial group theory, potential analysis, and theoretical computer science. This volume brings together original surveys and research-expository papers from renowned and leading experts, many of whom spoke at the workshop 'Groups, Graphs and Random Walks' celebrating the sixtieth birthday of Wolfgang Woess in Cortona, Italy. Topics include: growth and amenability of groups; Schrödinger operators and symbolic dynamics; ergodic theorems; Thompson's group F; Poisson boundaries; probability theory on buildings and groups of Lie type; structure trees for edge cuts in networks; and mathematical crystallography. In what is currently a fast-growing area of mathematics, this book provides an up-to-date and valuable reference for both researchers and graduate students, from which future research activities will undoubted...
Interaction Graphs: Exponentials
Seiller, Thomas
2013-01-01
This paper is the fourth of a series exposing a systematic combinatorial approach to Girard's Geometry of Interaction program. This program aims at obtaining particular realizability models for linear logic that accounts for the dynamics of cut-elimination. This fourth paper tackles the complex issue of defining exponential connectives in this framework. In order to succeed in this, we use the notion of graphings, a generalization of graphs which was defined in earlier work. We explain how we...
DEFF Research Database (Denmark)
Bakhshesh, Davood; Barba, Luis; Bose, Prosenjit
2018-01-01
In this paper, we introduce a variation of the well-studied Yao graphs. Given a set of points S⊂R2 and an angle 0Yao graph cY(θ) with vertex set S and angle θ as follows. For each p,q∈S, we add an edge from p to q in cY(θ) if there exists a cone with apex p...
Uniform Single Valued Neutrosophic Graphs
Directory of Open Access Journals (Sweden)
S. Broumi
2017-09-01
Full Text Available In this paper, we propose a new concept named the uniform single valued neutrosophic graph. An illustrative example and some properties are examined. Next, we develop an algorithmic approach for computing the complement of the single valued neutrosophic graph. A numerical example is demonstrated for computing the complement of single valued neutrosophic graphs and uniform single valued neutrosophic graph.
Local Interaction on Random Graphs
Directory of Open Access Journals (Sweden)
Hans Haller
2010-08-01
Full Text Available We analyze dynamic local interaction in population games where the local interaction structure (modeled as a graph can change over time: A stochastic process generates a random sequence of graphs. This contrasts with models where the initial interaction structure (represented by a deterministic graph or the realization of a random graph cannot change over time.
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.
Categorical constructions in graph theory
Directory of Open Access Journals (Sweden)
Richard T. Bumby
1986-01-01
Full Text Available This paper presents some graph-theoretic questions from the viewpoint of the portion of category theory which has become common knowledge. In particular, the reader is encouraged to consider whether there is only one natural category of graphs and how theories of directed graphs and undirected graphs are related.
O'Brien, O A; McCarthy, M; Gibney, E R; McAuliffe, F M
2014-07-01
Overweight and obesity are associated with increased risk of adverse maternal and fetal outcomes. However, the actuality of delivering effective lifestyle interventions in clinical practice is hampered by a high demand for resources. The use of technology to assist lifestyle interventions needs to be explored as a valid method of reducing strain on resources, and enhancing the effectiveness and population reach of interventions. The aim was to systematically review the literature on the use of technology-supported lifestyle interventions for healthy pregnant women and their impact on maternal outcomes. Online databases and registries were searched in March 2013. Primary outcomes of selected English language studies were fasting maternal glucose, incidence of gestational diabetes mellitus (GDM) and maternal gestational weight gain. Secondary outcomes were intervention uptake and acceptance, and dietary or physical activity modification. Studies whose subjects were diagnosed with GDM prior to intervention were excluded. The minimal number of eligible studies and varying outcomes precluded formal meta-analysis of the data. Initially, 203 articles were identified and screened. Seven articles, including five randomised controlled trials, met inclusion criteria for the current review. Results demonstrate several potential benefits associated with technology-supported interventions in pregnancy, despite minimal search results. Although communication technology holds potential as a safe therapeutic tool for the support of lifestyle interventions in pregnancy, there is a paucity of data on its effectiveness. Further RCTs examining the effectiveness of communication technology are required, particularly among those most likely to benefit from lifestyle interventions, such as overweight and obese pregnant women.
Commuting projections on graphs
Energy Technology Data Exchange (ETDEWEB)
Vassilevski, Panayot S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing; Zikatanov, Ludmil T. [Pennsylvania State Univ., University Park, PA (United States). Dept. of Mathematics
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 ℓ_{2}-projection Q_{H} 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 Q_{H} commute with the discrete divergence operator, i.e., we have div π _{H} = Q_{H} 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.
Bollobás, Béla
1998-01-01
The time has now come when graph theory should be part of the education of every serious student of mathematics and computer science, both for its own sake and to enhance the appreciation of mathematics as a whole. This book is an in-depth account of graph theory, written with such a student in mind; it reflects the current state of the subject and emphasizes connections with other branches of pure mathematics. The volume grew out of the author's earlier book, Graph Theory -- An Introductory Course, but its length is well over twice that of its predecessor, allowing it to reveal many exciting new developments in the subject. Recognizing that graph theory is one of several courses competing for the attention of a student, the book contains extensive descriptive passages designed to convey the flavor of the subject and to arouse interest. In addition to a modern treatment of the classical areas of graph theory such as coloring, matching, extremal theory, and algebraic graph theory, the book presents a detailed ...
Hierarchy of graph matchbox manifolds
Lukina, Olga
2011-01-01
We study a class of graph foliated spaces, or graph matchbox manifolds, initially constructed by Kenyon and Ghys. For graph foliated spaces we introduce a quantifier of dynamical complexity which we call its level. We develop the fusion construction, which allows us to associate to every two graph foliated spaces a third one which contains the former two in its closure. Although the underlying idea of the fusion is simple, it gives us a powerful tool to study graph foliated spaces. Using fusi...
Linear representation of a graph
Directory of Open Access Journals (Sweden)
Eduardo Montenegro
2019-10-01
Full Text Available In this paper the linear representation of a graph is defined. A linear representation of a graph is a subgroup of $GL(p,\\mathbb{R}$, the group of invertible matrices of order $ p $ and real coefficients. It will be demonstrated that every graph admits a linear representation. In this paper, simple and finite graphs will be used, framed in the graphs theory's area
Proxy Graph: Visual Quality Metrics of Big Graph Sampling.
Nguyen, Quan Hoang; Hong, Seok-Hee; Eades, Peter; Meidiana, Amyra
2017-06-01
Data sampling has been extensively studied for large scale graph mining. Many analyses and tasks become more efficient when performed on graph samples of much smaller size. The use of proxy objects is common in software engineering for analysis and interaction with heavy objects or systems. In this paper, we coin the term 'proxy graph' and empirically investigate how well a proxy graph visualization can represent a big graph. Our investigation focuses on proxy graphs obtained by sampling; this is one of the most common proxy approaches. Despite the plethora of data sampling studies, this is the first evaluation of sampling in the context of graph visualization. For an objective evaluation, we propose a new family of quality metrics for visual quality of proxy graphs. Our experiments cover popular sampling techniques. Our experimental results lead to guidelines for using sampling-based proxy graphs in visualization.
Gastin, Paul B; Cayzer, Cassy; Dwyer, Dan; Robertson, Sam
2018-03-01
The purpose of this study was to assess the validity of the ActiGraph GT3X+ (GT3X+) and the BodyMedia SenseWear Armband (SWA) to estimate energy expenditure (EE) during physical activity and field sport movements. Criterion validity. Twenty-six active adults completed a single 90min session involving alternating intervals of exercise (5min) and recovery (10min). Exercise involved walking (4km/h), jogging (8km/h), running (12km/h) or a sport-simulated circuit (three intervals). Participants wore two triaxial accelerometers (GT3X+ and SWA) and a portable gas analyser (MetaMax 3B), used as the criterion measure. Total EE was significantly underestimated (p<0.01) by the GT3X+ (mean bias±SD: -374.5±132.84kJ; % difference=-29.3%) and SWA (-244.3±148.0kJ; -18.2%). Overestimations were made by both accelerometers during the walk (GT3X+: 27.4±30.8kJ; SWA: 32.1±15.4kJ) and jog (38.0±30.0kJ; 34.5±31.6kJ). Underestimations were evident during the run (-41.2±25.1kJ; -43.8±33.5kJ) and circuit (C1: GTX+: -127.2±41.6kJ; SWA: -86.1±40.2kJ). Error of estimation increased in magnitude as the intensity of exercise increased (GT3X+: 40.8-143.0kJ; SWA: 35.5-102.0kJ). The ActiGraph GT3X+ and BodyMedia SWA do not provide valid EE estimates across a range of exercise modalities and intensities when compared to a criterion measure. Poor accuracy and large precision errors, particularly during high intensity and intermittent movement patterns, suggest these devices have limitations and should be used cautiously in the field. Copyright © 2017 Sports Medicine Australia. Published by Elsevier Ltd. All rights reserved.
The STAPL Parallel Graph Library
Harshvardhan,
2013-01-01
This paper describes the stapl Parallel Graph Library, a high-level framework that abstracts the user from data-distribution and parallelism details and allows them to concentrate on parallel graph algorithm development. It includes a customizable distributed graph container and a collection of commonly used parallel graph algorithms. The library introduces pGraph pViews that separate algorithm design from the container implementation. It supports three graph processing algorithmic paradigms, level-synchronous, asynchronous and coarse-grained, and provides common graph algorithms based on them. Experimental results demonstrate improved scalability in performance and data size over existing graph libraries on more than 16,000 cores and on internet-scale graphs containing over 16 billion vertices and 250 billion edges. © Springer-Verlag Berlin Heidelberg 2013.
Fundamentals of algebraic graph transformation
Ehrig, Hartmut; Prange, Ulrike; Taentzer, Gabriele
2006-01-01
Graphs are widely used to represent structural information in the form of objects and connections between them. Graph transformation is the rule-based manipulation of graphs, an increasingly important concept in computer science and related fields. This is the first textbook treatment of the algebraic approach to graph transformation, based on algebraic structures and category theory. Part I is an introduction to the classical case of graph and typed graph transformation. In Part II basic and advanced results are first shown for an abstract form of replacement systems, so-called adhesive high-level replacement systems based on category theory, and are then instantiated to several forms of graph and Petri net transformation systems. Part III develops typed attributed graph transformation, a technique of key relevance in the modeling of visual languages and in model transformation. Part IV contains a practical case study on model transformation and a presentation of the AGG (attributed graph grammar) tool envir...
Quantitative graph theory mathematical foundations and applications
Dehmer, Matthias
2014-01-01
The first book devoted exclusively to quantitative graph theory, Quantitative Graph Theory: Mathematical Foundations and Applications presents and demonstrates existing and novel methods for analyzing graphs quantitatively. Incorporating interdisciplinary knowledge from graph theory, information theory, measurement theory, and statistical techniques, this book covers a wide range of quantitative-graph theoretical concepts and methods, including those pertaining to real and random graphs such as:Comparative approaches (graph similarity or distance)Graph measures to characterize graphs quantitat
Ribes, Luis
2017-01-01
This book offers a detailed introduction to graph theoretic methods in profinite groups and applications to abstract groups. It is the first to provide a comprehensive treatment of the subject. The author begins by carefully developing relevant notions in topology, profinite groups and homology, including free products of profinite groups, cohomological methods in profinite groups, and fixed points of automorphisms of free pro-p groups. The final part of the book is dedicated to applications of the profinite theory to abstract groups, with sections on finitely generated subgroups of free groups, separability conditions in free and amalgamated products, and algorithms in free groups and finite monoids. Profinite Graphs and Groups will appeal to students and researchers interested in profinite groups, geometric group theory, graphs and connections with the theory of formal languages. A complete reference on the subject, the book includes historical and bibliographical notes as well as a discussion of open quest...
White, AT
1985-01-01
The field of topological graph theory has expanded greatly in the ten years since the first edition of this book appeared. The original nine chapters of this classic work have therefore been revised and updated. Six new chapters have been added, dealing with: voltage graphs, non-orientable imbeddings, block designs associated with graph imbeddings, hypergraph imbeddings, map automorphism groups and change ringing.Thirty-two new problems have been added to this new edition, so that there are now 181 in all; 22 of these have been designated as ``difficult'''' and 9 as ``unsolved''''. Three of the four unsolved problems from the first edition have been solved in the ten years between editions; they are now marked as ``difficult''''.
Graph theory and interconnection networks
Hsu, Lih-Hsing
2008-01-01
The advancement of large scale integrated circuit technology has enabled the construction of complex interconnection networks. Graph theory provides a fundamental tool for designing and analyzing such networks. Graph Theory and Interconnection Networks provides a thorough understanding of these interrelated topics. After a brief introduction to graph terminology, the book presents well-known interconnection networks as examples of graphs, followed by in-depth coverage of Hamiltonian graphs. Different types of problems illustrate the wide range of available methods for solving such problems. The text also explores recent progress on the diagnosability of graphs under various models.
Endomorphisms of graph algebras
DEFF Research Database (Denmark)
Conti, Roberto; Hong, Jeong Hee; Szymanski, Wojciech
2012-01-01
We initiate a systematic investigation of endomorphisms of graph C*-algebras C*(E), extending several known results on endomorphisms of the Cuntz algebras O_n. Most but not all of this study is focused on endomorphisms which permute the vertex projections and globally preserve the diagonal MASA D......_E of C*(E). Our results pertain both automorphisms and proper endomorphisms. Firstly, the Weyl group and the restricted Weyl group of a graph C*-algebra are introduced and investigated. In particular, criteria of outerness for automorphisms in the restricted Weyl group are found. We also show...
Stevanovic, Dragan
2015-01-01
Spectral Radius of Graphs provides a thorough overview of important results on the spectral radius of adjacency matrix of graphs that have appeared in the literature in the preceding ten years, most of them with proofs, and including some previously unpublished results of the author. The primer begins with a brief classical review, in order to provide the reader with a foundation for the subsequent chapters. Topics covered include spectral decomposition, the Perron-Frobenius theorem, the Rayleigh quotient, the Weyl inequalities, and the Interlacing theorem. From this introduction, the
Handbook of graph grammars and computing by graph transformation
Engels, G; Kreowski, H J; Rozenberg, G
1999-01-01
Graph grammars originated in the late 60s, motivated by considerations about pattern recognition and compiler construction. Since then, the list of areas which have interacted with the development of graph grammars has grown quite impressively. Besides the aforementioned areas, it includes software specification and development, VLSI layout schemes, database design, modeling of concurrent systems, massively parallel computer architectures, logic programming, computer animation, developmental biology, music composition, visual languages, and many others.The area of graph grammars and graph tran
Topics in graph theory graphs and their Cartesian product
Imrich, Wilfried; Rall, Douglas F
2008-01-01
From specialists in the field, you will learn about interesting connections and recent developments in the field of graph theory by looking in particular at Cartesian products-arguably the most important of the four standard graph products. Many new results in this area appear for the first time in print in this book. Written in an accessible way, this book can be used for personal study in advanced applications of graph theory or for an advanced graph theory course.
Using Graph Transformations and Graph Abstractions for Software Verification
Zambon, Eduardo; Rensink, Arend
In this paper we describe our intended approach for the verification of software written in imperative programming languages. We base our approach on model checking of graph transition systems, where each state is a graph and the transitions are specified by graph transformation rules. We believe
Robustness of random graphs based on graph spectra.
Wu, Jun; Barahona, Mauricio; Tan, Yue-Jin; Deng, Hong-Zhong
2012-12-01
It has been recently proposed that the robustness of complex networks can be efficiently characterized through the natural connectivity, a spectral property of the graph which corresponds to the average Estrada index. The natural connectivity corresponds to an average eigenvalue calculated from the graph spectrum and can also be interpreted as the Helmholtz free energy of the network. In this article, we explore the use of this index to characterize the robustness of Erdős-Rényi (ER) random graphs, random regular graphs, and regular ring lattices. We show both analytically and numerically that the natural connectivity of ER random graphs increases linearly with the average degree. It is also shown that ER random graphs are more robust than the corresponding random regular graphs with the same number of vertices and edges. However, the relative robustness of ER random graphs and regular ring lattices depends on the average degree and graph size: there is a critical graph size above which regular ring lattices are more robust than random graphs. We use our analytical results to derive this critical graph size as a function of the average degree.
Codes related to line graphs of triangular graphs and permutation ...
African Journals Online (AJOL)
For any prime p, we consider p-ary linear codes obtained from the row span of incidence matrices of line graphs of triangular graphs and adjacency matrices of their line graphs. We determine parameters of the codes, their automorphism groups and exhibit permutation decoding sets (PD-sets) for partial permutation ...
González-Díaz, Humberto; Herrera-Ibatá, Diana María; Duardo-Sánchez, Aliuska; Munteanu, Cristian R; Orbegozo-Medina, Ricardo Alfredo; Pazos, Alejandro
2014-03-24
This work is aimed at describing the workflow for a methodology that combines chemoinformatics and pharmacoepidemiology methods and at reporting the first predictive model developed with this methodology. The new model is able to predict complex networks of AIDS prevalence in the US counties, taking into consideration the social determinants and activity/structure of anti-HIV drugs in preclinical assays. We trained different Artificial Neural Networks (ANNs) using as input information indices of social networks and molecular graphs. We used a Shannon information index based on the Gini coefficient to quantify the effect of income inequality in the social network. We obtained the data on AIDS prevalence and the Gini coefficient from the AIDSVu database of Emory University. We also used the Balaban information indices to quantify changes in the chemical structure of anti-HIV drugs. We obtained the data on anti-HIV drug activity and structure (SMILE codes) from the ChEMBL database. Last, we used Box-Jenkins moving average operators to quantify information about the deviations of drugs with respect to data subsets of reference (targets, organisms, experimental parameters, protocols). The best model found was a Linear Neural Network (LNN) with values of Accuracy, Specificity, and Sensitivity above 0.76 and AUROC > 0.80 in training and external validation series. This model generates a complex network of AIDS prevalence in the US at county level with respect to the preclinical activity of anti-HIV drugs in preclinical assays. To train/validate the model and predict the complex network we needed to analyze 43,249 data points including values of AIDS prevalence in 2,310 counties in the US vs ChEMBL results for 21,582 unique drugs, 9 viral or human protein targets, 4,856 protocols, and 10 possible experimental measures.
AN EFFECTIVE RECOMMENDATIONS BY DIFFUSION ALGORITHM FOR WEB GRAPH MINING
Directory of Open Access Journals (Sweden)
S. Vasukipriya
2013-04-01
Full Text Available The information on the World Wide Web grows in an explosive rate. Societies are relying more on the Web for their miscellaneous needs of information. Recommendation systems are active information filtering systems that attempt to present the information items like movies, music, images, books recommendations, tags recommendations, query suggestions, etc., to the users. Various kinds of data bases are used for the recommendations; fundamentally these data bases can be molded in the form of many types of graphs. Aiming at provided that a general framework on effective DR (Recommendations by Diffusion algorithm for web graphs mining. First introduce a novel graph diffusion model based on heat diffusion. This method can be applied to both undirected graphs and directed graphs. Then it shows how to convert different Web data sources into correct graphs in our models.
Visualizing automorphisms of graph algebras
DEFF Research Database (Denmark)
Avery, James Emil; Johansen, Rune; Szymanski, Wojciech
2018-01-01
Graph C*-algebras have been celebrated as C*-algebras that can be seen, because many important properties may be determined by looking at the underlying graph. This paper introduces the permutation graph for a permutative endomorphism of a graph C*-algebra as a labeled directed multigraph...... that gives a visual representation of the endomorphism and facilitates computations. Combinatorial criteria have previously been developed for deciding when such an endomorphism is an automorphism, but here the question is reformulated in terms of the permutation graph and new proofs are given. Furthermore......, it is shown how to use permutation graphs to efficiently generate exhaustive collections of permutative automorphisms. Permutation graphs provide a natural link to the textile systems representing induced endomorphisms on the edge shift of the given graph, and this allows the powerful tools of the theory...
Rensink, Arend; Schmidt, David
2004-01-01
Graphs are an intuitive model for states of a (software) system that include pointer structures | for instance, object-oriented programs. However, a naive encoding results in large individual states and large, or even unbounded, state spaces. As usual, some form of abstraction is necessary in order
Rensink, Arend; Schmidt, D.A.
2004-01-01
Abstract. Graphs are an intuitive model for states of a (software) system that include pointer structures — for instance, object-oriented programs. However, a naive encoding results in large individual states and large, or even unbounded, state spaces. As usual, some form of abstraction is necessary
Dujmović, Vida; Sidiropoulos, Anastasios; Wood, David R.
2015-01-01
Bourgain and Yehudayoff recently constructed $O(1)$-monotone bipartite expanders. By combining this result with a generalisation of the unraveling method of Kannan, we construct 3-monotone bipartite expanders, which is best possible. We then show that the same graphs admit 3-page book embeddings, 2-queue layouts, 4-track layouts, and have simple thickness 2. All these results are best possible.
S.M. Heditniemi (Sandra); R.C. Laskar (R.C.); H.M. Mulder (Martyn)
2012-01-01
textabstractLet $G = (V,E)$ be a graph. A partition $\\pi = \\{V_1, V_2, \\ldots, V_k \\}$ of the vertices $V$ of $G$ into $k$ {\\it color classes} $V_i$, with $1 \\leq i \\leq k$, is called a {\\it quorum coloring} if for every vertex $v \\in V$, at least half of the vertices in the closed neighborhood
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…
Grabmayer, C.A.; van Oostrom, V.
2014-01-01
We report on work in progress on `nested term graphs' for formalizing higher-order terms (e.g. finite or infinite lambda-terms), including those expressing recursion (e.g. terms in the lambda-calculus with letrec). The idea is to represent the nested scope structure of a higher-order term by a
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 8; Issue 9. Decoding Codes on Graphs - Low Density Parity Check Codes. A S Madhu Aditya Nori. General Article Volume 8 Issue 9 September 2003 pp 49-59. Fulltext. Click here to view fulltext PDF. Permanent link:
Energy Technology Data Exchange (ETDEWEB)
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.
Temporal Representation in Semantic Graphs
Energy Technology Data Exchange (ETDEWEB)
Levandoski, J J; Abdulla, G M
2007-08-07
A wide range of knowledge discovery and analysis applications, ranging from business to biological, make use of semantic graphs when modeling relationships and concepts. Most of the semantic graphs used in these applications are assumed to be static pieces of information, meaning temporal evolution of concepts and relationships are not taken into account. Guided by the need for more advanced semantic graph queries involving temporal concepts, this paper surveys the existing work involving temporal representations in semantic graphs.
On dominator colorings in graphs
Indian Academy of Sciences (India)
Graph coloring and domination are two major areas in graph theory that have been ... independent set if no two vertices in S are adjacent. ... independent set. The corona G1 ◦ G2 of two graphs G1 and G2 is defined to be the graph. G obtained by taking one copy of G1 and |V(G1)| copies of G2, and then joining the i-th.
Hamiltonian paths on Platonic graphs
Directory of Open Access Journals (Sweden)
Brian Hopkins
2004-07-01
Full Text Available We develop a combinatorial method to show that the dodecahedron graph has, up to rotation and reflection, a unique Hamiltonian cycle. Platonic graphs with this property are called topologically uniquely Hamiltonian. The same method is used to demonstrate topologically distinct Hamiltonian cycles on the icosahedron graph and to show that a regular graph embeddable on the 2-holed torus is topologically uniquely Hamiltonian.
Energy Technology Data Exchange (ETDEWEB)
Winlaw, Manda [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); De Sterck, Hans [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Sanders, Geoffrey [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2015-10-26
In very simple terms a network can be de ned as a collection of points joined together by lines. Thus, networks can be used to represent connections between entities in a wide variety of elds including engi- neering, science, medicine, and sociology. Many large real-world networks share a surprising number of properties, leading to a strong interest in model development research and techniques for building synthetic networks have been developed, that capture these similarities and replicate real-world graphs. Modeling these real-world networks serves two purposes. First, building models that mimic the patterns and prop- erties of real networks helps to understand the implications of these patterns and helps determine which patterns are important. If we develop a generative process to synthesize real networks we can also examine which growth processes are plausible and which are not. Secondly, high-quality, large-scale network data is often not available, because of economic, legal, technological, or other obstacles [7]. Thus, there are many instances where the systems of interest cannot be represented by a single exemplar network. As one example, consider the eld of cybersecurity, where systems require testing across diverse threat scenarios and validation across diverse network structures. In these cases, where there is no single exemplar network, the systems must instead be modeled as a collection of networks in which the variation among them may be just as important as their common features. By developing processes to build synthetic models, so-called graph generators, we can build synthetic networks that capture both the essential features of a system and realistic variability. Then we can use such synthetic graphs to perform tasks such as simulations, analysis, and decision making. We can also use synthetic graphs to performance test graph analysis algorithms, including clustering algorithms and anomaly detection algorithms.
Nullspace embeddings for outerplanar graphs
L. Lovász (László); A. Schrijver (Alexander)
2017-01-01
textabstractWe study relations between geometric embeddings of graphs and the spectrum of associated matrices, focusing on outerplanar embeddings of graphs. For a simple connected graph G=(V,E), we define a "good" G-matrix as a V×V matrix with negative entries corresponding to adjacent nodes, zero
Nullspace embeddings for outerplanar graphs
L. Lovász (László); A. Schrijver (Alexander); M. Loebl (Martin); J. Nešetřil (Jaroslav); R. Thomas (Robin)
2017-01-01
htmlabstractWe study relations between geometric embeddings of graphs and the spectrum of associated matrices, focusing on outerplanar embeddings of graphs. For a simple connected graph G = (V, E), we define a "good” G-matrix as a V × V matrix with negative
Nullspace embeddings for outerplanar graphs
Lovász, L.; Schrijver, A.; Loebl, M.; Nešetřil, J.; Thomas, R.
2017-01-01
We study relations between geometric embeddings of graphs and the spectrum of associated matrices, focusing on outerplanar embeddings of graphs. For a simple connected graph G = (V, E), we define a “good” G-matrix as a V × V matrix with negative entries corresponding to adjacent nodes, zero entries
Pattern-Based Graph Abstraction
Rensink, Arend; Zambon, Eduardo; Ehrig, H; Engels, G.; Kreowski, H.J.; Rozenberg, G.
We present a new abstraction technique for the exploration of graph transformation systems with infinite state spaces. This technique is based on patterns, simple graphs describing structures of interest that should be preserved by the abstraction. Patterns are collected into pattern graphs, layered
Generalised compositionality in graph transformation
Ghamarian, A.H.; Rensink, Arend; Ehrig, H; Engels, G.; Kreowski, H.J.; Rozenberg, G.
We present a notion of composition applying both to graphs and to rules, based on graph and rule interfaces along which they are glued. The current paper generalises a previous result in two different ways. Firstly, rules do not have to form pullbacks with their interfaces; this enables graph
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…
Mining and Indexing Graph Databases
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.…
Graph transformation tool contest 2008
Rensink, Arend; van Gorp, Pieter
This special section is the outcome of the graph transformation tool contest organised during the Graph-Based Tools (GraBaTs) 2008 workshop, which took place as a satellite event of the International Conference on Graph Transformation (ICGT) 2008. The contest involved two parts: three “off-line case
Submanifolds weakly associated with graphs
Indian Academy of Sciences (India)
We establish an interesting link between differential geometry and graph theory by defining submanifolds weakly associated with graphs. We prove that, in a local sense, every submanifold satisfies such an association, and other general results. Finally, we study submanifolds associated with graphs either in low ...
Asteroidal Quadruples in non Rooted Path Graphs
Directory of Open Access Journals (Sweden)
Gutierrez Marisa
2015-11-01
Full Text Available A directed path graph is the intersection graph of a family of directed subpaths of a directed tree. A rooted path graph is the intersection graph of a family of directed subpaths of a rooted tree. Rooted path graphs are directed path graphs. Several characterizations are known for directed path graphs: one by forbidden induced subgraphs and one by forbidden asteroids. It is an open problem to find such characterizations for rooted path graphs. For this purpose, we are studying in this paper directed path graphs that are non rooted path graphs. We prove that such graphs always contain an asteroidal quadruple.
Green Globs: A Microcomputer Application for Graphing of Equations.
Dugdale, Sharon
This paper outlines the development of an activity that uses the computer's unique capabilities to provide students with a meaningful and highly motivating experience with the graphing of equations. The basic design of the game calls for the computer to display a coordinate grid on which it graphs any equations that are typed in by the student.…
Harary, Frank
2015-01-01
Presented in 1962-63 by experts at University College, London, these lectures offer a variety of perspectives on graph theory. Although the opening chapters form a coherent body of graph theoretic concepts, this volume is not a text on the subject but rather an introduction to the extensive literature of graph theory. The seminar's topics are geared toward advanced undergraduate students of mathematics.Lectures by this volume's editor, Frank Harary, include ""Some Theorems and Concepts of Graph Theory,"" ""Topological Concepts in Graph Theory,"" ""Graphical Reconstruction,"" and other introduc
Domination criticality in product graphs
Directory of Open Access Journals (Sweden)
M.R. Chithra
2015-07-01
Full Text Available A connected dominating set is an important notion and has many applications in routing and management of networks. Graph products have turned out to be a good model of interconnection networks. This motivated us to study the Cartesian product of graphs G with connected domination number, γc(G=2,3 and characterize such graphs. Also, we characterize the k−γ-vertex (edge critical graphs and k−γc-vertex (edge critical graphs for k=2,3 where γ denotes the domination number of G. We also discuss the vertex criticality in grids.
Dynamic Representations of Sparse Graphs
DEFF Research Database (Denmark)
Brodal, Gerth Stølting; Fagerberg, Rolf
1999-01-01
We present a linear space data structure for maintaining graphs with bounded arboricity—a large class of sparse graphs containing e.g. planar graphs and graphs of bounded treewidth—under edge insertions, edge deletions, and adjacency queries. The data structure supports adjacency queries in worst...... case O(c) time, and edge insertions and edge deletions in amortized O(1) and O(c+log n) time, respectively, where n is the number of nodes in the graph, and c is the bound on the arboricity....
Graph Creation, Visualisation and Transformation
Directory of Open Access Journals (Sweden)
Maribel Fernández
2010-03-01
Full Text Available We describe a tool to create, edit, visualise and compute with interaction nets - a form of graph rewriting systems. The editor, called GraphPaper, allows users to create and edit graphs and their transformation rules using an intuitive user interface. The editor uses the functionalities of the TULIP system, which gives us access to a wealth of visualisation algorithms. Interaction nets are not only a formalism for the specification of graphs, but also a rewrite-based computation model. We discuss graph rewriting strategies and a language to express them in order to perform strategic interaction net rewriting.
Towards Scalable Graph Computation on Mobile Devices
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
Towards Scalable Graph Computation on Mobile Devices.
Chen, Yiqi; Lin, Zhiyuan; Pienta, Robert; Kahng, Minsuk; Chau, Duen Horng
2014-10-01
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.
Graph Sampling for Covariance Estimation
Chepuri, Sundeep Prabhakar
2017-04-25
In this paper the focus is on subsampling as well as reconstructing the second-order statistics of signals residing on nodes of arbitrary undirected graphs. Second-order stationary graph signals may be obtained by graph filtering zero-mean white noise and they admit a well-defined power spectrum whose shape is determined by the frequency response of the graph filter. Estimating the graph power spectrum forms an important component of stationary graph signal processing and related inference tasks such as Wiener prediction or inpainting on graphs. The central result of this paper is that by sampling a significantly smaller subset of vertices and using simple least squares, we can reconstruct the second-order statistics of the graph signal from the subsampled observations, and more importantly, without any spectral priors. To this end, both a nonparametric approach as well as parametric approaches including moving average and autoregressive models for the graph power spectrum are considered. The results specialize for undirected circulant graphs in that the graph nodes leading to the best compression rates are given by the so-called minimal sparse rulers. A near-optimal greedy algorithm is developed to design the subsampling scheme for the non-parametric and the moving average models, whereas a particular subsampling scheme that allows linear estimation for the autoregressive model is proposed. Numerical experiments on synthetic as well as real datasets related to climatology and processing handwritten digits are provided to demonstrate the developed theory.
Hendrix, William; Jenkins, John; Padmanabhan, Kanchana; Chakraborty, Arpan
2014-01-01
Practical Graph Mining with R presents a "do-it-yourself" approach to extracting interesting patterns from graph data. It covers many basic and advanced techniques for the identification of anomalous or frequently recurring patterns in a graph, the discovery of groups or clusters of nodes that share common patterns of attributes and relationships, the extraction of patterns that distinguish one category of graphs from another, and the use of those patterns to predict the category of new graphs. Hands-On Application of Graph Data Mining Each chapter in the book focuses on a graph mining task, such as link analysis, cluster analysis, and classification. Through applications using real data sets, the book demonstrates how computational techniques can help solve real-world problems. The applications covered include network intrusion detection, tumor cell diagnostics, face recognition, predictive toxicology, mining metabolic and protein-protein interaction networks, and community detection in social networks. De...
Canonical Labelling of Site Graphs
Directory of Open Access Journals (Sweden)
Nicolas Oury
2013-06-01
Full Text Available We investigate algorithms for canonical labelling of site graphs, i.e. graphs in which edges bind vertices on sites with locally unique names. We first show that the problem of canonical labelling of site graphs reduces to the problem of canonical labelling of graphs with edge colourings. We then present two canonical labelling algorithms based on edge enumeration, and a third based on an extension of Hopcroft's partition refinement algorithm. All run in quadratic worst case time individually. However, one of the edge enumeration algorithms runs in sub-quadratic time for graphs with "many" automorphisms, and the partition refinement algorithm runs in sub-quadratic time for graphs with "few" bisimulation equivalences. This suite of algorithms was chosen based on the expectation that graphs fall in one of those two categories. If that is the case, a combined algorithm runs in sub-quadratic worst case time. Whether this expectation is reasonable remains an interesting open problem.
Directory of Open Access Journals (Sweden)
Burhan Selçuk
2017-06-01
Full Text Available Hypercube is a popular interconnection network. Due to the popularity of hypercube, more researchers pay a great effort to develop the different variants of hypercube. In this paper, we have proposed a variant of hypercube which is called as “Connected Cubic Network Graphs”, and have investigated the Hamilton-like properties of Connected Cubic Network Graphs (CCNG. Firstly, we defined CCNG and showed the characteristic analyses of CCNG. Then, we showed that the CCNG has the properties of Hamilton graph, and can be labeled using a Gray coding based recursive algorithm. Finally, we gave the comparison results, a routing algorithm and a bitonic sort algorithm for CCNG. In case of sparsity and cost, CCNG is better than Hypercube.
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…
Directory of Open Access Journals (Sweden)
Falcon Seth
2007-09-01
Full Text Available Abstract 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.
2010-12-02
evaluating the function ΘP (A) for any fixed A,P is equivalent to solving the so-called Quadratic Assignment Problem ( QAP ), and thus we can employ various...tractable linear programming, spectral, and SDP relaxations of QAP [40, 11, 33]. In particular we discuss recent work [14] on exploiting group...symmetry in SDP relaxations of QAP , which is useful for approximately computing elementary convex graph invariants in many interesting cases. Finally in
Technology-Supported Art as a "Way to Participation"
Directory of Open Access Journals (Sweden)
Molly Bathje MS, OTR/L
2014-04-01
Full Text Available Brianna Vitale provided the painting featured on the cover of the Spring 2014 issue of The Open Journal of Occupational Therapy. Brianna completed the painting, titled “Flamingo,” using a mouth joystick (joust to draw the image on her computer and an assistive device to translate her computer artwork into the watercolor painting. At 12 years old, Brianna has been living for the past 9 years with tetraplegia, the result of a spinal cord injury (SCI. Through technology and with the support of family, friends, and health care professionals, Brianna energetically engages in a variety of creative, social, and philanthropic activities.
Zhou, Feng; de la Torre, Fernando
2015-11-19
Graph matching (GM) is a fundamental problem in computer science, and it plays a central role to solve correspondence problems in computer vision. GM problems that incorporate pairwise constraints can be formulated as a quadratic assignment problem (QAP). Although widely used, solving the correspondence problem through GM has two main limitations: (1) the QAP is NP-hard and difficult to approximate; (2) GM algorithms do not incorporate geometric constraints between nodes that are natural in computer vision problems. To address aforementioned problems, this paper proposes factorized graph matching (FGM). FGM factorizes the large pairwise affinity matrix into smaller matrices that encode the local structure of each graph and the pairwise affinity between edges. Four are the benefits that follow from this factorization: (1) There is no need to compute the costly (in space and time) pairwise affinity matrix; (2) The factorization allows the use of a path-following optimization algorithm, that leads to improved optimization strategies and matching performance; (3) Given the factorization, it becomes straight-forward to incorporate geometric transformations (rigid and non-rigid) to the GM problem. (4) Using a matrix formulation for the GM problem and the factorization, it is easy to reveal commonalities and differences between different GM methods. The factorization also provides a clean connection with other matching algorithms such as iterative closest point; Experimental results on synthetic and real databases illustrate how FGM outperforms state-of-the-art algorithms for GM. The code is available at http://humansensing.cs.cmu.edu/fgm.
A graph-based mathematical morphology reader
Najman, Laurent; Cousty, Jean
2014-01-01
This survey paper aims at providing a "literary" anthology of mathematical morphology on graphs. It describes in the English language many ideas stemming from a large number of different papers, hence providing a unified view of an active and diverse field of research.
Technology support in nursing education: clickers in the classroom.
Berry, Janice
2009-01-01
Research has shown that the present generation of students has a preference for digital literacy, experiential learning, interactivity, and immediacy; therefore, greater use of technology is being brought into university courses to aid in student involvement. Student Response Systems, called clickers, were incorporated as a teaching methodology to enhance student interaction and learning in a didactic pediatric nursing course. This course was taught over Interactive Television (ITV) with students at a distant site as well as face to face, creating the challenge of whole-class engagement. Clickers were used to actively engage students at both sites simultaneously and give immediate feedback to students regarding understanding of lecture material. Clickers also allowed small-group problem solving of questions. Exam grades and level of participation in case studies were monitored and exam scores and final scores were compared to those of a previous class. Student t-tests demonstrated that one of three course exams and final course grades were significantly higher for the students who used clickers in the classroom. Satisfaction feedback also supported the use of clickers as a tool to engage students and enhance learning outcomes.
Graphs cospectral with a friendship graph or its complement
Directory of Open Access Journals (Sweden)
Alireza Abdollahi
2013-12-01
Full Text Available Let $n$ be any positive integer and let $F_n$ be the friendship (or Dutch windmill graph with $2n+1$ vertices and $3n$ edges. Here we study graphs with the same adjacency spectrum as the $F_n$. Two graphs are called cospectral if the eigenvalues multiset of their adjacency matrices are the same. Let $G$ be a graph cospectral with $F_n$. Here we prove that if $G$ has no cycle of length $4$ or $5$, then $Gcong F_n$. Moreover if $G$ is connected and planar then $Gcong F_n$.All but one of connected components of $G$ are isomorphic to $K_2$.The complement $overline{F_n}$ of the friendship graph is determined by its adjacency eigenvalues, that is, if $overline{F_n}$ is cospectral with a graph $H$, then $Hcong overline{F_n}$.
TECHNOLOGY SUPPORTED LEARNING PLATFORM: Moodle Integrated Academic Course
Directory of Open Access Journals (Sweden)
Saziye YAMAN
2010-04-01
Full Text Available It is substantially accepted that constructivism proposes knowledge as “not a fixed object”; constructed by an individual through her own experiences. As a learning theory, constructivism in education emphasizes collaborative learning, such as authentic challenging projects involving in students, teachers and experts in the learning community. Its goal is to create learning communities that are more closely related to the collaborative practice of the real world as strongly reflected in social constructivist idea. The technologies used in the filed of education will support learning through collaborative practices, using learners’ experiences for “meaning making”. The challenge now is to extend the educational networks so that it offers access to learning resources, online storage and tools for communication and management not just within the limitation of school and time. Through learning platforms, such as Moodle, teachers and administrators may bring hardware, software and supporting services together to enable more effective conditions among teachers and students. In this study, Moodle was used to support the 4th grade pre-service language teachers’ (student teachers one of the academic courses, named as “Field Experience”. The student teachers were expected to prepare graduation theses in the field of English language teaching. Moodle was integrated as a technological learning aid and used as online support throughout a semester course. So, we will discuss how Moodle was integrated as a learning platform, while discussing, the use of Moodle as a “course supporter” process, steps and the sample activities will be presented as well.
Dickson, Diane
2015-05-01
Linking theory to practice is an area of concern for ultrasound students, clinical mentors and academic staff. The link between theory and practice requires a robust clinical mentorship scheme in addition to careful curricula design considerations to improve student outcomes. The introduction of interactive technology in education provides ripe opportunity to improve feedback to students to support the link between theory and practice. A series of three interactive learning and teaching activities were designed and delivered to a PostGraduate Ultrasound cohort, after which, evaluation was performed to answer the research question: Which interactive technologies support the link between theory and practice through improved feedback mechanisms? An action research methodology was adopted involving an enquiry based literature review, planning, design and action process. Data were collected following action of three interactive teaching and learning sessions within the Medical Ultrasound cohort of 2013/2014 at Glasgow Caledonian University via a paper based questionnaire. A 100% response rate was achieved (n = 14). All three interactive learning and teaching sessions were considered with 100% highest point agreement to support the link between ultrasound theory and practice via feedback. Students found all three designed and facilitated sessions valuable and relevant to their learning, which in turn provided positive experiences which were perceived to support the link between theory and practice through feedback. These activities can be considered valuable in Postgraduate Ultrasound education.
X-Graphs: Language and Algorithms for Heterogeneous Graph Streams
2017-09-01
parallel implementations for many key graph algorithms, conversions between tables and graphs and Python language bindings. SNAP is widely deployed...1. We have used Delite to develop a suite of DSLs for data analysis (query processing, machine learning , and graph processing). Approved for Public...range of users, interested in network analysis: support for Python - a major programming language for data scientists, documentation, tutorials, and
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
Graphs Theory and Applications
Fournier, Jean-Claude
2008-01-01
This book provides a pedagogical and comprehensive introduction to graph theory and its applications. It contains all the standard basic material and develops significant topics and applications, such as: colorings and the timetabling problem, matchings and the optimal assignment problem, and Hamiltonian cycles and the traveling salesman problem, to name but a few. Exercises at various levels are given at the end of each chapter, and a final chapter presents a few general problems with hints for solutions, thus providing the reader with the opportunity to test and refine their knowledge on the
Solved and unsolved problems of chemical graph theory
International Nuclear Information System (INIS)
Trinajstic, N.; Klein, D.J.; Randic, M.
1986-01-01
The development of several novel graph theoretical concepts and their applications in different branches of chemistry are reviewed. After a few introductory remarks they follow with an outline of selected important graph theoretical invariants, introducing some new results and indicating some open problems. They continue with discussing the problem of graph characterization and construction of graphs of chemical interest, with a particular emphasis on large systems. Finally they consider various problems and difficulties associated with special subgraphs, including subgraphs representing Kekule valence structures. The paper ends with a brief review of structure-property and structure-activity correlations, the topic which is one of prime motivations for application of graph theory to chemistry
Kanstrup, Anne Marie; Bertelsen, Pernille; Nohr, Christian
The aim of this paper is to identify characteristics of patients' contributions to innovation in health information technology (HIT). The paper outlines a theoretical definition of patient innovation and presents an analysis of four digital prototypes and 22 low-fidelity mock-ups designed by people affected by the chronic illness diabetes mellitus. Seventeen families (a total of 60 people) with one or more diabetic family members participated in design activities in a four-year research project focused on the design of digital support for everyday living with diabetes. Our analysis documented the originality of the analysed patient designs and identified three characteristics of patients' designs: socio-technical networks, objects with associated personal meanings and technology supporting the expression of identity. The paper concludes that patient innovation is defined by what is perceived as new by patients and/or others within the social system of adaptation. The analysed patient designs are original (as distinct from replications of or improvements on known products), and their characteristics are innovative contributions to the social system of everyday living with diabetes (i.e. they are perceived as new to the patients in the research study). The results of the analysis contribute to the credentials of patients as key actors in HIT innovation and call for participatory approaches in health informatics.
Nested Dynamic Condition Response Graphs
DEFF Research Database (Denmark)
Hildebrandt, Thomas; Mukkamala, Raghava Rao; Slaats, Tijs
2012-01-01
We present an extension of the recently introduced declarative process model Dynamic Condition Response Graphs ( DCR Graphs) to allow nested subgraphs and a new milestone relation between events. The extension was developed during a case study carried out jointly with our industrial partner...... Exformatics, a danish provider of case and workflow management systems. We formalize the semantics by giving first a map from Nested to (flat) DCR Graphs with milestones, and then extending the previously given mapping from DCR Graphs to Buchi-automata to include the milestone relation....
Spectral partitioning in equitable graphs.
Barucca, Paolo
2017-06-01
Graph partitioning problems emerge in a wide variety of complex systems, ranging from biology to finance, but can be rigorously analyzed and solved only for a few graph ensembles. Here, an ensemble of equitable graphs, i.e., random graphs with a block-regular structure, is studied, for which analytical results can be obtained. In particular, the spectral density of this ensemble is computed exactly for a modular and bipartite structure. Kesten-McKay's law for random regular graphs is found analytically to apply also for modular and bipartite structures when blocks are homogeneous. An exact solution to graph partitioning for two equal-sized communities is proposed and verified numerically, and a conjecture on the absence of an efficient recovery detectability transition in equitable graphs is suggested. A final discussion summarizes results and outlines their relevance for the solution of graph partitioning problems in other graph ensembles, in particular for the study of detectability thresholds and resolution limits in stochastic block models.
Energy Technology Data Exchange (ETDEWEB)
Maunz, Peter Lukas Wilhelm [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Sterk, Jonathan David [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Lobser, Daniel [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Parekh, Ojas D. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Ryan-Anderson, Ciaran [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2016-01-01
In recent years, advanced network analytics have become increasingly important to na- tional security with applications ranging from cyber security to detection and disruption of ter- rorist networks. While classical computing solutions have received considerable investment, the development of quantum algorithms to address problems, such as data mining of attributed relational graphs, is a largely unexplored space. Recent theoretical work has shown that quan- tum algorithms for graph analysis can be more efficient than their classical counterparts. Here, we have implemented a trapped-ion-based two-qubit quantum information proces- sor to address these goals. Building on Sandia's microfabricated silicon surface ion traps, we have designed, realized and characterized a quantum information processor using the hyperfine qubits encoded in two 171 Yb + ions. We have implemented single qubit gates using resonant microwave radiation and have employed Gate set tomography (GST) to characterize the quan- tum process. For the first time, we were able to prove that the quantum process surpasses the fault tolerance thresholds of some quantum codes by demonstrating a diamond norm distance of less than 1 . 9 x 10 [?] 4 . We used Raman transitions in order to manipulate the trapped ions' motion and realize two-qubit gates. We characterized the implemented motion sensitive and insensitive single qubit processes and achieved a maximal process infidelity of 6 . 5 x 10 [?] 5 . We implemented the two-qubit gate proposed by Molmer and Sorensen and achieved a fidelity of more than 97 . 7%.
ILIGRA : An Efficient Inverse Line Graph Algorithm
Liu, D.; Trajanovski, S.; Van Mieghem, P.
2014-01-01
This paper presents a new and efficient algorithm, ILIGRA, for inverse line graph construction. Given a line graph H, ILIGRA constructs its root graph G with the time complexity being linear in the number of nodes in H. If ILIGRA does not know whether the given graph H is a line graph, it firstly
On Graph Rewriting, Reduction and Evaluation
DEFF Research Database (Denmark)
Zerny, Ian
2010-01-01
We inter-derive two prototypical styles of graph reduction: reduction machines à la Turner and graph rewriting systems à la Barendregt et al. To this end, we adapt Danvy et al.'s mechanical program derivations from the world of terms to the world of graphs. We also outline how to inter......-derive a third style of graph reduction: a graph evaluator....
ON BIPOLAR SINGLE VALUED NEUTROSOPHIC GRAPHS
Broumi, Said; Talea, Mohamed; Bakali, Assia; Smarandache, Florentin
2016-01-01
In this article, we combine the concept of bipolar neutrosophic set and graph theory. We introduce the notions of bipolar single valued neutrosophic graphs, strong bipolar single valued neutrosophic graphs, complete bipolar single valued neutrosophic graphs, regular bipolar single valued neutrosophic graphs and investigate some of their related properties.
Using Graph Transformations and Graph Abstractions for Software Verification
Zambon, Eduardo; Ehrig, Hartmut; Rensink, Arend; Rozenberg, Grzegorz; Schurr, Andy
In this abstract we present an overview of our intended approach for the verification of software written in imperative programming languages. This approach is based on model checking of graph transition systems (GTS), where each program state is modeled as a graph and the exploration engine is
Kirchhoff index of graphs and some graph operations
Indian Academy of Sciences (India)
We define the -repetition of to be the graph obtained by joining y i to x j for each i ∈ V ( T ) and each child of . In this paper, we compute the Kirchhoff index of the -repetition of in terms of parameters of and . Also we study how K f ( G ) behaves under some graph operations such as joining vertices or ...
Graph Theory. 2. Vertex Descriptors and Graph Coloring
Directory of Open Access Journals (Sweden)
Lorentz JÄNTSCHI
2002-12-01
Full Text Available This original work presents the construction of a set of ten sequence matrices and their applications for ordering vertices in graphs. For every sequence matrix three ordering criteria are applied: lexicographic ordering, based on strings of numbers, corresponding to every vertex, extracted as rows from sequence matrices; ordering by the sum of path lengths from a given vertex; and ordering by the sum of paths, starting from a given vertex. We also examine a graph that has different orderings for the above criteria. We then proceed to demonstrate that every criterion induced its own partition of graph vertex. We propose the following theoretical result: both LAVS and LVDS criteria generate identical partitioning of vertices in any graph. Finally, a coloring of graph vertices according to introduced ordering criteria was proposed.
An Application of Cartesian Graphing to Seismic Exploration.
Robertson, Douglas Frederick
1992-01-01
Describes how college students enrolled in a course in elementary algebra apply graphing and algebra to data collected from a seismic profile to uncover the structure of a subterranean rock formation. Includes steps guiding the activity. (MDH)
Chordal Graphs and Semidefinite Optimization
DEFF Research Database (Denmark)
Vandenberghe, Lieven; Andersen, Martin Skovgaard
2015-01-01
Chordal graphs play a central role in techniques for exploiting sparsity in large semidefinite optimization problems and in related con-vex optimization problems involving sparse positive semidefinite matrices. Chordal graph properties are also fundamental to several classical results in combinat...
DYNAMICALLY MAINTAINING THE VISIBILITY GRAPH
VEGTER, G
1991-01-01
An algorithm is presented to maintain the visibility graph of a set of N line segments in the plane in O(log2 N + K log N) time, where K is the total number of arcs of the visibility graph that are destroyed or created upon insertion or deletion of a line segment. The line segments should be
A cluster algorithm for graphs
S. van Dongen
2000-01-01
textabstractA cluster algorithm for graphs called the emph{Markov Cluster algorithm (MCL~algorithm) is introduced. The algorithm provides basically an interface to an algebraic process defined on stochastic matrices, called the MCL~process. The graphs may be both weighted (with nonnegative weight)
The planar cubic Cayley graphs
Georgakopoulos, Agelos
2018-01-01
The author obtains a complete description of the planar cubic Cayley graphs, providing an explicit presentation and embedding for each of them. This turns out to be a rich class, comprising several infinite families. He obtains counterexamples to conjectures of Mohar, Bonnington and Watkins. The author's analysis makes the involved graphs accessible to computation, corroborating a conjecture of Droms.
The planar cubic cayley graphs
Georgakopoulos, Agelos
2018-01-01
The author obtains a complete description of the planar cubic Cayley graphs, providing an explicit presentation and embedding for each of them. This turns out to be a rich class, comprising several infinite families. He obtains counterexamples to conjectures of Mohar, Bonnington and Watkins. The author's analysis makes the involved graphs accessible to computation, corroborating a conjecture of Droms.
Hoede, C.; Liu, X
1998-01-01
In continuation of the paper of Hoede and Li on word graphs for a set of prepositions, word graphs are given for adjectives, adverbs and Chinese classifier words. It is argued that these three classes of words belong to a general class of words that may be called adwords. These words express the
2005-06-01
relationship, trust, etc.) between people. • User Psychology : Clickstream graphs are bipartite graphs connecting Internet users to the websites they visit...document groups (say, science fiction novels and thrillers ), based on the word groups that occur most frequently in them. A user who prefers one
Bell inequalities for graph states
International Nuclear Information System (INIS)
Toth, G.; Hyllus, P.; Briegel, H.J.; Guehne, O.
2005-01-01
Full text: In the last years graph states have attracted an increasing interest in the field of quantum information theory. Graph states form a family of multi-qubit states which comprises many popular states such as the GHZ states and the cluster states. They also play an important role in applications. For instance, measurement based quantum computation uses graph states as resources. From a theoretical point of view, it is remarkable that graph states allow for a simple description in terms of stabilizing operators. In this contribution, we investigate the non-local properties of graph states. We derive a family of Bell inequalities which require three measurement settings for each party and are maximally violated by graph states. In turn, any graph state violates at least one of the inequalities. We show that for certain types of graph states the violation of these inequalities increases exponentially with the number of qubits. We also discuss connections to other entanglement properties such as the positively of the partial transpose or the geometric measure of entanglement. (author)
Submanifolds weakly associated with graphs
Indian Academy of Sciences (India)
theory by defining submanifolds weakly associated with graphs. We prove that, in a local sense, every submanifold satisfies such an association, and other general results. Finally, we study submanifolds associated with graphs either in low dimensions or belonging to some special families. Keywords. Almost Hermitian ...
Subgraph Enumeration in Massive Graphs
DEFF Research Database (Denmark)
Silvestri, Francesco
We consider the problem of enumerating all instances of a given sample graph in a large data graph. Our focus is on determining the input/output (I/O) complexity of this problem. Let $E$ be the number of edges in the data graph, $k=\\BO{1}$ be the number of vertexes in the sample graph, $B......$ be the block length, and $M$ be the main memory size. The main result of the paper is a randomized algorithm that enumerates all instances of the sample graph in $\\BO{E^{k/2}/\\left(BM^{k/2-1}\\right)}$ expected I/Os if the maximum vertex degree of the data graph is $\\sqrt{EM}$. Under some assumptions, the same...... bound also applies with high probability. Our algorithm is I/O optimal, in the worst-case, when the sample graph belongs to the Alon class, which includes cliques, cycles and every graph with a perfect matching: indeed, we show that any algorithm enumerating $T$ instances must always use $\\BOM...
A Collection of Features for Semantic Graphs
Energy Technology Data Exchange (ETDEWEB)
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.
Directory of Open Access Journals (Sweden)
Marco Raberto
Full Text Available 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.
RJSplot: Interactive Graphs with R.
Barrios, David; Prieto, Carlos
2018-03-01
Data visualization techniques provide new methods for the generation of interactive graphs. These graphs allow a better exploration and interpretation of data but their creation requires advanced knowledge of graphical libraries. Recent packages have enabled the integration of interactive graphs in R. However, R provides limited graphical packages that allow the generation of interactive graphs for computational biology applications. The present project has joined the analytical power of R with the interactive graphical features of JavaScript in a new R package (RJSplot). It enables the easy generation of interactive graphs in R, provides new visualization capabilities, and contributes to the advance of computational biology analytical methods. At present, 16 interactive graphics are available in RJSplot, such as the genome viewer, Manhattan plots, 3D plots, heatmaps, dendrograms, networks, and so on. The RJSplot package is freely available online at http://rjsplot.net. © 2018 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.
Quantum chaos on discrete graphs
Energy Technology Data Exchange (ETDEWEB)
Smilansky, Uzy [Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100 (Israel); Isaac Newton Institute for Mathematical Sciences, 20 Clarkson Road, Cambridge CB3 0EH (United Kingdom)
2007-07-06
Adapting a method developed for the study of quantum chaos on quantum (metric) graphs (Kottos and Smilansky 1997 Phys. Rev. Lett. 79 4794, Kottos and Smilansky 1999 Ann. Phys., NY 274 76), spectral {zeta} functions and trace formulae for discrete Laplacians on graphs are derived. This is achieved by expressing the spectral secular equation in terms of the periodic orbits of the graph and obtaining functions which belong to the class of {zeta} functions proposed originally by Ihara (1966 J. Mat. Soc. Japan 18 219) and expanded by subsequent authors (Stark and Terras 1996 Adv. Math. 121 124, Kotani and Sunada 2000 J. Math. Sci. Univ. Tokyo 7 7). Finally, a model of 'classical dynamics' on the discrete graph is proposed. It is analogous to the corresponding classical dynamics derived for quantum graphs (Kottos and Smilansky 1997 Phys. Rev. Lett. 79 4794, Kottos and Smilansky 1999 Ann. Phys., NY 274 76). (fast track communication)
Directory of Open Access Journals (Sweden)
I. Sahul Hamid
2016-07-01
Full Text Available A set D of vertices of a graph G is called a dominating set of G if every vertex in V(G−D is adjacent to a vertex in D. A dominating set S such that the subgraph 〈S〉 induced by S has at least one isolated vertex is called an isolate dominating set. An isolate dominating set none of whose proper subset is an isolate dominating set is a minimal isolate dominating set. The minimum and maximum cardinality of a minimal isolate dominating set are called the isolate domination number γ0 and the upper isolate domination number Γ0 respectively. In this paper we initiate a study on these parameters.
Environmental evolutionary graph theory.
Maciejewski, Wes; Puleo, Gregory J
2014-11-07
Understanding the influence of an environment on the evolution of its resident population is a major challenge in evolutionary biology. Great progress has been made in homogeneous population structures while heterogeneous structures have received relatively less attention. Here we present a structured population model where different individuals are best suited to different regions of their environment. The underlying structure is a graph: individuals occupy vertices, which are connected by edges. If an individual is suited for their vertex, they receive an increase in fecundity. This framework allows attention to be restricted to the spatial arrangement of suitable habitat. We prove some basic properties of this model and find some counter-intuitive results. Notably, (1) the arrangement of suitable sites is as important as their proportion, and (2) decreasing the proportion of suitable sites may result in a decrease in the fixation time of an allele. Copyright © 2014 Elsevier Ltd. All rights reserved.
On characterizing terrain visibility graphs
Directory of Open Access Journals (Sweden)
William Evans
2015-06-01
Full Text Available A terrain is an $x$-monotone polygonal line in the $xy$-plane. Two vertices of a terrain are mutually visible if and only if there is no terrain vertex on or above the open line segment connecting them. A graph whose vertices represent terrain vertices and whose edges represent mutually visible pairs of terrain vertices is called a terrain visibility graph. We would like to find properties that are both necessary and sufficient for a graph to be a terrain visibility graph; that is, we would like to characterize terrain visibility graphs.Abello et al. [Discrete and Computational Geometry, 14(3:331--358, 1995] showed that all terrain visibility graphs are “persistent”. They showed that the visibility information of a terrain point set implies some ordering requirements on the slopes of the lines connecting pairs of points in any realization, and as a step towards showing sufficiency, they proved that for any persistent graph $M$ there is a total order on the slopes of the (pseudo lines in a generalized configuration of points whose visibility graph is $M$.We give a much simpler proof of this result by establishing an orientation to every triple of vertices, reflecting some slope ordering requirements that are consistent with $M$ being the visibility graph, and prove that these requirements form a partial order. We give a faster algorithm to construct a total order on the slopes. Our approach attempts to clarify the implications of the graph theoretic properties on the ordering of the slopes, and may be interpreted as defining properties on an underlying oriented matroid that we show is a restricted type of $3$-signotope.
Graph embedding with rich information through heterogeneous graph
Sun, Guolei
2017-11-12
Graph embedding, aiming to learn low-dimensional representations for nodes in graphs, has attracted increasing attention due to its critical application including node classification, link prediction and clustering in social network analysis. Most existing algorithms for graph embedding only rely on the topology information and fail to use the copious information in nodes as well as edges. As a result, their performance for many tasks may not be satisfactory. In this thesis, we proposed a novel and general framework for graph embedding with rich text information (GERI) through constructing a heterogeneous network, in which we integrate node and edge content information with graph topology. Specially, we designed a novel biased random walk to explore the constructed heterogeneous network with the notion of flexible neighborhood. Our sampling strategy can compromise between BFS and DFS local search on heterogeneous graph. To further improve our algorithm, we proposed semi-supervised GERI (SGERI), which learns graph embedding in an discriminative manner through heterogeneous network with label information. The efficacy of our method is demonstrated by extensive comparison experiments with 9 baselines over multi-label and multi-class classification on various datasets including Citeseer, Cora, DBLP and Wiki. It shows that GERI improves the Micro-F1 and Macro-F1 of node classification up to 10%, and SGERI improves GERI by 5% in Wiki.
On some properties of doughnut graphs
Directory of Open Access Journals (Sweden)
Md. Rezaul Karim
2016-08-01
Full Text Available The class of doughnut graphs is a subclass of 5-connected planar graphs. It is known that a doughnut graph admits a straight-line grid drawing with linear area, the outerplanarity of a doughnut graph is 3, and a doughnut graph is k-partitionable. In this paper we show that a doughnut graph exhibits a recursive structure. We also give an efficient algorithm for finding a shortest path between any pair of vertices in a doughnut graph. We also propose a nice application of a doughnut graph based on its properties.
Completeness and regularity of generalized fuzzy graphs.
Samanta, Sovan; Sarkar, Biswajit; Shin, Dongmin; Pal, Madhumangal
2016-01-01
Fuzzy graphs are the backbone of many real systems like networks, image, scheduling, etc. But, due to some restriction on edges, fuzzy graphs are limited to represent for some systems. Generalized fuzzy graphs are appropriate to avoid such restrictions. In this study generalized fuzzy graphs are introduced. In this study, matrix representation of generalized fuzzy graphs is described. Completeness and regularity are two important parameters of graph theory. Here, regular and complete generalized fuzzy graphs are introduced. Some properties of them are discussed. After that, effective regular graphs are exemplified.
Comparison and Enumeration of Chemical Graphs
Akutsu, Tatsuya; Nagamochi, Hiroshi
2013-01-01
Chemical compounds are usually represented as graph structured data in computers. In this review article, we overview several graph classes relevant to chemical compounds and the computational complexities of several fundamental problems for these graph classes. In particular, we consider the following problems: determining whether two chemical graphs are identical, determining whether one input chemical graph is a part of the other input chemical graph, finding a maximum common part of two input graphs, finding a reaction atom mapping, enumerating possible chemical graphs, and enumerating stereoisomers. We also discuss the relationship between the fifth problem and kernel functions for chemical compounds. PMID:24688697
Colored graphs and matrix integrals
International Nuclear Information System (INIS)
Artamkin, I.V.
2007-12-01
In this article we discuss two different asymptotic expansions of matrix integrals. The original approach using the so-called Feynman diagram techniques leads to sums over isomorphism classes of ribbon graphs. Asymptotic expansions of more general Gaussian integrals are sums over isomorphism classes of colored graphs without ribbon structure. Here we derive the former expansion from the latter one. This provides an independent proof for the expansion used by Kontsevich. It might be very interesting to compare the algebra arising in these two approaches. The asymptotic expansion using ribbon graphs leads to the tau function of the KDV hierarchy while the sums over colored graphs satisfy simple partial differential equations which generalize the Burgers equation. We describe the general approach using colored graphs in the second section. In the third section we specialize the results of the second section for the matrix integral. In this section we also derive the expansion over ribbon graphs. The proof is based on simple topological considerations which are contained in section 5. In the last section we give an explicit calculation of the first term of the expansion using colored graphs
Hierarchy of modular graph identities
Energy Technology Data Exchange (ETDEWEB)
D’Hoker, Eric; Kaidi, Justin [Mani L. Bhaumik Institute for Theoretical Physics, Department of Physics and Astronomy,University of California,Los Angeles, CA 90095 (United States)
2016-11-09
The low energy expansion of Type II superstring amplitudes at genus one is organized in terms of modular graph functions associated with Feynman graphs of a conformal scalar field on the torus. In earlier work, surprising identities between two-loop graphs at all weights, and between higher-loop graphs of weights four and five were constructed. In the present paper, these results are generalized in two complementary directions. First, all identities at weight six and all dihedral identities at weight seven are obtained and proven. Whenever the Laurent polynomial at the cusp is available, the form of these identities confirms the pattern by which the vanishing of the Laurent polynomial governs the full modular identity. Second, the family of modular graph functions is extended to include all graphs with derivative couplings and worldsheet fermions. These extended families of modular graph functions are shown to obey a hierarchy of inhomogeneous Laplace eigenvalue equations. The eigenvalues are calculated analytically for the simplest infinite sub-families and obtained by Maple for successively more complicated sub-families. The spectrum is shown to consist solely of eigenvalues s(s−1) for positive integers s bounded by the weight, with multiplicities which exhibit rich representation-theoretic patterns.
Identifying vertex covers in graphs
DEFF Research Database (Denmark)
Henning, Michael A.; Yeo, Anders
2012-01-01
An identifying vertex cover in a graph G is a subset T of vertices in G that has a nonempty intersection with every edge of G such that T distinguishes the edges, that is, e∩T ≠ 0 for every edge e in G and e∩T ≠ f∩T for every two distinct edges e and f in G. The identifying vertex cover number TD......(G) of G is the minimum size of an identifying vertex cover in G. We observe that TD(G)+ρ(G) = |V (G)|, where ρ(G) denotes the packing number of G. We conjecture that if G is a graph of order n and size m with maximum degree Δ, then TD(G) ≤(Δ(Δ-1)/ Δ2+1)n + (2/Δ2+1) m. If the conjecture is true......, then the bound is best possible for all Δ ≥ 1. We prove this conjecture when Δ ≥ 1 and G is a Δ-regular graph. The three known Moore graphs of diameter 2, namely the 5-cycle, the Petersen graph and the Hoffman-Singleton graph, are examples of regular graphs that achieves equality in the upper bound. We also...
Learning How to Design a Technology Supported Inquiry-Based Learning Environment
Hakverdi-Can, Meral; Sonmez, Duygu
2012-01-01
This paper describes a study focusing on pre-service teachers' experience of learning how to design a technology supported inquiry-based learning environment using the Internet. As part of their elective course, pre-service science teachers were asked to develop a WebQuest environment targeting middle school students. A WebQuest is an…
Godzicki, Linda; Godzicki, Nicole; Krofel, Mary; Michaels, Rachel
2013-01-01
This action research project report was conducted in order to increase motivation and engagement in elementary and middle school students through technology-supported learning environments. The study was conducted from August 27, 2012, through December 14, 2012 with 116 participating students in first-, fourth-, fifth- and eighth-grade classes. To…
Rinaldi, Vera D.; Lorr, Nancy A.; Williams, Kimberly
2017-01-01
Monitoring of student learning through systematic formative assessment is important for adjusting pedagogical strategies. However, traditional formative assessments, such as quizzes and written assignments, may not be sufficiently timely for making adjustments to a learning process. Technology supported formative assessment tools assess student…
Ben-Moussa, M.; Rubo, M.; Debracque, C.; Lange, W.G.
2017-01-01
The present paper explores the benefits and the capabilities of various emerging state-of-the-art interactive 3D and Internet of Things (IoT) technologies and investigates how these technologies can be exploited to develop a more effective technology supported exposure therapy solution for Social
Proceedings of the 1st Workshop on Technology Support for Self-Organized Learners
Kalz, Marco; Koper, Rob; Hornung-Prähauser, Veronika; Luckmann, Michaela
2008-01-01
Kalz, M., Koper, R., Hornung-Prähauser, V., & Luckmann, M. (Eds.) (2008). Proceedings of the 1st Workshop on Technology Support for Self-Organized Learners. June, 2-3, 2008, Salzburg, Austria: CEUR Workshop Proceedings, ISSN 1613-0073. Available at http://ceur-ws.org/Vol-349.
Healthcare professional behaviour change using technological supports: A realist literature review
Directory of Open Access Journals (Sweden)
Chris Keyworth
2015-10-01
Technological supports aiming to change the behaviour of healthcare professionals show considerable promise, particularly those involving computer-generated reminders and feedback. Due to the lack of theoretically-informed interventions, we were unable to draw conclusions around the effectiveness of theory-behaviour change interventions in this context. Interventions currently lack consistency in delivery method and content, which future research should address.
Energy Technology Data Exchange (ETDEWEB)
NONE
1998-12-01
This final technical report was prepared by Rolls-Royce Allison summarizing the multiyear activities of the Advanced Turbine Technology Applications Project (ATTAP) and the Hybrid Vehicle Turbine Engine Technology Support (HVTE-TS) project. The ATTAP program was initiated in October 1987 and continued through 1993 under sponsorship of the US Department of Energy (DOE), Energy Conservation and Renewable Energy, Office of Transportation Technologies, Propulsion Systems, Advanced Propulsion Division. ATTAP was intended to advance the technological readiness of the automotive ceramic gas turbine engine. The target application was the prime power unit coupled to conventional transmissions and powertrains. During the early 1990s, hybrid electric powered automotive propulsion systems became the focus of development and demonstration efforts by the US auto industry and the Department of energy. Thus in 1994, the original ATTAP technology focus was redirected to meet the needs of advanced gas turbine electric generator sets. As a result, the program was restructured to provide the required hybrid vehicle turbine engine technology support and the project renamed HVTE-TS. The overall objective of the combined ATTAP and HVTE-TS projects was to develop and demonstrate structural ceramic components that have the potential for competitive automotive engine life cycle cost and for operating 3,500 hr in an advanced high temperature turbine engine environment. This report describes materials characterization and ceramic component development, ceramic components, hot gasifier rig testing, test-bed engine testing, combustion development, insulation development, and regenerator system development. 130 figs., 12 tabs.
Fast construction of voxel-level functional connectivity graphs.
Loewe, Kristian; Grueschow, Marcus; Stoppel, Christian M; Kruse, Rudolf; Borgelt, Christian
2014-06-19
Graph-based analysis of fMRI data has recently emerged as a promising approach to study brain networks. Based on the assessment of synchronous fMRI activity at separate brain sites, functional connectivity graphs are constructed and analyzed using graph-theoretical concepts. Most previous studies investigated region-level graphs, which are computationally inexpensive, but bring along the problem of choosing sensible regions and involve blurring of more detailed information. In contrast, voxel-level graphs provide the finest granularity attainable from the data, enabling analyses at superior spatial resolution. They are, however, associated with considerable computational demands, which can render high-resolution analyses infeasible. In response, many existing studies investigating functional connectivity at the voxel-level reduced the computational burden by sacrificing spatial resolution. Here, a novel, time-efficient method for graph construction is presented that retains the original spatial resolution. Performance gains are instead achieved through data reduction in the temporal domain based on dichotomization of voxel time series combined with tetrachoric correlation estimation and efficient implementation. By comparison with graph construction based on Pearson's r, the technique used by the majority of previous studies, we find that the novel approach produces highly similar results an order of magnitude faster. Its demonstrated performance makes the proposed approach a sensible and efficient alternative to customary practice. An open source software package containing the created programs is freely available for download.
XML Graphs in Program Analysis
DEFF Research Database (Denmark)
Møller, Anders; Schwartzbach, Michael I.
2011-01-01
XML graphs have shown to be a simple and effective formalism for representing sets of XML documents in program analysis. It has evolved through a six year period with variants tailored for a range of applications. We present a unified definition, outline the key properties including validation...... of XML graphs against different XML schema languages, and provide a software package that enables others to make use of these ideas. We also survey the use of XML graphs for program analysis with four very different languages: XACT (XML in Java), Java Servlets (Web application programming), XSugar...... (transformations between XML and non-XML data), and XSLT (stylesheets for transforming XML documents)....
Large networks and graph limits
Lovász, László
2012-01-01
Recently, it became apparent that a large number of the most interesting structures and phenomena of the world can be described by networks. Developing a mathematical theory of very large networks is an important challenge. This book describes one recent approach to this theory, the limit theory of graphs, which has emerged over the last decade. The theory has rich connections with other approaches to the study of large networks, such as "property testing" in computer science and regularity partition in graph theory. It has several applications in extremal graph theory, including the exact for
Kirchhoff index of graphs and some graph operations
Indian Academy of Sciences (India)
Abstract. Let T be a rooted tree, G a connected graph, x,y ∈ V(G) be fixed and Gi's be |V(T )| disjoint copies of G with xi and yi denoting the corresponding copies of x and y in Gi, respectively. We define the T -repetition of G to be the graph obtained by joining yi to xj for each i ∈ V(T ) and each child j of i. In this paper, we ...
Zhao, Jian; Glueck, Michael; Breslav, Simon; Chevalier, Fanny; Khan, Azam
2017-01-01
User-authored annotations of data can support analysts in the activity of hypothesis generation and sensemaking, where it is not only critical to document key observations, but also to communicate insights between analysts. We present annotation graphs, a dynamic graph visualization that enables meta-analysis of data based on user-authored annotations. The annotation graph topology encodes annotation semantics, which describe the content of and relations between data selections, comments, and tags. We present a mixed-initiative approach to graph layout that integrates an analyst's manual manipulations with an automatic method based on similarity inferred from the annotation semantics. Various visual graph layout styles reveal different perspectives on the annotation semantics. Annotation graphs are implemented within C8, a system that supports authoring annotations during exploratory analysis of a dataset. We apply principles of Exploratory Sequential Data Analysis (ESDA) in designing C8, and further link these to an existing task typology in the visualization literature. We develop and evaluate the system through an iterative user-centered design process with three experts, situated in the domain of analyzing HCI experiment data. The results suggest that annotation graphs are effective as a method of visually extending user-authored annotations to data meta-analysis for discovery and organization of ideas.
Graph theory and combinatorial optimization
Marcotte, Odile; Avis, David
2006-01-01
A current treatment of cutting-edge topics in Graph Theory and Combinatorial Optimization by leading researchersIncludes heuristic advances and novel approaches to solving combinatorial optimization problems.
Open Graphs and Computational Reasoning
Directory of Open Access Journals (Sweden)
Lucas Dixon
2010-06-01
Full Text Available We present a form of algebraic reasoning for computational objects which are expressed as graphs. Edges describe the flow of data between primitive operations which are represented by vertices. These graphs have an interface made of half-edges (edges which are drawn with an unconnected end and enjoy rich compositional principles by connecting graphs along these half-edges. In particular, this allows equations and rewrite rules to be specified between graphs. Particular computational models can then be encoded as an axiomatic set of such rules. Further rules can be derived graphically and rewriting can be used to simulate the dynamics of a computational system, e.g. evaluating a program on an input. Examples of models which can be formalised in this way include traditional electronic circuits as well as recent categorical accounts of quantum information.
Graph Model Based Indoor Tracking
DEFF Research Database (Denmark)
Jensen, Christian Søndergaard; Lu, Hua; Yang, Bin
2009-01-01
The tracking of the locations of moving objects in large indoor spaces is important, as it enables a range of applications related to, e.g., security and indoor navigation and guidance. This paper presents a graph model based approach to indoor tracking that offers a uniform data management...... infrastructure for different symbolic positioning technologies, e.g., Bluetooth and RFID. More specifically, the paper proposes a model of indoor space that comprises a base graph and mappings that represent the topology of indoor space at different levels. The resulting model can be used for one or several...... indoor positioning technologies. Focusing on RFID-based positioning, an RFID specific reader deployment graph model is built from the base graph model. This model is then used in several algorithms for constructing and refining trajectories from raw RFID readings. Empirical studies with implementations...
Generating random networks and graphs
Coolen, Ton; Roberts, Ekaterina
2017-01-01
This book supports researchers who need to generate random networks, or who are interested in the theoretical study of random graphs. The coverage includes exponential random graphs (where the targeted probability of each network appearing in the ensemble is specified), growth algorithms (i.e. preferential attachment and the stub-joining configuration model), special constructions (e.g. geometric graphs and Watts Strogatz models) and graphs on structured spaces (e.g. multiplex networks). The presentation aims to be a complete starting point, including details of both theory and implementation, as well as discussions of the main strengths and weaknesses of each approach. It includes extensive references for readers wishing to go further. The material is carefully structured to be accessible to researchers from all disciplines while also containing rigorous mathematical analysis (largely based on the techniques of statistical mechanics) to support those wishing to further develop or implement the theory of rand...
Submanifolds weakly associated with graphs
Indian Academy of Sciences (India)
Leuven: Katholieke Universiteit Leuven). (1990). [5] Etayo F, On quasi-slant submanifolds of an almost Hermitian manifold, Publ. Math. Debrecen 53 (1998) 217–223. [6] Harary F, Graph Theory (Reading: Addison-Wesley) (1972). [7] Papaghiuc N ...
Graph anomalies in cyber communications
Energy Technology Data Exchange (ETDEWEB)
Vander Wiel, Scott A [Los Alamos National Laboratory; Storlie, Curtis B [Los Alamos National Laboratory; Sandine, Gary [Los Alamos National Laboratory; Hagberg, Aric A [Los Alamos National Laboratory; Fisk, Michael [Los Alamos National Laboratory
2011-01-11
Enterprises monitor cyber traffic for viruses, intruders and stolen information. Detection methods look for known signatures of malicious traffic or search for anomalies with respect to a nominal reference model. Traditional anomaly detection focuses on aggregate traffic at central nodes or on user-level monitoring. More recently, however, traffic is being viewed more holistically as a dynamic communication graph. Attention to the graph nature of the traffic has expanded the types of anomalies that are being sought. We give an overview of several cyber data streams collected at Los Alamos National Laboratory and discuss current work in modeling the graph dynamics of traffic over the network. We consider global properties and local properties within the communication graph. A method for monitoring relative entropy on multiple correlated properties is discussed in detail.
A contribution to queens graphs
DEFF Research Database (Denmark)
Barat, Janos
A graph $G$ is a queens graph if the vertices of $G$ can be mapped to queens on the chessboard such that two vertices are adjacent if and only if the corresponding queens attack each other, i.e. they are in horizontal, vertical or diagonal position. We prove a conjecture of Beineke, Broere...... and Henning that the Cartesian product of an odd cycle and a path is a queens graph. We show that the same does not hold for two odd cycles. % is not representable in the same way. The representation of the Cartesian product of an odd cycle and an even cycle remains an open problem. We also prove...... constructively that any finite subgraph of the grid or the hexagonal grid is a queens graph....
SOUR graphs for efficient completion
Lynch, Christopher; Strogova, Polina
1998-01-01
International audience; We introduce a data structure called \\emphSOUR graphs and present an efficient Knuth-Bendix completion procedure based on it. \\emphSOUR graphs allow for a maximal structure sharing of terms in rewriting systems. The term representation is a dag representation, except that edges are labelled with equational constraints and variable renamings. The rewrite rules correspond to rewrite edges, the unification problems to unification edges. The Critical Pair and Simplificatio...
Rectilinear Graphs and Angular Resolution
Bodlaender, H.L.; Tel, G.
2003-01-01
In this note we show that a planar graph with angular resolution at least π/2 can be drawn with all angles an integer multiple of π/2, that is, in a rectilinear manner. Moreover, we show that for d ≠ 4, d › 2, having an angular resolution of 2π/d does not imply that the graph can be drawn with all
Graph theory and its applications
Gross, Jonathan L
2006-01-01
Gross and Yellen take a comprehensive approach to graph theory that integrates careful exposition of classical developments with emerging methods, models, and practical needs. Their unparalleled treatment provides a text ideal for a two-semester course and a variety of one-semester classes, from an introductory one-semester course to courses slanted toward classical graph theory, operations research, data structures and algorithms, or algebra and topology.
On dominator colorings in graphs
Indian Academy of Sciences (India)
A dominator coloring of a graph G is a proper coloring of G in which every vertex dominates every vertex of at least one color class. The minimum number of colors required for a dominator coloring of G is called the dominator chromatic number of G and is denoted by χd(G). In this paper we present several results on graphs ...
a generalization of total graphs
Indian Academy of Sciences (India)
8
Abstract. Let R be a commutative ring with nonzero identity, Ln(R) be the set of all lower triangular n × n matrices, and U be a triangular subset of. Rn i.e. the product of any lower triangular matrix with the transpose of any element of U, belongs to U. The graph GTn. U (Rn) is a simple graph whose ver- tices consists of all ...
Port-Hamiltonian Systems on Open Graphs
Schaft, A.J. van der; Maschke, B.M.
2010-01-01
In this talk we discuss how to define in an intrinsic manner port-Hamiltonian dynamics on open graphs. Open graphs are graphs where some of the vertices are boundary vertices (terminals), which allow interconnection with other systems. We show that a directed graph carries two natural Dirac
A Modal-Logic Based Graph Abstraction
Bauer, J.; Boneva, I.B.; Kurban, M.E.; Rensink, Arend; Ehrig, H; Heckel, R.; Rozenberg, G.; Taentzer, G.
2008-01-01
Infinite or very large state spaces often prohibit the successful verification of graph transformation systems. Abstract graph transformation is an approach that tackles this problem by abstracting graphs to abstract graphs of bounded size and by lifting application of productions to abstract
Summary 2: Graph Grammar Verification through Abstraction
Baldan, P.; Koenig, B.; Rensink, A.; Rensink, Arend; König, B.; Montanari, U.; Gardner, P.
2005-01-01
Until now there have been few contributions concerning the verification of graph grammars, specifically of infinite-state graph grammars. This paper compares two existing approaches, based on abstractions of graph transformation systems. While in the unfolding approach graph grammars are
On Graph Rewriting, Reduction and Evaluation
DEFF Research Database (Denmark)
Zerny, Ian
2009-01-01
We inter-derive two prototypical styles of graph reduction: reduction machines à la Turner and graph rewriting systems à la Barendregt. To this end, we adapt Danvy et al.'s mechanical program derivations from the world of terms to the world of graphs. We also inter-derive a graph evaluator....
Graphs with branchwidth at most three
Bodlaender, H.L.; Thilikos, D.M.
1997-01-01
In this paper we investigate both the structure of graphs with branchwidth at most three, as well as algorithms to recognise such graphs. We show that a graph has branchwidth at most three, if and only if it has treewidth at most three and does not contain the three-dimensional binary cube graph
A faithful functor among algebras and graphs
Falcón Ganfornina, Óscar Jesús; Falcón Ganfornina, Raúl Manuel; Núñez Valdés, Juan; Pacheco Martínez, Ana María; Villar Liñán, María Trinidad; Vigo Aguiar, Jesús (Coordinador)
2016-01-01
The problem of identifying a functor between the categories of algebras and graphs is currently open. Based on a known algorithm that identifies isomorphisms of Latin squares with isomorphism of vertex-colored graphs, we describe here a pair of graphs that enable us to find a faithful functor between finite-dimensional algebras over finite fields and these graphs.
Constructing Dense Graphs with Unique Hamiltonian Cycles
Lynch, Mark A. M.
2012-01-01
It is not difficult to construct dense graphs containing Hamiltonian cycles, but it is difficult to generate dense graphs that are guaranteed to contain a unique Hamiltonian cycle. This article presents an algorithm for generating arbitrarily large simple graphs containing "unique" Hamiltonian cycles. These graphs can be turned into dense graphs…
Hard graphs for the maximum clique problem
Hoede, C.
1988-01-01
The maximum clique problem is one of the NP-complete problems. There are graphs for which a reduction technique exists that transforms the problem for these graphs into one for graphs with specific properties in polynomial time. The resulting graphs do not grow exponentially in order and number.
Dynamic Programming on Nominal Graphs
Directory of Open Access Journals (Sweden)
Nicklas Hoch
2015-04-01
Full Text Available Many optimization problems can be naturally represented as (hyper graphs, where vertices correspond to variables and edges to tasks, whose cost depends on the values of the adjacent variables. Capitalizing on the structure of the graph, suitable dynamic programming strategies can select certain orders of evaluation of the variables which guarantee to reach both an optimal solution and a minimal size of the tables computed in the optimization process. In this paper we introduce a simple algebraic specification with parallel composition and restriction whose terms up to structural axioms are the graphs mentioned above. In addition, free (unrestricted vertices are labelled with variables, and the specification includes operations of name permutation with finite support. We show a correspondence between the well-known tree decompositions of graphs and our terms. If an axiom of scope extension is dropped, several (hierarchical terms actually correspond to the same graph. A suitable graphical structure can be found, corresponding to every hierarchical term. Evaluating such a graphical structure in some target algebra yields a dynamic programming strategy. If the target algebra satisfies the scope extension axiom, then the result does not depend on the particular structure, but only on the original graph. We apply our approach to the parking optimization problem developed in the ASCENS e-mobility case study, in collaboration with Volkswagen. Dynamic programming evaluations are particularly interesting for autonomic systems, where actual behavior often consists of propagating local knowledge to obtain global knowledge and getting it back for local decisions.
Chromatic polynomials of random graphs
International Nuclear Information System (INIS)
Van Bussel, Frank; Fliegner, Denny; Timme, Marc; Ehrlich, Christoph; Stolzenberg, Sebastian
2010-01-01
Chromatic polynomials and related graph invariants are central objects in both graph theory and statistical physics. Computational difficulties, however, have so far restricted studies of such polynomials to graphs that were either very small, very sparse or highly structured. Recent algorithmic advances (Timme et al 2009 New J. Phys. 11 023001) now make it possible to compute chromatic polynomials for moderately sized graphs of arbitrary structure and number of edges. Here we present chromatic polynomials of ensembles of random graphs with up to 30 vertices, over the entire range of edge density. We specifically focus on the locations of the zeros of the polynomial in the complex plane. The results indicate that the chromatic zeros of random graphs have a very consistent layout. In particular, the crossing point, the point at which the chromatic zeros with non-zero imaginary part approach the real axis, scales linearly with the average degree over most of the density range. While the scaling laws obtained are purely empirical, if they continue to hold in general there are significant implications: the crossing points of chromatic zeros in the thermodynamic limit separate systems with zero ground state entropy from systems with positive ground state entropy, the latter an exception to the third law of thermodynamics.
Graph Quasicontinuous Functions and Densely Continuous Forms
Directory of Open Access Journals (Sweden)
Lubica Hola
2017-07-01
Full Text Available Let $X, Y$ be topological spaces. A function $f: X \\to Y$ is said to be graph quasicontinuous if there is a quasicontinuous function $g: X \\to Y$ with the graph of $g$ contained in the closure of the graph of $f$. There is a close relation between the notions of graph quasicontinuous functions and minimal usco maps as well as the notions of graph quasicontinuous functions and densely continuous forms. Every function with values in a compact Hausdorff space is graph quasicontinuous; more generally every locally compact function is graph quasicontinuous.
On P-transitive graphs and applications
Directory of Open Access Journals (Sweden)
Giacomo Lenzi
2011-06-01
Full Text Available We introduce a new class of graphs which we call P-transitive graphs, lying between transitive and 3-transitive graphs. First we show that the analogue of de Jongh-Sambin Theorem is false for wellfounded P-transitive graphs; then we show that the mu-calculus fixpoint hierarchy is infinite for P-transitive graphs. Both results contrast with the case of transitive graphs. We give also an undecidability result for an enriched mu-calculus on P-transitive graphs. Finally, we consider a polynomial time reduction from the model checking problem on arbitrary graphs to the model checking problem on P-transitive graphs. All these results carry over to 3-transitive graphs.
Phage, Itumeleng B.; Lemmer, Miriam; Hitge, Mariette
2017-01-01
Students' graph comprehension may be affected by the background of the students who are the readers or interpreters of the graph, their knowledge of the context in which the graph is set, and the inferential processes required by the graph operation. This research study investigated these aspects of graph comprehension for 152 first year…
Analyzing Social Media Relationships in Context with Discussion Graphs
DEFF Research Database (Denmark)
Kiciman, Emre; Choudhury, Munmun De; Counts, Scott
2013-01-01
We present discussion graphs, a hyper-graph-based representation of social media discussions that captures both the structural features of the relationships among entities as well as the context of the discussions from which they were derived. Building on previous analyses of social media networks....... First, we extend standard hyper-graph representations of networks to include the distribution of contexts surrounding discussions in social media networks. Second, we demonstrate how this context is useful for understanding the results of common graph measures and analyses, such as network centrality...... and pseudo-cliques, when applied to the analysis of textual social media content. We apply our framework across several domains captured in Twitter, including the mining of peoples' statements about their locations and activities and discussions of the U.S. 2012 elections....
Geometry of Graph Edit Distance Spaces
Jain, Brijnesh J.
2015-01-01
In this paper we study the geometry of graph spaces endowed with a special class of graph edit distances. The focus is on geometrical results useful for statistical pattern recognition. The main result is the Graph Representation Theorem. It states that a graph is a point in some geometrical space, called orbit space. Orbit spaces are well investigated and easier to explore than the original graph space. We derive a number of geometrical results from the orbit space representation, translate ...
GraphMeta: Managing HPC Rich Metadata in Graphs
Energy Technology Data Exchange (ETDEWEB)
Dai, Dong; Chen, Yong; Carns, Philip; Jenkins, John; Zhang, Wei; Ross, Robert
2016-01-01
High-performance computing (HPC) systems face increasingly critical metadata management challenges, especially in the approaching exascale era. These challenges arise not only from exploding metadata volumes, but also from increasingly diverse metadata, which contains data provenance and arbitrary user-defined attributes in addition to traditional POSIX metadata. This ‘rich’ metadata is becoming critical to supporting advanced data management functionality such as data auditing and validation. In our prior work, we identified a graph-based model as a promising solution to uniformly manage HPC rich metadata due to its flexibility and generality. However, at the same time, graph-based HPC rich metadata anagement also introduces significant challenges to the underlying infrastructure. In this study, we first identify the challenges on the underlying infrastructure to support scalable, high-performance rich metadata management. Based on that, we introduce GraphMeta, a graphbased engine designed for this use case. It achieves performance scalability by introducing a new graph partitioning algorithm and a write-optimal storage engine. We evaluate GraphMeta under both synthetic and real HPC metadata workloads, compare it with other approaches, and demonstrate its advantages in terms of efficiency and usability for rich metadata management in HPC systems.
PRIVATE GRAPHS – ACCESS RIGHTS ON GRAPHS FOR SEAMLESS NAVIGATION
Directory of Open Access Journals (Sweden)
W. Dorner
2016-06-01
Full Text Available After the success of GNSS (Global Navigational Satellite Systems and navigation services for public streets, indoor seems to be the next big development in navigational services, relying on RTLS – Real Time Locating Services (e.g. WIFI and allowing seamless navigation. In contrast to navigation and routing services on public streets, seamless navigation will cause an additional challenge: how to make routing data accessible to defined users or restrict access rights for defined areas or only to parts of the graph to a defined user group? The paper will present case studies and data from literature, where seamless and especially indoor navigation solutions are presented (hospitals, industrial complexes, building sites, but the problem of restricted access rights was only touched from a real world, but not a technical perspective. The analysis of case studies will show, that the objective of navigation and the different target groups for navigation solutions will demand well defined access rights and require solutions, how to make only parts of a graph to a user or application available to solve a navigational task. The paper will therefore introduce the concept of private graphs, which is defined as a graph for navigational purposes covering the street, road or floor network of an area behind a public street and suggest different approaches how to make graph data for navigational purposes available considering access rights and data protection, privacy and security issues as well.
2006-06-01
with EADS Defence and Security Systems UK. Stone, R.; Guest, R.; Ch’ng, E .; McCririe, C.; Collis, C.; Mannur, R.; Rehmi, I. (2006) Serious Gaming ...RTO-MP-HFM-136 8 - 1 Serious Gaming Technologies Support Human Factors Investigations of Advanced Interfaces for Semi-Autonomous Vehicles...University of Birmingham Electronic , Electrical & Computer Engineering Department Edgbaston Birmingham, B15 2TT UK r.j.stone@bham.ac.uk ABSTRACT
Directory of Open Access Journals (Sweden)
Andreas P. Braun
2016-04-01
Full Text Available Box graphs succinctly and comprehensively characterize singular fibers of elliptic fibrations in codimension two and three, as well as flop transitions connecting these, in terms of representation theoretic data. We develop a framework that provides a systematic map between a box graph and a crepant algebraic resolution of the singular elliptic fibration, thus allowing an explicit construction of the fibers from a singular Weierstrass or Tate model. The key tool is what we call a fiber face diagram, which shows the relevant information of a (partial toric triangulation and allows the inclusion of more general algebraic blowups. We shown that each such diagram defines a sequence of weighted algebraic blowups, thus providing a realization of the fiber defined by the box graph in terms of an explicit resolution. We show this correspondence explicitly for the case of SU(5 by providing a map between box graphs and fiber faces, and thereby a sequence of algebraic resolutions of the Tate model, which realizes each of the box graphs.
Hierarchical organisation of causal graphs
International Nuclear Information System (INIS)
Dziopa, P.
1993-01-01
This paper deals with the design of a supervision system using a hierarchy of models formed by graphs, in which the variables are the nodes and the causal relations between the variables of the arcs. To obtain a representation of the variables evolutions which contains only the relevant features of their real evolutions, the causal relations are completed with qualitative transfer functions (QTFs) which produce roughly the behaviour of the classical transfer functions. Major improvements have been made in the building of the hierarchical organization. First, the basic variables of the uppermost level and the causal relations between them are chosen. The next graph is built by adding intermediary variables to the upper graph. When the undermost graph has been built, the transfer functions parameters corresponding to its causal relations are identified. The second task consists in the upwelling of the information from the undermost graph to the uppermost one. A fusion procedure of the causal relations has been designed to compute the QFTs relevant for each level. This procedure aims to reduce the number of parameters needed to represent an evolution at a high level of abstraction. These techniques have been applied to the hierarchical modelling of nuclear process. (authors). 8 refs., 12 figs
Integer Flows and Circuit Covers of Graphs and Signed Graphs
Cheng, Jian
The work in Chapter 2 is motivated by Tutte and Jaeger's pioneering work on converting modulo flows into integer-valued flows for ordinary graphs. For a signed graphs (G, sigma), we first prove that for each k ∈ {2, 3}, if (G, sigma) is (k - 1)-edge-connected and contains an even number of negative edges when k = 2, then every modulo k-flow of (G, sigma) can be converted into an integer-valued ( k + 1)-ow with a larger or the same support. We also prove that if (G, sigma) is odd-(2p+1)-edge-connected, then (G, sigma) admits a modulo circular (2 + 1/ p)-flows if and only if it admits an integer-valued circular (2 + 1/p)-flows, which improves all previous result by Xu and Zhang (DM2005), Schubert and Steffen (EJC2015), and Zhu (JCTB2015). Shortest circuit cover conjecture is one of the major open problems in graph theory. It states that every bridgeless graph G contains a set of circuits F such that each edge is contained in at least one member of F and the length of F is at most 7/5∥E(G)∥. This concept was recently generalized to signed graphs by Macajova et al. (JGT2015). In Chapter 3, we improve their upper bound from 11∥E( G)∥ to 14/3 ∥E(G)∥, and if G is 2-edgeconnected and has even negativeness, then it can be further reduced to 11/3 ∥E(G)∥. Tutte's 3-flow conjecture has been studied by many graph theorists in the last several decades. As a new approach to this conjecture, DeVos and Thomassen considered the vectors as ow values and found that there is a close relation between vector S1-flows and integer 3-NZFs. Motivated by their observation, in Chapter 4, we prove that if a graph G admits a vector S1-flow with rank at most two, then G admits an integer 3-NZF. The concept of even factors is highly related to the famous Four Color Theorem. We conclude this dissertation in Chapter 5 with an improvement of a recent result by Chen and Fan (JCTB2016) on the upperbound of even factors. We show that if a graph G contains an even factor, then it
Algorithms for Planar Graphs and Graphs in Metric Spaces
DEFF Research Database (Denmark)
Wulff-Nilsen, Christian
preprocessing time, an O(n log n) time algorithm for the replacement paths problem, and a min st-cut oracle with nearlinear preprocessing time. We also give improved time bounds for computing various graph invariants such as diameter and girth. In the second part, we consider stretch factor problems...... a graph with new edges while minimizing stretch factor. The third and final part of the thesis deals with the Steiner tree problem in the plane equipped with a weighted fixed orientation metric. Here, we give an improved theoretical analysis of the strength of pruning techniques applied by many Steiner...
An algebraic approach to graph codes
DEFF Research Database (Denmark)
Pinero, Fernando
theory as evaluation codes. Chapter three consists of the introduction to graph based codes, such as Tanner codes and graph codes. In Chapter four, we compute the dimension of some graph based codes with a result combining graph based codes and subfield subcodes. Moreover, some codes in chapter four...... are optimal or best known for their parameters. In chapter five we study some graph codes with Reed–Solomon component codes. The underlying graph is well known and widely used for its good characteristics. This helps us to compute the dimension of the graph codes. We also introduce a combinatorial concept...... related to the iterative encoding of graph codes with MDS component code. The last chapter deals with affine Grassmann codes and Grassmann codes. We begin with some previously known codes and prove that they are also Tanner codes of the incidence graph of the point–line partial geometry...
An original approach to the mathematical concept of graph from braid crafts
Directory of Open Access Journals (Sweden)
Albanese Veronica
2016-01-01
Full Text Available In previous researches we found that a community of Argentinean artisans models its own practices of braiding using graphs. Inspired by these findings, we designed an educational activity to introduce the concept of graphs. The study of graphs helps students to develop combinatorial and systematic thinking as well as skills to model reality and abstract and generalize patterns from particular situations. The tasks proposed aim to construct the concept of graphs, then identify characteristics that allow some graphs to be models of braids and finally use them to invent more graphs for new braids. The activity performed in a secondary school teachers’ educational course, had quite satisfactory results due to the number of braids invented and the small amount of mistakes made by the participants.
Nodal Statistics on Quantum Graphs
Alon, Lior; Band, Ram; Berkolaiko, Gregory
2018-03-01
It has been suggested that the distribution of the suitably normalized number of zeros of Laplacian eigenfunctions contains information about the geometry of the underlying domain. We study this distribution (more precisely, the distribution of the "nodal surplus") for Laplacian eigenfunctions of a metric graph. The existence of the distribution is established, along with its symmetry. One consequence of the symmetry is that the graph's first Betti number can be recovered as twice the average nodal surplus of its eigenfunctions. Furthermore, for graphs with disjoint cycles it is proven that the distribution has a universal form—it is binomial over the allowed range of values of the surplus. To prove the latter result, we introduce the notion of a local nodal surplus and study its symmetry and dependence properties, establishing that the local nodal surpluses of disjoint cycles behave like independent Bernoulli variables.
Graph modeling systems and methods
Neergaard, Mike
2015-10-13
An apparatus and a method for vulnerability and reliability modeling are provided. The method generally includes constructing a graph model of a physical network using a computer, the graph model including a plurality of terminating vertices to represent nodes in the physical network, a plurality of edges to represent transmission paths in the physical network, and a non-terminating vertex to represent a non-nodal vulnerability along a transmission path in the physical network. The method additionally includes evaluating the vulnerability and reliability of the physical network using the constructed graph model, wherein the vulnerability and reliability evaluation includes a determination of whether each terminating and non-terminating vertex represents a critical point of failure. The method can be utilized to evaluate wide variety of networks, including power grid infrastructures, communication network topologies, and fluid distribution systems.
Feder, Tomás
2009-06-01
Results on graph turnpike problem without distinctness, including its NP-completeness, and an O(m+n log n) algorithm, is presented. The usual turnpike problem has all pairwise distances given, but does not specify which pair of vertices w e corresponds to. There are two other problems that can be viewed as special cases of the graph turnpike problem, including the bandwidth problem and the low-distortion graph embedding problem. The aim for the turnpike problem in the NP-complete is to orient the edges with weights w i in either direction so that when the whole cycle is transversed in the real line, it returns to a chosen starting point for the cycle. An instance of the turnpike problem with or without distinctness is uniquely mappable if there exists at most one solution up to translation and choice of orientation.
Negation switching invariant signed graphs
Directory of Open Access Journals (Sweden)
Deepa Sinha
2014-04-01
Full Text Available A signed graph (or, $sigraph$ in short is a graph G in which each edge x carries a value $\\sigma(x \\in \\{-, +\\}$ called its sign. Given a sigraph S, the negation $\\eta(S$ of the sigraph S is a sigraph obtained from S by reversing the sign of every edge of S. Two sigraphs $S_{1}$ and $S_{2}$ on the same underlying graph are switching equivalent if it is possible to assign signs `+' (`plus' or `-' (`minus' to vertices of $S_{1}$ such that by reversing the sign of each of its edges that has received opposite signs at its ends, one obtains $S_{2}$. In this paper, we characterize sigraphs which are negation switching invariant and also see for what sigraphs, S and $\\eta (S$ are signed isomorphic.
The fascinating world of graph theory
Benjamin, Arthur; Zhang, Ping
2015-01-01
Graph theory goes back several centuries and revolves around the study of graphs-mathematical structures showing relations between objects. With applications in biology, computer science, transportation science, and other areas, graph theory encompasses some of the most beautiful formulas in mathematics-and some of its most famous problems. The Fascinating World of Graph Theory explores the questions and puzzles that have been studied, and often solved, through graph theory. This book looks at graph theory's development and the vibrant individuals responsible for the field's growth. Introducin
An intersection graph of straight lines
DEFF Research Database (Denmark)
Thomassen, Carsten
2002-01-01
G. Ehrlich, S. Even, and R.E. Tarjan conjectured that the graph obtained from a complete 3 partite graph K4,4,4 by deleting the edges of four disjoint triangles is not the intersection graph of straight line segments in the plane. We show that it is.......G. Ehrlich, S. Even, and R.E. Tarjan conjectured that the graph obtained from a complete 3 partite graph K4,4,4 by deleting the edges of four disjoint triangles is not the intersection graph of straight line segments in the plane. We show that it is....
Graph-based modelling in engineering
Rysiński, Jacek
2017-01-01
This book presents versatile, modern and creative applications of graph theory in mechanical engineering, robotics and computer networks. Topics related to mechanical engineering include e.g. machine and mechanism science, mechatronics, robotics, gearing and transmissions, design theory and production processes. The graphs treated are simple graphs, weighted and mixed graphs, bond graphs, Petri nets, logical trees etc. The authors represent several countries in Europe and America, and their contributions show how different, elegant, useful and fruitful the utilization of graphs in modelling of engineering systems can be. .
Graph Processing on GPUs: A Survey
DEFF Research Database (Denmark)
Shi, Xuanhua; Zheng, Zhigao; Zhou, Yongluan
2018-01-01
In the big data era, much real-world data can be naturally represented as graphs. Consequently, many application domains can be modeled as graph processing. Graph processing, especially the processing of the large-scale graphs with the number of vertices and edges in the order of billions or even......, utilizing GPU to accelerate graph processing proves to be a promising solution. This article surveys the key issues of graph processing on GPUs, including data layout, memory access pattern, workload mapping, and specific GPU programming. In this article, we summarize the state-of-the-art research on GPU...
Ménoret, Mathilde; Farrugia, Nicolas; Pasdeloup, Bastien; Gripon, Vincent
2017-01-01
Graph Signal Processing (GSP) is a promising framework to analyze multi-dimensional neuroimaging datasets, while taking into account both the spatial and functional dependencies between brain signals. In the present work, we apply dimensionality reduction techniques based on graph representations of the brain to decode brain activity from real and simulated fMRI datasets. We introduce seven graphs obtained from a) geometric structure and/or b) functional connectivity between brain areas at re...
Graph topologies on closed multifunctions
Directory of Open Access Journals (Sweden)
Giuseppe Di Maio
2003-10-01
Full Text Available In this paper we study function space topologies on closed multifunctions, i.e. closed relations on X x Y using various hypertopologies. The hypertopologies are in essence, graph topologies i.e topologies on functions considered as graphs which are subsets of X x Y . We also study several topologies, including one that is derived from the Attouch-Wets filter on the range. We state embedding theorems which enable us to generalize and prove some recent results in the literature with the use of known results in the hyperspace of the range space and in the function space topologies of ordinary functions.
XML Graphs in Program Analysis
DEFF Research Database (Denmark)
Møller, Anders; Schwartzbach, Michael Ignatieff
2007-01-01
XML graphs have shown to be a simple and effective formalism for representing sets of XML documents in program analysis. It has evolved through a six year period with variants tailored for a range of applications. We present a unified definition, outline the key properties including validation...... of XML graphs against different XML schema languages, and provide a software package that enables others to make use of these ideas. We also survey four very different applications: XML in Java, Java Servlets and JSP, transformations between XML and non-XML data, and XSLT....
Andersson, Mattias
2011-01-01
A star graph consists of a vertex to which a set of edges are connected. Such an object can be used to, among other things, model the electromagnetic properties of quantum wires. A scalar field theory is constructed on the star graph and its properties are investigated. It turns out that there exist Kirchoff's rules for the conserved charges in the system leading to restrictions of the possible type of boundary conditions at the vertex. Scale invariant boundary conditions are investigated in...
Completely Described Undirected Graph Structure
Directory of Open Access Journals (Sweden)
G. S. Ivanova
2016-01-01
Full Text Available The objects of research are undirected graphs. The paper considers a problem of their isomorphism. A literature analysis of its solution, has shown that there is no way to define a complete graph invariant in the form of unique structural characteristics of each its vertex, which has a computational complexity of definition better than О (n 4 .The work objective is to provide the characteristics of the graph structure, which could be used to solve the problem of their isomorphism for a time better than О (n 4 . As such characteristics, the paper proposes to use the set of codes of tree roots of all the shortest - in terms of the number of edges - paths from each vertex to the others, uniquely defining the structure of each tree. It proves the theorem that it is possible to reduce the problem of isomorphism of the undirected graphs to the isomorphism problem of their splitting into the trees of all the shortest - in terms of the number of edges - paths of each vertex to the others. An algorithm to construct the shortest paths from each vertex to all others and to compute codes of their vertices has been developed. As the latter, are used Aho-codes, which find application in recognising the isomorphism of trees. The computational complexity to obtain structural characteristics of vertices has been estimated to be about О (n 3 .The pilot studies involved the full-scale experiment using the developed complex programmes to generate raw data, i.e. analytic representation of the graph with the number of vertices equal to 1200, and a programme to provide codes of the tree roots. To have an estimate of - "the worst" in terms of time - complexity of expansion algorithm of graphs into trees of the shortest paths and define the codes of their roots has been an experimentally studied how the number of tree vertices depends on the graph density. For the worst case was obtained a dependence of the number of tree vertices on the number of graph vertices
Some Invariants of Jahangir Graphs
Directory of Open Access Journals (Sweden)
Mobeen Munir
2017-01-01
Full Text Available In this report, we compute closed forms of M-polynomial, first and second Zagreb polynomials and forgotten polynomial for Jahangir graphs Jn,m for all values of m and n. From the M-polynomial, we recover many degree-based topological indices such as first and second Zagreb indices, modified Zagreb index, Symmetric division index, etc. We also compute harmonic index, first and second multiple Zagreb indices and forgotten index of Jahangir graphs. Our results are extensions of many existing results.
Graph abstraction and abstract graph transformations (Amended version)
Boneva, I.B.; Kreiker, Jörg; Kurban, M.E.; Rensink, Arend; Zambon, Eduardo
2012-01-01
Many important systems such as concurrent heap-manipulating programs, communication networks, or distributed algorithms, are hard to verify due to their inherent dynamics and unboundedness. Graphs are an intuitive representation for the states of these systems, where transitions can be conveniently
Multiple graph regularized protein domain ranking
Wang, Jim Jing-Yan
2012-11-19
Background: Protein domain ranking is a fundamental task in structural biology. Most protein domain ranking methods rely on the pairwise comparison of protein domains while neglecting the global manifold structure of the protein domain database. Recently, graph regularized ranking that exploits the global structure of the graph defined by the pairwise similarities has been proposed. However, the existing graph regularized ranking methods are very sensitive to the choice of the graph model and parameters, and this remains a difficult problem for most of the protein domain ranking methods.Results: To tackle this problem, we have developed the Multiple Graph regularized Ranking algorithm, MultiG-Rank. Instead of using a single graph to regularize the ranking scores, MultiG-Rank approximates the intrinsic manifold of protein domain distribution by combining multiple initial graphs for the regularization. Graph weights are learned with ranking scores jointly and automatically, by alternately minimizing an objective function in an iterative algorithm. Experimental results on a subset of the ASTRAL SCOP protein domain database demonstrate that MultiG-Rank achieves a better ranking performance than single graph regularized ranking methods and pairwise similarity based ranking methods.Conclusion: The problem of graph model and parameter selection in graph regularized protein domain ranking can be solved effectively by combining multiple graphs. This aspect of generalization introduces a new frontier in applying multiple graphs to solving protein domain ranking applications. 2012 Wang et al; licensee BioMed Central Ltd.
Multiple graph regularized protein domain ranking.
Wang, Jim Jing-Yan; Bensmail, Halima; Gao, Xin
2012-11-19
Protein domain ranking is a fundamental task in structural biology. Most protein domain ranking methods rely on the pairwise comparison of protein domains while neglecting the global manifold structure of the protein domain database. Recently, graph regularized ranking that exploits the global structure of the graph defined by the pairwise similarities has been proposed. However, the existing graph regularized ranking methods are very sensitive to the choice of the graph model and parameters, and this remains a difficult problem for most of the protein domain ranking methods. To tackle this problem, we have developed the Multiple Graph regularized Ranking algorithm, MultiG-Rank. Instead of using a single graph to regularize the ranking scores, MultiG-Rank approximates the intrinsic manifold of protein domain distribution by combining multiple initial graphs for the regularization. Graph weights are learned with ranking scores jointly and automatically, by alternately minimizing an objective function in an iterative algorithm. Experimental results on a subset of the ASTRAL SCOP protein domain database demonstrate that MultiG-Rank achieves a better ranking performance than single graph regularized ranking methods and pairwise similarity based ranking methods. The problem of graph model and parameter selection in graph regularized protein domain ranking can be solved effectively by combining multiple graphs. This aspect of generalization introduces a new frontier in applying multiple graphs to solving protein domain ranking applications.
Multiple graph regularized protein domain ranking
Directory of Open Access Journals (Sweden)
Wang Jim
2012-11-01
Full Text Available Abstract Background Protein domain ranking is a fundamental task in structural biology. Most protein domain ranking methods rely on the pairwise comparison of protein domains while neglecting the global manifold structure of the protein domain database. Recently, graph regularized ranking that exploits the global structure of the graph defined by the pairwise similarities has been proposed. However, the existing graph regularized ranking methods are very sensitive to the choice of the graph model and parameters, and this remains a difficult problem for most of the protein domain ranking methods. Results To tackle this problem, we have developed the Multiple Graph regularized Ranking algorithm, MultiG-Rank. Instead of using a single graph to regularize the ranking scores, MultiG-Rank approximates the intrinsic manifold of protein domain distribution by combining multiple initial graphs for the regularization. Graph weights are learned with ranking scores jointly and automatically, by alternately minimizing an objective function in an iterative algorithm. Experimental results on a subset of the ASTRAL SCOP protein domain database demonstrate that MultiG-Rank achieves a better ranking performance than single graph regularized ranking methods and pairwise similarity based ranking methods. Conclusion The problem of graph model and parameter selection in graph regularized protein domain ranking can be solved effectively by combining multiple graphs. This aspect of generalization introduces a new frontier in applying multiple graphs to solving protein domain ranking applications.
Graph reconstruction with a betweenness oracle
DEFF Research Database (Denmark)
Abrahamsen, Mikkel; Bodwin, Greg; Rotenberg, Eva
2016-01-01
Graph reconstruction algorithms seek to learn a hidden graph by repeatedly querying a blackbox oracle for information about the graph structure. Perhaps the most well studied and applied version of the problem uses a distance oracle, which can report the shortest path distance between any pair....... Despite this, we are able to develop betweenness reconstruction algorithms that match the current state of the art for distance reconstruction, and even improve it for certain types of graphs. We obtain the following algorithms: 1. Reconstruction of general graphs in O(n2) queries 2. Reconstruction...... of degree-bounded graphs in Õ(n3/2) queries 3. Reconstruction of geodetic degree-bounded graphs in Õ(n) queries In addition to being a fundamental graph theoretic problem with some natural applications, our new results shed light on some avenues for progress in the distance reconstruction problem....
Use of Spatial Transformations in Graph Comprehension
National Research Council Canada - National Science Library
Trickett, Susan B; Trafton, J. G
2004-01-01
Current theories of graph comprehension are largely silent about the processes by which inferences are made from graphs, although it is apparent that people are able to make such inferences. In Trickett & Trafton (2004...
Humidity Graphs for All Seasons.
Esmael, F.
1982-01-01
In a previous article in this journal (Vol. 17, p358, 1979), a wet-bulb depression table was recommended for two simple experiments to determine relative humidity. However, the use of a graph is suggested because it gives the relative humidity directly from the wet and dry bulb readings. (JN)
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 12; Issue 1. A Problem in Graph Theory. K P Savithri. Think It Over Volume 12 Issue 1 January 2007 pp 81-81. Fulltext. Click here to view fulltext PDF. Permanent link: http://www.ias.ac.in/article/fulltext/reso/012/01/0081-0081. Author Affiliations.
Box graphs and singular fibers
International Nuclear Information System (INIS)
Hayashi, Hirotaka; Lawrie, Craig; Morrison, David R.; Schäfer-Nameki, Sakura
2014-01-01
We determine the higher codimension fibers of elliptically fibered Calabi-Yau fourfolds with section by studying the three-dimensional N=2 supersymmetric gauge theory with matter which describes the low energy effective theory of M-theory compactified on the associated Weierstrass model, a singular model of the fourfold. Each phase of the Coulomb branch of this theory corresponds to a particular resolution of the Weierstrass model, and we show that these have a concise description in terms of decorated box graphs based on the representation graph of the matter multiplets, or alternatively by a class of convex paths on said graph. Transitions between phases have a simple interpretation as “flopping' of the path, and in the geometry correspond to actual flop transitions. This description of the phases enables us to enumerate and determine the entire network between them, with various matter representations for all reductive Lie groups. Furthermore, we observe that each network of phases carries the structure of a (quasi-)minuscule representation of a specific Lie algebra. Interpreted from a geometric point of view, this analysis determines the generators of the cone of effective curves as well as the network of flop transitions between crepant resolutions of singular elliptic Calabi-Yau fourfolds. From the box graphs we determine all fiber types in codimensions two and three, and we find new, non-Kodaira, fiber types for E 6 , E 7 and E 8
Ancestral Genres of Mathematical Graphs
Gerofsky, Susan
2011-01-01
Drawing from sources in gesture studies, cognitive science, the anthropology of religion and art/architecture history, this article explores cultural, bodily and cosmological resonances carried (unintentionally) by mathematical graphs on Cartesian coordinates. Concepts of asymmetric bodily spaces, grids, orthogonality, mapping and sacred spaces…
Constructing Knowledge Graphs of Depression
Huang, Zhisheng; Yang, Jie; van Harmelen, Frank; Hu, Qing
2017-01-01
Knowledge Graphs have been shown to be useful tools for integrating multiple medical knowledge sources, and to support such tasks as medical decision making, literature retrieval, determining healthcare quality indicators, co-morbodity analysis and many others. A large number of medical knowledge
Contracting a planar graph efficiently
DEFF Research Database (Denmark)
Holm, Jacob; Italiano, Giuseppe F.; Karczmarz, Adam
2017-01-01
We present a data structure that can maintain a simple planar graph under edge contractions in linear total time. The data structure supports adjacency queries and provides access to neighbor lists in O(1) time. Moreover, it can report all the arising self-loops and parallel edges. By applying th...
Fixation Time for Evolutionary Graphs
Nie, Pu-Yan; Zhang, Pei-Ai
Evolutionary graph theory (EGT) is recently proposed by Lieberman et al. in 2005. EGT is successful for explaining biological evolution and some social phenomena. It is extremely important to consider the time of fixation for EGT in many practical problems, including evolutionary theory and the evolution of cooperation. This study characterizes the time to asymptotically reach fixation.
Indian Academy of Sciences (India)
Examples: Some explicit computations. Throughout this section, we will assume that ( , μ) is a finite, connected, weighted graph. The adjacency matrix of (which, by abuse of notation, will also be denoted by ) is, as usual, the symmetric matrix with rows and columns indexed by the vertex set V of and. (v, w) = |{e ∈ E : s(e) = v, ...
Affect and Graphing Calculator Use
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…
On dominator colorings in graphs
Indian Academy of Sciences (India)
A dominator coloring of a graph is a proper coloring of in which every vertex dominates every vertex of at least one color class. The minimum number of colors required for a dominator coloring of is called the dominator chromatic number of and is denoted by d ( G ) . In this paper we present several results on ...
Czech Academy of Sciences Publication Activity Database
Hussein, A.; Krejčiřík, David; Siegl, P.
2015-01-01
Roč. 367, č. 4 (2015), s. 2921-2957 ISSN 0002-9947 R&D Projects: GA ČR GAP203/11/0701 Institutional support: RVO:61389005 Keywords : Laplacians on metric graphs * non-self-adjoint boundary conditions * similarity transforms to self-adjoint operators * Riesz basis Subject RIV: BE - Theoretical Physics Impact factor: 1.196, year: 2015
Application of graph database for analytical tasks
Günzl, Richard
2014-01-01
This diploma thesis is about graph databases, which belong to the category of database systems known as NoSQL databases, but graph databases are beyond NoSQL databases. Graph databases are useful in many cases thanks to native storing of interconnections between data, which brings advantageous properties in comparison with traditional relational database system, especially in querying. The main goal of the thesis is: to describe principles, properties and advantages of graph database; to desi...
Bond graph modeling of centrifugal compression systems
Uddin, Nur; Gravdahl, Jan Tommy
2015-01-01
A novel approach to model unsteady fluid dynamics in a compressor network by using a bond graph is presented. The model is intended in particular for compressor control system development. First, we develop a bond graph model of a single compression system. Bond graph modeling offers a different perspective to previous work by modeling the compression system based on energy flow instead of fluid dynamics. Analyzing the bond graph model explains the energy flow during compressor surge. Two pri...
A Graph Calculus for Predicate Logic
Directory of Open Access Journals (Sweden)
Paulo A. S. Veloso
2013-03-01
Full Text Available We introduce a refutation graph calculus for classical first-order predicate logic, which is an extension of previous ones for binary relations. One reduces logical consequence to establishing that a constructed graph has empty extension, i. e. it represents bottom. Our calculus establishes that a graph has empty extension by converting it to a normal form, which is expanded to other graphs until we can recognize conflicting situations (equivalent to a formula and its negation.
Unsupervised Deep Haar Scattering on Graphs
Chen, Xu; Cheng, Xiuyuan; Mallat, Stéphane
2014-01-01
The classification of high-dimensional data defined on graphs is particularly difficult when the graph geometry is unknown. We introduce a Haar scattering transform on graphs, which computes invariant signal descriptors. It is implemented with a deep cascade of additions, subtractions and absolute values, which iteratively compute orthogonal Haar wavelet transforms. Multiscale neighborhoods of unknown graphs are estimated by minimizing an average total variation, with a pair matching algorith...
A graph-graph approach to the analysis of the set of associative rules
Belim, S. V.; Smirnova, T. B.; Mironenko, A. N.
2018-01-01
The article proposes a method for processing a set of associative rules, which makes it possible to identify additional relationships between the set of objects under study. The proposed approach consists of three stages. At the first stage, associative rules are revealed from the statistical data. At the second stage, constructed weighted oriented graph of relationships between the objects of the system. The third stage analyses the graph and identifies the community (community), which allows you to determine the groups of the most related objects. As an example, is given an analysis of the activities of public organizations. The result of the work is a method that allows to identify patterns from the analysis of a set of associative rules, and not just from a separate associative rule.
On m-Neighbourly Irregular Instuitionistic Fuzzy Graphs
N.R.Santhi Maheswari; C.Sekar
2016-01-01
In this paper, m-neighbourly irregular intuitionistic fuzzy graphs and m- neighbourly totally irregular intuitionistic fuzzy graphs are defined. Relation between m-neighbourly irregular intuitionistic fuzzy graph and m-neighbourly totally irregular intuitionistic fuzzy graph are discussed.
Construction of cycle double covers for certain classes of graphs
Hoede, C.; Kriesell, M.; Uttuggadewa, S.
2000-01-01
We introduce two classes of graphs, Indonesian graphs and $k$-doughnut graphs. Cycle double covers are constructed for these classes. In case of doughnut graphs this is done for the values $k=1,2,3$ and 4.
Graph Partitioning Models for Parallel Computing
Energy Technology Data Exchange (ETDEWEB)
Hendrickson, B.; Kolda, T.G.
1999-03-02
Calculations can naturally be described as graphs in which vertices represent computation and edges reflect data dependencies. By partitioning the vertices of a graph, the calculation can be divided among processors of a parallel computer. However, the standard methodology for graph partitioning minimizes the wrong metric and lacks expressibility. We survey several recently proposed alternatives and discuss their relative merits.
Modeling Software Evolution using Algebraic Graph Rewriting
Ciraci, S.; van den Broek, P.M.; Avgeriou, P.; Zdun, U.; Borne, I.
We show how evolution requests can be formalized using algebraic graph rewriting. In particular, we present a way to convert the UML class diagrams to colored graphs. Since changes in software may effect the relation between the methods of classes, our colored graph representation also employs the
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…
A Type Graph Model for Java Programs
Rensink, Arend; Zambon, Eduardo
2009-01-01
In this report we present a type graph that models all executable constructs of the Java programming language. Such a model is useful for any graph-based technique that relies on a representation of Java programs as graphs. The model can be regarded as a common representation to which all Java
A Type Graph Model for Java Programs
Rensink, Arend; Zambon, Eduardo; Lee, D.; Lopes, A.; Poetzsch-Heffter, A.
2009-01-01
In this work we present a type graph that models all executable constructs of the Java programming language. Such a model is useful for any graph-based technique that relies on a representation of Java programs as graphs. The model can be regarded as a common representation to which all Java syntax
Cycles in weighted graphs and related topics
Zhang, Shenggui
2002-01-01
This thesis contains results on paths andcycles in graphs andon a more or less relatedtopic, the vulnerability of graphs. In the first part of the thesis, Chapters 2 through 5, we concentrate on paths andcycles in weightedgraphs. A number of sufficient conditions are presentedfor graphs to contain
Collaborative Robotic Instruction: A Graph Teaching Experience
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…
Integral complete r-partite graphs
Wang, Ligong; Li, Xueliang; Hoede, C.
2004-01-01
A graph is called integral if all the eigenvalues of its adjacency matrix are integers. In this paper, we give a useful sufficient and necessary condition for complete r-partite graphs to be integral, from which we can construct infinite many new classes of such integral graphs. It is proved that
Verification Techniques for Graph Rewriting (Tutorial)
Rensink, Arend; Abdulla, Parosh Aziz; Gadducci, Fabio; König, Barbara; Vafeiadis, Viktor
This tutorial paints a high-level picture of the concepts involved in verification of graph transformation systems. We distinguish three fundamentally different application scenarios for graph rewriting: (1) as grammars (in which case we are interested in the language, or set, of terminal graphs for
Graph Transformation Semantics for a QVT Language
Rensink, Arend; Nederpel, Ronald; Bruni, Roberto; Varró, Dániel
It has been claimed by many in the graph transformation community that model transformation, as understood in the context of Model Driven Architecture, can be seen as an application of graph transformation. In this paper we substantiate this claim by giving a graph transformation-based semantics to
A new cluster algorithm for graphs
S. van Dongen
1998-01-01
textabstractA new cluster algorithm for graphs called the emph{Markov Cluster algorithm ($MCL$ algorithm) is introduced. The graphs may be both weighted (with nonnegative weight) and directed. Let~$G$~be such a graph. The $MCL$ algorithm simulates flow in $G$ by first identifying $G$ in a
Girth 5 graphs from relative difference sets
DEFF Research Database (Denmark)
Jørgensen, Leif Kjær
We consider the problem of construction of graphs with given degree and girth 5 and as few vertices as possible. We give a construction of a family of girth 5 graphs based on relative difference sets. This family contains the smallest known graph of degree 8 and girth 5 which was constructed by G...
Destroying longest cycles in graphs and digraphs
DEFF Research Database (Denmark)
Van Aardt, Susan A.; Burger, Alewyn P.; Dunbar, Jean E.
2015-01-01
In 1978, C. Thomassen proved that in any graph one can destroy all the longest cycles by deleting at most one third of the vertices. We show that for graphs with circumference k≤8 it suffices to remove at most 1/k of the vertices. The Petersen graph demonstrates that this result cannot be extended...
Structure of simplicial complexes of graphs representing ...
Indian Academy of Sciences (India)
Abstract. Mapping time series onto graphs and the use of graph theory methods opens up the possibility to study the structure of the phase space manifolds underlying the fluctuations of a dynamical variable. Here, we go beyond the standard graph measures and analyze the higher-order structures such as triangles, ...
Strongly 2-connected orientations of graphs
DEFF Research Database (Denmark)
Thomassen, Carsten
2014-01-01
We prove that a graph admits a strongly 2-connected orientation if and only if it is 4-edge-connected, and every vertex-deleted subgraph is 2-edge-connected. In particular, every 4-connected graph has such an orientation while no cubic 3-connected graph has such an orientation....
So Many Graphs, So Little Time
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…
On topological indices for small RNA graphs.
Churkin, Alexander; Gabdank, Idan; Barash, Danny
2012-12-01
The secondary structure of RNAs can be represented by graphs at various resolutions. While it was shown that RNA secondary structures can be represented by coarse grain tree-graphs and meaningful topological indices can be used to distinguish between various structures, small RNAs are needed to be represented by full graphs. No meaningful topological index has yet been suggested for the analysis of such type of RNA graphs. Recalling that the second eigenvalue of the Laplacian matrix can be used to track topological changes in the case of coarse grain tree-graphs, it is plausible to assume that a topological index such as the Wiener index that represents all Laplacian eigenvalues may provide a similar guide for full graphs. However, by its original definition, the Wiener index was defined for acyclic graphs. Nevertheless, similarly to cyclic chemical graphs, small RNA graphs can be analyzed using elementary cuts, which enables the calculation of topological indices for small RNAs in an intuitive way. We show how to calculate a structural descriptor that is suitable for cyclic graphs, the Szeged index, for small RNA graphs by elementary cuts. We discuss potential uses of such a procedure that considers all eigenvalues of the associated Laplacian matrices to quantify the topology of small RNA graphs. Copyright © 2012 Elsevier Ltd. All rights reserved.
47 CFR 80.761 - Conversion graphs.
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 is...
Graphs with many valencies and few eigenvalues
van Dam, Edwin; Koolen, J.H.; Xia, Zheng-Jiang
Dom de Caen posed the question whether connected graphs with three distinct eigenvalues have at most three distinct valencies. We do not answer this question, but instead construct connected graphs with four and five distinct eigenvalues and arbitrarily many distinct valencies. The graphs with four
Algorithms and Data Structures for Graphs
DEFF Research Database (Denmark)
Rotenberg, Eva
A graph consists of a set of vertices and a set of edges between vertices. Graphs are a popular mathematical model for road maps, communication networks, electrical circuits, social networks, disease transmission networks, job assignments, resource allocation, and more. A special class of graphs ...
On 3-Chromatic Distance-Regular Graphs
Blokhuis, A.; Brouwer, A.E.; Haemers, W.H.
2006-01-01
We give some necessary conditions for a graph to be 3-chromatic in terms of the spectrum of the adjacency matrix.For all known distance-regular graphs it is determined whether they are 3-chromatic.A start is made with the classification of 3-chromatic distance-regular graphs, and it is shown that
The Effectiveness of Technology-Supported Exercise Therapy for Low Back Pain: A Systematic Review.
Matheve, Thomas; Brumagne, Simon; Timmermans, Annick A A
2017-05-01
Various technological systems have been developed to assist exercise therapy for low back pain. The aim of this systematic review was to provide an overview and to assess the effectiveness of the available technology-supported exercise therapy (TSET) programs for low back pain. The electronic databases Pubmed, Embase, Cochrane Central Register of Controlled Trials, PEDro, IEEE, and ACM were searched until January 2016. Randomized controlled trials (RCTs) using electronic technological systems simultaneously with exercise therapy for patients with low back pain were included. Twenty-five RCTs met the inclusion criteria. Seventeen studies involved patients with chronic low back pain, and electromyography biofeedback was the most prevalent type of technological support. This review shows that TSET seems to improve pain, disability, and quality of life for patients with low back pain, and that a standard treatment combined with an additional TSET program might be superior to a standard treatment alone. However, TSET seems not more effective compared to other interventions or a placebo intervention for improving these outcomes, which may partially be explained by the analytical approach of the current TSET-programs. For most technologies, only a limited number of RCTs are available, making it difficult to draw firm conclusions about the effectiveness of individual technological systems.
Abstract graph-like space and vector-valued metric graphs
Post, Olaf
2016-01-01
In this note we present some abstract ideas how one can construct spaces from building blocks according to a graph. The coupling is expressed via boundary pairs, and can be applied to very different spaces such as discrete graphs, quantum graphs or graph-like manifolds. We show a spectral analysis of graph-like spaces, and consider as a special case vector-valued quantum graphs. Moreover, we provide a prototype of a convergence theorem for shrinking graph-like spaces with Dirichlet boundary c...
Kirchhoff index of graphs and some graph operations
Indian Academy of Sciences (India)
Recently this concept has got a wide attention from different authors especially those interested ..... In this section, we pay attention to edge deletions and subdivisions and also joining vertices. Using Proposition 2.5 we ... Let H be the complete graph on x,y,z with ρxy(H ) = r , ρxz(H ) = a and ρyz(H ) = b. In K, {x,y} is a vertex ...
Bars, Lines, & Pies: A Graphing Skills Program. Expect the Unexpected with Math[R
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,…
"Cheers for Rates of Change"--An Introductory Lab Used to Relate Graphs to Physical Systems
Forrest, Doug; Whalen, Mary Battershell
2012-01-01
Students entering physics courses in high school have seen graphs for years in math and science classes, but often do not have a deep understanding of the physical meaning of the graphs. This introductory activity is designed to allow students to collect data for a real world or physical situation (the height versus volume of water held in…
Cofinite graphs and their profinite completions
Directory of Open Access Journals (Sweden)
Amrita Acharyya
2017-10-01
Full Text Available We generalize the idea of cofinite groups, due to B. Hartley, [2]. First we define cofinite spaces in general. Then, as a special situation, we study cofinite graphs and their uniform completions.The idea of constructing a cofinite graph starts with defining a uniform topological graph $\\Gamma$, in an appropriate fashion. We endow abstract graphs with uniformities corresponding to separating filter bases of equivalence relations with finitely many equivalence classes over $\\Gamma$. It is established that for any cofinite graph there exists a unique cofinite completion.
Cycle decompositions: From graphs to continua.
Georgakopoulos, Agelos
2012-01-30
We generalise a fundamental graph-theoretical fact, stating that every element of the cycle space of a graph is a sum of edge-disjoint cycles, to arbitrary continua. To achieve this we replace graph cycles by topological circles, and replace the cycle space of a graph by a new homology group for continua which is a quotient of the first singular homology group [Formula: see text]. This homology seems to be particularly apt for studying spaces with infinitely generated [Formula: see text], e.g. infinite graphs or fractals.
Modelling complex networks by random hierarchical graphs
Directory of Open Access Journals (Sweden)
M.Wróbel
2008-06-01
Full Text Available Numerous complex networks contain special patterns, called network motifs. These are specific subgraphs, which occur oftener than in randomized networks of Erdős-Rényi type. We choose one of them, the triangle, and build a family of random hierarchical graphs, being Sierpiński gasket-based graphs with random "decorations". We calculate the important characteristics of these graphs - average degree, average shortest path length, small-world graph family characteristics. They depend on probability of decorations. We analyze the Ising model on our graphs and describe its critical properties using a renormalization-group technique.
Subsampling for graph power spectrum estimation
Chepuri, Sundeep Prabhakar
2016-10-06
In this paper we focus on subsampling stationary random signals that reside on the vertices of undirected graphs. Second-order stationary graph signals are obtained by filtering white noise and they admit a well-defined power spectrum. Estimating the graph power spectrum forms a central component of stationary graph signal processing and related inference tasks. We show that by sampling a significantly smaller subset of vertices and using simple least squares, we can reconstruct the power spectrum of the graph signal from the subsampled observations, without any spectral priors. In addition, a near-optimal greedy algorithm is developed to design the subsampling scheme.
On 4-critical t-perfect graphs
Benchetrit, Yohann
2016-01-01
It is an open question whether the chromatic number of $t$-perfect graphs is bounded by a constant. The largest known value for this parameter is 4, and the only example of a 4-critical $t$-perfect graph, due to Laurent and Seymour, is the complement of the line graph of the prism $\\Pi$ (a graph is 4-critical if it has chromatic number 4 and all its proper induced subgraphs are 3-colorable). In this paper, we show a new example of a 4-critical $t$-perfect graph: the complement of the line gra...
Constrained Graph Optimization: Interdiction and Preservation Problems
Energy Technology Data Exchange (ETDEWEB)
Schild, Aaron V [Los Alamos National Laboratory
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.
On a programming language for graph algorithms
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.
Modes of Convergence for Term Graph Rewriting
DEFF Research Database (Denmark)
Bahr, Patrick
2012-01-01
Term graph rewriting provides a simple mechanism to finitely represent restricted forms of infinitary term rewriting. The correspondence between infinitary term rewriting and term graph rewriting has been studied to some extent. However, this endeavour is impaired by the lack of an appropriate...... counterpart of infinitary rewriting on the side of term graphs. We aim to fill this gap by devising two modes of convergence based on a partial order respectively a metric on term graphs. The thus obtained structures generalise corresponding modes of convergence that are usually studied in infinitary term...... rewriting. We argue that this yields a common framework in which both term rewriting and term graph rewriting can be studied. In order to substantiate our claim, we compare convergence on term graphs and on terms. In particular, we show that the modes of convergence on term graphs are conservative...
Modes of Convergence for Term Graph Rewriting
DEFF Research Database (Denmark)
Bahr, Patrick
2011-01-01
Term graph rewriting provides a simple mechanism to finitely represent restricted forms of infinitary term rewriting. The correspondence between infinitary term rewriting and term graph rewriting has been studied to some extent. However, this endeavour is impaired by the lack of an appropriate...... counterpart of infinitary rewriting on the side of term graphs. We aim to fill this gap by devising two modes of convergence based on a partial order resp. a metric on term graphs. The thus obtained structures generalise corresponding modes of convergence that are usually studied in infinitary term rewriting....... We argue that this yields a common framework in which both term rewriting and term graph rewriting can be studied. In order to substantiate our claim, we compare convergence on term graphs and on terms. In particular, we show that the resulting infinitary calculi of term graph rewriting exhibit...
On the centrality of some graphs
Directory of Open Access Journals (Sweden)
Vecdi Aytac
2017-10-01
Full Text Available A central issue in the analysis of complex networks is the assessment of their stability and vulnerability. A variety of measures have been proposed in the literature to quantify the stability of networks and a number of graph-theoretic parameters have been used to derive formulas for calculating network reliability. Different measures for graph vulnerability have been introduced so far to study different aspects of the graph behavior after removal of vertices or links such as connectivity, toughness, scattering number, binding number, residual closeness and integrity. In this paper, we consider betweenness centrality of a graph. Betweenness centrality of a vertex of a graph is portion of the shortest paths all pairs of vertices passing through a given vertex. In this paper, we obtain exact values for betweenness centrality for some wheel related graphs namely gear, helm, sunflower and friendship graphs.
A kaleidoscopic view of graph colorings
Zhang, Ping
2016-01-01
This book describes kaleidoscopic topics that have developed in the area of graph colorings. Unifying current material on graph coloring, this book describes current information on vertex and edge colorings in graph theory, including harmonious colorings, majestic colorings, kaleidoscopic colorings and binomial colorings. Recently there have been a number of breakthroughs in vertex colorings that give rise to other colorings in a graph, such as graceful labelings of graphs that have been reconsidered under the language of colorings. The topics presented in this book include sample detailed proofs and illustrations, which depicts elements that are often overlooked. This book is ideal for graduate students and researchers in graph theory, as it covers a broad range of topics and makes connections between recent developments and well-known areas in graph theory.
Software for Graph Analysis and Visualization
Directory of Open Access Journals (Sweden)
M. I. Kolomeychenko
2014-01-01
Full Text Available This paper describes the software for graph storage, analysis and visualization. The article presents a comparative analysis of existing software for analysis and visualization of graphs, describes the overall architecture of application and basic principles of construction and operation of the main modules. Furthermore, a description of the developed graph storage oriented to storage and processing of large-scale graphs is presented. The developed algorithm for finding communities and implemented algorithms of autolayouts of graphs are the main functionality of the product. The main advantage of the developed software is high speed processing of large size networks (up to millions of nodes and links. Moreover, the proposed graph storage architecture is unique and has no analogues. The developed approaches and algorithms are optimized for operating with big graphs and have high productivity.
Fibonacci number of the tadpole graph
Directory of Open Access Journals (Sweden)
Joe DeMaio
2014-10-01
Full Text Available In 1982, Prodinger and Tichy defined the Fibonacci number of a graph G to be the number of independent sets of the graph G. They did so since the Fibonacci number of the path graph Pn is the Fibonacci number F(n+2 and the Fibonacci number of the cycle graph Cn is the Lucas number Ln. The tadpole graph Tn,k is the graph created by concatenating Cn and Pk with an edge from any vertex of Cn to a pendant of Pk for integers n=3 and k=0. This paper establishes formulae and identities for the Fibonacci number of the tadpole graph via algebraic and combinatorial methods.
Triangle Counting in Dynamic Graph Streams
DEFF Research Database (Denmark)
Bulteau, Laurent; Froese, Vincent; Pagh, Rasmus
2015-01-01
Estimating the number of triangles in graph streams using a limited amount of memory has become a popular topic in the last decade. Different variations of the problem have been studied, depending on whether the graph edges are provided in an arbitrary order or as incidence lists. However......, with a few exceptions, the algorithms have considered insert-only streams. We present a new algorithm estimating the number of triangles in dynamic graph streams where edges can be both inserted and deleted. We show that our algorithm achieves better time and space complexity than previous solutions...... for various graph classes, for example sparse graphs with a relatively small number of triangles. Also, for graphs with constant transitivity coefficient, a common situation in real graphs, this is the first algorithm achieving constant processing time per edge. The result is achieved by a novel approach...
The optimal graph partitioning problem
DEFF Research Database (Denmark)
Sørensen, Michael Malmros; Holm, Søren
1993-01-01
In this paper we consider the problem of partitioning the set of nodes in a graph in at most p classes, such that the sum of node weights in any class is not greater than the class capacity b, and such that the sum of edge weights, for edges connecting nodes in the same class, is maximal. This pr......In this paper we consider the problem of partitioning the set of nodes in a graph in at most p classes, such that the sum of node weights in any class is not greater than the class capacity b, and such that the sum of edge weights, for edges connecting nodes in the same class, is maximal...
Significance evaluation in factor graphs
DEFF Research Database (Denmark)
Madsen, Tobias; Hobolth, Asger; Jensen, Jens Ledet
2017-01-01
in genomics and the multiple-testing issues accompanying them, accurate significance evaluation is of great importance. We here address the problem of evaluating statistical significance of observations from factor graph models. Results Two novel numerical approximations for evaluation of statistical...... significance are presented. First a method using importance sampling. Second a saddlepoint approximation based method. We develop algorithms to efficiently compute the approximations and compare them to naive sampling and the normal approximation. The individual merits of the methods are analysed both from....... Conclusions The applicability of saddlepoint approximation and importance sampling is demonstrated on known models in the factor graph framework. Using the two methods we can substantially improve computational cost without compromising accuracy. This contribution allows analyses of large datasets...
3-biplacement of bipartite graphs
Directory of Open Access Journals (Sweden)
Lech Adamus
2008-01-01
Full Text Available Let \\(G=(L,R;E\\ be a bipartite graph with color classes \\(L\\ and \\(R\\ and edge set \\(E\\. A set of two bijections \\(\\{\\varphi_1 , \\varphi_2\\}\\, \\(\\varphi_1 , \\varphi_2 :L \\cup R \\to L \\cup R\\, is said to be a \\(3\\-biplacement of \\(G\\ if \\(\\varphi_1(L= \\varphi_2(L = L\\ and \\(E \\cap \\varphi_1^*(E=\\emptyset\\, \\(E \\cap \\varphi_2^*(E=\\emptyset\\, \\(\\varphi_1^*(E \\cap \\varphi_2^*(E=\\emptyset\\, where \\(\\varphi_1^*\\, \\(\\varphi_2^*\\ are the maps defined on \\(E\\, induced by \\(\\varphi_1\\, \\(\\varphi_2\\, respectively. We prove that if \\(|L| = p\\, \\(|R| = q\\, \\(3 \\leq p \\leq q\\, then every graph \\(G=(L,R;E\\ of size at most \\(p\\ has a \\(3\\-biplacement.
Zhang, Ping
2015-01-01
A comprehensive treatment of color-induced graph colorings is presented in this book, emphasizing vertex colorings induced by edge colorings. The coloring concepts described in this book depend not only on the property required of the initial edge coloring and the kind of objects serving as colors, but also on the property demanded of the vertex coloring produced. For each edge coloring introduced, background for the concept is provided, followed by a presentation of results and open questions dealing with this topic. While the edge colorings discussed can be either proper or unrestricted, the resulting vertex colorings are either proper colorings or rainbow colorings. This gives rise to a discussion of irregular colorings, strong colorings, modular colorings, edge-graceful colorings, twin edge colorings and binomial colorings. Since many of the concepts described in this book are relatively recent, the audience for this book is primarily mathematicians interested in learning some new areas of graph colorings...
Reachability Games on Automatic Graphs
Neider, Daniel
In this work we study two-person reachability games on finite and infinite automatic graphs. For the finite case we empirically show that automatic game encodings are competitive to well-known symbolic techniques such as BDDs, SAT and QBF formulas. For the infinite case we present a novel algorithm utilizing algorithmic learning techniques, which allows to solve huge classes of automatic reachability games.
Decomposing a graph into bistars
DEFF Research Database (Denmark)
Thomassen, Carsten
2013-01-01
Bárat and the present author conjectured that, for each tree T, there exists a natural number kT such that the following holds: If G is a kT-edge-connected graph such that |E(T)| divides |E(G)|, then G has a T-decomposition, that is, a decomposition of the edge set into trees each of which...
Parallel External Memory Graph Algorithms
DEFF Research Database (Denmark)
Arge, Lars Allan; Goodrich, Michael T.; Sitchinava, Nodari
2010-01-01
In this paper, we study parallel I/O efficient graph algorithms in the Parallel External Memory (PEM) model, one o f the private-cache chip multiprocessor (CMP) models. We study the fundamental problem of list ranking which leads to efficient solutions to problems on trees, such as computing lowest...... an optimal speedup of Â¿(P) in parallel I/O complexity and parallel computation time, compared to the single-processor external memory counterparts....
Quantum information processing with graph states
International Nuclear Information System (INIS)
Schlingemann, Dirk-Michael
2005-04-01
Graph states are multiparticle states which are associated with graphs. Each vertex of the graph corresponds to a single system or particle. The links describe quantum correlations (entanglement) between pairs of connected particles. Graph states were initiated independently by two research groups: On the one hand, graph states were introduced by Briegel and Raussendorf as a resource for a new model of one-way quantum computing, where algorithms are implemented by a sequence of measurements at single particles. On the other hand, graph states were developed by the author of this thesis and ReinhardWerner in Braunschweig, as a tool to build quantum error correcting codes, called graph codes. The connection between the two approaches was fully realized in close cooperation of both research groups. This habilitation thesis provides a survey of the theory of graph codes, focussing mainly, but not exclusively on the author's own research work. We present the theoretical and mathematical background for the analysis of graph codes. The concept of one-way quantum computing for general graph states is discussed. We explicitly show how to realize the encoding and decoding device of a graph code on a one-way quantum computer. This kind of implementation is to be seen as a mathematical description of a quantum memory device. In addition to that, we investigate interaction processes, which enable the creation of graph states on very large systems. Particular graph states can be created, for instance, by an Ising type interaction between next neighbor particles which sits at the points of an infinitely extended cubic lattice. Based on the theory of quantum cellular automata, we give a constructive characterization of general interactions which create a translationally invariant graph state. (orig.)
Topological structure of dictionary graphs
International Nuclear Information System (INIS)
Fuks, Henryk; Krzeminski, Mark
2009-01-01
We investigate the topological structure of the subgraphs of dictionary graphs constructed from WordNet and Moby thesaurus data. In the process of learning a foreign language, the learner knows only a subset of all words of the language, corresponding to a subgraph of a dictionary graph. When this subgraph grows with time, its topological properties change. We introduce the notion of the pseudocore and argue that the growth of the vocabulary roughly follows decreasing pseudocore numbers-that is, one first learns words with a high pseudocore number followed by smaller pseudocores. We also propose an alternative strategy for vocabulary growth, involving decreasing core numbers as opposed to pseudocore numbers. We find that as the core or pseudocore grows in size, the clustering coefficient first decreases, then reaches a minimum and starts increasing again. The minimum occurs when the vocabulary reaches a size between 10 3 and 10 4 . A simple model exhibiting similar behavior is proposed. The model is based on a generalized geometric random graph. Possible implications for language learning are discussed.
Dynkin graphs and quadrilateral singularities
Urabe, Tohsuke
1993-01-01
The study of hypersurface quadrilateral singularities can be reduced to the study of elliptic K3 surfaces with a singular fiber of type I * 0 (superscript *, subscript 0), and therefore these notes consider, besides the topics of the title, such K3 surfaces too. The combinations of rational double points that can occur on fibers in the semi-universal deformations of quadrilateral singularities are examined, to show that the possible combinations can be described by a certain law from the viewpoint of Dynkin graphs. This is equivalent to saying that the possible combinations of singular fibers in elliptic K3 surfaces with a singular fiber of type I * 0 (superscript *, subscript 0) can be described by a certain law using classical Dynkin graphs appearing in the theory of semi-simple Lie groups. Further, a similar description for thecombination of singularities on plane sextic curves is given. Standard knowledge of algebraic geometry at the level of graduate students is expected. A new method based on graphs wil...
Hybrid vehicle turbine engine technology support (HVTE-TS) project. 1995--1996 annual report
Energy Technology Data Exchange (ETDEWEB)
NONE
1996-12-31
This report presents a summary of technical work accomplished on the Hybrid Vehicle Turbine Engine--Technology Support (HVTE-TS) Project during calendar years 1995 and 1996. Work was performed under an initial National Aeronautics and Space Administration (NASA) contract DEN3-336. As of September 1996 the contract administration was transferred to the US Department of Energy (DoE) Chicago Operations Office, and renumbered as DE-AC02-96EE50553. The purpose of the HVTE-TS program is to develop gas turbine engine technology in support of DoE and automotive industry programs exploring the use of gas turbine generator sets in hybrid-electric automotive propulsion systems. The program focus is directed to the development of four key technologies to be applied to advanced turbogenerators for hybrid vehicles: Structural ceramic materials and processes; Low emissions combustion systems; Regenerators and seals systems; and Insulation systems and processes. 60 figs., 9 tabs.
Anderson, Lori S; Enge, Karmin J
2012-10-01
School nurses care for children with a variety of health-related conditions and they need information about managing these conditions, which is accessible, current, and useful. The goal of this literature review was to gather and synthesize information on technology-supported resources and to determine which met the educational needs of school nurses. Successful online educational programs were interactive and self-directed. The most common barriers were lack of time to find educational information, lack of knowledge about computers, technology, the Internet and specific programs, and lack of administrative support from school officials to use technology to access information and evidence for practice. Recommendations for successful use of technology to meet practicing school nurse's educational needs are offered.
Rinaldi, Vera D; Lorr, Nancy A; Williams, Kimberly
2017-07-01
Monitoring of student learning through systematic formative assessment is important for adjusting pedagogical strategies. However, traditional formative assessments, such as quizzes and written assignments, may not be sufficiently timely for making adjustments to a learning process. Technology supported formative assessment tools assess student knowledge, allow for immediate feedback, facilitate classroom dialogues, and have the potential to modify student learning strategies. As an attempt to integrate technology supported formative assessment in the laboratory section of an upper-level histology course, the interactive application Learning Catalytics TM , a cloud-based assessment system, was used. This study conducted during the 2015 Histology courses at Cornell University concluded that this application is helpful for identifying student misconceptions "on-the-go," engaging otherwise marginalized students, and forming a new communication venue between students and instructors. There was no overall difference between grades from topics that used the application and grades from those that did not, and students reported that it only slightly helped improve their understanding of the topic (3.8 ± 0.99 on a five-point Likert scale). However, they highly recommended using it (4.2 ± 0.71). The major limitation was regarding the image display and graphical resolution of this application. Even though students embrace the use of technology, 39% reported benefits of having the traditional light microscope available. This cohort of students led instructors to conclude that the newest tools are not always better, but rather can complement traditional instruction methods. Anat Sci Educ 10: 328-338. © 2016 American Association of Anatomists. © 2016 American Association of Anatomists.
Three Syntactic Theories for Combinatory Graph Reduction
DEFF Research Database (Denmark)
Danvy, Olivier; Zerny, Ian
2011-01-01
We present a purely syntactic theory of graph reduction for the canonical combinators S, K, and I, where graph vertices are represented with evaluation contexts and let expressions. We express this syntactic theory as a reduction semantics, which we refocus into the first storeless abstract machine...... for combinatory graph reduction, which we refunctionalize into the first storeless natural semantics for combinatory graph reduction.We then factor out the introduction of let expressions to denote as many graph vertices as possible upfront instead of on demand, resulting in a second syntactic theory, this one...... of term graphs in the sense of Barendregt et al. The corresponding storeless abstract machine and natural semantics follow mutatis mutandis. We then interpret let expressions as operations over a global store (thus shifting, in Strachey's words, from denotable entities to storable entities), resulting...
Double-Critical Graphs and Complete Minors
DEFF Research Database (Denmark)
Kawarabayashi, Ken-ichi; Pedersen, Anders Sune; Toft, Bjarne
2010-01-01
A connected $k$-chromatic graph $G$ is double-critical if for all edges $uv$ of $G$ the graph $G - u - v$ is $(k-2)$-colourable. The only known double-critical $k$-chromatic graph is the complete $k$-graph $K_k$. The conjecture that there are no other double-critical graphs is a special case...... of a conjecture from 1966, due to Erd\\H{o}s and Lov\\'asz. The conjecture has been verified for $k \\leq 5$. We prove for $k=6$ and $k=7$ that any non-complete double-critical $k$-chromatic graph is $6$-connected and has $K_k$ as a minor. Udgivelsesdato: 07.06....
Alliances and Bisection Width for Planar Graphs
DEFF Research Database (Denmark)
Olsen, Martin; Revsbæk, Morten
2013-01-01
An alliance in a graph is a set of vertices (allies) such that each vertex in the alliance has at least as many allies (counting the vertex itself) as non-allies in its neighborhood of the graph. We show that any planar graph with minimum degree at least 4 can be split into two alliances...... in polynomial time. We base this on a proof of an upper bound of n on the bisection width for 4-connected planar graphs with an odd number of vertices. This improves a recently published n + 1 upper bound on the bisection width of planar graphs without separating triangles and supports the folklore conjecture...... that a general upper bound of n exists for the bisection width of planar graphs....
Well-covered graphs and factors
DEFF Research Database (Denmark)
Randerath, Bert; Vestergaard, Preben D.
2006-01-01
A maximum independent set of vertices in a graph is a set of pairwise nonadjacent vertices of largest cardinality α. Plummer defined a graph to be well-covered, if every independent set is contained in a maximum independent set of G. Every well-covered graph G without isolated vertices has...... a perfect [1,2]-factor F_G, i.e. a spanning subgraph such that each component is 1-regular og 2-regular. Here, we characterize all well-covered graphs G satisfying α(G)=α(F_G) for some perfect [1,2]-factor F_G. This class contains all well-covered graphs G without isolated vertices of order n with α ≥ (n...... - 1)/2, and in particular all very well-covered graphs....
Fast Generation of Sparse Random Kernel Graphs.
Hagberg, Aric; Lemons, Nathan
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 (n(logn)2). As a practical example we show how to generate samples of power-law degree distribution graphs with tunable assortativity.
2-domination number of generalized Petersen graphs
Indian Academy of Sciences (India)
35
2Department of Computer Science, Yazd University, Yazd, Iran. Abstract. Let G = (V,E) be a graph. A subset S ⊆ V is a k-dominating set of. G if each vertex ... on the area of domination in graphs and its applications we refer the reader to [6, 7]. The generalized Petersen graph P(n, k)=(V,E) is defined as follows: V = {v1,v2,...
On path hypercompositions in graphs and automata
Directory of Open Access Journals (Sweden)
Massouros Christos G.
2016-01-01
Full Text Available The paths in graphs define hypercompositions in the set of their vertices and therefore it is feasible to associate hypercompositional structures to each graph. Similarly, the strings of letters from their alphabet, define hypercompositions in the automata, which in turn define the associated hypergroups to the automata. The study of the associated hypercompositional structures gives results in both, graphs and automata theory.
Visibility graphs and landscape visibility analysis
O Sullivan, D.; Turner, A.
2001-01-01
Visibility analysis based on viewsheds is one of the most frequently used GIS analysis tools. In this paper we present an approach to visibility analysis based on the visibility graph. A visibility graph records the pattern of mutual visibility relations in a landscape, and provides a convenient way of storing and further analysing the results of multiple viewshed analyses for a particular landscape region. We describe how a visibility graph may be calculated for a landscape. We then give exa...
Steiner Distance in Graphs--A Survey
Mao, Yaping
2017-01-01
For a connected graph $G$ of order at least $2$ and $S\\subseteq V(G)$, the \\emph{Steiner distance} $d_G(S)$ among the vertices of $S$ is the minimum size among all connected subgraphs whose vertex sets contain $S$. In this paper, we summarize the known results on the Steiner distance parameters, including Steiner distance, Steiner diameter, Steiner center, Steiner median, Steiner interval, Steiner distance hereditary graph, Steiner distance stable graph, average Steiner distance, and Steiner ...
Designing a Cross-organizational Case Management System using Dynamic Condition Response Graphs
DEFF Research Database (Denmark)
Hildebrandt, Thomas; Mukkamala, Raghava Rao; Slaats, Tijs
2011-01-01
We present a case study of the use of Dynamic Con- dition Response (DCR) Graphs, a recently introduced declarative business process model, in the design of a cross-organizational case management system being developed by Exformatics A/S, a danish provider of knowledge and workflow management...... systems. We show how DCR Graphs allow to capture directly both the behavioral constraints identified during meetings with the customer and the operational execution as markings of the graph. In comparison, imperative models such as BPMN, Petri Net, UML Sequence or Activity diagrams are only good.......0 standard. The case study motivated an extension of the DCR Graphs model to nested graphs and the development of graphical design and simulation tools to increase the understanding of the models. The study also revealed a number of challenges for future research in techniques for model-driven design...
Xu, Kexiang; Trinajstić, Nenad
2015-01-01
This is the first book to focus on the topological index, the Harary index, of a graph, including its mathematical properties, chemical applications and some related and attractive open problems. This book is dedicated to Professor Frank Harary (1921—2005), the grandmaster of graph theory and its applications. It has be written by experts in the field of graph theory and its applications. For a connected graph G, as an important distance-based topological index, the Harary index H(G) is defined as the sum of the reciprocals of the distance between any two unordered vertices of the graph G. In this book, the authors report on the newest results on the Harary index of a graph. These results mainly concern external graphs with respect to the Harary index; the relations to other topological indices; its properties and applications to pure graph theory and chemical graph theory; and two significant variants, i.e., additively and multiplicatively weighted Harary indices. In the last chapter, we present a number o...
Interactive Graph Layout of a Million Nodes
Directory of Open Access Journals (Sweden)
Peng Mi
2016-12-01
Full Text Available Sensemaking of large graphs, specifically those with millions of nodes, is a crucial task in many fields. Automatic graph layout algorithms, augmented with real-time human-in-the-loop interaction, can potentially support sensemaking of large graphs. However, designing interactive algorithms to achieve this is challenging. In this paper, we tackle the scalability problem of interactive layout of large graphs, and contribute a new GPU-based force-directed layout algorithm that exploits graph topology. This algorithm can interactively layout graphs with millions of nodes, and support real-time interaction to explore alternative graph layouts. Users can directly manipulate the layout of vertices in a force-directed fashion. The complexity of traditional repulsive force computation is reduced by approximating calculations based on the hierarchical structure of multi-level clustered graphs. We evaluate the algorithm performance, and demonstrate human-in-the-loop layout in two sensemaking case studies. Moreover, we summarize lessons learned for designing interactive large graph layout algorithms on the GPU.
Evolutionary Games of Multiplayer Cooperation on Graphs
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
Mechatronic modeling and simulation using bond graphs
Das, Shuvra
2009-01-01
Introduction to Mechatronics and System ModelingWhat Is Mechatronics?What Is a System and Why Model Systems?Mathematical Modeling Techniques Used in PracticeSoftwareBond Graphs: What Are They?Engineering SystemsPortsGeneralized VariablesBond GraphsBasic Components in SystemsA Brief Note about Bond Graph Power DirectionsSummary of Bond Direction RulesDrawing Bond Graphs for Simple Systems: Electrical and MechanicalSimplification Rules for Junction StructureDrawing Bond Graphs for Electrical SystemsDrawing Bond Graphs for Mechanical SystemsCausalityDrawing Bond Graphs for Hydraulic and Electronic Components and SystemsSome Basic Properties and Concepts for FluidsBond Graph Model of Hydraulic SystemsElectronic SystemsDeriving System Equations from Bond GraphsSystem VariablesDeriving System EquationsTackling Differential CausalityAlgebraic LoopsSolution of Model Equations and Their InterpretationZeroth Order SystemsFirst Order SystemsSecond Order SystemTransfer Functions and Frequency ResponsesNumerical Solution ...
DEFF Research Database (Denmark)
Jensen, T.R.; Thomassen, Carsten
2000-01-01
If k is a prime power, and G is a graph with n vertices, then a k-coloring of G may be considered as a vector in GF(k)(n). We prove that the subspace of GF(3)(n) spanned by all 3-colorings of a planar triangle-free graph with n vertices has dimension n. In particular, any such graph has at least n...... - 1 nonequivalent 3-colorings, and the addition of any edge or any vertex of degree 3 results in a 3-colorable graph. (C) 2000 John Wiley & Sons, Inc....
Evolutionary Games of Multiplayer Cooperation on Graphs.
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.
A Reduction of the Graph Reconstruction Conjecture
Directory of Open Access Journals (Sweden)
Monikandan S.
2014-08-01
Full Text Available A graph is said to be reconstructible if it is determined up to isomor- phism from the collection of all its one-vertex deleted unlabeled subgraphs. Reconstruction Conjecture (RC asserts that all graphs on at least three vertices are reconstructible. In this paper, we prove that interval-regular graphs and some new classes of graphs are reconstructible and show that RC is true if and only if all non-geodetic and non-interval-regular blocks G with diam(G = 2 or diam(Ḡ = diam(G = 3 are reconstructible
Visual Adjacency Lists for Dynamic Graphs.
Hlawatsch, Marcel; Burch, Michael; Weiskopf, Daniel
2014-11-01
We present a visual representation for dynamic, weighted graphs based on the concept of adjacency lists. Two orthogonal axes are used: one for all nodes of the displayed graph, the other for the corresponding links. Colors and labels are employed to identify the nodes. The usage of color allows us to scale the visualization to single pixel level for large graphs. In contrast to other techniques, we employ an asymmetric mapping that results in an aligned and compact representation of links. Our approach is independent of the specific properties of the graph to be visualized, but certain graphs and tasks benefit from the asymmetry. As we show in our results, the strength of our technique is the visualization of dynamic graphs. In particular, sparse graphs benefit from the compact representation. Furthermore, our approach uses visual encoding by size to represent weights and therefore allows easy quantification and comparison. We evaluate our approach in a quantitative user study that confirms the suitability for dynamic and weighted graphs. Finally, we demonstrate our approach for two examples of dynamic graphs.
Chemical graph-theoretic cluster expansions
International Nuclear Information System (INIS)
Klein, D.J.
1986-01-01
A general computationally amenable chemico-graph-theoretic cluster expansion method is suggested as a paradigm for incorporation of chemical structure concepts in a systematic manner. The cluster expansion approach is presented in a formalism general enough to cover a variety of empirical, semiempirical, and even ab initio applications. Formally such approaches for the utilization of chemical structure-related concepts may be viewed as discrete analogues of Taylor series expansions. The efficacy of the chemical structure concepts then is simply bound up in the rate of convergence of the cluster expansions. In many empirical applications, e.g., boiling points, chromatographic separation coefficients, and biological activities, this rate of convergence has been observed to be quite rapid. More note will be made here of quantum chemical applications. Relations to questions concerning size extensivity of energies and size consistency of wave functions are addressed
Analytical Treatment of Higher-Order Graphs: A Path Ordinal Method for Solving Graphs
Directory of Open Access Journals (Sweden)
Hala Kamal
2017-11-01
Full Text Available Analytical treatment of the composition of higher-order graphs representing linear relations between variables is developed. A path formalism to deal with problems in graph theory is introduced. It is shown how paths in the composed graph representing individual contributions to variables relation can be enumerated and represented by ordinals. The method allows for one to extract partial information and gives an alternative to classical graph approach.
Applications of Multivalued Contractions on Graphs to Graph-Directed Iterated Function Systems
Directory of Open Access Journals (Sweden)
T. Dinevari
2015-01-01
Full Text Available We apply a fixed point result for multivalued contractions on complete metric spaces endowed with a graph to graph-directed iterated function systems. More precisely, we construct a suitable metric space endowed with a graph G and a suitable G-contraction such that its fixed points permit us to obtain more information on the attractor of a graph-directed iterated function system.
Decomposing a planar graph into an independent set and a 3-degenerate graph
DEFF Research Database (Denmark)
Thomassen, Carsten
2000-01-01
We prove the conjecture made by O.V.Borodin in 1976 that the vertex set of every planar graph can be decomposed into an independent set and aset inducing a $3$-degenerate graph.......We prove the conjecture made by O.V.Borodin in 1976 that the vertex set of every planar graph can be decomposed into an independent set and aset inducing a $3$-degenerate graph....
Decomposing a planar graph into an independent set and a 3-degenerate graph
DEFF Research Database (Denmark)
Thomassen, Carsten
2001-01-01
We prove the conjecture made by O. V. Borodin in 1976 that the vertex set of every planar graph can be decomposed into an independent set and a set inducing a 3-degenerate graph. (C) 2001 Academic Press.......We prove the conjecture made by O. V. Borodin in 1976 that the vertex set of every planar graph can be decomposed into an independent set and a set inducing a 3-degenerate graph. (C) 2001 Academic Press....
Ben-Moussa, Maher; Rubo, Marius; Debracque, Coralie; Lange, Wolf-Gero
2017-01-01
The present paper explores the benefits and the capabilities of various emerging state-of-the-art interactive 3D and Internet of Things technologies and investigates how these technologies can be exploited to develop a more effective technology supported exposure therapy solution for social anxiety disorder. “DJINNI” is a conceptual design of an in vivo augmented reality (AR) exposure therapy mobile support system that exploits several capturing technologies and integrates the patient’s state and situation by vision-based, audio-based, and physiology-based analysis as well as by indoor/outdoor localization techniques. DJINNI also comprises an innovative virtual reality exposure therapy system that is adaptive and customizable to the demands of the in vivo experience and therapeutic progress. DJINNI follows a gamification approach where rewards and achievements are utilized to motivate the patient to progress in her/his treatment. The current paper reviews the state of the art of technologies needed for such a solution and recommends how these technologies could be integrated in the development of an individually tailored and yet feasible and effective AR/virtual reality-based exposure therapy. Finally, the paper outlines how DJINNI could be part of classical cognitive behavioral treatment and how to validate such a setup. PMID:28503155
Directory of Open Access Journals (Sweden)
Maher Ben-Moussa
2017-04-01
Full Text Available The present paper explores the benefits and the capabilities of various emerging state-of-the-art interactive 3D and Internet of Things technologies and investigates how these technologies can be exploited to develop a more effective technology supported exposure therapy solution for social anxiety disorder. “DJINNI” is a conceptual design of an in vivo augmented reality (AR exposure therapy mobile support system that exploits several capturing technologies and integrates the patient’s state and situation by vision-based, audio-based, and physiology-based analysis as well as by indoor/outdoor localization techniques. DJINNI also comprises an innovative virtual reality exposure therapy system that is adaptive and customizable to the demands of the in vivo experience and therapeutic progress. DJINNI follows a gamification approach where rewards and achievements are utilized to motivate the patient to progress in her/his treatment. The current paper reviews the state of the art of technologies needed for such a solution and recommends how these technologies could be integrated in the development of an individually tailored and yet feasible and effective AR/virtual reality-based exposure therapy. Finally, the paper outlines how DJINNI could be part of classical cognitive behavioral treatment and how to validate such a setup.
Ben-Moussa, Maher; Rubo, Marius; Debracque, Coralie; Lange, Wolf-Gero
2017-01-01
The present paper explores the benefits and the capabilities of various emerging state-of-the-art interactive 3D and Internet of Things technologies and investigates how these technologies can be exploited to develop a more effective technology supported exposure therapy solution for social anxiety disorder. "DJINNI" is a conceptual design of an in vivo augmented reality (AR) exposure therapy mobile support system that exploits several capturing technologies and integrates the patient's state and situation by vision-based, audio-based, and physiology-based analysis as well as by indoor/outdoor localization techniques. DJINNI also comprises an innovative virtual reality exposure therapy system that is adaptive and customizable to the demands of the in vivo experience and therapeutic progress. DJINNI follows a gamification approach where rewards and achievements are utilized to motivate the patient to progress in her/his treatment. The current paper reviews the state of the art of technologies needed for such a solution and recommends how these technologies could be integrated in the development of an individually tailored and yet feasible and effective AR/virtual reality-based exposure therapy. Finally, the paper outlines how DJINNI could be part of classical cognitive behavioral treatment and how to validate such a setup.
Muller, Angela M; Mérillat, Susan; Jäncke, Lutz
2016-02-15
A major part of our knowledge about the functioning of the aging brain comes from task-induced activation paradigms. However, the aging brain's intrinsic functional organization may be already a limiting factor for the outcome of an actual behavior. In order to get a better understanding of how this functional baseline configuration of the aging brain may affect cognitive performance, we analyzed task-free fMRI data of older 186 participants (mean age=70.4, 97 female) and their performance data in verbal fluency: First, we conducted an intrinsic connectivity contrast analysis (ICC) for the purpose of evaluating the brain regions whose degree of connectedness was significantly correlated with fluency performance. Secondly, using connectivity analyses we investigated how the clusters from the ICC functionally related to the other major resting-state networks. Apart from the importance of intact fronto-parietal long-range connections, the preserved capacity of the DMN for a finely attuned interaction with the executive-control network and the language network seems to be crucial for successful verbal fluency performance in older people. We provide further evidence that the right frontal regions might be more prominently affected by age-related decline. Copyright © 2015 Elsevier Inc. All rights reserved.
Embedding graphs in Lorentzian spacetime.
Directory of Open Access Journals (Sweden)
James R Clough
Full Text Available Geometric approaches to network analysis combine simply defined models with great descriptive power. In this work we provide a method for embedding directed acyclic graphs (DAG into Minkowski spacetime using Multidimensional scaling (MDS. First we generalise the classical MDS algorithm, defined only for metrics with a Riemannian signature, to manifolds of any metric signature. We then use this general method to develop an algorithm which exploits the causal structure of a DAG to assign space and time coordinates in a Minkowski spacetime to each vertex. As in the causal set approach to quantum gravity, causal connections in the discrete graph correspond to timelike separation in the continuous spacetime. The method is demonstrated by calculating embeddings for simple models of causal sets and random DAGs, as well as real citation networks. We find that the citation networks we test yield significantly more accurate embeddings that random DAGs of the same size. Finally we suggest a number of applications in citation analysis such as paper recommendation, identifying missing citations and fitting citation models to data using this geometric approach.
Feature Tracking Using Reeb Graphs
Energy Technology Data Exchange (ETDEWEB)
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.
Representing vertex-transitive Vertex-transitive graphs on Groupoids
African Journals Online (AJOL)
Vertex-transitive graphs are one of the most favoured class of graphs in modelling scientific phenomena if symmetry is at issue. An understanding of these graphs should, therefore, be an obvious undertaking. Here, we present a characterisation of vertex-transitive graphs as left loop graphs and expose the measure of ...
Graph compositions and flats of cycle matroids | Mphako-Banda ...
African Journals Online (AJOL)
We give an alternative method for counting the number of graph compositions of any graph G. In particular we show that counting the number of graph compositions of a graph G is equivalent to counting the number of flats of its cycle matroid. Then we give one condition for non isomorphic graphs to have the same number ...
Distance-regular Cayley graphs with least eigenvalue -2
van Dam, Edwin; Abdollahi, Alireza; Jazaeri, Mojtaba
2017-01-01
We classify the distance-regular Cayley graphs with least eigenvalue −2 and diameter at most three. Besides sporadic examples, these comprise of the lattice graphs, certain triangular graphs, and line graphs of incidence graphs of certain projective planes. In addition, we classify the possible
Geometric aspects of 2-walk-regular graphs
Camara Vallejo, M.; van Dam, E.R.; Koolen, J.H.; Park, J.
2013-01-01
A t-walk-regular graph is a graph for which the number of walks of given length between two vertices depends only on the distance between these two vertices, as long as this distance is at most t. Such graphs generalize distance-regular graphs and t-arc-transitive graphs. In this paper, we will
On cyclic orthogonal double covers of circulant graphs by special infinite graphs
Directory of Open Access Journals (Sweden)
R. El-Shanawany
2017-12-01
Full Text Available In this article, a technique to construct cyclic orthogonal double covers (CODCs of regular circulant graphs by certain infinite graph classes such as complete bipartite and tripartite graphs and disjoint union of butterfly and K1,2n−10 is introduced.
Helping Students Make Sense of Graphs: An Experimental Trial of SmartGraphs Software
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…
Spatial legend compatibility within versus between graphs in multiple graph comprehension.
Riechelmann, Eva; Huestegge, Lynn
2018-02-01
Previous research has shown that spatial compatibility between the data region and the legend of a graph is beneficial for comprehension. However, in multiple graphs, data-legend compatibility can come at the cost of spatial between-graph legend incompatibility. Here we aimed at determining which type of compatibility is most important for performance: global (legend-legend) compatibility between graphs, or local (data-legend) compatibility within graphs. Additionally, a baseline condition (incompatible) was included. Participants chose one out of several line graphs from a multiple panel as the answer to a data-related question. Compatibility type and the number of graphs per panel were varied. Whereas Experiment 1 involved simple graphs with only two lines/legend entries within each graph, Experiment 2 explored more complex graphs. The results indicated that compatibility speeds up comprehension, at least when a certain threshold of graph complexity is exceeded. Furthermore, we found evidence for an advantage of local over global data-legend compatibility under specific conditions. Taken together, the results further support the idea that compatibility principles strongly determine the ease of integration processes in graph comprehension and should thus be considered in multiple-panel design.
Enabling Graph Appliance for Genome Assembly
Energy Technology Data Exchange (ETDEWEB)
Singh, Rina [ORNL; Graves, Jeffrey A [ORNL; Lee, Sangkeun (Matt) [ORNL; Sukumar, Sreenivas R [ORNL; Shankar, Mallikarjun [ORNL
2015-01-01
In recent years, there has been a huge growth in the amount of genomic data available as reads generated from various genome sequencers. The number of reads generated can be huge, ranging from hundreds to billions of nucleotide, each varying in size. Assembling such large amounts of data is one of the challenging computational problems for both biomedical and data scientists. Most of the genome assemblers developed have used de Bruijn graph techniques. A de Bruijn graph represents a collection of read sequences by billions of vertices and edges, which require large amounts of memory and computational power to store and process. This is the major drawback to de Bruijn graph assembly. Massively parallel, multi-threaded, shared memory systems can be leveraged to overcome some of these issues. The objective of our research is to investigate the feasibility and scalability issues of de Bruijn graph assembly on Cray s Urika-GD system; Urika-GD is a high performance graph appliance with a large shared memory and massively multithreaded custom processor designed for executing SPARQL queries over large-scale RDF data sets. However, to the best of our knowledge, there is no research on representing a de Bruijn graph as an RDF graph or finding Eulerian paths in RDF graphs using SPARQL for potential genome discovery. In this paper, we address the issues involved in representing a de Bruin graphs as RDF graphs and propose an iterative querying approach for finding Eulerian paths in large RDF graphs. We evaluate the performance of our implementation on real world ebola genome datasets and illustrate how genome assembly can be accomplished with Urika-GD using iterative SPARQL queries.
Probability on graphs random processes on graphs and lattices
Grimmett, Geoffrey
2018-01-01
This introduction to some of the principal models in the theory of disordered systems leads the reader through the basics, to the very edge of contemporary research, with the minimum of technical fuss. Topics covered include random walk, percolation, self-avoiding walk, interacting particle systems, uniform spanning tree, random graphs, as well as the Ising, Potts, and random-cluster models for ferromagnetism, and the Lorentz model for motion in a random medium. This new edition features accounts of major recent progress, including the exact value of the connective constant of the hexagonal lattice, and the critical point of the random-cluster model on the square lattice. The choice of topics is strongly motivated by modern applications, and focuses on areas that merit further research. Accessible to a wide audience of mathematicians and physicists, this book can be used as a graduate course text. Each chapter ends with a range of exercises.
Real Graphs from Real Data: Experiencing the Concepts of Measurement and Uncertainty
Farmer, Stuart
2012-01-01
A simple activity using cheap and readily available materials is described that allows students to experience first hand many of the concepts of measurement, uncertainty and graph drawing without laborious measuring or calculation. (Contains 9 figures.)
Recruitment of the ventral and dorsal streams in statistical graph comprehension: An fMRI study.
Li, Mi; Lu, Shengfu; Zhong, Ning
2015-01-01
Although many previous studies have focused on statistical graph comprehension in cognitive psychology, there is no consensus among them. Brain neuroimaging studies on the statistical graph comprehension are useful to account for the cognitive mechanism of interpreting statistical graphic information. The present study used two experimental conditions, a statistical graph (SG) and a statistical graph with text (SGT), and one control condition, a text (ST), where the ST task was a verbal description of the information from the SG, and when the SGT is a mixed graph + textual description. We used fMRI to investigate the brain activity of 36 normal subjects while they passively viewed the statistical information presented in visual forms as SG, ST or SGT. The results showed that compared with the control tasks, both SG and SGT consistently activated ventral and dorsal streams and that compared with SGT, SG significantly activated the ventral stream but not the dorsal stream. These results suggest that the portions of the ventral and dorsal streams related to object recognition are commonly involved in statistical graph comprehension. These findings provide neuroimaging evidence for the cognitive processing of statistical graphs.
Digital video, learning styles, and student understanding of kinematics graphs
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
Graphs, Ideal Flow, and the Transportation Network
Teknomo, Kardi
2016-01-01
This lecture discusses the mathematical relationship between network structure and network utilization of transportation network. Network structure means the graph itself. Network utilization represent the aggregation of trajectories of agents in using the network graph. I show the similarity and relationship between the structural pattern of the network and network utilization.
Radio Channel Modelling Using Stochastic Propagation Graphs
DEFF Research Database (Denmark)
Pedersen, Troels; Fleury, Bernard Henri
2007-01-01
In this contribution the radio channel model proposed in [1] is extended to include multiple transmitters and receivers. The propagation environment is modelled using random graphs where vertices of a graph represent scatterers and edges model the wave propagation between scatterers. Furthermore...
The Minimum Distance of Graph Codes
DEFF Research Database (Denmark)
Høholdt, Tom; Justesen, Jørn
2011-01-01
We study codes constructed from graphs where the code symbols are associated with the edges and the symbols connected to a given vertex are restricted to be codewords in a component code. In particular we treat such codes from bipartite expander graphs coming from Euclidean planes and other...
Geometric classification of simple graph algebras
DEFF Research Database (Denmark)
Sørensen, Adam Peder Wie
2013-01-01
Inspired by Franks’ classification of irreducible shifts of finite type, we provide a short list of allowed moves on graphs that preserve the stable isomorphism class of the associated C ∗ -algebras. We show that if two graphs have stably isomorphic and simple unital algebras then we can use...
From concatenated codes to graph codes
DEFF Research Database (Denmark)
Justesen, Jørn; Høholdt, Tom
2004-01-01
We consider codes based on simple bipartite expander graphs. These codes may be seen as the first step leading from product type concatenated codes to more complex graph codes. We emphasize constructions of specific codes of realistic lengths, and study the details of decoding by message passing...
Three Syntactic Theories for Combinatory Graph Reduction
DEFF Research Database (Denmark)
Danvy, Olivier; Zerny, Ian
2013-01-01
here therefore properly account for combinatory graph reduction As We Know It. These three syntactic theories scale to handling the Y combinator. This article therefore illustrates the scientic consensus of theoreticians and implementors about graph reduction: it is the same combinatory elephant....
Edge Cover Domination in Mangoldt Graph
African Journals Online (AJOL)
Bheema
Domination theory of graphs has many applications in. Engineering and Communication Networks. For these applications, the arithmetic graphs associated with certain number theoretic arithmetic functions like the Euler totient function Φ(n), the divison function d(n), the quadratic residue function and the Mangoldt function ...
Attitudes towards Graphing Calculators in Developmental Mathematics
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…
A Graph Library Extension of SVG
DEFF Research Database (Denmark)
Nørmark, Kurt
2007-01-01
be aggregated as a single node, and an entire graph can be embedded in a single node. In addition, a number of different graph animations are described. The starting point of the SVG extension is a library that provides an exact of mirror of SVG 1.1 in the functional programming language Scheme. Each element...
Eigenvalues and expansion of bipartite graphs
DEFF Research Database (Denmark)
Høholdt, Tom; Janwa, Heeralal
2012-01-01
We prove lower bounds on the largest and second largest eigenvalue of the adjacency matrix of bipartite graphs and give necessary and sufficient conditions for equality. We give several examples of classes that are optimal with respect to the bouns. We prove that BIBD-graphs are characterized by ...
Student Reasoning about Graphs in Different Contexts
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…
Acyclicity in edge-colored graphs
DEFF Research Database (Denmark)
Gutin, Gregory; Jones, Mark; Sheng, Bin
2017-01-01
A walk W in edge-colored graphs is called properly colored (PC) if every pair of consecutive edges in W is of different color. We introduce and study five types of PC acyclicity in edge-colored graphs such that graphs of PC acyclicity of type i is a proper superset of graphs of acyclicity of type i......+1, i=1,2,3,4. The first three types are equivalent to the absence of PC cycles, PC closed trails, and PC closed walks, respectively. While graphs of types 1, 2 and 3 can be recognized in polynomial time, the problem of recognizing graphs of type 4 is, somewhat surprisingly, NP-hard even for 2-edge-colored...... graphs (i.e., when only two colors are used). The same problem with respect to type 5 is polynomial-time solvable for all edge-colored graphs. Using the five types, we investigate the border between intractability and tractability for the problems of finding the maximum number of internally vertex...
Sobolev spaces on graphs | Ostrovskii | Quaestiones Mathematicae
African Journals Online (AJOL)
The present paper is devoted to discrete analogues of Sobolev spaces of smooth functions. The discrete analogues that we consider are spaces of functions on vertex sets of graphs. Such spaces have applications in Graph Theory, Metric Geometry and Convex Geometry. We present known and prove some new results on ...
Pattern Perception and the Comprehension of Graphs.
Pinker, Steven
Three experiments tested the hypothesis that graphs convey information effectively because they can display global trends as geometric patterns that visual systems encode easily. A novel type of graph was invented in which angles/lengths of line segments joined end-to-end represented variables of rainfall and temperature of a set of months. It was…
Knowledge graph analysis of particles in Japanese
Hoede, C.
2005-01-01
The theory of knowledge graphs is a structuralistic theory of language. Its ontology consists of eight types of binary relationships and four types of so-called frames. The relationships connect so-called tokens, that represent semantic units. In this way a graph structure arises. Japanese particles
Graph coarsening and clustering on the GPU
Fagginger Auer, B.O.; Bisseling, R.H.
2013-01-01
Agglomerative clustering is an effective greedy way to quickly generate graph clusterings of high modularity in a small amount of time. In an effort to use the power offered by multi-core CPU and GPU hardware to solve the clustering problem, we introduce a fine-grained sharedmemory parallel graph
Chain graph models and their causal interpretations
DEFF Research Database (Denmark)
Lauritzen, Steffen Lilholt; Richardson, Thomas S.
2002-01-01
, interpretations of chain graphs that are often invoked, implicitly or explicitly. These interpretations also lead to flawed methods for applying background knowledge to model selection. We present a valid interpretation by showing how the distribution corresponding to a chain graph may be generated from...... traditionally been used to model feed-back in econometrics....
Dynamic planar embeddings of dynamic graphs
DEFF Research Database (Denmark)
Holm, Jacob; Rotenberg, Eva
2017-01-01
, exploiting that the complement of a spanning tree of a connected plane graph is a spanning tree of the dual graph. The primal and dual trees are interpreted as having the same Euler tour, and a main idea of the new algorithm is an elegant interaction between top trees over the two trees via their common...
Dynamic planar embeddings of dynamic graphs
DEFF Research Database (Denmark)
Holm, Jacob; Rotenberg, Eva
2015-01-01
that the complement of a spanning tree of a connected plane graph is a spanning tree of the dual graph. The primal and dual trees are interpreted as having the same Euler tour, and a main idea of the new algorithm is an elegant interaction between top trees over the two trees via their common Euler tour....
Connected domination stable graphs upon edge addition ...
African Journals Online (AJOL)
A set S of vertices in a graph G is a connected dominating set of G if S dominates G and the subgraph induced by S is connected. We study the graphs for which adding any edge does not change the connected domination number. Keywords: Connected domination, connected domination stable, edge addition ...
A Ring Construction Using Finite Directed Graphs
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…
Toughness and Triangle-Free Graphs
Bauer, D.; van den Heuvel, J.; Schmeichel, E.
1995-01-01
In this paper, we prove that there exist triangle-free graphs with arbitrarily large toughness, thereby settling a longstanding open question. We also explore the problem of whether there exists a t-tough, n/(t + 1)-regular, triangle-free graph on n vertices for various values of t, and provide a
Declarative Process Mining for DCR Graphs
DEFF Research Database (Denmark)
Debois, Søren; Hildebrandt, Thomas T.; Laursen, Paw Høvsgaard
2017-01-01
We investigate process mining for the declarative Dynamic Condition Response (DCR) graphs process modelling language. We contribute (a) a process mining algorithm for DCR graphs, (b) a proposal for a set of metrics quantifying output model quality, and (c) a preliminary example-based comparison...
Graph Bundling by Kernel Density Estimation
Hurter, C.; Ersoy, O.; Telea, A.
We present a fast and simple method to compute bundled layouts of general graphs. For this, we first transform a given graph drawing into a density map using kernel density estimation. Next, we apply an image sharpening technique which progressively merges local height maxima by moving the convolved
The direct algorithm for solving of the graph isomorphism problem
Faizullin, Rashit T.; Prolubnikov, Alexander V.
2005-01-01
We propose an algorithm for solving of the graph isomorphism problem. Also, we introduce the new class of graphs for which the graph isomorphism problem can be solved polynomially using the algorithm.
Proof-graphs for Minimal Implicational Logic
Directory of Open Access Journals (Sweden)
Marcela Quispe-Cruz
2014-03-01
Full Text Available It is well-known that the size of propositional classical proofs can be huge. Proof theoretical studies discovered exponential gaps between normal or cut free proofs and their respective non-normal proofs. The aim of this work is to study how to reduce the weight of propositional deductions. We present the formalism of proof-graphs for purely implicational logic, which are graphs of a specific shape that are intended to capture the logical structure of a deduction. The advantage of this formalism is that formulas can be shared in the reduced proof. In the present paper we give a precise definition of proof-graphs for the minimal implicational logic, together with a normalization procedure for these proof-graphs. In contrast to standard tree-like formalisms, our normalization does not increase the number of nodes, when applied to the corresponding minimal proof-graph representations.
A model of language inflection graphs
Fukś, Henryk; Farzad, Babak; Cao, Yi
2014-01-01
Inflection graphs are highly complex networks representing relationships between inflectional forms of words in human languages. For so-called synthetic languages, such as Latin or Polish, they have particularly interesting structure due to the abundance of inflectional forms. We construct the simplest form of inflection graphs, namely a bipartite graph in which one group of vertices corresponds to dictionary headwords and the other group to inflected forms encountered in a given text. We, then, study projection of this graph on the set of headwords. The projection decomposes into a large number of connected components, to be called word groups. Distribution of sizes of word group exhibits some remarkable properties, resembling cluster distribution in a lattice percolation near the critical point. We propose a simple model which produces graphs of this type, reproducing the desired component distribution and other topological features.
Algorithms for Graph Rigidity and Scene Analysis
DEFF Research Database (Denmark)
Berg, Alex Rune; Jordán, Tibor
2003-01-01
We investigate algorithmic questions and structural problems concerning graph families defined by `edge-counts'. Motivated by recent developments in the unique realization problem of graphs, we give an efficient algorithm to compute the rigid, redundantly rigid, M-connected, and globally rigid...... components of a graph. Our algorithm is based on (and also extends and simplifies) the idea of Hendrickson and Jacobs, as it uses orientations as the main algorithmic tool. We also consider families of bipartite graphs which occur in parallel drawings and scene analysis. We verify a conjecture of Whiteley...... by showing that 2d-connected bipartite graphs are d-tight. We give a new algorithm for finding a maximal d-sharp subgraph. We also answer a question of Imai and show that finding a maximum size d-sharp subgraph is NP-hard....
On The Roman Domination Stable Graphs
Directory of Open Access Journals (Sweden)
Hajian Majid
2017-11-01
Full Text Available A Roman dominating function (or just RDF on a graph G = (V,E is a function f : V → {0, 1, 2} satisfying the condition that every vertex u for which f(u = 0 is adjacent to at least one vertex v for which f(v = 2. The weight of an RDF f is the value f(V (G = Pu2V (G f(u. The Roman domination number of a graph G, denoted by R(G, is the minimum weight of a Roman dominating function on G. A graph G is Roman domination stable if the Roman domination number of G remains unchanged under removal of any vertex. In this paper we present upper bounds for the Roman domination number in the class of Roman domination stable graphs, improving bounds posed in [V. Samodivkin, Roman domination in graphs: the class RUV R, Discrete Math. Algorithms Appl. 8 (2016 1650049].
Disease management research using event graphs.
Allore, H G; Schruben, L W
2000-08-01
Event Graphs, conditional representations of stochastic relationships between discrete events, simulate disease dynamics. In this paper, we demonstrate how Event Graphs, at an appropriate abstraction level, also extend and organize scientific knowledge about diseases. They can identify promising treatment strategies and directions for further research and provide enough detail for testing combinations of new medicines and interventions. Event Graphs can be enriched to incorporate and validate data and test new theories to reflect an expanding dynamic scientific knowledge base and establish performance criteria for the economic viability of new treatments. To illustrate, an Event Graph is developed for mastitis, a costly dairy cattle disease, for which extensive scientific literature exists. With only a modest amount of imagination, the methodology presented here can be seen to apply modeling to any disease, human, plant, or animal. The Event Graph simulation presented here is currently being used in research and in a new veterinary epidemiology course. Copyright 2000 Academic Press.
Pixels to Graphs by Associative Embedding
Newell, Alejandro
2017-06-22
Graphs are a useful abstraction of image content. Not only can graphs represent details about individual objects in a scene but they can capture the interactions between pairs of objects. We present a method for training a convolutional neural network such that it takes in an input image and produces a full graph. This is done end-to-end in a single stage with the use of associative embeddings. The network learns to simultaneously identify all of the elements that make up a graph and piece them together. We benchmark on the Visual Genome dataset, and report a Recall@50 of 9.7% compared to the prior state-of-the-art at 3.4%, a nearly threefold improvement on the challenging task of scene graph generation.
Pristine transfinite graphs and permissive electrical networks
Zemanian, Armen H
2001-01-01
A transfinite graph or electrical network of the first rank is obtained conceptually by connecting conventionally infinite graphs and networks together at their infinite extremities. This process can be repeated to obtain a hierarchy of transfiniteness whose ranks increase through the countable ordinals. This idea, which is of recent origin, has enriched the theories of graphs and networks with radically new constructs and research problems. The book provides a more accessible introduction to the subject that, though sacrificing some generality, captures the essential ideas of transfiniteness for graphs and networks. Thus, for example, some results concerning discrete potentials and random walks on transfinite networks can now be presented more concisely. Conversely, the simplifications enable the development of many new results that were previously unavailable. Topics and features: *A simplified exposition provides an introduction to transfiniteness for graphs and networks.*Various results for conventional g...
Graph Mining Meets the Semantic Web
Energy Technology Data Exchange (ETDEWEB)
Lee, Sangkeun (Matt) [ORNL; Sukumar, Sreenivas R [ORNL; Lim, Seung-Hwan [ORNL
2015-01-01
The Resource Description Framework (RDF) and SPARQL Protocol and RDF Query Language (SPARQL) were introduced about a decade ago to enable flexible schema-free data interchange on the Semantic Web. Today, data scientists use the framework as a scalable graph representation for integrating, querying, exploring and analyzing data sets hosted at different sources. With increasing adoption, the need for graph mining capabilities for the Semantic Web has emerged. We address that need through implementation of three popular iterative Graph Mining algorithms (Triangle count, Connected component analysis, and PageRank). We implement these algorithms as SPARQL queries, wrapped within Python scripts. We evaluate the performance of our implementation on 6 real world data sets and show graph mining algorithms (that have a linear-algebra formulation) can indeed be unleashed on data represented as RDF graphs using the SPARQL query interface.
OPEX: Optimized Eccentricity Computation in Graphs
Energy Technology Data Exchange (ETDEWEB)
Henderson, Keith [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2011-11-14
Real-world graphs have many properties of interest, but often these properties are expensive to compute. We focus on eccentricity, radius and diameter in this work. These properties are useful measures of the global connectivity patterns in a graph. Unfortunately, computing eccentricity for all nodes is O(n2) for a graph with n nodes. We present OPEX, a novel combination of optimizations which improves computation time of these properties by orders of magnitude in real-world experiments on graphs of many different sizes. We run OPEX on graphs with up to millions of links. OPEX gives either exact results or bounded approximations, unlike its competitors which give probabilistic approximations or sacrifice node-level information (eccentricity) to compute graphlevel information (diameter).
Relations between the set-complexity and the structure of graphs and their sub-graphs.
Ignac, Tomasz M; Sakhanenko, Nikita A; Galas, David J
2012-09-21
: We describe some new conceptual tools for the rigorous, mathematical description of the "set-complexity" of graphs. This set-complexity has been shown previously to be a useful measure for analyzing some biological networks, and in discussing biological information in a quantitative fashion. The advances described here allow us to define some significant relationships between the set-complexity measure and the structure of graphs, and of their component sub-graphs. We show here that modular graph structures tend to maximize the set-complexity of graphs. We point out the relationship between modularity and redundancy, and discuss the significance of set-complexity in this regard. We specifically discuss the relationship between complexity and entropy in the case of complete-bipartite graphs, and present a new method for constructing highly complex, binary graphs. These results can be extended to the case of ternary graphs, and to other multi-edge graphs, which are fundamentally more relevant to biological structures and systems. Finally, our results lead us to an approach for extracting high complexity modular graphs from large, noisy graphs with low information content. We illustrate this approach with two examples.
Perfect secure domination in graphs
Directory of Open Access Journals (Sweden)
S.V. Divya Rashmi
2017-07-01
Full Text Available Let $G=(V,E$ be a graph. A subset $S$ of $V$ is a dominating set of $G$ if every vertex in $Vsetminus S$ is adjacent to a vertex in $S.$ A dominating set $S$ is called a secure dominating set if for each $vin Vsetminus S$ there exists $uin S$ such that $v$ is adjacent to $u$ and $S_1=(Ssetminus{u}cup {v}$ is a dominating set. If further the vertex $uin S$ is unique, then $S$ is called a perfect secure dominating set. The minimum cardinality of a perfect secure dominating set of $G$ is called the perfect secure domination number of $G$ and is denoted by $gamma_{ps}(G.$ In this paper we initiate a study of this parameter and present several basic results.
Toughness Condition for a Graph to Be a Fractional (g,f,n-Critical Deleted Graph
Directory of Open Access Journals (Sweden)
Wei Gao
2014-01-01
Full Text Available A graph G is called a fractional (g,f-deleted graph if G-{e} admits a fractional (g,f-factor for any e∈E(G. A graph G is called a fractional (g,f,n-critical deleted graph if, after deleting any n vertices from G, the resulting graph is still a fractional (g,f-deleted graph. The toughness, as the parameter for measuring the vulnerability of communication networks, has received significant attention in computer science. In this paper, we present the relationship between toughness and fractional (g,f,n-critical deleted graphs. It is determined that G is fractional (g,f,n-critical deleted if t(G≥((b2-1+bn/a.
Kumar, David Devraj
2017-01-01
This paper reports an analysis of an interactive technology-supported, problem-based learning (PBL) project in science, technology, engineering and mathematics (STEM) from a Learning Sciences perspective using the Selected Learning Sciences Interest Areas (SLSIA). The SLSIA was adapted from the "What kinds of topics do ISLS [International…
Tas, Said
2017-01-01
In this research, it is aimed to investigate classroom management problems of middle school 6th and 7th grade teachers in traditional and technology-supported classrooms and differences between them. For this purpose the opinions of the students in the 4th grade of Primary Education Department in Faculty of Education of Süleyman Demirel University…
Rosé, Carolyn Penstein; Ferschke, Oliver
2016-01-01
This article offers a vision for technology supported collaborative and discussion-based learning at scale. It begins with historical work in the area of tutorial dialogue systems. It traces the history of that area of the field of Artificial Intelligence in Education as it has made an impact on the field of Computer-Supported Collaborative…
Inferring ontology graph structures using OWL reasoning.
Rodríguez-García, Miguel Ángel; Hoehndorf, Robert
2018-01-05
Ontologies are representations of a conceptualization of a domain. Traditionally, ontologies in biology were represented as directed acyclic graphs (DAG) which represent the backbone taxonomy and additional relations between classes. These graphs are widely exploited for data analysis in the form of ontology enrichment or computation of semantic similarity. More recently, ontologies are developed in a formal language such as the Web Ontology Language (OWL) and consist of a set of axioms through which classes are defined or constrained. While the taxonomy of an ontology can be inferred directly from the axioms of an ontology as one of the standard OWL reasoning tasks, creating general graph structures from OWL ontologies that exploit the ontologies' semantic content remains a challenge. We developed a method to transform ontologies into graphs using an automated reasoner while taking into account all relations between classes. Searching for (existential) patterns in the deductive closure of ontologies, we can identify relations between classes that are implied but not asserted and generate graph structures that encode for a large part of the ontologies' semantic content. We demonstrate the advantages of our method by applying it to inference of protein-protein interactions through semantic similarity over the Gene Ontology and demonstrate that performance is increased when graph structures are inferred using deductive inference according to our method. Our software and experiment results are available at http://github.com/bio-ontology-research-group/Onto2Graph . Onto2Graph is a method to generate graph structures from OWL ontologies using automated reasoning. The resulting graphs can be used for improved ontology visualization and ontology-based data analysis.
Inferring ontology graph structures using OWL reasoning
Rodriguez-Garcia, Miguel Angel
2018-01-05
Ontologies are representations of a conceptualization of a domain. Traditionally, ontologies in biology were represented as directed acyclic graphs (DAG) which represent the backbone taxonomy and additional relations between classes. These graphs are widely exploited for data analysis in the form of ontology enrichment or computation of semantic similarity. More recently, ontologies are developed in a formal language such as the Web Ontology Language (OWL) and consist of a set of axioms through which classes are defined or constrained. While the taxonomy of an ontology can be inferred directly from the axioms of an ontology as one of the standard OWL reasoning tasks, creating general graph structures from OWL ontologies that exploit the ontologies\\' semantic content remains a challenge.We developed a method to transform ontologies into graphs using an automated reasoner while taking into account all relations between classes. Searching for (existential) patterns in the deductive closure of ontologies, we can identify relations between classes that are implied but not asserted and generate graph structures that encode for a large part of the ontologies\\' semantic content. We demonstrate the advantages of our method by applying it to inference of protein-protein interactions through semantic similarity over the Gene Ontology and demonstrate that performance is increased when graph structures are inferred using deductive inference according to our method. Our software and experiment results are available at http://github.com/bio-ontology-research-group/Onto2Graph .Onto2Graph is a method to generate graph structures from OWL ontologies using automated reasoning. The resulting graphs can be used for improved ontology visualization and ontology-based data analysis.
Spanners for geometric intersection graphs with applications
Directory of Open Access Journals (Sweden)
Martin Fürer
2012-05-01
Full Text Available A ball graph is an intersection graph of a set of balls with arbitrary radii. Given a real numbert>1, we say that a subgraph G' of a graph G is a t-spanner of G, if for every pair of verticesu,v in G, there exists a path in G' of length at most t times the distance between u and v inG. In this paper, we consider the problem of efficiently constructing sparse spanners of ball graphs which supports fast shortest path distance queries.We present the first algorithm for constructing spanners of ball graphs. For a ball graph in Rk, we construct a (1+ε-spanner for any ε>0 with O(nε-k+1 edges in O(n2ℓ+δε-k logℓ S time, using an efficient partitioning of space into hypercubes and solving intersection problems. Here ℓ=1-1/(⌊k/2⌋+2, δ is any positive constant, and S is the ratio between the largest and smallest radius. For the special case when the balls all have unit size, we show that the complexity of constructing a (1+ε-spanner is almost equal to the complexity of constructing a Euclidean minimum spanning tree. The algorithm extends naturally to other disk-likeobjects, also in higher dimensions.The algorithm uses an efficient subdivision of space to construct a sparse graph having many of the same distance properties as the input ball graph. Additionally, the constructed spanners have a small vertex separator decomposition (hereditary. In dimension k=2, the disk graph spanner has an O(n1/2ε-3/2+ε-3log S separator. The presence of a small separator is then exploited to obtain very efficient data structures for approximate distance queries. The results on geometric graph separators might be of independent interest. For example, since complete Euclidean graphs are just a special case of (unit ball graphs, our results also provide a new approach for constructing spanners with small separators in these graphs.
Discriminative graph embedding for label propagation.
Nguyen, Canh Hao; Mamitsuka, Hiroshi
2011-09-01
In many applications, the available information is encoded in graph structures. This is a common problem in biological networks, social networks, web communities and document citations. We investigate the problem of classifying nodes' labels on a similarity graph given only a graph structure on the nodes. Conventional machine learning methods usually require data to reside in some Euclidean spaces or to have a kernel representation. Applying these methods to nodes on graphs would require embedding the graphs into these spaces. By embedding and then learning the nodes on graphs, most methods are either flexible with different learning objectives or efficient enough for large scale applications. We propose a method to embed a graph into a feature space for a discriminative purpose. Our idea is to include label information into the embedding process, making the space representation tailored to the task. We design embedding objective functions that the following learning formulations become spectral transforms. We then reformulate these spectral transforms into multiple kernel learning problems. Our method, while being tailored to the discriminative tasks, is efficient and can scale to massive data sets. We show the need of discriminative embedding on some simulations. Applying to biological network problems, our method is shown to outperform baselines.
Pathfinder: Visual Analysis of Paths in Graphs
Partl, C.; Gratzl, S.; Streit, M.; Wassermann, A. M.; Pfister, H.; Schmalstieg, D.; Lex, A.
2016-01-01
The analysis of paths in graphs is highly relevant in many domains. Typically, path-related tasks are performed in node-link layouts. Unfortunately, graph layouts often do not scale to the size of many real world networks. Also, many networks are multivariate, i.e., contain rich attribute sets associated with the nodes and edges. These attributes are often critical in judging paths, but directly visualizing attributes in a graph layout exacerbates the scalability problem. In this paper, we present visual analysis solutions dedicated to path-related tasks in large and highly multivariate graphs. We show that by focusing on paths, we can address the scalability problem of multivariate graph visualization, equipping analysts with a powerful tool to explore large graphs. We introduce Pathfinder (Figure 1), a technique that provides visual methods to query paths, while considering various constraints. The resulting set of paths is visualized in both a ranked list and as a node-link diagram. For the paths in the list, we display rich attribute data associated with nodes and edges, and the node-link diagram provides topological context. The paths can be ranked based on topological properties, such as path length or average node degree, and scores derived from attribute data. Pathfinder is designed to scale to graphs with tens of thousands of nodes and edges by employing strategies such as incremental query results. We demonstrate Pathfinder's fitness for use in scenarios with data from a coauthor network and biological pathways. PMID:27942090
Approximate von Neumann entropy for directed graphs.
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.
Pathfinder: Visual Analysis of Paths in Graphs.
Partl, C; Gratzl, S; Streit, M; Wassermann, A M; Pfister, H; Schmalstieg, D; Lex, A
2016-06-01
The analysis of paths in graphs is highly relevant in many domains. Typically, path-related tasks are performed in node-link layouts. Unfortunately, graph layouts often do not scale to the size of many real world networks. Also, many networks are multivariate, i.e., contain rich attribute sets associated with the nodes and edges. These attributes are often critical in judging paths, but directly visualizing attributes in a graph layout exacerbates the scalability problem. In this paper, we present visual analysis solutions dedicated to path-related tasks in large and highly multivariate graphs. We show that by focusing on paths, we can address the scalability problem of multivariate graph visualization, equipping analysts with a powerful tool to explore large graphs. We introduce Pathfinder (Figure 1), a technique that provides visual methods to query paths, while considering various constraints. The resulting set of paths is visualized in both a ranked list and as a node-link diagram. For the paths in the list, we display rich attribute data associated with nodes and edges, and the node-link diagram provides topological context. The paths can be ranked based on topological properties, such as path length or average node degree, and scores derived from attribute data. Pathfinder is designed to scale to graphs with tens of thousands of nodes and edges by employing strategies such as incremental query results. We demonstrate Pathfinder's fitness for use in scenarios with data from a coauthor network and biological pathways.
A GRAPH-BASED INVESTIGATION OF BITCOIN TRANSACTIONS
Zhao, Chen; Guan, Yong
2015-01-01
Part 2: INTERNET CRIME INVESTIGATIONS; International audience; The Bitcoin global cryptocurrency system has been the subject of several criminal cases. The Bitcoin network is a peer-to-peer system that has participants from all over the Internet. The Bitcoin protocol requires participating nodes to retain and update all transaction records; this ensures that all Bitcoin activities are accessible from a consistent transaction history database. This chapter describes a graph-based method for an...
Analysis, Modeling and Simulation of Mechatronic Systems using the Bond Graph Method
Directory of Open Access Journals (Sweden)
A. Alabakhshizadeh
2011-01-01
Full Text Available The Bond Graph is the proper choice of physical system used for: (i Modeling which can be applied to systems combining multidisciplinary energy domains, (ii Analysis to provide a great value proposition for finding the algebraic loops within the system enabling the process of troubleshooting and eliminating the defects by using the proper component(s to fix the causality conflict even without being acquainted in the proper system, and (iii Simulation facilitated through derived state space equations from the Bond Graph model is solved using industrial simulation software, such as 20-Sim. The Bond Graph technique is a graphical language of modeling, in which component energy ports are connected by bonds that specify the transfer of energy between system components. Following a brief introduction of the Bond Graph methodology and techniques, two separate case studies are comprehensively addressed. The first case study is a systematic implementation of a fourth order electrical system and conversion to mechanical system while the second case study presents modeling of the Dielectric Electro Active Polymer (DEAP actuator. Building the systematic Bond Graph of multifaceted system and ease of switching between different domains are aims of the first case study while the second study shows how a complex mechatronic system could be analyzed and built by the Bond Graph. The respective Bond Graphs in each case is evaluated in the light of mathematical equations and simulations. Excellent correlation has been achieved between the simulation results and proper system equations.
A first course in graph theory
Chartrand, Gary
2012-01-01
This comprehensive text offers undergraduates a remarkably student-friendly introduction to graph theory. Written by two of the field's most prominent experts, it takes an engaging approach that emphasizes graph theory's history. Unique examples and lucid proofs provide a sound yet accessible treatment that stimulates interest in an evolving subject and its many applications.Optional sections designated as ""excursion"" and ""exploration"" present interesting sidelights of graph theory and touch upon topics that allow students the opportunity to experiment and use their imaginations. Three app
NOUS: A Knowledge Graph Management System
Energy Technology Data Exchange (ETDEWEB)
2017-06-26
Knowledge graphs represent information as entities and relationships between them. For tasks such as natural language question answering or automated analysis of text, a knowledge graph provides valuable context to establish the specific type of entities being discussed. It allow us to derive better context about newly arriving information and leads to intelligent reasoning capabilities. We address two primary needs: A) Automated construction of knowledge graphs is a technically challenging, expensive process; and B) The ability to synthesize new information by monitoring newly emerging knowledge is a transformational capability that does not exist in state of the art systems.
The total irregularity of a graph
DEFF Research Database (Denmark)
Abdo, H.; Brandt, S.; Dimitrov, D.
2014-01-01
In this note a new measure of irregularity of a graph G is introduced. It is named the total irregularity of a graph and is defined as irr(t)(G) - 1/2 Sigma(u, v is an element of V(G)) vertical bar d(G)(u) - d(G)(v)vertical bar, where d(G)(u) denotes the degree of a vertex u is an element of V......(G). All graphs with maximal total irregularity are determined. It is also shown that among all trees of the same order the star has the maximal total irregularity....
Crossed products for interactions and graph algebras
DEFF Research Database (Denmark)
Kwasniewski, Bartosz
2014-01-01
. These results cover the case of crossed products by endomorphisms with hereditary ranges and complemented kernels. As model examples of interactions not coming from endomorphisms we introduce and study in detail interactions arising from finite graphs. The interaction (V,H) associated to a graph E acts...... on the core F_E of the graph algebra C*(E). By describing a partial homeomorphism dual to (V,H) we find the fundamental structure theorems for C*(E), such as Cuntz–Krieger uniqueness theorem, as results concerning reversible noncommutative dynamics on F_E . We also provide a new approach to calculation of K...
A heterogeneous graph-based recommendation simulator
Energy Technology Data Exchange (ETDEWEB)
Yeonchan, Ahn [Seoul National University; Sungchan, Park [Seoul National University; Lee, Matt Sangkeun [ORNL; Sang-goo, Lee [Seoul National University
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.
Integer sequence discovery from small graphs.
Hoppe, Travis; Petrone, Anna
2016-03-11
We have exhaustively enumerated all simple, connected graphs of a finite order and have computed a selection of invariants over this set. Integer sequences were constructed from these invariants and checked against the Online Encyclopedia of Integer Sequences (OEIS). 141 new sequences were added and six sequences were extended. From the graph database, we were able to programmatically suggest relationships among the invariants. It will be shown that we can readily visualize any sequence of graphs with a given criteria. The code has been released as an open-source framework for further analysis and the database was constructed to be extensible to invariants not considered in this work.
Bouvier, Tom
2014-01-01
In this thesis, we study some width parameters on graphs, beyond tree-width and clique-width. Our first investigation is a comparative study between the tree-width of a graph and the clique-width of the associated incidence graph, from which we extract some strong algorithmic results. Then we present a few structural properties over a recently defined width called special tree-width and which takes its definition through both tree-width and clique-width. Finally, we end our journey with a mor...
Integer sequence discovery from small graphs
Hoppe, Travis; Petrone, Anna
2015-01-01
We have exhaustively enumerated all simple, connected graphs of a finite order and have computed a selection of invariants over this set. Integer sequences were constructed from these invariants and checked against the Online Encyclopedia of Integer Sequences (OEIS). 141 new sequences were added and six sequences were extended. From the graph database, we were able to programmatically suggest relationships among the invariants. It will be shown that we can readily visualize any sequence of graphs with a given criteria. The code has been released as an open-source framework for further analysis and the database was constructed to be extensible to invariants not considered in this work. PMID:27034526
Assessing statistical significance in causal graphs.
Chindelevitch, Leonid; Loh, Po-Ru; Enayetallah, Ahmed; Berger, Bonnie; Ziemek, Daniel
2012-02-20
Causal graphs are an increasingly popular tool for the analysis of biological datasets. In particular, signed causal graphs--directed graphs whose edges additionally have a sign denoting upregulation or downregulation--can be used to model regulatory networks within a cell. Such models allow prediction of downstream effects of regulation of biological entities; conversely, they also enable inference of causative agents behind observed expression changes. However, due to their complex nature, signed causal graph models present special challenges with respect to assessing statistical significance. In this paper we frame and solve two fundamental computational problems that arise in practice when computing appropriate null distributions for hypothesis testing. First, we show how to compute a p-value for agreement between observed and model-predicted classifications of gene transcripts as upregulated, downregulated, or neither. Specifically, how likely are the classifications to agree to the same extent under the null distribution of the observed classification being randomized? This problem, which we call "Ternary Dot Product Distribution" owing to its mathematical form, can be viewed as a generalization of Fisher's exact test to ternary variables. We present two computationally efficient algorithms for computing the Ternary Dot Product Distribution and investigate its combinatorial structure analytically and numerically to establish computational complexity bounds.Second, we develop an algorithm for efficiently performing random sampling of causal graphs. This enables p-value computation under a different, equally important null distribution obtained by randomizing the graph topology but keeping fixed its basic structure: connectedness and the positive and negative in- and out-degrees of each vertex. We provide an algorithm for sampling a graph from this distribution uniformly at random. We also highlight theoretical challenges unique to signed causal graphs
Identifying Codes on Directed De Bruijn Graphs
2015-08-27
JOURNAL ARTICLE (POST PRINT) 3. DATES COVERED (From - To) JUN 2013 – AUG 2015 4. TITLE AND SUBTITLE IDENTIFYING CODES ON DIRECTED DE BRUIJN GRAPHS 5a...owner. 14. ABSTRACT For a directed graph G, a t-identifying code is a subset S ⊆ V (G) with the property that for each vertex v ∈ V (G) the set of...vertices of S reachable from v by a directed path of length at most t is both non-empty and unique. A graph is called t- identifiable if there exists a
High Dimensional Spectral Graph Theory and Non-backtracking Random Walks on Graphs
Kempton, Mark
This thesis has two primary areas of focus. First we study connection graphs, which are weighted graphs in which each edge is associated with a d-dimensional rotation matrix for some fixed dimension d, in addition to a scalar weight. Second, we study non-backtracking random walks on graphs, which are random walks with the additional constraint that they cannot return to the immediately previous state at any given step. Our work in connection graphs is centered on the notion of consistency, that is, the product of rotations moving from one vertex to another is independent of the path taken, and a generalization called epsilon-consistency. We present higher dimensional versions of the combinatorial Laplacian matrix and normalized Laplacian matrix from spectral graph theory, and give results characterizing the consistency of a connection graph in terms of the spectra of these matrices. We generalize several tools from classical spectral graph theory, such as PageRank and effective resistance, to apply to connection graphs. We use these tools to give algorithms for sparsification, clustering, and noise reduction on connection graphs. In non-backtracking random walks, we address the question raised by Alon et. al. concerning how the mixing rate of a non-backtracking random walk to its stationary distribution compares to the mixing rate for an ordinary random walk. Alon et. al. address this question for regular graphs. We take a different approach, and use a generalization of Ihara's Theorem to give a new proof of Alon's result for regular graphs, and to extend the result to biregular graphs. Finally, we give a non-backtracking version of Polya's Random Walk Theorem for 2-dimensional grids.
Encoding !-tensors as !-graphs with neighbourhood orders
Directory of Open Access Journals (Sweden)
David Quick
2015-11-01
Full Text Available Diagrammatic reasoning using string diagrams provides an intuitive language for reasoning about morphisms in a symmetric monoidal category. To allow working with infinite families of string diagrams, !-graphs were introduced as a method to mark repeated structure inside a diagram. This led to !-graphs being implemented in the diagrammatic proof assistant Quantomatic. Having a partially automated program for rewriting diagrams has proven very useful, but being based on !-graphs, only commutative theories are allowed. An enriched abstract tensor notation, called !-tensors, has been used to formalise the notion of !-boxes in non-commutative structures. This work-in-progress paper presents a method to encode !-tensors as !-graphs with some additional structure. This will allow us to leverage the existing code from Quantomatic and quickly provide various tools for non-commutative diagrammatic reasoning.
Density conditions for triangles in multipartite graphs
DEFF Research Database (Denmark)
Bondy, Adrian; Shen, Jin; Thomassé, Stephan
2006-01-01
subgraphs in G. We investigate in particular the case where G is a complete multipartite graph. We prove that a finite tripartite graph with all edge densities greater than the golden ratio has a triangle and that this bound is best possible. Also we show that an infinite-partite graph with finite parts has......We consider the problem of finding a large or dense triangle-free subgraph in a given graph G. In response to a question of P. Erdos, we prove that, if the minimum degree of G is at least 9 vertical bar V(G)vertical bar/10, the largest triangle-free subgraphs are precisely the largest bipartite...... a triangle, provided that the edge density between any two parts is greater than 1/2....
Approximation properties of fine hyperbolic graphs
Indian Academy of Sciences (India)
is called the metric invariant translation approximation property for a countable dis- crete metric space. Moreover ... Uniform Roe algebras; fine hyperbolic graph; metric invariant translation approximation property. ..... ate Studies in Mathematics, Volume 88 (2008) (Rhode Island: American Mathematical. Society Providence).
Kansas Data Access and Support Center — Digital line graph (DLG) data are digital representations of cartographic information. DLG's of map features are converted to digital form from maps and related...
Determining X-chains in graph states
International Nuclear Information System (INIS)
Wu, Jun-Yi; Kampermann, Hermann; Bruß, Dagmar
2016-01-01
The representation of graph states in the X-basis as well as the calculation of graph state overlaps can efficiently be performed by using the concept of X-chains (Wu et al 2015 Phys. Rev. A 92 012322). We present a necessary and sufficient criterion for X-chains and show that they can efficiently be determined by the Bareiss algorithm. An analytical approach for searching X-chain groups of a graph state is proposed. Furthermore we generalize the concept of X-chains to so-called Euler chains, whose induced subgraphs are Eulerian. This approach helps to determine if a given vertex set is an X-chain and we show how Euler chains can be used in the construction of multipartite Bell inequalities for graph states. (paper)
Joint embeddings of scene graphs and images
Belilovsky, Eugene; Blaschko, Matthew; Kiros, Jamie Ryan; Urtasun, Raquel; Zemel, Richard
2017-01-01
Belilovsky E., Blaschko M., Kiros J.R., Urtasun R., Zemel R., ''Joint embeddings of scene graphs and images'', 5th international conference on learning representations workshop track - ICLR 2017, 5 pp., April 24-26, 2017, Toulon, France.
Use of Attack Graphs in Security Systems
Directory of Open Access Journals (Sweden)
Vivek Shandilya
2014-01-01
Full Text Available Attack graphs have been used to model the vulnerabilities of the systems and their potential exploits. The successful exploits leading to the partial/total failure of the systems are subject of keen security interest. Considerable effort has been expended in exhaustive modeling, analyses, detection, and mitigation of attacks. One prominent methodology involves constructing attack graphs of the pertinent system for analysis and response strategies. This not only gives the simplified representation of the system, but also allows prioritizing the security properties whose violations are of greater concern, for both detection and repair. We present a survey and critical study of state-of-the-art technologies in attack graph generation and use in security system. Based on our research, we identify the potential, challenges, and direction of the current research in using attack graphs.
Bipartite graph partitioning and data clustering
Energy Technology Data Exchange (ETDEWEB)
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.
Strong sum distance in fuzzy graphs.
Tom, Mini; Sunitha, Muraleedharan Shetty
2015-01-01
In this paper the idea of strong sum distance which is a metric, in a fuzzy graph is introduced. Based on this metric the concepts of eccentricity, radius, diameter, center and self centered fuzzy graphs are studied. Some properties of eccentric nodes, peripheral nodes and central nodes are obtained. A characterisation of self centered complete fuzzy graph is obtained and conditions under which a fuzzy cycle is self centered are established. We have proved that based on this metric, an eccentric node of a fuzzy tree G is a fuzzy end node of G and a node is an eccentric node of a fuzzy tree if and only if it is a peripheral node of G and the center of a fuzzy tree consists of either one or two neighboring nodes. The concepts of boundary nodes and interior nodes in a fuzzy graph based on strong sum distance are introduced. Some properties of boundary nodes, interior nodes and complete nodes are studied.
Spanners for geometric intersection graphs with applications
Martin Fürer; Shiva Prasad Kasiviswanathan
2012-01-01
A ball graph is an intersection graph of a set of balls with arbitrary radii. Given a real numbert>1, we say that a subgraph G' of a graph G is a t-spanner of G, if for every pair of verticesu,v in G, there exists a path in G' of length at most t times the distance between u and v inG. In this paper, we consider the problem of efficiently constructing sparse spanners of ball graphs which supports fast shortest path distance queries.We present the first algorithm for constructing spanners o...
Fixation probability on clique-based graphs
Choi, Jeong-Ok; Yu, Unjong
2018-02-01
The fixation probability of a mutant in the evolutionary dynamics of Moran process is calculated by the Monte-Carlo method on a few families of clique-based graphs. It is shown that the complete suppression of fixation can be realized with the generalized clique-wheel graph in the limit of small wheel-clique ratio and infinite size. The family of clique-star is an amplifier, and clique-arms graph changes from amplifier to suppressor as the fitness of the mutant increases. We demonstrate that the overall structure of a graph can be more important to determine the fixation probability than the degree or the heat heterogeneity. The dependence of the fixation probability on the position of the first mutant is discussed.
PERANCANGAN SISTEM PENJADWALAN PEMBELAJARAN MENGGUNAKAN GRAPH COLORING
Directory of Open Access Journals (Sweden)
Taufik Hidayatulloh
2016-03-01
Full Text Available Abstract - In learning scheduling problem often faced by schools in the new academic year. Sometimes collisions on the schedule was not found when the learning process has begun, so it is necessary to re-schedule on the schedule. And this resulted in the teaching and learning first weeks less to run well. Researchers previously have used various methods to solve the scheduling as Tabu search, Simulated Annealing, Network Flow, Graph Coloring. Graph Coloring (coloring of a graph is the simplest method and the experimental results indicate that the development of methods of scheduling Graph Coloring deliver results that meet an average of 93% across the specified constraints. At the time of split schedules that require extra energy at the start of learning did not experience a collision. With this system is expected to facilitate the allocation of space, teachers, lessons to avoid a collision. Keywords: Information Systems, Scheduling, graph coloring Abstraksi - Dalam masalah penjadwalan pembelajaran sering dihadapi sekolah pada tahun ajaran baru. Terkadang tabrakan pada jadwal itu baru ditemukan ketika proses belajar mengajar telah dimulai, sehingga perlu dilakukan penjadwalan ulang pada jadwal tersebut. Dan hal ini mengakibatkan kegiatan belajar mengajar pada minggu-minggu pertama kurang dapat berjalan dengan baik. Para peneliti sebelumnya telah menggunakan berbagai metode untuk memecahkan penjadwalan seperti Tabu search, Simulated Annealing, Network Flow, Graph Coloring. Graph Coloring (pewarnaan graf merupakan metode yang paling sederhana dan hasil percobaan menunjukkan bahwa pengembangan metode Graph Coloring memberikan hasil penjadwalan yang memenuhi rata-rata 93% seluruh constraints yang ditentukan. Pada saat membagi jadwal memerlukan energi ekstra agar pada saat di mulai pembelajaran tidak mengalami tabrakan. Dengan sistem ini diharapkan dapat mempermudah dalam mengalokasikan ruangan, guru, pelajaran agar tidak mengalami tabrakan. Kata
Bounds on Gromov hyperbolicity constant in graphs
Indian Academy of Sciences (India)
is a topic of recent and increasing interest in graph theory; see, for instance [3–5, 8–10,. 15–17, 18–20, 22, 23, 25–27]. The theory ..... the Laplace matrix μ∗, we have δ(G) ≤ n(μ∗ − d0) μ∗ . Proof. ..... [27] Tourís E, Graphs and Gromov hyperbolicity of non-constant negatively curved surfaces,. J. Math. Anal. Appl. 380 (2011) ...
Exploring and Making Sense of Large Graphs
2015-08-01
149 7.5.1 Enron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 7.5.2 Brain Connectivity Graph Clustering...graph (top) and the Enron email network (bottom). The distribution of structures discovered by VOG and VOG-TOP100 are denoted by blue crosses and red...100 most important of the 250 identified structures. . . . . . . . . . . . . . . 43 3.14 Enron : Adjacency matrix of the top near-bipartite core found
Gromov hyperbolicity in lexicographic product graphs
Indian Academy of Sciences (India)
41
In particular, we obtain the sharp inequalities δ(G1) ≤ δ(G1 ◦ G2) ≤ δ(G1)+3/2 if G1 is not a trivial graph, and we .... provides a family of graphs for which the first inequality is attained; besides, Theorems 3.20 and 3.24 characterize ...... [56] Verbeek, K. and Suri, S., Metric embeddings, hyperbolic space and social networks.
Recognizing Cuneiform Signs Using Graph Based Methods
Kriege, Nils M.; Fey, Matthias; Fisseler, Denis; Mutzel, Petra; Weichert, Frank
2018-01-01
The cuneiform script constitutes one of the earliest systems of writing and is realized by wedge-shaped marks on clay tablets. A tremendous number of cuneiform tablets have already been discovered and are incrementally digitalized and made available to automated processing. As reading cuneiform script is still a manual task, we address the real-world application of recognizing cuneiform signs by two graph based methods with complementary runtime characteristics. We present a graph model for c...
Topics on tournaments in graph theory
Moon, John W
2015-01-01
Tournaments, in this context, are directed graphs ― an important and interesting topic in graph theory. This concise volume collects a substantial amount of information on tournaments from throughout the mathematical literature. Suitable for advanced undergraduate students of mathematics, the straightforward treatment requires a basic familiarity with finite mathematics. The fundamental definitions and results appear in the earlier sections, and most of the later sections can be read independently of each other. Subjects include irreducible and strong tournaments, cycles and strong subtourname
Data transfer using complete bipartite graph
Chandrasekaran, V. M.; Praba, B.; Manimaran, A.; Kailash, G.
2017-11-01
Information exchange extent is an estimation of the amount of information sent between two focuses on a framework in a given time period. It is an extremely significant perception in present world. There are many ways of message passing in the present situations. Some of them are through encryption, decryption, by using complete bipartite graph. In this paper, we recommend a method for communication using messages through encryption of a complete bipartite graph.
Querying 3D Data by Adjacency Graphs
Bore, Nils; Jensfelt, Patric; Folkesson, John
2015-01-01
The need for robots to search the 3D data they have saved is becoming more apparent. We present an approach for finding structures in 3D models such as those built by robots of their environment. The method extracts geometric primitives from point cloud data. An attributed graph over these primitives forms our representation of the surface structures. Recurring substructures are found with frequent graph mining techniques. We investigate if a model invariant to changes in size and reflection ...
Outer-totalistic cellular automata on graphs
International Nuclear Information System (INIS)
Marr, Carsten; Huett, Marc-Thorsten
2009-01-01
We present an intuitive formalism for implementing cellular automata on arbitrary topologies. By that means, we identify a symmetry operation in the class of elementary cellular automata. Moreover, we determine the subset of topologically sensitive elementary cellular automata and find that the overall number of complex patterns decreases under increasing neighborhood size in regular graphs. As exemplary applications, we apply the formalism to complex networks and compare the potential of scale-free graphs and metabolic networks to generate complex dynamics
Domination versus disjunctive domination in graphs | Henning ...
African Journals Online (AJOL)
A dominating set in a graph G is a set S of vertices of G such that every vertex not in S is adjacent to a vertex of S. The domination number of G is the minimum cardinality of a dominating set of G. For a positive integer b, a set S of vertices in a graph G is a b-disjunctive dominating set in G if every vertex v not in S is adjacent ...
Determinantal spanning forests on planar graphs
Kenyon, Richard
2017-01-01
We generalize the uniform spanning tree to construct a family of determinantal measures on essential spanning forests on periodic planar graphs in which every component tree is bi-infinite. Like the uniform spanning tree, these measures arise naturally from the laplacian on the graph. More generally these results hold for the "massive" laplacian determinant which counts rooted spanning forests with weight $M$ per finite component. These measures typically have a form of conformal invariance, ...
Optimizing spread dynamics on graphs by message passing
International Nuclear Information System (INIS)
Altarelli, F; Braunstein, A; Dall’Asta, L; Zecchina, R
2013-01-01
Cascade processes are responsible for many important phenomena in natural and social sciences. Simple models of irreversible dynamics on graphs, in which nodes activate depending on the state of their neighbors, have been successfully applied to describe cascades in a large variety of contexts. Over the past decades, much effort has been devoted to understanding the typical behavior of the cascades arising from initial conditions extracted at random from some given ensemble. However, the problem of optimizing the trajectory of the system, i.e. of identifying appropriate initial conditions to maximize (or minimize) the final number of active nodes, is still considered to be practically intractable, with the only exception being models that satisfy a sort of diminishing returns property called submodularity. Submodular models can be approximately solved by means of greedy strategies, but by definition they lack cooperative characteristics which are fundamental in many real systems. Here we introduce an efficient algorithm based on statistical physics for the optimization of trajectories in cascade processes on graphs. We show that for a wide class of irreversible dynamics, even in the absence of submodularity, the spread optimization problem can be solved efficiently on large networks. Analytic and algorithmic results on random graphs are complemented by the solution of the spread maximization problem on a real-world network (the Epinions consumer reviews network). (paper)
Towards Translating Graph Transformation Approaches by Model Transformations
Hermann, F.; Kastenberg, H.; Modica, T.; Karsai, G.; Taentzer, G.
2006-01-01
Recently, many researchers are working on semantics preserving model transformation. In the field of graph transformation one can think of translating graph grammars written in one approach to a behaviourally equivalent graph grammar in another approach. In this paper we translate graph grammars
On the Recognition of Fuzzy Circular Interval Graphs
Oriolo, Gianpaolo; Pietropaoli, Ugo; Stauffer, Gautier
2011-01-01
Fuzzy circular interval graphs are a generalization of proper circular arc graphs and have been recently introduced by Chudnovsky and Seymour as a fundamental subclass of claw-free graphs. In this paper, we provide a polynomial-time algorithm for recognizing such graphs, and more importantly for building a suitable representation.
Graphs whose Complement and Square are Isomorphic (extended version)
DEFF Research Database (Denmark)
Pedersen, Anders Sune; Milanic, Martin; Verret, Gabriel
2013-01-01
We study square-complementary graphs, that is, graphs whose comple- ment and square are isomorphic. We prove several necessary conditions for a graph to be square-complementary, describe ways of building new square-complementary graphs from existing ones, construct innite families of square-compl...
Pre-Service Elementary Teachers' Understandings of Graphs
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…
On convex relaxation of graph isomorphism
Aflalo, Yonathan; Bronstein, Alexander; Kimmel, Ron
2015-01-01
We consider the problem of exact and inexact matching of weighted undirected graphs, in which a bijective correspondence is sought to minimize a quadratic weight disagreement. This computationally challenging problem is often relaxed as a convex quadratic program, in which the space of permutations is replaced by the space of doubly stochastic matrices. However, the applicability of such a relaxation is poorly understood. We define a broad class of friendly graphs characterized by an easily verifiable spectral property. We prove that for friendly graphs, the convex relaxation is guaranteed to find the exact isomorphism or certify its inexistence. This result is further extended to approximately isomorphic graphs, for which we develop an explicit bound on the amount of weight disagreement under which the relaxation is guaranteed to find the globally optimal approximate isomorphism. We also show that in many cases, the graph matching problem can be further harmlessly relaxed to a convex quadratic program with only n separable linear equality constraints, which is substantially more efficient than the standard relaxation involving 2n equality and n2 inequality constraints. Finally, we show that our results are still valid for unfriendly graphs if additional information in the form of seeds or attributes is allowed, with the latter satisfying an easy to verify spectral characteristic. PMID:25713342
Probabilistic Graph Layout for Uncertain Network Visualization.
Schulz, Christoph; Nocaj, Arlind; Goertler, Jochen; Deussen, Oliver; Brandes, Ulrik; Weiskopf, Daniel
2017-01-01
We present a novel uncertain network visualization technique based on node-link diagrams. Nodes expand spatially in our probabilistic graph layout, depending on the underlying probability distributions of edges. The visualization is created by computing a two-dimensional graph embedding that combines samples from the probabilistic graph. A Monte Carlo process is used to decompose a probabilistic graph into its possible instances and to continue with our graph layout technique. Splatting and edge bundling are used to visualize point clouds and network topology. The results provide insights into probability distributions for the entire network-not only for individual nodes and edges. We validate our approach using three data sets that represent a wide range of network types: synthetic data, protein-protein interactions from the STRING database, and travel times extracted from Google Maps. Our approach reveals general limitations of the force-directed layout and allows the user to recognize that some nodes of the graph are at a specific position just by chance.
Quantum complexity of graph and algebraic problems
Energy Technology Data Exchange (ETDEWEB)
Doern, Sebastian
2008-02-04
This thesis is organized as follows: In Chapter 2 we give some basic notations, definitions and facts from linear algebra, graph theory, group theory and quantum computation. In Chapter 3 we describe three important methods for the construction of quantum algorithms. We present the quantum search algorithm by Grover, the quantum amplitude amplification and the quantum walk search technique by Magniez et al. These three tools are the basis for the development of our new quantum algorithms for graph and algebra problems. In Chapter 4 we present two tools for proving quantum query lower bounds. We present the quantum adversary method by Ambainis and the polynomial method introduced by Beals et al. The quantum adversary tool is very useful to prove good lower bounds for many graph and algebra problems. The part of the thesis containing the original results is organized in two parts. In the first part we consider the graph problems. In Chapter 5 we give a short summary of known quantum graph algorithms. In Chapter 6 to 8 we study the complexity of our new algorithms for matching problems, graph traversal and independent set problems on quantum computers. In the second part of our thesis we present new quantum algorithms for algebraic problems. In Chapter 9 to 10 we consider group testing problems and prove quantum complexity bounds for important problems from linear algebra. (orig.)
Multiple graph regularized nonnegative matrix factorization
Wang, Jim Jing-Yan
2013-10-01
Non-negative matrix factorization (NMF) has been widely used as a data representation method based on components. To overcome the disadvantage of NMF in failing to consider the manifold structure of a data set, graph regularized NMF (GrNMF) has been proposed by Cai et al. by constructing an affinity graph and searching for a matrix factorization that respects graph structure. Selecting a graph model and its corresponding parameters is critical for this strategy. This process is usually carried out by cross-validation or discrete grid search, which are time consuming and prone to overfitting. In this paper, we propose a GrNMF, called MultiGrNMF, in which the intrinsic manifold is approximated by a linear combination of several graphs with different models and parameters inspired by ensemble manifold regularization. Factorization metrics and linear combination coefficients of graphs are determined simultaneously within a unified object function. They are alternately optimized in an iterative algorithm, thus resulting in a novel data representation algorithm. Extensive experiments on a protein subcellular localization task and an Alzheimer\\'s disease diagnosis task demonstrate the effectiveness of the proposed algorithm. © 2013 Elsevier Ltd. All rights reserved.
Quantum complexity of graph and algebraic problems
International Nuclear Information System (INIS)
Doern, Sebastian
2008-01-01
This thesis is organized as follows: In Chapter 2 we give some basic notations, definitions and facts from linear algebra, graph theory, group theory and quantum computation. In Chapter 3 we describe three important methods for the construction of quantum algorithms. We present the quantum search algorithm by Grover, the quantum amplitude amplification and the quantum walk search technique by Magniez et al. These three tools are the basis for the development of our new quantum algorithms for graph and algebra problems. In Chapter 4 we present two tools for proving quantum query lower bounds. We present the quantum adversary method by Ambainis and the polynomial method introduced by Beals et al. The quantum adversary tool is very useful to prove good lower bounds for many graph and algebra problems. The part of the thesis containing the original results is organized in two parts. In the first part we consider the graph problems. In Chapter 5 we give a short summary of known quantum graph algorithms. In Chapter 6 to 8 we study the complexity of our new algorithms for matching problems, graph traversal and independent set problems on quantum computers. In the second part of our thesis we present new quantum algorithms for algebraic problems. In Chapter 9 to 10 we consider group testing problems and prove quantum complexity bounds for important problems from linear algebra. (orig.)
Graph representation of protein free energy landscape
International Nuclear Information System (INIS)
Li, Minghai; Duan, Mojie; Fan, Jue; Huo, Shuanghong; Han, Li
2013-01-01
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
Sparse graphs using exchangeable random measures.
Caron, François; Fox, Emily B
2017-11-01
Statistical network modelling has focused on representing the graph as a discrete structure, namely the adjacency matrix. When assuming exchangeability of this array-which can aid in modelling, computations and theoretical analysis-the Aldous-Hoover theorem informs us that the graph is necessarily either dense or empty. We instead consider representing the graph as an exchangeable random measure and appeal to the Kallenberg representation theorem for this object. We explore using completely random measures (CRMs) to define the exchangeable random measure, and we show how our CRM construction enables us to achieve sparse graphs while maintaining the attractive properties of exchangeability. We relate the sparsity of the graph to the Lévy measure defining the CRM. For a specific choice of CRM, our graphs can be tuned from dense to sparse on the basis of a single parameter. We present a scalable Hamiltonian Monte Carlo algorithm for posterior inference, which we use to analyse network properties in a range of real data sets, including networks with hundreds of thousands of nodes and millions of edges.
On the Laplacian spectral radii of Halin graphs.
Jia, Huicai; Xue, Jie
2017-01-01
Let T be a tree with at least four vertices, none of which has degree 2, embedded in the plane. A Halin graph is a plane graph constructed by connecting the leaves of T into a cycle. Thus the cycle C forms the outer face of the Halin graph, with the tree inside it. Let G be a Halin graph with order n . Denote by [Formula: see text] the Laplacian spectral radius of G . This paper determines all the Halin graphs with [Formula: see text]. Moreover, we obtain the graphs with the first three largest Laplacian spectral radius among all the Halin graphs on n vertices.