Quantization of gauge fields, graph polynomials and graph homology

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kreimer, Dirk, E-mail: kreimer@physik.hu-berlin.de; Sars, Matthias; Suijlekom, Walter D. van

2013-09-15

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

BRAPH: A graph theory software for the analysis of brain connectivity

PubMed Central

Mijalkov, Mite; Kakaei, Ehsan; Pereira, Joana B.; Westman, Eric; Volpe, Giovanni

2017-01-01

The brain is a large-scale complex network whose workings rely on the interaction between its various regions. In the past few years, the organization of the human brain network has been studied extensively using concepts from graph theory, where the brain is represented as a set of nodes connected by edges. This representation of the brain as a connectome can be used to assess important measures that reflect its topological architecture. We have developed a freeware MatLab-based software (BRAPH–BRain Analysis using graPH theory) for connectivity analysis of brain networks derived from structural magnetic resonance imaging (MRI), functional MRI (fMRI), positron emission tomography (PET) and electroencephalogram (EEG) data. BRAPH allows building connectivity matrices, calculating global and local network measures, performing non-parametric permutations for group comparisons, assessing the modules in the network, and comparing the results to random networks. By contrast to other toolboxes, it allows performing longitudinal comparisons of the same patients across different points in time. Furthermore, even though a user-friendly interface is provided, the architecture of the program is modular (object-oriented) so that it can be easily expanded and customized. To demonstrate the abilities of BRAPH, we performed structural and functional graph theory analyses in two separate studies. In the first study, using MRI data, we assessed the differences in global and nodal network topology in healthy controls, patients with amnestic mild cognitive impairment, and patients with Alzheimer’s disease. In the second study, using resting-state fMRI data, we compared healthy controls and Parkinson’s patients with mild cognitive impairment. PMID:28763447

BRAPH: A graph theory software for the analysis of brain connectivity.

PubMed

Mijalkov, Mite; Kakaei, Ehsan; Pereira, Joana B; Westman, Eric; Volpe, Giovanni

2017-01-01

The brain is a large-scale complex network whose workings rely on the interaction between its various regions. In the past few years, the organization of the human brain network has been studied extensively using concepts from graph theory, where the brain is represented as a set of nodes connected by edges. This representation of the brain as a connectome can be used to assess important measures that reflect its topological architecture. We have developed a freeware MatLab-based software (BRAPH-BRain Analysis using graPH theory) for connectivity analysis of brain networks derived from structural magnetic resonance imaging (MRI), functional MRI (fMRI), positron emission tomography (PET) and electroencephalogram (EEG) data. BRAPH allows building connectivity matrices, calculating global and local network measures, performing non-parametric permutations for group comparisons, assessing the modules in the network, and comparing the results to random networks. By contrast to other toolboxes, it allows performing longitudinal comparisons of the same patients across different points in time. Furthermore, even though a user-friendly interface is provided, the architecture of the program is modular (object-oriented) so that it can be easily expanded and customized. To demonstrate the abilities of BRAPH, we performed structural and functional graph theory analyses in two separate studies. In the first study, using MRI data, we assessed the differences in global and nodal network topology in healthy controls, patients with amnestic mild cognitive impairment, and patients with Alzheimer's disease. In the second study, using resting-state fMRI data, we compared healthy controls and Parkinson's patients with mild cognitive impairment.

Change of Brain Functional Connectivity in Patients With Spinal Cord Injury: Graph Theory Based Approach.

PubMed

Min, Yu-Sun; Chang, Yongmin; Park, Jang Woo; Lee, Jong-Min; Cha, Jungho; Yang, Jin-Ju; Kim, Chul-Hyun; Hwang, Jong-Moon; Yoo, Ji-Na; Jung, Tae-Du

2015-06-01

To investigate the global functional reorganization of the brain following spinal cord injury with graph theory based approach by creating whole brain functional connectivity networks from resting state-functional magnetic resonance imaging (rs-fMRI), characterizing the reorganization of these networks using graph theoretical metrics and to compare these metrics between patients with spinal cord injury (SCI) and age-matched controls. Twenty patients with incomplete cervical SCI (14 males, 6 females; age, 55±14.1 years) and 20 healthy subjects (10 males, 10 females; age, 52.9±13.6 years) participated in this study. To analyze the characteristics of the whole brain network constructed with functional connectivity using rs-fMRI, graph theoretical measures were calculated including clustering coefficient, characteristic path length, global efficiency and small-worldness. Clustering coefficient, global efficiency and small-worldness did not show any difference between controls and SCIs in all density ranges. The normalized characteristic path length to random network was higher in SCI patients than in controls and reached statistical significance at 12%-13% of density (p<0.05, uncorrected). The graph theoretical approach in brain functional connectivity might be helpful to reveal the information processing after SCI. These findings imply that patients with SCI can build on preserved competent brain control. Further analyses, such as topological rearrangement and hub region identification, will be needed for better understanding of neuroplasticity in patients with SCI.

Graph Theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sanfilippo, Antonio P.

2005-12-27

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

GAT: a graph-theoretical analysis toolbox for analyzing between-group differences in large-scale structural and functional brain networks.

PubMed

Hosseini, S M Hadi; Hoeft, Fumiko; Kesler, Shelli R

2012-01-01

In recent years, graph theoretical analyses of neuroimaging data have increased our understanding of the organization of large-scale structural and functional brain networks. However, tools for pipeline application of graph theory for analyzing topology of brain networks is still lacking. In this report, we describe the development of a graph-analysis toolbox (GAT) that facilitates analysis and comparison of structural and functional network brain networks. GAT provides a graphical user interface (GUI) that facilitates construction and analysis of brain networks, comparison of regional and global topological properties between networks, analysis of network hub and modules, and analysis of resilience of the networks to random failure and targeted attacks. Area under a curve (AUC) and functional data analyses (FDA), in conjunction with permutation testing, is employed for testing the differences in network topologies; analyses that are less sensitive to the thresholding process. We demonstrated the capabilities of GAT by investigating the differences in the organization of regional gray-matter correlation networks in survivors of acute lymphoblastic leukemia (ALL) and healthy matched Controls (CON). The results revealed an alteration in small-world characteristics of the brain networks in the ALL survivors; an observation that confirm our hypothesis suggesting widespread neurobiological injury in ALL survivors. Along with demonstration of the capabilities of the GAT, this is the first report of altered large-scale structural brain networks in ALL survivors.

Graph Theory and Its Application in Educational Research: A Review and Integration.

ERIC Educational Resources Information Center

Tatsuoka, Maurice M.

1986-01-01

A nontechnical exposition of graph theory is presented, followed by survey of the literature on applications of graph theory in research in education and related disciplines. Applications include order-theoretic studies of the dimensionality of data sets, the investigation of hierarchical structures in various domains, and cluster analysis.…

Applying graphs and complex networks to football metric interpretation.

PubMed

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

2018-02-01

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

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

NASA Astrophysics Data System (ADS)

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

2016-05-01

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

Kevin Bacon and Graph Theory

ERIC Educational Resources Information Center

Hopkins, Brian

2004-01-01

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

Flying through Graphs: An Introduction to Graph Theory.

ERIC Educational Resources Information Center

McDuffie, Amy Roth

2001-01-01

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

Panconnectivity of Locally Connected K(1,3)-Free Graphs

DTIC Science & Technology

1989-10-15

Graph Theory, 3 (1979) p. 351-356. 22 7. Cun-Quan Zhang, Cycles of Given Lengths in KI, 3-Free Graphs, Discrete Math ., (1988) to appear. I. f 2.f 𔃽. AA A V V / (S. ...Locally Connected and Hamiltonian-Connected Graphs, Isreal J. Math., 33 (1979) p. 5-8. 4. V. Chvatal and P. Erd6s, A Note on Hamiltonian Circuits, Discrete ... Math ., 2 (1972) p. 111-113. 5. S. V. Kanetkar and P. R. Rao, Connected and Locally 2- Connected, K1.3-Free Graphs are Panconnected, J. Graph Theory, 8

Graph Theory and Brain Connectivity in Alzheimer's Disease.

PubMed

delEtoile, Jon; Adeli, Hojjat

2017-04-01

This article presents a review of recent advances in neuroscience research in the specific area of brain connectivity as a potential biomarker of Alzheimer's disease with a focus on the application of graph theory. The review will begin with a brief overview of connectivity and graph theory. Then resent advances in connectivity as a biomarker for Alzheimer's disease will be presented and analyzed.

On the 2-Extendability of Planar Graphs

DTIC Science & Technology

1989-01-01

connectivity for n-extend- ability of regular graphs, 1988, submitted. [6] L. Lov~isz and M.D. Plummer, Matching Theory, Ann. Discrete Math . 29, North...Holland, Amsterdam, 1986. [7] M.D. Plummer, On n-extendable graphs, Discrete Math . 31, 1980, 201-210. [8] M.D. Plummer, A theorem on matchings in the...plane, Graph Theory in Memory of G.A. Dirac, Ann. Discrete Math . 41, North-Holland, Amsterdam, 1989, 347-354. [9] C. Thomassen, Girth in graphs, J

Using Combinatorica/Mathematica for Student Projects in Random Graph Theory

ERIC Educational Resources Information Center

Pfaff, Thomas J.; Zaret, Michele

2006-01-01

We give an example of a student project that experimentally explores a topic in random graph theory. We use the "Combinatorica" package in "Mathematica" to estimate the minimum number of edges needed in a random graph to have a 50 percent chance that the graph is connected. We provide the "Mathematica" code and compare it to the known theoretical…

Graph theory and the Virasoro master equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Obers, N.A.J.

1991-04-01

A brief history of affine Lie algebra, the Virasoro algebra and its culmination in the Virasoro master equations is given. By studying ansaetze of the master equation, we obtain exact solutions and gain insight in the structure of large slices of affine-Virasoro space. We find an isomorphism between the constructions in the ansatz SO(n){sub diag}, which is a set of unitary, generically irrational affine-Virasoro constructions on SO(n), and the unlabelled graphs, while, conversely, a group-theoretic and conformal field-theoretic identification is obtained for every graph of graph theory. We also define a class of magic'' Lie group bases in which themore » Virasoro master equation admits a simple metric ansatz (gmetric), whose structure is visible in the high-level expansion. When a magic basis is real on compact g, the corresponding g{sub metric} is a large system of unitary, generically irrational conformal field theories. Examples in this class include the graph-theory ansatz SO(n){sub diag} in the Cartesian basis of SO(n), and the ansatz SU(n){sub metric} in the Pauli-like basis of SU(n). Finally, we define the sine-area graphs'' of SU(n), which label the conformal field theories of SU(n){sub metric}, and we note that, in similar fashion, each magic basis of g defines a generalized graph theory on g which labels the conformal field theories of g{sub metric}. 24 figs., 4 tabs.« less

A brief historical introduction to Euler's formula for polyhedra, topology, graph theory and networks

NASA Astrophysics Data System (ADS)

Debnath, Lokenath

2010-09-01

This article is essentially devoted to a brief historical introduction to Euler's formula for polyhedra, topology, theory of graphs and networks with many examples from the real-world. Celebrated Königsberg seven-bridge problem and some of the basic properties of graphs and networks for some understanding of the macroscopic behaviour of real physical systems are included. We also mention some important and modern applications of graph theory or network problems from transportation to telecommunications. Graphs or networks are effectively used as powerful tools in industrial, electrical and civil engineering, communication networks in the planning of business and industry. Graph theory and combinatorics can be used to understand the changes that occur in many large and complex scientific, technical and medical systems. With the advent of fast large computers and the ubiquitous Internet consisting of a very large network of computers, large-scale complex optimization problems can be modelled in terms of graphs or networks and then solved by algorithms available in graph theory. Many large and more complex combinatorial problems dealing with the possible arrangements of situations of various kinds, and computing the number and properties of such arrangements can be formulated in terms of networks. The Knight's tour problem, Hamilton's tour problem, problem of magic squares, the Euler Graeco-Latin squares problem and their modern developments in the twentieth century are also included.

Less Is Less: A Systematic Review of Graph Use in Meta-Analyses

ERIC Educational Resources Information Center

Schild, Anne H. E.; Voracek, Martin

2013-01-01

Graphs are an essential part of scientific communication. Complex datasets, of which meta-analyses are textbook examples, benefit the most from visualization. Although a number of graph options for meta-analyses exist, the extent to which these are used was hitherto unclear. A systematic review on graph use in meta-analyses in three disciplines…

Interval Graph Limits

PubMed Central

Diaconis, Persi; Holmes, Susan; Janson, Svante

2015-01-01

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

Matching Theory - A Sampler: From Denes Koenig to the Present

DTIC Science & Technology

1991-01-01

1079. [1131 , Matching Theory, Ann. Discrete Math . 29, North- Holland, Amsterdam, 1986. [114 ] M. Luby, A simple parallel algorithm for the maximal...311. [135 ]M.D. Plummer, On n-extendable graphs, Discrete Math . 31, 1980, 201-210. [1361 , Matching extension and the genus of a graph, J. Combin...Theory Ser. B, 44, 1988, 329-837. [137] , A theorem on matchings in the plane, Graph Theory in Memory of G.A. Dirac, Ann. Discrete Math . 41, North

Graph-based linear scaling electronic structure theory.

PubMed

Niklasson, Anders M N; Mniszewski, Susan M; Negre, Christian F A; Cawkwell, Marc J; Swart, Pieter J; Mohd-Yusof, Jamal; Germann, Timothy C; Wall, Michael E; Bock, Nicolas; Rubensson, Emanuel H; Djidjev, Hristo

2016-06-21

We show how graph theory can be combined with quantum theory to calculate the electronic structure of large complex systems. The graph formalism is general and applicable to a broad range of electronic structure methods and materials, including challenging systems such as biomolecules. The methodology combines well-controlled accuracy, low computational cost, and natural low-communication parallelism. This combination addresses substantial shortcomings of linear scaling electronic structure theory, in particular with respect to quantum-based molecular dynamics simulations.

Graph-based linear scaling electronic structure theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Niklasson, Anders M. N., E-mail: amn@lanl.gov; Negre, Christian F. A.; Cawkwell, Marc J.

2016-06-21

We show how graph theory can be combined with quantum theory to calculate the electronic structure of large complex systems. The graph formalism is general and applicable to a broad range of electronic structure methods and materials, including challenging systems such as biomolecules. The methodology combines well-controlled accuracy, low computational cost, and natural low-communication parallelism. This combination addresses substantial shortcomings of linear scaling electronic structure theory, in particular with respect to quantum-based molecular dynamics simulations.

The investigation of social networks based on multi-component random graphs

NASA Astrophysics Data System (ADS)

Zadorozhnyi, V. N.; Yudin, E. B.

2018-01-01

The methods of non-homogeneous random graphs calibration are developed for social networks simulation. The graphs are calibrated by the degree distributions of the vertices and the edges. The mathematical foundation of the methods is formed by the theory of random graphs with the nonlinear preferential attachment rule and the theory of Erdôs-Rényi random graphs. In fact, well-calibrated network graph models and computer experiments with these models would help developers (owners) of the networks to predict their development correctly and to choose effective strategies for controlling network projects.

A PVS Graph Theory Library

NASA Technical Reports Server (NTRS)

Butler, Ricky W.; Sjogren, Jon A.

1998-01-01

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

Graph theory and the Virasoro master equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Obers, N.A.J.

1991-01-01

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

Band connectivity for topological quantum chemistry: Band structures as a graph theory problem

NASA Astrophysics Data System (ADS)

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

2018-01-01

The conventional theory of solids is well suited to describing band structures locally near isolated points in momentum space, but struggles to capture the full, global picture necessary for understanding topological phenomena. In part of a recent paper [B. Bradlyn et al., Nature (London) 547, 298 (2017), 10.1038/nature23268], we have introduced the way to overcome this difficulty by formulating the problem of sewing together many disconnected local k .p band structures across the Brillouin zone in terms of graph theory. In this paper, we give the details of our full theoretical construction. We show that crystal symmetries strongly constrain the allowed connectivities of energy bands, and we employ graph theoretic techniques such as graph connectivity to enumerate all the solutions to these constraints. The tools of graph theory allow us to identify disconnected groups of bands in these solutions, and so identify topologically distinct insulating phases.

Using Zipf-Mandelbrot law and graph theory to evaluate animal welfare

NASA Astrophysics Data System (ADS)

de Oliveira, Caprice G. L.; Miranda, José G. V.; Japyassú, Hilton F.; El-Hani, Charbel N.

2018-02-01

This work deals with the construction and testing of metrics of welfare based on behavioral complexity, using assumptions derived from Zipf-Mandelbrot law and graph theory. To test these metrics we compared yellow-breasted capuchins (Sapajus xanthosternos) (Wied-Neuwied, 1826) (PRIMATES CEBIDAE) found in two institutions, subjected to different captive conditions: a Zoobotanical Garden (hereafter, ZOO; n = 14), in good welfare condition, and a Wildlife Rescue Center (hereafter, WRC; n = 8), in poor welfare condition. In the Zipf-Mandelbrot-based analysis, the power law exponent was calculated using behavior frequency values versus behavior rank value. These values allow us to evaluate variations in individual behavioral complexity. For each individual we also constructed a graph using the sequence of behavioral units displayed in each recording (average recording time per individual: 4 h 26 min in the ZOO, 4 h 30 min in the WRC). Then, we calculated the values of the main graph attributes, which allowed us to analyze the complexity of the connectivity of the behaviors displayed in the individuals' behavioral sequences. We found significant differences between the two groups for the slope values in the Zipf-Mandelbrot analysis. The slope values for the ZOO individuals approached -1, with graphs representing a power law, while the values for the WRC individuals diverged from -1, differing from a power law pattern. Likewise, we found significant differences for the graph attributes average degree, weighted average degree, and clustering coefficient when comparing the ZOO and WRC individual graphs. However, no significant difference was found for the attributes modularity and average path length. Both analyses were effective in detecting differences between the patterns of behavioral complexity in the two groups. The slope values for the ZOO individuals indicated a higher behavioral complexity when compared to the WRC individuals. Similarly, graph construction and the calculation of its attributes values allowed us to show that the complexity of the connectivity among the behaviors was higher in the ZOO than in the WRC individual graphs. These results show that the two measuring approaches introduced and tested in this paper were capable of capturing the differences in welfare levels between the two conditions, as shown by differences in behavioral complexity.

Matching Extension and Connectivity in Graphs. 1. Introduction and Terminology,

DTIC Science & Technology

1986-01-01

minimal elementary bipartite graphs, J. Combin. Theory Ser. B 23, 1977, 127-138. 1986. Matching Theory, Ann. Discrete Math ., North-Holland, Amsterdam, 1986...to appear). M. D. PLUMMER 1980. On n-extendable graphs, Discrete Math . 31, 1980, 201-210. 1985. A theorem on matchings in the plane, Conference in...memory of Gabriel Dirac, Ann. Discrete Math ., North-Holland, Amsterdam, to appear. 1986a. Matching extension in bipartite graphs, preprint, 1986. 1986b

Applying Graph Theory to Problems in Air Traffic Management

NASA Technical Reports Server (NTRS)

Farrahi, Amir Hossein; Goldbert, Alan; Bagasol, Leonard Neil; Jung, Jaewoo

2017-01-01

Graph theory is used to investigate three different problems arising in air traffic management. First, using a polynomial reduction from a graph partitioning problem, it is shown that both the airspace sectorization problem and its incremental counterpart, the sector combination problem are NP-hard, in general, under several simple workload models. Second, using a polynomial time reduction from maximum independent set in graphs, it is shown that for any fixed e, the problem of finding a solution to the minimum delay scheduling problem in traffic flow management that is guaranteed to be within n1-e of the optimal, where n is the number of aircraft in the problem instance, is NP-hard. Finally, a problem arising in precision arrival scheduling is formulated and solved using graph reachability. These results demonstrate that graph theory provides a powerful framework for modeling, reasoning about, and devising algorithmic solutions to diverse problems arising in air traffic management.

Applying Graph Theory to Problems in Air Traffic Management

NASA Technical Reports Server (NTRS)

Farrahi, Amir H.; Goldberg, Alan T.; Bagasol, Leonard N.; Jung, Jaewoo

2017-01-01

Graph theory is used to investigate three different problems arising in air traffic management. First, using a polynomial reduction from a graph partitioning problem, it isshown that both the airspace sectorization problem and its incremental counterpart, the sector combination problem are NP-hard, in general, under several simple workload models. Second, using a polynomial time reduction from maximum independent set in graphs, it is shown that for any fixed e, the problem of finding a solution to the minimum delay scheduling problem in traffic flow management that is guaranteed to be within n1-e of the optimal, where n is the number of aircraft in the problem instance, is NP-hard. Finally, a problem arising in precision arrival scheduling is formulated and solved using graph reachability. These results demonstrate that graph theory provides a powerful framework for modeling, reasoning about, and devising algorithmic solutions to diverse problems arising in air traffic management.

A Ring Construction Using Finite Directed Graphs

ERIC Educational Resources Information Center

Bardzell, Michael

2012-01-01

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

Guidelines for the CSMP K-6 Curriculum in Graph Theory.

ERIC Educational Resources Information Center

Deskins, W. E.; And Others

This volume is designed for teachers preparing to teach upper elementary students using the Comprehensive School Mathematics Program (CSMP) curriculum. It begins with a discussion of the importance of graph theory in mathematics and science. A mathematical development of graph-theoretic concepts and theorems is presented, followed by a set of…

A simple proof of orientability in colored group field theory.

PubMed

Caravelli, Francesco

2012-01-01

Group field theory is an emerging field at the boundary between Quantum Gravity, Statistical Mechanics and Quantum Field Theory and provides a path integral for the gluing of n-simplices. Colored group field theory has been introduced in order to improve the renormalizability of the theory and associates colors to the faces of the simplices. The theory of crystallizations is instead a field at the boundary between graph theory and combinatorial topology and deals with n-simplices as colored graphs. Several techniques have been introduced in order to study the topology of the pseudo-manifold associated to the colored graph. Although of the similarity between colored group field theory and the theory of crystallizations, the connection between the two fields has never been made explicit. In this short note we use results from the theory of crystallizations to prove that color in group field theories guarantees orientability of the piecewise linear pseudo-manifolds associated to each graph generated perturbatively. Colored group field theories generate orientable pseudo-manifolds. The origin of orientability is the presence of two interaction vertices in the action of colored group field theories. In order to obtain the result, we made the connection between the theory of crystallizations and colored group field theory.

Counting the number of Feynman graphs in QCD

NASA Astrophysics Data System (ADS)

Kaneko, T.

2018-05-01

Information about the number of Feynman graphs for a given physical process in a given field theory is especially useful for confirming the result of a Feynman graph generator used in an automatic system of perturbative calculations. A method of counting the number of Feynman graphs with weight of symmetry factor was established based on zero-dimensional field theory, and was used in scalar theories and QED. In this article this method is generalized to more complicated models by direct calculation of generating functions on a computer algebra system. This method is applied to QCD with and without counter terms, where many higher order are being calculated automatically.

Graph theory findings in the pathophysiology of temporal lobe epilepsy

PubMed Central

Chiang, Sharon; Haneef, Zulfi

2014-01-01

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

Generalized graph states based on Hadamard matrices

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cui, Shawn X.; Yu, Nengkun; Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario N1G 2W1

2015-07-15

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

A Brief Historical Introduction to Euler's Formula for Polyhedra, Topology, Graph Theory and Networks

ERIC Educational Resources Information Center

Debnath, Lokenath

2010-01-01

This article is essentially devoted to a brief historical introduction to Euler's formula for polyhedra, topology, theory of graphs and networks with many examples from the real-world. Celebrated Konigsberg seven-bridge problem and some of the basic properties of graphs and networks for some understanding of the macroscopic behaviour of real…

Detecting labor using graph theory on connectivity matrices of uterine EMG.

PubMed

Al-Omar, S; Diab, A; Nader, N; Khalil, M; Karlsson, B; Marque, C

2015-08-01

Premature labor is one of the most serious health problems in the developed world. One of the main reasons for this is that no good way exists to distinguish true labor from normal pregnancy contractions. The aim of this paper is to investigate if the application of graph theory techniques to multi-electrode uterine EMG signals can improve the discrimination between pregnancy contractions and labor. To test our methods we first applied them to synthetic graphs where we detected some differences in the parameters results and changes in the graph model from pregnancy-like graphs to labor-like graphs. Then, we applied the same methods to real signals. We obtained the best differentiation between pregnancy and labor through the same parameters. Major improvements in differentiating between pregnancy and labor were obtained using a low pass windowing preprocessing step. Results show that real graphs generally became more organized when moving from pregnancy, where the graph showed random characteristics, to labor where the graph became a more small-world like graph.

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

PubMed

Gnutzmann, Sven; Waltner, Daniel

2016-12-01

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

Applying network theory to animal movements to identify properties of landscape space use.

PubMed

Bastille-Rousseau, Guillaume; Douglas-Hamilton, Iain; Blake, Stephen; Northrup, Joseph M; Wittemyer, George

2018-04-01

Network (graph) theory is a popular analytical framework to characterize the structure and dynamics among discrete objects and is particularly effective at identifying critical hubs and patterns of connectivity. The identification of such attributes is a fundamental objective of animal movement research, yet network theory has rarely been applied directly to animal relocation data. We develop an approach that allows the analysis of movement data using network theory by defining occupied pixels as nodes and connection among these pixels as edges. We first quantify node-level (local) metrics and graph-level (system) metrics on simulated movement trajectories to assess the ability of these metrics to pull out known properties in movement paths. We then apply our framework to empirical data from African elephants (Loxodonta africana), giant Galapagos tortoises (Chelonoidis spp.), and mule deer (Odocoileous hemionus). Our results indicate that certain node-level metrics, namely degree, weight, and betweenness, perform well in capturing local patterns of space use, such as the definition of core areas and paths used for inter-patch movement. These metrics were generally applicable across data sets, indicating their robustness to assumptions structuring analysis or strategies of movement. Other metrics capture local patterns effectively, but were sensitive to specified graph properties, indicating case specific applications. Our analysis indicates that graph-level metrics are unlikely to outperform other approaches for the categorization of general movement strategies (central place foraging, migration, nomadism). By identifying critical nodes, our approach provides a robust quantitative framework to identify local properties of space use that can be used to evaluate the effect of the loss of specific nodes on range wide connectivity. Our network approach is intuitive, and can be implemented across imperfectly sampled or large-scale data sets efficiently, providing a framework for conservationists to analyze movement data. Functions created for the analyses are available within the R package moveNT. © 2018 by the Ecological Society of America.

Graph Theory and the High School Student.

ERIC Educational Resources Information Center

Chartrand, Gary; Wall, Curtiss E.

1980-01-01

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

Graph theory findings in the pathophysiology of temporal lobe epilepsy.

PubMed

Chiang, Sharon; Haneef, Zulfi

2014-07-01

Temporal lobe epilepsy (TLE) is the most common form of adult epilepsy. Accumulating evidence has shown that TLE is a disorder of abnormal epileptogenic networks, rather than focal sources. Graph theory allows for a network-based representation of TLE brain networks, and has potential to illuminate characteristics of brain topology conducive to TLE pathophysiology, including seizure initiation and spread. We review basic concepts which we believe will prove helpful in interpreting results rapidly emerging from graph theory research in TLE. In addition, we summarize the current state of graph theory findings in TLE as they pertain its pathophysiology. Several common findings have emerged from the many modalities which have been used to study TLE using graph theory, including structural MRI, diffusion tensor imaging, surface EEG, intracranial EEG, magnetoencephalography, functional MRI, cell cultures, simulated models, and mouse models, involving increased regularity of the interictal network configuration, altered local segregation and global integration of the TLE network, and network reorganization of temporal lobe and limbic structures. As different modalities provide different views of the same phenomenon, future studies integrating data from multiple modalities are needed to clarify findings and contribute to the formation of a coherent theory on the pathophysiology of TLE. Copyright © 2014 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved.

A preliminary study on atrial epicardial mapping signals based on Graph Theory.

PubMed

Sun, Liqian; Yang, Cuiwei; Zhang, Lin; Chen, Ying; Wu, Zhong; Shao, Jun

2014-07-01

In order to get a better understanding of atrial fibrillation, we introduced a method based on Graph Theory to interpret the relations of different parts of the atria. Atrial electrograms under sinus rhythm and atrial fibrillation were collected from eight living mongrel dogs with cholinergic AF model. These epicardial signals were acquired from 95 unipolar electrodes attached to the surface of the atria and four pulmonary veins. Then, we analyzed the electrode correlations using Graph Theory. The topology, the connectivity and the parameters of graphs during different rhythms were studied. Our results showed that the connectivity of graphs varied from sinus rhythm to atrial fibrillation and there were parameter gradients in various parts of the atria. The results provide spatial insight into the interaction between different parts of the atria and the method may have its potential for studying atrial fibrillation. Copyright © 2014 IPEM. Published by Elsevier Ltd. All rights reserved.

Graph Theory-Based Pinning Synchronization of Stochastic Complex Dynamical Networks.

PubMed

Li, Xiao-Jian; Yang, Guang-Hong

2017-02-01

This paper is concerned with the adaptive pinning synchronization problem of stochastic complex dynamical networks (CDNs). Based on algebraic graph theory and Lyapunov theory, pinning controller design conditions are derived, and the rigorous convergence analysis of synchronization errors in the probability sense is also conducted. Compared with the existing results, the topology structures of stochastic CDN are allowed to be unknown due to the use of graph theory. In particular, it is shown that the selection of nodes for pinning depends on the unknown lower bounds of coupling strengths. Finally, an example on a Chua's circuit network is given to validate the effectiveness of the theoretical results.

Computing Role Assignments of Proper Interval Graphs in Polynomial Time

NASA Astrophysics Data System (ADS)

Heggernes, Pinar; van't Hof, Pim; Paulusma, Daniël

A homomorphism from a graph G to a graph R is locally surjective if its restriction to the neighborhood of each vertex of G is surjective. Such a homomorphism is also called an R-role assignment of G. Role assignments have applications in distributed computing, social network theory, and topological graph theory. The Role Assignment problem has as input a pair of graphs (G,R) and asks whether G has an R-role assignment. This problem is NP-complete already on input pairs (G,R) where R is a path on three vertices. So far, the only known non-trivial tractable case consists of input pairs (G,R) where G is a tree. We present a polynomial time algorithm that solves Role Assignment on all input pairs (G,R) where G is a proper interval graph. Thus we identify the first graph class other than trees on which the problem is tractable. As a complementary result, we show that the problem is Graph Isomorphism-hard on chordal graphs, a superclass of proper interval graphs and trees.

Eigenanalysis and Graph Theory Combined to Determine the Seasonal and Solar-Cycle Variations of Polar Magnetic Fields

NASA Astrophysics Data System (ADS)

Shore, R. M.; Freeman, M. P.; Gjerloev, J. W.

2017-12-01

We apply the meteorological analysis method of Empirical Orthogonal Functions (EOF) to ground magnetometer measurements, and subsequently use graph theory to classify the results. The EOF method is used to characterise and separate contributions to the variability of the Earth's external magnetic field (EMF) in the northern polar region. EOFs decompose the noisy EMF data into a small number of independent spatio-temporal basis functions, which collectively describe the majority of the magnetic field variance. We use these basis functions (computed monthly) to infill where data are missing, providing a self-consistent description of the EMF at 5-minute resolution spanning 1997-2009 (solar cycle 23). The EOF basis functions are calculated independently for each of the 144 months (i.e. 1997-2009) analysed. Since (by definition) the basis vectors are ranked by their contribution to the total variance, their rank will change from month to month. We use graph theory to find clusters of quantifiably-similar spatial basis functions, and thereby track similar patterns throughout the span of 144 months. We find that the discovered clusters can be associated with well-known individual Disturbance Polar (DP)-type equivalent current systems (e.g. DP2, DP1, DPY, NBZ), or with the motion of these systems. Via this method, we thus describe the varying behaviour of these current systems over solar cycle 23. We present their seasonal and solar cycle variations and examine the response of each current system to solar wind driving.

An impatient evolutionary algorithm with probabilistic tabu search for unified solution of some NP-hard problems in graph and set theory via clique finding.

PubMed

Guturu, Parthasarathy; Dantu, Ram

2008-06-01

Many graph- and set-theoretic problems, because of their tremendous application potential and theoretical appeal, have been well investigated by the researchers in complexity theory and were found to be NP-hard. Since the combinatorial complexity of these problems does not permit exhaustive searches for optimal solutions, only near-optimal solutions can be explored using either various problem-specific heuristic strategies or metaheuristic global-optimization methods, such as simulated annealing, genetic algorithms, etc. In this paper, we propose a unified evolutionary algorithm (EA) to the problems of maximum clique finding, maximum independent set, minimum vertex cover, subgraph and double subgraph isomorphism, set packing, set partitioning, and set cover. In the proposed approach, we first map these problems onto the maximum clique-finding problem (MCP), which is later solved using an evolutionary strategy. The proposed impatient EA with probabilistic tabu search (IEA-PTS) for the MCP integrates the best features of earlier successful approaches with a number of new heuristics that we developed to yield a performance that advances the state of the art in EAs for the exploration of the maximum cliques in a graph. Results of experimentation with the 37 DIMACS benchmark graphs and comparative analyses with six state-of-the-art algorithms, including two from the smaller EA community and four from the larger metaheuristics community, indicate that the IEA-PTS outperforms the EAs with respect to a Pareto-lexicographic ranking criterion and offers competitive performance on some graph instances when individually compared to the other heuristic algorithms. It has also successfully set a new benchmark on one graph instance. On another benchmark suite called Benchmarks with Hidden Optimal Solutions, IEA-PTS ranks second, after a very recent algorithm called COVER, among its peers that have experimented with this suite.

Chemical Applications of Graph Theory: Part I. Fundamentals and Topological Indices.

ERIC Educational Resources Information Center

Hansen, Peter J.; Jurs, Peter C.

1988-01-01

Explores graph theory and use of topological indices to predict boiling points. Lists three indices: Wiener Number, Randic Branching Index and Molecular Connectivity, and Molecular Identification numbers. Warns of inadequacies with stereochemistry. (ML)

Causal inference, probability theory, and graphical insights.

PubMed

Baker, Stuart G

2013-11-10

Causal inference from observational studies is a fundamental topic in biostatistics. The causal graph literature typically views probability theory as insufficient to express causal concepts in observational studies. In contrast, the view here is that probability theory is a desirable and sufficient basis for many topics in causal inference for the following two reasons. First, probability theory is generally more flexible than causal graphs: Besides explaining such causal graph topics as M-bias (adjusting for a collider) and bias amplification and attenuation (when adjusting for instrumental variable), probability theory is also the foundation of the paired availability design for historical controls, which does not fit into a causal graph framework. Second, probability theory is the basis for insightful graphical displays including the BK-Plot for understanding Simpson's paradox with a binary confounder, the BK2-Plot for understanding bias amplification and attenuation in the presence of an unobserved binary confounder, and the PAD-Plot for understanding the principal stratification component of the paired availability design. Published 2013. This article is a US Government work and is in the public domain in the USA.

The Data-Ink Ratio and Accuracy of Information Derived from Newspaper Graphs: An Experimental Test of the Theory.

ERIC Educational Resources Information Center

Kelly, James D.

A study tested the data-ink ratio theory, which holds that a reader's recall of quantitative data displayed in a graph containing a substantial amount of non-data-ink will be significantly less than recall from a graph containing little non-data-ink, as it might apply to graphics used in mass circulation newspapers. The experiment employed a…

Quantum Experiments and Graphs: Multiparty States as Coherent Superpositions of Perfect Matchings.

PubMed

Krenn, Mario; Gu, Xuemei; Zeilinger, Anton

2017-12-15

We show a surprising link between experimental setups to realize high-dimensional multipartite quantum states and graph theory. In these setups, the paths of photons are identified such that the photon-source information is never created. We find that each of these setups corresponds to an undirected graph, and every undirected graph corresponds to an experimental setup. Every term in the emerging quantum superposition corresponds to a perfect matching in the graph. Calculating the final quantum state is in the #P-complete complexity class, thus it cannot be done efficiently. To strengthen the link further, theorems from graph theory-such as Hall's marriage problem-are rephrased in the language of pair creation in quantum experiments. We show explicitly how this link allows one to answer questions about quantum experiments (such as which classes of entangled states can be created) with graph theoretical methods, and how to potentially simulate properties of graphs and networks with quantum experiments (such as critical exponents and phase transitions).

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

ERIC Educational Resources Information Center

Xi, Xiaoming

2010-01-01

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

Brain Graph Topology Changes Associated with Anti-Epileptic Drug Use

PubMed Central

Levin, Harvey S.; Chiang, Sharon

2015-01-01

Abstract Neuroimaging studies of functional connectivity using graph theory have furthered our understanding of the network structure in temporal lobe epilepsy (TLE). Brain network effects of anti-epileptic drugs could influence such studies, but have not been systematically studied. Resting-state functional MRI was analyzed in 25 patients with TLE using graph theory analysis. Patients were divided into two groups based on anti-epileptic medication use: those taking carbamazepine/oxcarbazepine (CBZ/OXC) (n=9) and those not taking CBZ/OXC (n=16) as a part of their medication regimen. The following graph topology metrics were analyzed: global efficiency, betweenness centrality (BC), clustering coefficient, and small-world index. Multiple linear regression was used to examine the association of CBZ/OXC with graph topology. The two groups did not differ from each other based on epilepsy characteristics. Use of CBZ/OXC was associated with a lower BC. Longer epilepsy duration was also associated with a lower BC. These findings can inform graph theory-based studies in patients with TLE. The changes observed are discussed in relation to the anti-epileptic mechanism of action and adverse effects of CBZ/OXC. PMID:25492633

Graph-based network analysis of resting-state functional MRI.

PubMed

Wang, Jinhui; Zuo, Xinian; He, Yong

2010-01-01

In the past decade, resting-state functional MRI (R-fMRI) measures of brain activity have attracted considerable attention. Based on changes in the blood oxygen level-dependent signal, R-fMRI offers a novel way to assess the brain's spontaneous or intrinsic (i.e., task-free) activity with both high spatial and temporal resolutions. The properties of both the intra- and inter-regional connectivity of resting-state brain activity have been well documented, promoting our understanding of the brain as a complex network. Specifically, the topological organization of brain networks has been recently studied with graph theory. In this review, we will summarize the recent advances in graph-based brain network analyses of R-fMRI signals, both in typical and atypical populations. Application of these approaches to R-fMRI data has demonstrated non-trivial topological properties of functional networks in the human brain. Among these is the knowledge that the brain's intrinsic activity is organized as a small-world, highly efficient network, with significant modularity and highly connected hub regions. These network properties have also been found to change throughout normal development, aging, and in various pathological conditions. The literature reviewed here suggests that graph-based network analyses are capable of uncovering system-level changes associated with different processes in the resting brain, which could provide novel insights into the understanding of the underlying physiological mechanisms of brain function. We also highlight several potential research topics in the future.

Less is less: a systematic review of graph use in meta-analyses.

PubMed

Schild, Anne H E; Voracek, Martin

2013-09-01

Graphs are an essential part of scientific communication. Complex datasets, of which meta-analyses are textbook examples, benefit the most from visualization. Although a number of graph options for meta-analyses exist, the extent to which these are used was hitherto unclear. A systematic review on graph use in meta-analyses in three disciplines (medicine, psychology, and business) and nine journals was conducted. Interdisciplinary differences, which are mirrored in the respective journals, were revealed, that is, graph use correlates with external factors rather than methodological considerations. There was only limited variation in graph types (with forest plots as the most important representatives), and diagnostic plots were very rare. Although an increase in graph use over time could be observed, it is unlikely that this phenomenon is specific to meta-analyses. There is a gaping discrepancy between available graphic methods and their application in meta-analyses. This may be rooted in a number of factors, namely, (i) insufficient dissemination of new developments, (ii) unsatisfactory implementation in software packages, and (iii) minor attention on graphics in meta-analysis reporting guidelines. Using visualization methods to their full capacity is a further step in using meta-analysis to its full potential. Copyright © 2013 John Wiley & Sons, Ltd.

Measuring Graph Comprehension, Critique, and Construction in Science

NASA Astrophysics Data System (ADS)

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

2016-08-01

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

Matching Extension in Regular Graphs

DTIC Science & Technology

1989-01-01

Plummer, Matching Theory, Ann. Discrete Math . 29, North- Holland, Amsterdam, 1986. [101 , The matching structure of graphs: some recent re- sults...maximums d’un graphe, These, Dr. troisieme cycle, Univ. Grenoble, 1978. [12 ] D. Naddef and W.R. Pulleyblank, Matching in regular graphs, Discrete Math . 34...1981, 283-291. [13 1 M.D. Plummer, On n-extendable graphs, Discrete Math . 31, 1980, 201-210. . [ 141 ,Matching extension in planar graphs IV

Clinical correlates of graph theory findings in temporal lobe epilepsy.

PubMed

Haneef, Zulfi; Chiang, Sharon

2014-11-01

Temporal lobe epilepsy (TLE) is considered a brain network disorder, additionally representing the most common form of pharmaco-resistant epilepsy in adults. There is increasing evidence that seizures in TLE arise from abnormal epileptogenic networks, which extend beyond the clinico-radiologically determined epileptogenic zone and may contribute to the failure rate of 30-50% following epilepsy surgery. Graph theory allows for a network-based representation of TLE brain networks using several neuroimaging and electrophysiologic modalities, and has potential to provide clinicians with clinically useful biomarkers for diagnostic and prognostic purposes. We performed a review of the current state of graph theory findings in TLE as they pertain to localization of the epileptogenic zone, prediction of pre- and post-surgical seizure frequency and cognitive performance, and monitoring cognitive decline in TLE. Although different neuroimaging and electrophysiologic modalities have yielded occasionally conflicting results, several potential biomarkers have been characterized for identifying the epileptogenic zone, pre-/post-surgical seizure prediction, and assessing cognitive performance. For localization, graph theory measures of centrality have shown the most potential, including betweenness centrality, outdegree, and graph index complexity, whereas for prediction of seizure frequency, measures of synchronizability have shown the most potential. The utility of clustering coefficient and characteristic path length for assessing cognitive performance in TLE is also discussed. Future studies integrating data from multiple modalities and testing predictive models are needed to clarify findings and develop graph theory for its clinical utility. Copyright © 2014 British Epilepsy Association. Published by Elsevier Ltd. All rights reserved.

Clinical correlates of graph theory findings in temporal lobe epilepsy

PubMed Central

Haneef, Zulfi; Chiang, Sharon

2014-01-01

Purpose Temporal lobe epilepsy (TLE) is considered a brain network disorder, additionally representing the most common form of pharmaco-resistant epilepsy in adults. There is increasing evidence that seizures in TLE arise from abnormal epileptogenic networks, which extend beyond the clinico-radiologically determined epileptogenic zone and may contribute to the failure rate of 30–50% following epilepsy surgery. Graph theory allows for a network-based representation of TLE brain networks using several neuroimaging and electrophysiologic modalities, and has potential to provide clinicians with clinically useful biomarkers for diagnostic and prognostic purposes. Methods We performed a review of the current state of graph theory findings in TLE as they pertain to localization of the epileptogenic zone, prediction of pre- and post-surgical seizure frequency and cognitive performance, and monitoring cognitive decline in TLE. Results Although different neuroimaging and electrophysiologic modalities have yielded occasionally conflicting results, several potential biomarkers have been characterized for identifying the epileptogenic zone, pre-/post-surgical seizure prediction, and assessing cognitive performance. For localization, graph theory measures of centrality have shown the most potential, including betweenness centrality, outdegree, and graph index complexity, whereas for prediction of seizure frequency, measures of synchronizability have shown the most potential. The utility of clustering coefficient and characteristic path length for assessing cognitive performance in TLE is also discussed. Conclusions Future studies integrating data from multiple modalities and testing predictive models are needed to clarify findings and develop graph theory for its clinical utility. PMID:25127370

Applications of graph theory in protein structure identification

PubMed Central

2011-01-01

There is a growing interest in the identification of proteins on the proteome wide scale. Among different kinds of protein structure identification methods, graph-theoretic methods are very sharp ones. Due to their lower costs, higher effectiveness and many other advantages, they have drawn more and more researchers’ attention nowadays. Specifically, graph-theoretic methods have been widely used in homology identification, side-chain cluster identification, peptide sequencing and so on. This paper reviews several methods in solving protein structure identification problems using graph theory. We mainly introduce classical methods and mathematical models including homology modeling based on clique finding, identification of side-chain clusters in protein structures upon graph spectrum, and de novo peptide sequencing via tandem mass spectrometry using the spectrum graph model. In addition, concluding remarks and future priorities of each method are given. PMID:22165974

Revealing Long-Range Interconnected Hubs in Human Chromatin Interaction Data Using Graph Theory

NASA Astrophysics Data System (ADS)

Boulos, R. E.; Arneodo, A.; Jensen, P.; Audit, B.

2013-09-01

We use graph theory to analyze chromatin interaction (Hi-C) data in the human genome. We show that a key functional feature of the genome—“master” replication origins—corresponds to DNA loci of maximal network centrality. These loci form a set of interconnected hubs both within chromosomes and between different chromosomes. Our results open the way to a fruitful use of graph theory concepts to decipher DNA structural organization in relation to genome functions such as replication and transcription. This quantitative information should prove useful to discriminate between possible polymer models of nuclear organization.

NEFI: Network Extraction From Images

PubMed Central

Dirnberger, M.; Kehl, T.; Neumann, A.

2015-01-01

Networks are amongst the central building blocks of many systems. Given a graph of a network, methods from graph theory enable a precise investigation of its properties. Software for the analysis of graphs is widely available and has been applied to study various types of networks. In some applications, graph acquisition is relatively simple. However, for many networks data collection relies on images where graph extraction requires domain-specific solutions. Here we introduce NEFI, a tool that extracts graphs from images of networks originating in various domains. Regarding previous work on graph extraction, theoretical results are fully accessible only to an expert audience and ready-to-use implementations for non-experts are rarely available or insufficiently documented. NEFI provides a novel platform allowing practitioners to easily extract graphs from images by combining basic tools from image processing, computer vision and graph theory. Thus, NEFI constitutes an alternative to tedious manual graph extraction and special purpose tools. We anticipate NEFI to enable time-efficient collection of large datasets. The analysis of these novel datasets may open up the possibility to gain new insights into the structure and function of various networks. NEFI is open source and available at http://nefi.mpi-inf.mpg.de. PMID:26521675

A Note on Hamiltonian Graphs

ERIC Educational Resources Information Center

Skurnick, Ronald; Davi, Charles; Skurnick, Mia

2005-01-01

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

Creating single-subject design graphs in Microsoft Excel 2007.

PubMed

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

2009-01-01

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

CREATING SINGLE-SUBJECT DESIGN GRAPHS IN MICROSOFT EXCELTM 2007

PubMed Central

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

2009-01-01

Over 10 years have passed since the publication of Carr and Burkholder's (1998) technical article on how to construct single-subject graphs using Microsoft Excel. Over the course of the past decade, the Excel program has undergone a series of revisions that make the Carr and Burkholder paper somewhat difficult to follow with newer versions. The present article provides task analyses for constructing various types of commonly used single-subject design graphs in Microsoft Excel 2007. The task analyses were evaluated using a between-subjects design that compared the graphing skills of 22 behavior-analytic graduate students using Excel 2007 and either the Carr and Burkholder or newly developed task analyses. Results indicate that the new task analyses yielded more accurate and faster graph construction than the Carr and Burkholder instructions. PMID:19949515

Faster Parameterized Algorithms for Minor Containment

NASA Astrophysics Data System (ADS)

Adler, Isolde; Dorn, Frederic; Fomin, Fedor V.; Sau, Ignasi; Thilikos, Dimitrios M.

The theory of Graph Minors by Robertson and Seymour is one of the deepest and significant theories in modern Combinatorics. This theory has also a strong impact on the recent development of Algorithms, and several areas, like Parameterized Complexity, have roots in Graph Minors. Until very recently it was a common belief that Graph Minors Theory is mainly of theoretical importance. However, it appears that many deep results from Robertson and Seymour's theory can be also used in the design of practical algorithms. Minor containment testing is one of algorithmically most important and technical parts of the theory, and minor containment in graphs of bounded branchwidth is a basic ingredient of this algorithm. In order to implement minor containment testing on graphs of bounded branchwidth, Hicks [NETWORKS 04] described an algorithm, that in time O(3^{k^2}\\cdot (h+k-1)!\\cdot m) decides if a graph G with m edges and branchwidth k, contains a fixed graph H on h vertices as a minor. That algorithm follows the ideas introduced by Robertson and Seymour in [J'CTSB 95]. In this work we improve the dependence on k of Hicks' result by showing that checking if H is a minor of G can be done in time O(2^{(2k +1 )\\cdot log k} \\cdot h^{2k} \\cdot 2^{2h^2} \\cdot m). Our approach is based on a combinatorial object called rooted packing, which captures the properties of the potential models of subgraphs of H that we seek in our dynamic programming algorithm. This formulation with rooted packings allows us to speed up the algorithm when G is embedded in a fixed surface, obtaining the first single-exponential algorithm for minor containment testing. Namely, it runs in time 2^{O(k)} \\cdot h^{2k} \\cdot 2^{O(h)} \\cdot n, with n = |V(G)|. Finally, we show that slight modifications of our algorithm permit to solve some related problems within the same time bounds, like induced minor or contraction minor containment.

Rapid geodesic mapping of brain functional connectivity: implementation of a dedicated co-processor in a field-programmable gate array (FPGA) and application to resting state functional MRI.

PubMed

Minati, Ludovico; Cercignani, Mara; Chan, Dennis

2013-10-01

Graph theory-based analyses of brain network topology can be used to model the spatiotemporal correlations in neural activity detected through fMRI, and such approaches have wide-ranging potential, from detection of alterations in preclinical Alzheimer's disease through to command identification in brain-machine interfaces. However, due to prohibitive computational costs, graph-based analyses to date have principally focused on measuring connection density rather than mapping the topological architecture in full by exhaustive shortest-path determination. This paper outlines a solution to this problem through parallel implementation of Dijkstra's algorithm in programmable logic. The processor design is optimized for large, sparse graphs and provided in full as synthesizable VHDL code. An acceleration factor between 15 and 18 is obtained on a representative resting-state fMRI dataset, and maps of Euclidean path length reveal the anticipated heterogeneous cortical involvement in long-range integrative processing. These results enable high-resolution geodesic connectivity mapping for resting-state fMRI in patient populations and real-time geodesic mapping to support identification of imagined actions for fMRI-based brain-machine interfaces. Copyright © 2013 IPEM. Published by Elsevier Ltd. All rights reserved.

Radiation Induced Chromatin Conformation Changes Analysed by Fluorescent Localization Microscopy, Statistical Physics, and Graph Theory

PubMed Central

Müller, Patrick; Hillebrandt, Sabina; Krufczik, Matthias; Bach, Margund; Kaufmann, Rainer; Hausmann, Michael; Heermann, Dieter W.

2015-01-01

It has been well established that the architecture of chromatin in cell nuclei is not random but functionally correlated. Chromatin damage caused by ionizing radiation raises complex repair machineries. This is accompanied by local chromatin rearrangements and structural changes which may for instance improve the accessibility of damaged sites for repair protein complexes. Using stably transfected HeLa cells expressing either green fluorescent protein (GFP) labelled histone H2B or yellow fluorescent protein (YFP) labelled histone H2A, we investigated the positioning of individual histone proteins in cell nuclei by means of high resolution localization microscopy (Spectral Position Determination Microscopy = SPDM). The cells were exposed to ionizing radiation of different doses and aliquots were fixed after different repair times for SPDM imaging. In addition to the repair dependent histone protein pattern, the positioning of antibodies specific for heterochromatin and euchromatin was separately recorded by SPDM. The present paper aims to provide a quantitative description of structural changes of chromatin after irradiation and during repair. It introduces a novel approach to analyse SPDM images by means of statistical physics and graph theory. The method is based on the calculation of the radial distribution functions as well as edge length distributions for graphs defined by a triangulation of the marker positions. The obtained results show that through the cell nucleus the different chromatin re-arrangements as detected by the fluorescent nucleosomal pattern average themselves. In contrast heterochromatic regions alone indicate a relaxation after radiation exposure and re-condensation during repair whereas euchromatin seemed to be unaffected or behave contrarily. SPDM in combination with the analysis techniques applied allows the systematic elucidation of chromatin re-arrangements after irradiation and during repair, if selected sub-regions of nuclei are investigated. PMID:26042422

Radiation induced chromatin conformation changes analysed by fluorescent localization microscopy, statistical physics, and graph theory.

PubMed

Zhang, Yang; Máté, Gabriell; Müller, Patrick; Hillebrandt, Sabina; Krufczik, Matthias; Bach, Margund; Kaufmann, Rainer; Hausmann, Michael; Heermann, Dieter W

2015-01-01

It has been well established that the architecture of chromatin in cell nuclei is not random but functionally correlated. Chromatin damage caused by ionizing radiation raises complex repair machineries. This is accompanied by local chromatin rearrangements and structural changes which may for instance improve the accessibility of damaged sites for repair protein complexes. Using stably transfected HeLa cells expressing either green fluorescent protein (GFP) labelled histone H2B or yellow fluorescent protein (YFP) labelled histone H2A, we investigated the positioning of individual histone proteins in cell nuclei by means of high resolution localization microscopy (Spectral Position Determination Microscopy = SPDM). The cells were exposed to ionizing radiation of different doses and aliquots were fixed after different repair times for SPDM imaging. In addition to the repair dependent histone protein pattern, the positioning of antibodies specific for heterochromatin and euchromatin was separately recorded by SPDM. The present paper aims to provide a quantitative description of structural changes of chromatin after irradiation and during repair. It introduces a novel approach to analyse SPDM images by means of statistical physics and graph theory. The method is based on the calculation of the radial distribution functions as well as edge length distributions for graphs defined by a triangulation of the marker positions. The obtained results show that through the cell nucleus the different chromatin re-arrangements as detected by the fluorescent nucleosomal pattern average themselves. In contrast heterochromatic regions alone indicate a relaxation after radiation exposure and re-condensation during repair whereas euchromatin seemed to be unaffected or behave contrarily. SPDM in combination with the analysis techniques applied allows the systematic elucidation of chromatin re-arrangements after irradiation and during repair, if selected sub-regions of nuclei are investigated.

Magic bases, metric ansaetze and generalized graph theories in the Virasoro master equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Halpern, M.B.; Obers, N.A.

1991-11-15

The authors define a class of magic Lie group bases in which the Virasoro master equation admits a class of simple metric ansaetze (g{sub metric}), whose structure is visible in the high-level expansion. When a magic basis is real on compact g, the corresponding g{sub metric} is a large system of unitary, generically irrational conformal field theories. Examples in this class include the graph-theory ansatz SO(n){sub diag} in the Cartesian basis of So(n) and the ansatz SU(n){sub metric} in the Pauli-like basis of SU(n). A new phenomenon is observed in the high-level comparison of SU(n){sub metric}: Due to the trigonometricmore » structure constants of the Pauli-like basis, irrational central charge is clearly visible at finite order of the expansion. They also define the sine-area graphs of SU(n), which label the conformal field theories of SU(n){sub metric} and note that, in a similar fashion, each magic basis of g defines a generalize graph theory on g which labels the conformal field theories of g{sub metric}.« less

Introduction and Terminology 2-Extendability in 3-Polytopes.

DTIC Science & Technology

1985-01-01

and D.A. Holton, On defect-d matchings in graphs, Discrete Math ., 13, 1975, 41-54. [LGH2] (-), Erratum: "On defect-d matchings, Discrete Mlath., 14...Matching Theory, Vol. 29, knn. Discrete Math ., North- Holland, Amsterdam, 1986. [Plell J. Plesnik, Connectivity of regular graphs and the existence of 1...Plu2] -- ), A theorem on mnatchings in the plane, Graph Theo~ry in Memory of G..4. Dirac, Ann. Discrete Math ., North-Holland. Amisterdarni. to appear

Tutte polynomial in functional magnetic resonance imaging

NASA Astrophysics Data System (ADS)

García-Castillón, Marlly V.

2015-09-01

Methods of graph theory are applied to the processing of functional magnetic resonance images. Specifically the Tutte polynomial is used to analyze such kind of images. Functional Magnetic Resonance Imaging provide us connectivity networks in the brain which are represented by graphs and the Tutte polynomial will be applied. The problem of computing the Tutte polynomial for a given graph is #P-hard even for planar graphs. For a practical application the maple packages "GraphTheory" and "SpecialGraphs" will be used. We will consider certain diagram which is depicting functional connectivity, specifically between frontal and posterior areas, in autism during an inferential text comprehension task. The Tutte polynomial for the resulting neural networks will be computed and some numerical invariants for such network will be obtained. Our results show that the Tutte polynomial is a powerful tool to analyze and characterize the networks obtained from functional magnetic resonance imaging.

Differentials on graph complexes II: hairy graphs

NASA Astrophysics Data System (ADS)

Khoroshkin, Anton; Willwacher, Thomas; Živković, Marko

2017-10-01

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

A Single Session of rTMS Enhances Small-Worldness in Writer's Cramp: Evidence from Simultaneous EEG-fMRI Multi-Modal Brain Graph.

PubMed

Bharath, Rose D; Panda, Rajanikant; Reddam, Venkateswara Reddy; Bhaskar, M V; Gohel, Suril; Bhardwaj, Sujas; Prajapati, Arvind; Pal, Pramod Kumar

2017-01-01

Background and Purpose : Repetitive transcranial magnetic stimulation (rTMS) induces widespread changes in brain connectivity. As the network topology differences induced by a single session of rTMS are less known we undertook this study to ascertain whether the network alterations had a small-world morphology using multi-modal graph theory analysis of simultaneous EEG-fMRI. Method : Simultaneous EEG-fMRI was acquired in duplicate before (R1) and after (R2) a single session of rTMS in 14 patients with Writer's Cramp (WC). Whole brain neuronal and hemodynamic network connectivity were explored using the graph theory measures and clustering coefficient, path length and small-world index were calculated for EEG and resting state fMRI (rsfMRI). Multi-modal graph theory analysis was used to evaluate the correlation of EEG and fMRI clustering coefficients. Result : A single session of rTMS was found to increase the clustering coefficient and small-worldness significantly in both EEG and fMRI ( p < 0.05). Multi-modal graph theory analysis revealed significant modulations in the fronto-parietal regions immediately after rTMS. The rsfMRI revealed additional modulations in several deep brain regions including cerebellum, insula and medial frontal lobe. Conclusion : Multi-modal graph theory analysis of simultaneous EEG-fMRI can supplement motor physiology methods in understanding the neurobiology of rTMS in vivo . Coinciding evidence from EEG and rsfMRI reports small-world morphology for the acute phase network hyper-connectivity indicating changes ensuing low-frequency rTMS is probably not "noise".

K-theory of locally finite graph C∗-algebras

NASA Astrophysics Data System (ADS)

Iyudu, Natalia

2013-09-01

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

Exclusivity structures and graph representatives of local complementation orbits

NASA Astrophysics Data System (ADS)

Cabello, Adán; Parker, Matthew G.; Scarpa, Giannicola; Severini, Simone

2013-07-01

We describe a construction that maps any connected graph G on three or more vertices into a larger graph, H(G), whose independence number is strictly smaller than its Lovász number which is equal to its fractional packing number. The vertices of H(G) represent all possible events consistent with the stabilizer group of the graph state associated with G, and exclusive events are adjacent. Mathematically, the graph H(G) corresponds to the orbit of G under local complementation. Physically, the construction translates into graph-theoretic terms the connection between a graph state and a Bell inequality maximally violated by quantum mechanics. In the context of zero-error information theory, the construction suggests a protocol achieving the maximum rate of entanglement-assisted capacity, a quantum mechanical analogue of the Shannon capacity, for each H(G). The violation of the Bell inequality is expressed by the one-shot version of this capacity being strictly larger than the independence number. Finally, given the correspondence between graphs and exclusivity structures, we are able to compute the independence number for certain infinite families of graphs with the use of quantum non-locality, therefore highlighting an application of quantum theory in the proof of a purely combinatorial statement.

Spectral statistics of random geometric graphs

NASA Astrophysics Data System (ADS)

Dettmann, C. P.; Georgiou, O.; Knight, G.

2017-04-01

We use random matrix theory to study the spectrum of random geometric graphs, a fundamental model of spatial networks. Considering ensembles of random geometric graphs we look at short-range correlations in the level spacings of the spectrum via the nearest-neighbour and next-nearest-neighbour spacing distribution and long-range correlations via the spectral rigidity Δ3 statistic. These correlations in the level spacings give information about localisation of eigenvectors, level of community structure and the level of randomness within the networks. We find a parameter-dependent transition between Poisson and Gaussian orthogonal ensemble statistics. That is the spectral statistics of spatial random geometric graphs fits the universality of random matrix theory found in other models such as Erdős-Rényi, Barabási-Albert and Watts-Strogatz random graphs.

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

PubMed

Peña, Jorge; Rochat, Yannick

2012-01-01

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

Horizontal visibility graphs generated by type-I intermittency

NASA Astrophysics Data System (ADS)

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

2013-05-01

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

Scattering theory for graphs isomorphic to a regular tree at infinity

NASA Astrophysics Data System (ADS)

Colin de Verdière, Yves; Truc, Françoise

2013-06-01

We describe the spectral theory of the adjacency operator of a graph which is isomorphic to a regular tree at infinity. Using some combinatorics, we reduce the problem to a scattering problem for a finite rank perturbation of the adjacency operator on a regular tree. We develop this scattering theory using the classical recipes for Schrödinger operators in Euclidian spaces.

Spectral fluctuations of quantum graphs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pluhař, Z.; Weidenmüller, H. A.

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

2-Extendability in Two Classes of Claw-Free Graphs

DTIC Science & Technology

1992-01-01

extendability of planar graphs, Discrete Math ., 96, 1991, 81-99. [Lai M. Las Verguas, A note on matchings in graphs, Colloque sur la Thiorie des Graphes...43, 1987, 187-222. [LP L. Loviss and M.D. Plummet, Matching Theory, Ann. Discrete Math . 29, North-Holland, Amsterdam, 1986. [P11 M.D. Plummer, On n...extendable graphs, Discrete Math . 31, 1960, 201-210. [P21 Extending matchinp in planar graphs IV, Proc. of the Conference in honor of Cert Sabidussi, Ann

Reducing Abstraction When Learning Graph Theory

ERIC Educational Resources Information Center

Hazzan, Orit; Hadar, Irit

2005-01-01

This article presents research on students' understanding of basic concepts in Graph Theory. Students' understanding is analyzed through the lens of the theoretical framework of reducing abstraction (Hazzan, 1999). As it turns out, in spite of the relative simplicity of the concepts that are introduced in the introductory part of a traditional…

Algebraic Topology of Multi-Brain Connectivity Networks Reveals Dissimilarity in Functional Patterns during Spoken Communications

PubMed Central

Tadić, Bosiljka; Andjelković, Miroslav; Boshkoska, Biljana Mileva; Levnajić, Zoran

2016-01-01

Human behaviour in various circumstances mirrors the corresponding brain connectivity patterns, which are suitably represented by functional brain networks. While the objective analysis of these networks by graph theory tools deepened our understanding of brain functions, the multi-brain structures and connections underlying human social behaviour remain largely unexplored. In this study, we analyse the aggregate graph that maps coordination of EEG signals previously recorded during spoken communications in two groups of six listeners and two speakers. Applying an innovative approach based on the algebraic topology of graphs, we analyse higher-order topological complexes consisting of mutually interwoven cliques of a high order to which the identified functional connections organise. Our results reveal that the topological quantifiers provide new suitable measures for differences in the brain activity patterns and inter-brain synchronisation between speakers and listeners. Moreover, the higher topological complexity correlates with the listener’s concentration to the story, confirmed by self-rating, and closeness to the speaker’s brain activity pattern, which is measured by network-to-network distance. The connectivity structures of the frontal and parietal lobe consistently constitute distinct clusters, which extend across the listener’s group. Formally, the topology quantifiers of the multi-brain communities exceed the sum of those of the participating individuals and also reflect the listener’s rated attributes of the speaker and the narrated subject. In the broader context, the presented study exposes the relevance of higher topological structures (besides standard graph measures) for characterising functional brain networks under different stimuli. PMID:27880802

Survey on Ontology Mapping

NASA Astrophysics Data System (ADS)

Zhu, Junwu

To create a sharable semantic space in which the terms from different domain ontology or knowledge system, Ontology mapping become a hot research point in Semantic Web Community. In this paper, motivated factors of ontology mapping research are given firstly, and then 5 dominating theories and methods, such as information accessing technology, machine learning, linguistics, structure graph and similarity, are illustrated according their technology class. Before we analyses the new requirements and takes a long view, the contributions of these theories and methods are summarized in details. At last, this paper suggest to design a group of semantic connector with the ability of migration learning for OWL-2 extended with constrains and the ontology mapping theory of axiom, so as to provide a new methodology for ontology mapping.

Assessing cortical synchronization during transcranial direct current stimulation: A graph-theoretical analysis.

PubMed

Mancini, Matteo; Brignani, Debora; Conforto, Silvia; Mauri, Piercarlo; Miniussi, Carlo; Pellicciari, Maria Concetta

2016-10-15

Transcranial direct current stimulation (tDCS) is a neuromodulation technique that can alter cortical excitability and modulate behaviour in a polarity-dependent way. Despite the widespread use of this method in the neuroscience field, its effects on ongoing local or global (network level) neuronal activity are still not foreseeable. A way to shed light on the neuronal mechanisms underlying the cortical connectivity changes induced by tDCS is provided by the combination of tDCS with electroencephalography (EEG). In this study, twelve healthy subjects underwent online tDCS-EEG recording (i.e., simultaneous), during resting-state, using 19 EEG channels. The protocol involved anodal, cathodal and sham stimulation conditions, with the active and the reference electrodes in the left frontocentral area (FC3) and on the forehead over the right eyebrow, respectively. The data were processed using a network model, based on graph theory and the synchronization likelihood. The resulting graphs were analysed for four frequency bands (theta, alpha, beta and gamma) to evaluate the presence of tDCS-induced differences in synchronization patterns and graph theory measures. The resting state network connectivity resulted altered during tDCS, in a polarity-specific manner for theta and alpha bands. Anodal tDCS weakened synchronization with respect to the baseline over the fronto-central areas in the left hemisphere, for theta band (p<0.05). In contrast, during cathodal tDCS a significant increase in inter-hemispheric synchronization connectivity was observed over the centro-parietal, centro-occipital and parieto-occipital areas for the alpha band (p<0.05). Local graph measures showed a tDCS-induced polarity-specific differences that regarded modifications of network activities rather than specific region properties. Our results show that applying tDCS during the resting state modulates local synchronization as well as network properties in slow frequency bands, in a polarity-specific manner. Copyright © 2016 Elsevier Inc. All rights reserved.

Generalized graphs and unitary irrational central charge in the superconformal master equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Halpern, M.B.; Obers, N.A.

1991-12-01

For each magic basis of Lie {ital g}, it is known that the Virasoro master equation on affine {ital g} contains a generalized graph theory of conformal level-families. In this paper, it is found that the superconformal master equation on affine {ital g}{times}SO(dim {ital g}) similarly contains a generalized graph theory of superconformal level-families for each magic basis of {ital g}. The superconformal level-families satisfy linear equations on the generalized graphs, and the first exact unitary irrational solutions of the superconformal master equation are obtained on the sine-area graphs of {ital g}=SU({ital n}), including the simplest unitary irrational central chargesmore » {ital c}=6{ital nx}/({ital nx}+8 sin{sup 2}(rs{pi}/n)) yet observed in the program.« less

Mapping the functional connectome in traumatic brain injury: What can graph metrics tell us?

PubMed

Caeyenberghs, Karen; Verhelst, Helena; Clemente, Adam; Wilson, Peter H

2017-10-15

Traumatic brain injury (TBI) is associated with cognitive and motor deficits, and poses a significant personal, societal, and economic burden. One mechanism by which TBI is thought to affect cognition and behavior is through changes in functional connectivity. Graph theory is a powerful framework for quantifying topological features of neuroimaging-derived functional networks. The objective of this paper is to review studies examining functional connectivity in TBI with an emphasis on graph theoretical analysis that is proving to be valuable in uncovering network abnormalities in this condition. We review studies that have examined TBI-related alterations in different properties of the functional brain network, including global integration, segregation, centrality and resilience. We focus on functional data using task-related fMRI or resting-state fMRI in patients with TBI of different severity and recovery phase, and consider how graph metrics may inform rehabilitation and enhance efficacy. Moreover, we outline some methodological challenges associated with the examination of functional connectivity in patients with brain injury, including the sample size, parcellation scheme used, node definition and subgroup analyses. The findings suggest that TBI is associated with hyperconnectivity and a suboptimal global integration, characterized by increased connectivity degree and strength and reduced efficiency of functional networks. This altered functional connectivity, also evident in other clinical populations, is attributable to diffuse white matter pathology and reductions in gray and white matter volume. These functional alterations are implicated in post-concussional symptoms, posttraumatic stress and neurocognitive dysfunction after TBI. Finally, the effects of focal lesions have been found to depend critically on topological position and their role in the network. Graph theory is a unique and powerful tool for exploring functional connectivity in brain-injured patients. One limitation is that its results do not provide specific measures about the biophysical mechanism underlying TBI. Continued work in this field will hopefully see graph metrics used as biomarkers to provide more accurate diagnosis and help guide treatment at the individual patient level. Copyright © 2016. Published by Elsevier Inc.

A manifold learning approach to target detection in high-resolution hyperspectral imagery

NASA Astrophysics Data System (ADS)

Ziemann, Amanda K.

Imagery collected from airborne platforms and satellites provide an important medium for remotely analyzing the content in a scene. In particular, the ability to detect a specific material within a scene is of high importance to both civilian and defense applications. This may include identifying "targets" such as vehicles, buildings, or boats. Sensors that process hyperspectral images provide the high-dimensional spectral information necessary to perform such analyses. However, for a d-dimensional hyperspectral image, it is typical for the data to inherently occupy an m-dimensional space, with m << d. In the remote sensing community, this has led to a recent increase in the use of manifold learning, which aims to characterize the embedded lower-dimensional, non-linear manifold upon which the hyperspectral data inherently lie. Classic hyperspectral data models include statistical, linear subspace, and linear mixture models, but these can place restrictive assumptions on the distribution of the data; this is particularly true when implementing traditional target detection approaches, and the limitations of these models are well-documented. With manifold learning based approaches, the only assumption is that the data reside on an underlying manifold that can be discretely modeled by a graph. The research presented here focuses on the use of graph theory and manifold learning in hyperspectral imagery. Early work explored various graph-building techniques with application to the background model of the Topological Anomaly Detection (TAD) algorithm, which is a graph theory based approach to anomaly detection. This led towards a focus on target detection, and in the development of a specific graph-based model of the data and subsequent dimensionality reduction using manifold learning. An adaptive graph is built on the data, and then used to implement an adaptive version of locally linear embedding (LLE). We artificially induce a target manifold and incorporate it into the adaptive LLE transformation; the artificial target manifold helps to guide the separation of the target data from the background data in the new, lower-dimensional manifold coordinates. Then, target detection is performed in the manifold space.

Support Vector Machine Classification of Major Depressive Disorder Using Diffusion-Weighted Neuroimaging and Graph Theory

PubMed Central

Sacchet, Matthew D.; Prasad, Gautam; Foland-Ross, Lara C.; Thompson, Paul M.; Gotlib, Ian H.

2015-01-01

Recently, there has been considerable interest in understanding brain networks in major depressive disorder (MDD). Neural pathways can be tracked in the living brain using diffusion-weighted imaging (DWI); graph theory can then be used to study properties of the resulting fiber networks. To date, global abnormalities have not been reported in tractography-based graph metrics in MDD, so we used a machine learning approach based on “support vector machines” to differentiate depressed from healthy individuals based on multiple brain network properties. We also assessed how important specific graph metrics were for this differentiation. Finally, we conducted a local graph analysis to identify abnormal connectivity at specific nodes of the network. We were able to classify depression using whole-brain graph metrics. Small-worldness was the most useful graph metric for classification. The right pars orbitalis, right inferior parietal cortex, and left rostral anterior cingulate all showed abnormal network connectivity in MDD. This is the first use of structural global graph metrics to classify depressed individuals. These findings highlight the importance of future research to understand network properties in depression across imaging modalities, improve classification results, and relate network alterations to psychiatric symptoms, medication, and comorbidities. PMID:25762941

Support vector machine classification of major depressive disorder using diffusion-weighted neuroimaging and graph theory.

PubMed

Sacchet, Matthew D; Prasad, Gautam; Foland-Ross, Lara C; Thompson, Paul M; Gotlib, Ian H

2015-01-01

Recently, there has been considerable interest in understanding brain networks in major depressive disorder (MDD). Neural pathways can be tracked in the living brain using diffusion-weighted imaging (DWI); graph theory can then be used to study properties of the resulting fiber networks. To date, global abnormalities have not been reported in tractography-based graph metrics in MDD, so we used a machine learning approach based on "support vector machines" to differentiate depressed from healthy individuals based on multiple brain network properties. We also assessed how important specific graph metrics were for this differentiation. Finally, we conducted a local graph analysis to identify abnormal connectivity at specific nodes of the network. We were able to classify depression using whole-brain graph metrics. Small-worldness was the most useful graph metric for classification. The right pars orbitalis, right inferior parietal cortex, and left rostral anterior cingulate all showed abnormal network connectivity in MDD. This is the first use of structural global graph metrics to classify depressed individuals. These findings highlight the importance of future research to understand network properties in depression across imaging modalities, improve classification results, and relate network alterations to psychiatric symptoms, medication, and comorbidities.

Assessing the impact of background spectral graph construction techniques on the topological anomaly detection algorithm

NASA Astrophysics Data System (ADS)

Ziemann, Amanda K.; Messinger, David W.; Albano, James A.; Basener, William F.

2012-06-01

Anomaly detection algorithms have historically been applied to hyperspectral imagery in order to identify pixels whose material content is incongruous with the background material in the scene. Typically, the application involves extracting man-made objects from natural and agricultural surroundings. A large challenge in designing these algorithms is determining which pixels initially constitute the background material within an image. The topological anomaly detection (TAD) algorithm constructs a graph theory-based, fully non-parametric topological model of the background in the image scene, and uses codensity to measure deviation from this background. In TAD, the initial graph theory structure of the image data is created by connecting an edge between any two pixel vertices x and y if the Euclidean distance between them is less than some resolution r. While this type of proximity graph is among the most well-known approaches to building a geometric graph based on a given set of data, there is a wide variety of dierent geometrically-based techniques. In this paper, we present a comparative test of the performance of TAD across four dierent constructs of the initial graph: mutual k-nearest neighbor graph, sigma-local graph for two different values of σ > 1, and the proximity graph originally implemented in TAD.

Extracting Undimensional Chains from Multidimensional Datasets: A Graph Theory Approach.

ERIC Educational Resources Information Center

Yamomoto, Yoneo; Wise, Steven L.

An order-analysis procedure, which uses graph theory to extract efficiently nonredundant, unidimensional chains of items from multidimensional data sets and chain consistency as a criterion for chain membership is outlined in this paper. The procedure is intended as an alternative to the Reynolds (1976) procedure which is described as being…

Untangling Word Webs: Graph Theory and the Notion of Density in Second Language Word Association Networks.

ERIC Educational Resources Information Center

Wilks, Clarissa; Meara, Paul

2002-01-01

Examines the implications of the metaphor of the vocabulary network. Takes a formal approach to the exploration of this metaphor by applying the principles of graph theory to word association data to compare the relative densities of the first language and second language lexical networks. (Author/VWL)

Thinking Graphically: Connecting Vision and Cognition during Graph Comprehension

ERIC Educational Resources Information Center

Ratwani, Raj M.; Trafton, J. Gregory; Boehm-Davis, Deborah A.

2008-01-01

Task analytic theories of graph comprehension account for the perceptual and conceptual processes required to extract specific information from graphs. Comparatively, the processes underlying information integration have received less attention. We propose a new framework for information integration that highlights visual integration and cognitive…

Thinking graphically: Connecting vision and cognition during graph comprehension.

PubMed

Ratwani, Raj M; Trafton, J Gregory; Boehm-Davis, Deborah A

2008-03-01

Task analytic theories of graph comprehension account for the perceptual and conceptual processes required to extract specific information from graphs. Comparatively, the processes underlying information integration have received less attention. We propose a new framework for information integration that highlights visual integration and cognitive integration. During visual integration, pattern recognition processes are used to form visual clusters of information; these visual clusters are then used to reason about the graph during cognitive integration. In 3 experiments, the processes required to extract specific information and to integrate information were examined by collecting verbal protocol and eye movement data. Results supported the task analytic theories for specific information extraction and the processes of visual and cognitive integration for integrative questions. Further, the integrative processes scaled up as graph complexity increased, highlighting the importance of these processes for integration in more complex graphs. Finally, based on this framework, design principles to improve both visual and cognitive integration are described. PsycINFO Database Record (c) 2008 APA, all rights reserved

Claw-Free Maximal Planar Graphs

DTIC Science & Technology

1989-01-01

1976, 212-223. 110] M.D. Plummer, On n-extendable graphs, Discrete Math . 31, 1980, 201-210. 1111 , A theorem on matchings in the plane, Graph Theory...in Memory of G.A. Dirac, Ann. Discrete Math . 41, North-Holland, Amsterdam, 1989, 347-354. 1121 N. Sbihi, Algorithme de recherche d’un stable de...cardinalitA maximum dans un graphe sans 6toile, Discrete Math . 29, 1980, 53-76. 1131 D. Sumner, On Tutte’s factorization theorem, Graphs and Combinatorics

Proving relations between modular graph functions

NASA Astrophysics Data System (ADS)

Basu, Anirban

2016-12-01

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

Mild traumatic brain injury: graph-model characterization of brain networks for episodic memory.

PubMed

Tsirka, Vasso; Simos, Panagiotis G; Vakis, Antonios; Kanatsouli, Kassiani; Vourkas, Michael; Erimaki, Sofia; Pachou, Ellie; Stam, Cornelis Jan; Micheloyannis, Sifis

2011-02-01

Episodic memory is among the cognitive functions that can be affected in the acute phase following mild traumatic brain injury (MTBI). The present study used EEG recordings to evaluate global synchronization and network organization of rhythmic activity during the encoding and recognition phases of an episodic memory task varying in stimulus type (kaleidoscope images, pictures, words, and pseudowords). Synchronization of oscillatory activity was assessed using a linear and nonlinear connectivity estimator and network analyses were performed using algorithms derived from graph theory. Twenty five MTBI patients (tested within days post-injury) and healthy volunteers were closely matched on demographic variables, verbal ability, psychological status variables, as well as on overall task performance. Patients demonstrated sub-optimal network organization, as reflected by changes in graph parameters in the theta and alpha bands during both encoding and recognition. There were no group differences in spectral energy during task performance or on network parameters during a control condition (rest). Evidence of less optimally organized functional networks during memory tasks was more prominent for pictorial than for verbal stimuli. Copyright © 2010 Elsevier B.V. All rights reserved.

Stability and dynamical properties of material flow systems on random networks

NASA Astrophysics Data System (ADS)

Anand, K.; Galla, T.

2009-04-01

The theory of complex networks and of disordered systems is used to study the stability and dynamical properties of a simple model of material flow networks defined on random graphs. In particular we address instabilities that are characteristic of flow networks in economic, ecological and biological systems. Based on results from random matrix theory, we work out the phase diagram of such systems defined on extensively connected random graphs, and study in detail how the choice of control policies and the network structure affects stability. We also present results for more complex topologies of the underlying graph, focussing on finitely connected Erdös-Réyni graphs, Small-World Networks and Barabási-Albert scale-free networks. Results indicate that variability of input-output matrix elements, and random structures of the underlying graph tend to make the system less stable, while fast price dynamics or strong responsiveness to stock accumulation promote stability.

What Can Graph Theory Tell Us about Word Learning and Lexical Retrieval?

ERIC Educational Resources Information Center

Vitevitch, Michael S.

2008-01-01

Purpose: Graph theory and the new science of networks provide a mathematically rigorous approach to examine the development and organization of complex systems. These tools were applied to the mental lexicon to examine the organization of words in the lexicon and to explore how that structure might influence the acquisition and retrieval of…

Examining the Relationship between Comparative and Self-Focused Academic Data Visualizations in At-Risk College Students' Academic Motivation

ERIC Educational Resources Information Center

Aguilar, Stephen J.

2018-01-01

This qualitative study focuses on capturing students' understanding two visualizations often utilized by learning analytics-based educational technologies: bar graphs, and line graphs. It is framed by Achievement Goal Theory--a prominent theory of students' academic motivation--and utilizes interviews (n = 60) to investigate how students at risk…

On Edge Exchangeable Random Graphs

NASA Astrophysics Data System (ADS)

Janson, Svante

2017-06-01

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

Adjusting protein graphs based on graph entropy.

PubMed

Peng, Sheng-Lung; Tsay, Yu-Wei

2014-01-01

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

Adjusting protein graphs based on graph entropy

PubMed Central

2014-01-01

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

Chiral limit of N = 4 SYM and ABJM and integrable Feynman graphs

NASA Astrophysics Data System (ADS)

Caetano, João; Gürdoğan, Ömer; Kazakov, Vladimir

2018-03-01

We consider a special double scaling limit, recently introduced by two of the authors, combining weak coupling and large imaginary twist, for the γ-twisted N = 4 SYM theory. We also establish the analogous limit for ABJM theory. The resulting non-gauge chiral 4D and 3D theories of interacting scalars and fermions are integrable in the planar limit. In spite of the breakdown of conformality by double-trace interactions, most of the correlators for local operators of these theories are conformal, with non-trivial anomalous dimensions defined by specific, integrable Feynman diagrams. We discuss the details of this diagrammatics. We construct the doubly-scaled asymptotic Bethe ansatz (ABA) equations for multi-magnon states in these theories. Each entry of the mixing matrix of local conformal operators in the simplest of these theories — the bi-scalar model in 4D and tri-scalar model in 3D — is given by a single Feynman diagram at any given loop order. The related diagrams are in principle computable, up to a few scheme dependent constants, by integrability methods (quantum spectral curve or ABA). These constants should be fixed from direct computations of a few simplest graphs. This integrability-based method is advocated to be able to provide information about some high loop order graphs which are hardly computable by other known methods. We exemplify our approach with specific five-loop graphs.

Bipartite Graphs as Models of Population Structures in Evolutionary Multiplayer Games

PubMed Central

Peña, Jorge; Rochat, Yannick

2012-01-01

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

Bounds for percolation thresholds on directed and undirected graphs

NASA Astrophysics Data System (ADS)

Hamilton, Kathleen; Pryadko, Leonid

2015-03-01

Percolation theory is an efficient approach to problems with strong disorder, e.g., in quantum or classical transport, composite materials, and diluted magnets. Recently, the growing role of big data in scientific and industrial applications has led to a renewed interest in graph theory as a tool for describing complex connections in various kinds of networks: social, biological, technological, etc. In particular, percolation on graphs has been used to describe internet stability, spread of contagious diseases and computer viruses; related models describe market crashes and viral spread in social networks. We consider site-dependent percolation on directed and undirected graphs, and present several exact bounds for location of the percolation transition in terms of the eigenvalues of matrices associated with graphs, including the adjacency matrix and the Hashimoto matrix used to enumerate non-backtracking walks. These bounds correspond t0 a mean field approximation and become asymptotically exact for graphs with no short cycles. We illustrate this convergence numerically by simulating percolation on several families of graphs with different cycle lengths. This research was supported in part by the NSF Grant PHY-1416578 and by the ARO Grant W911NF-11-1-0027.

Phenotypic Graphs and Evolution Unfold the Standard Genetic Code as the Optimal

NASA Astrophysics Data System (ADS)

Zamudio, Gabriel S.; José, Marco V.

2018-03-01

In this work, we explicitly consider the evolution of the Standard Genetic Code (SGC) by assuming two evolutionary stages, to wit, the primeval RNY code and two intermediate codes in between. We used network theory and graph theory to measure the connectivity of each phenotypic graph. The connectivity values are compared to the values of the codes under different randomization scenarios. An error-correcting optimal code is one in which the algebraic connectivity is minimized. We show that the SGC is optimal in regard to its robustness and error-tolerance when compared to all random codes under different assumptions.

Identification of lethal reactions in the Esherichia coli metabolic network: Graph theory approach

NASA Astrophysics Data System (ADS)

Ghim, C.-M.; Goh, K.-I.; Kahng, B.; Kim, D.

2004-03-01

As a first step toward holistic modeling of cells, we analyze the biochemical reactions occurring in the genome-scale metabolism of Esherichia coli. To this end, we construct a directed bipartite graph by assigning metabolite or reaction to each node. We apply various measures of centrality, a well-known concept in the graph theory, and their modifications to the metabolic network, finding that there exist lethal reactions involved in the central metabolism. Such lethal reactions or associated enzymes under diverse environments in silico are identified and compared with earlier results obtained from flux balance analysis.

Promoting Graphical Thinking: Using Temperature and a Graphing Calculator to Teach Kinetics Concepts

ERIC Educational Resources Information Center

Cortes-Figueroa, Jose E.; Moore-Russo, Deborah A.

2004-01-01

A combination of graphical thinking with chemical and physical theories in the classroom is encouraged by using the Calculator-Based Laboratory System (CBL) with a temperature sensor and graphing calculator. The theory of first-order kinetics is logically explained with the aid of the cooling or heating of the metal bead of the CBL's temperature…

A Qualitative Analysis Framework Using Natural Language Processing and Graph Theory

ERIC Educational Resources Information Center

Tierney, Patrick J.

2012-01-01

This paper introduces a method of extending natural language-based processing of qualitative data analysis with the use of a very quantitative tool--graph theory. It is not an attempt to convert qualitative research to a positivist approach with a mathematical black box, nor is it a "graphical solution". Rather, it is a method to help qualitative…

Constructing Phylogenies.

ERIC Educational Resources Information Center

Bilardello, Nicholas; Valdes, Linda

1998-01-01

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

Young Children Communicate with Graphs

ERIC Educational Resources Information Center

Cathcart, W. George

1978-01-01

Graphing is an integrative skill because you can use it whether you are teaching measurement or geometry or number theory or most any other topic. It is also important as a mode of communication which can simplify a large amount of information. Here are five steps for effective presentation of graphing to young students. (Author/RK)

Application of Graph Theory to Cost-Effective Fire Protection of Chemical Plants During Domino Effects.

PubMed

Khakzad, Nima; Landucci, Gabriele; Reniers, Genserik

2017-09-01

In the present study, we have introduced a methodology based on graph theory and multicriteria decision analysis for cost-effective fire protection of chemical plants subject to fire-induced domino effects. By modeling domino effects in chemical plants as a directed graph, the graph centrality measures such as out-closeness and betweenness scores can be used to identify the installations playing a key role in initiating and propagating potential domino effects. It is demonstrated that active fire protection of installations with the highest out-closeness score and passive fire protection of installations with the highest betweenness score are the most effective strategies for reducing the vulnerability of chemical plants to fire-induced domino effects. We have employed a dynamic graph analysis to investigate the impact of both the availability and the degradation of fire protection measures over time on the vulnerability of chemical plants. The results obtained from the graph analysis can further be prioritized using multicriteria decision analysis techniques such as the method of reference point to find the most cost-effective fire protection strategy. © 2016 Society for Risk Analysis.

Graph theory applied to noise and vibration control in statistical energy analysis models.

PubMed

Guasch, Oriol; Cortés, Lluís

2009-06-01

A fundamental aspect of noise and vibration control in statistical energy analysis (SEA) models consists in first identifying and then reducing the energy flow paths between subsystems. In this work, it is proposed to make use of some results from graph theory to address both issues. On the one hand, linear and path algebras applied to adjacency matrices of SEA graphs are used to determine the existence of any order paths between subsystems, counting and labeling them, finding extremal paths, or determining the power flow contributions from groups of paths. On the other hand, a strategy is presented that makes use of graph cut algorithms to reduce the energy flow from a source subsystem to a receiver one, modifying as few internal and coupling loss factors as possible.

Some Recent Results on Graph Matching,

DTIC Science & Technology

1987-06-01

V. CHVATAL, Tough graphs and Hamiltonian circuits, Discrete Math . 5, 1973, 215-228. [El] J. EDMONDS, Paths, trees and flowers, Canad. J. Math. 17...Theory, Ann. Discrete Math . 29, North-Holland, Amsterdam, 1986. [N] D. NADDEF, Rank of maximum matchings in a graph, Math. Programming 22, 52-70. [NP...Optimization, Ann. Discrete Math . 16, North-Holland, Amsterdam, 1982, 241-260. [P1] M.D. PLUMMER, On n-extendable graphs, Discrete Math . 31, 1980, 201-210

Extending Matchings in Graphs: A Survey

DTIC Science & Technology

1990-01-01

private communication from, 1989. [11] D.A. Holton, D. Lou and M.D. Plummer, On the 2-extendability of planar graphs, Discrete Math ., (to appear). [12...222. [231 L. Lovasz and M.D. Plummer, Matching Theory, Ann. Discrete Math . 29, North- Holland, Amsterdam, 1986. [241 W.S. Massey, Algebraic Topology...Plummer, On n-extendable graphs, Discrete Math . 31, 1980, 201-210. [341 , Toughness and matching extension in graphs, Discrete Math . 72, 1988, 311-320

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Functional neural networks of honesty and dishonesty in children: Evidence from graph theory analysis.

PubMed

Ding, Xiao Pan; Wu, Si Jia; Liu, Jiangang; Fu, Genyue; Lee, Kang

2017-09-21

The present study examined how different brain regions interact with each other during spontaneous honest vs. dishonest communication. More specifically, we took a complex network approach based on the graph-theory to analyze neural response data when children are spontaneously engaged in honest or dishonest acts. Fifty-nine right-handed children between 7 and 12 years of age participated in the study. They lied or told the truth out of their own volition. We found that lying decreased both the global and local efficiencies of children's functional neural network. This finding, for the first time, suggests that lying disrupts the efficiency of children's cortical network functioning. Further, it suggests that the graph theory based network analysis is a viable approach to study the neural development of deception.

Brain Structure and Organization Five Decades After Childhood Onset Epilepsy

PubMed Central

Garcia-Ramos, Camille; Bobholz, Sam; Dabbs, Kevin; Hermann, Bruce; Joutsa, Juho; Rinne, Juha O.; Karrasch, Mira; Prabhakaran, Vivek; Shinnar, Shlomo; Sillanpää, Matti

2017-01-01

The purpose of this project was to characterize brain structure and organization in persons with active and remitted childhood onset epilepsy 50 years after diagnosis compared to healthy controls. Participants from a population-based investigation of uncomplicated childhood onset epilepsy were followed up 5 decades later. Forty-one participants had a history of childhood onset epilepsy (mean age of onset= 5.2 yrs, current chronological age= 56.0 yrs) and were compared to 48 population-based controls (mean age= 55.9 yrs). Of the epilepsy participants, 8 had persisting active epilepsy and in 33 the epilepsy had remitted. All participants underwent 3T MRI with subsequent vertex analysis of cortical volume, thickness, surface area and gyral complexity. In addition, cortical and subcortical volumes, including regions of the frontal, parietal, temporal, and occipital lobes, and subcortical structures including amygdala, thalamus, and hippocampus, were analyzed using graph theory techniques. There were modest group differences in traditional vertex-based analyses of cortical volume, thickness, surface area and gyral index, as well as across volumes of subcortical structures, after correction for multiple comparisons. Graph theory analyses revealed suboptimal topological structural organization with enhanced network segregation and reduced global integration in the epilepsy participants compared to controls, these patterns significantly more extreme in the active epilepsy group. Furthermore, both groups with epilepsy presented a greater number of higher Z-score regions in betweenness centrality (BC) than lower Z-score regions compared to controls. Also, contrary to the group with remitted epilepsy, patients with active epilepsy presented most of their high BC Z-score regions in subcortical areas including the amygdala, thalamus, hippocampus, pallidum and accumbens. Overall, this population-based investigation of long term outcome (5 decades) of childhood onset epilepsy reveals persisting abnormalities, especially when examined by graph theoretical measurements, and provides new insights into the very long term outcomes of active and remitted epilepsy. PMID:28370719

Altered small-world topology of structural brain networks in infants with intrauterine growth restriction and its association with later neurodevelopmental outcome.

PubMed

Batalle, Dafnis; Eixarch, Elisenda; Figueras, Francesc; Muñoz-Moreno, Emma; Bargallo, Nuria; Illa, Miriam; Acosta-Rojas, Ruthy; Amat-Roldan, Ivan; Gratacos, Eduard

2012-04-02

Intrauterine growth restriction (IUGR) due to placental insufficiency affects 5-10% of all pregnancies and it is associated with a wide range of short- and long-term neurodevelopmental disorders. Prediction of neurodevelopmental outcomes in IUGR is among the clinical challenges of modern fetal medicine and pediatrics. In recent years several studies have used magnetic resonance imaging (MRI) to demonstrate differences in brain structure in IUGR subjects, but the ability to use MRI for individual predictive purposes in IUGR is limited. Recent research suggests that MRI in vivo access to brain connectivity might have the potential to help understanding cognitive and neurodevelopment processes. Specifically, MRI based connectomics is an emerging approach to extract information from MRI data that exhaustively maps inter-regional connectivity within the brain to build a graph model of its neural circuitry known as brain network. In the present study we used diffusion MRI based connectomics to obtain structural brain networks of a prospective cohort of one year old infants (32 controls and 24 IUGR) and analyze the existence of quantifiable brain reorganization of white matter circuitry in IUGR group by means of global and regional graph theory features of brain networks. Based on global and regional analyses of the brain network topology we demonstrated brain reorganization in IUGR infants at one year of age. Specifically, IUGR infants presented decreased global and local weighted efficiency, and a pattern of altered regional graph theory features. By means of binomial logistic regression, we also demonstrated that connectivity measures were associated with abnormal performance in later neurodevelopmental outcome as measured by Bayley Scale for Infant and Toddler Development, Third edition (BSID-III) at two years of age. These findings show the potential of diffusion MRI based connectomics and graph theory based network characteristics for estimating differences in the architecture of neural circuitry and developing imaging biomarkers of poor neurodevelopment outcome in infants with prenatal diseases. Copyright © 2012 Elsevier Inc. All rights reserved.

Alterations in Anatomical Covariance in the Prematurely Born

PubMed Central

Scheinost, Dustin; Kwon, Soo Hyun; Lacadie, Cheryl; Vohr, Betty R.; Schneider, Karen C.; Papademetris, Xenophon; Constable, R. Todd; Ment, Laura R.

2017-01-01

Abstract Preterm (PT) birth results in long-term alterations in functional and structural connectivity, but the related changes in anatomical covariance are just beginning to be explored. To test the hypothesis that PT birth alters patterns of anatomical covariance, we investigated brain volumes of 25 PTs and 22 terms at young adulthood using magnetic resonance imaging. Using regional volumetrics, seed-based analyses, and whole brain graphs, we show that PT birth is associated with reduced volume in bilateral temporal and inferior frontal lobes, left caudate, left fusiform, and posterior cingulate for prematurely born subjects at young adulthood. Seed-based analyses demonstrate altered patterns of anatomical covariance for PTs compared with terms. PTs exhibit reduced covariance with R Brodmann area (BA) 47, Broca's area, and L BA 21, Wernicke's area, and white matter volume in the left prefrontal lobe, but increased covariance with R BA 47 and left cerebellum. Graph theory analyses demonstrate that measures of network complexity are significantly less robust in PTs compared with term controls. Volumes in regions showing group differences are significantly correlated with phonological awareness, the fundamental basis for reading acquisition, for the PTs. These data suggest both long-lasting and clinically significant alterations in the covariance in the PTs at young adulthood. PMID:26494796

Graph theory applied to the analysis of motor activity in patients with schizophrenia and depression

PubMed Central

Fasmer, Erlend Eindride; Berle, Jan Øystein; Oedegaard, Ketil J.; Hauge, Erik R.

2018-01-01

Depression and schizophrenia are defined only by their clinical features, and diagnostic separation between them can be difficult. Disturbances in motor activity pattern are central features of both types of disorders. We introduce a new method to analyze time series, called the similarity graph algorithm. Time series of motor activity, obtained from actigraph registrations over 12 days in depressed and schizophrenic patients, were mapped into a graph and we then applied techniques from graph theory to characterize these time series, primarily looking for changes in complexity. The most marked finding was that depressed patients were found to be significantly different from both controls and schizophrenic patients, with evidence of less regularity of the time series, when analyzing the recordings with one hour intervals. These findings support the contention that there are important differences in control systems regulating motor behavior in patients with depression and schizophrenia. The similarity graph algorithm we have described can easily be applied to the study of other types of time series. PMID:29668743

Graph theory applied to the analysis of motor activity in patients with schizophrenia and depression.

PubMed

Fasmer, Erlend Eindride; Fasmer, Ole Bernt; Berle, Jan Øystein; Oedegaard, Ketil J; Hauge, Erik R

2018-01-01

Depression and schizophrenia are defined only by their clinical features, and diagnostic separation between them can be difficult. Disturbances in motor activity pattern are central features of both types of disorders. We introduce a new method to analyze time series, called the similarity graph algorithm. Time series of motor activity, obtained from actigraph registrations over 12 days in depressed and schizophrenic patients, were mapped into a graph and we then applied techniques from graph theory to characterize these time series, primarily looking for changes in complexity. The most marked finding was that depressed patients were found to be significantly different from both controls and schizophrenic patients, with evidence of less regularity of the time series, when analyzing the recordings with one hour intervals. These findings support the contention that there are important differences in control systems regulating motor behavior in patients with depression and schizophrenia. The similarity graph algorithm we have described can easily be applied to the study of other types of time series.

Optimal Clustering in Graphs with Weighted Edges: A Unified Approach to the Threshold Problem.

ERIC Educational Resources Information Center

Goetschel, Roy; Voxman, William

1987-01-01

Relations on a finite set V are viewed as weighted graphs. Using the language of graph theory, two methods of partitioning V are examined: selecting threshold values and applying them to a maximal weighted spanning forest, and using a parametric linear program to obtain a most adhesive partition. (Author/EM)

Augmenting Conceptual Design Trajectory Tradespace Exploration with Graph Theory

NASA Technical Reports Server (NTRS)

Dees, Patrick D.; Zwack, Mathew R.; Steffens, Michael; Edwards, Stephen

2016-01-01

Within conceptual design changes occur rapidly due to a combination of uncertainty and shifting requirements. To stay relevant in this fluid time, trade studies must also be performed rapidly. In order to drive down analysis time while improving the information gained by these studies, surrogate models can be created to represent the complex output of a tool or tools within a specified tradespace. In order to create this model however, a large amount of data must be collected in a short amount of time. By this method, the historical approach of relying on subject matter experts to generate the data required is schedule infeasible. However, by implementing automation and distributed analysis the required data can be generated in a fraction of the time. Previous work focused on setting up a tool called multiPOST capable of orchestrating many simultaneous runs of an analysis tool assessing these automated analyses utilizing heuristics gleaned from the best practices of current subject matter experts. In this update to the previous work, elements of graph theory are included to further drive down analysis time by leveraging data previously gathered. It is shown to outperform the previous method in both time required, and the quantity and quality of data produced.

Brain network connectivity in women exposed to intimate partner violence: a graph theory analysis study.

PubMed

Roos, Annerine; Fouche, Jean-Paul; Stein, Dan J

2017-12-01

Evidence suggests that women who suffer from intimate partner violence (IPV) and posttraumatic stress disorder (PTSD) have structural and functional alterations in specific brain regions. Yet, little is known about how brain connectivity may be altered in individuals with IPV, but without PTSD. Women exposed to IPV (n = 18) and healthy controls (n = 18) underwent structural brain imaging using a Siemens 3T MRI. Global and regional brain network connectivity measures were determined, using graph theory analyses. Structural covariance networks were created using volumetric and cortical thickness data after controlling for intracranial volume, age and alcohol use. Nonparametric permutation tests were used to investigate group differences. Findings revealed altered connectivity on a global and regional level in the IPV group of regions involved in cognitive-emotional control, with principal involvement of the caudal anterior cingulate, the middle temporal gyrus, left amygdala and ventral diencephalon that includes the thalamus. To our knowledge, this is the first evidence showing different brain network connectivity in global and regional networks in women exposed to IPV, and without PTSD. Altered cognitive-emotional control in IPV may underlie adaptive neural mechanisms in environments characterized by potentially dangerous cues.

Applications of graph theory to landscape genetics

PubMed Central

Garroway, Colin J; Bowman, Jeff; Carr, Denis; Wilson, Paul J

2008-01-01

We investigated the relationships among landscape quality, gene flow, and population genetic structure of fishers (Martes pennanti) in ON, Canada. We used graph theory as an analytical framework considering each landscape as a network node. The 34 nodes were connected by 93 edges. Network structure was characterized by a higher level of clustering than expected by chance, a short mean path length connecting all pairs of nodes, and a resiliency to the loss of highly connected nodes. This suggests that alleles can be efficiently spread through the system and that extirpations and conservative harvest are not likely to affect their spread. Two measures of node centrality were negatively related to both the proportion of immigrants in a node and node snow depth. This suggests that central nodes are producers of emigrants, contain high-quality habitat (i.e., deep snow can make locomotion energetically costly) and that fishers were migrating from high to low quality habitat. A method of community detection on networks delineated five genetic clusters of nodes suggesting cryptic population structure. Our analyses showed that network models can provide system-level insight into the process of gene flow with implications for understanding how landscape alterations might affect population fitness and evolutionary potential. PMID:25567802

Matched signal detection on graphs: Theory and application to brain imaging data classification.

PubMed

Hu, Chenhui; Sepulcre, Jorge; Johnson, Keith A; Fakhri, Georges E; Lu, Yue M; Li, Quanzheng

2016-01-15

Motivated by recent progress in signal processing on graphs, we have developed a matched signal detection (MSD) theory for signals with intrinsic structures described by weighted graphs. First, we regard graph Laplacian eigenvalues as frequencies of graph-signals and assume that the signal is in a subspace spanned by the first few graph Laplacian eigenvectors associated with lower eigenvalues. The conventional matched subspace detector can be applied to this case. Furthermore, we study signals that may not merely live in a subspace. Concretely, we consider signals with bounded variation on graphs and more general signals that are randomly drawn from a prior distribution. For bounded variation signals, the test is a weighted energy detector. For the random signals, the test statistic is the difference of signal variations on associated graphs, if a degenerate Gaussian distribution specified by the graph Laplacian is adopted. We evaluate the effectiveness of the MSD on graphs both with simulated and real data sets. Specifically, we apply MSD to the brain imaging data classification problem of Alzheimer's disease (AD) based on two independent data sets: 1) positron emission tomography data with Pittsburgh compound-B tracer of 30 AD and 40 normal control (NC) subjects, and 2) resting-state functional magnetic resonance imaging (R-fMRI) data of 30 early mild cognitive impairment and 20 NC subjects. Our results demonstrate that the MSD approach is able to outperform the traditional methods and help detect AD at an early stage, probably due to the success of exploiting the manifold structure of the data. Copyright © 2015. Published by Elsevier Inc.

Local Higher-Order Graph Clustering

PubMed Central

Yin, Hao; Benson, Austin R.; Leskovec, Jure; Gleich, David F.

2018-01-01

Local graph clustering methods aim to find a cluster of nodes by exploring a small region of the graph. These methods are attractive because they enable targeted clustering around a given seed node and are faster than traditional global graph clustering methods because their runtime does not depend on the size of the input graph. However, current local graph partitioning methods are not designed to account for the higher-order structures crucial to the network, nor can they effectively handle directed networks. Here we introduce a new class of local graph clustering methods that address these issues by incorporating higher-order network information captured by small subgraphs, also called network motifs. We develop the Motif-based Approximate Personalized PageRank (MAPPR) algorithm that finds clusters containing a seed node with minimal motif conductance, a generalization of the conductance metric for network motifs. We generalize existing theory to prove the fast running time (independent of the size of the graph) and obtain theoretical guarantees on the cluster quality (in terms of motif conductance). We also develop a theory of node neighborhoods for finding sets that have small motif conductance, and apply these results to the case of finding good seed nodes to use as input to the MAPPR algorithm. Experimental validation on community detection tasks in both synthetic and real-world networks, shows that our new framework MAPPR outperforms the current edge-based personalized PageRank methodology. PMID:29770258

Quantitative evaluation of simulated functional brain networks in graph theoretical analysis.

PubMed

Lee, Won Hee; Bullmore, Ed; Frangou, Sophia

2017-02-01

There is increasing interest in the potential of whole-brain computational models to provide mechanistic insights into resting-state brain networks. It is therefore important to determine the degree to which computational models reproduce the topological features of empirical functional brain networks. We used empirical connectivity data derived from diffusion spectrum and resting-state functional magnetic resonance imaging data from healthy individuals. Empirical and simulated functional networks, constrained by structural connectivity, were defined based on 66 brain anatomical regions (nodes). Simulated functional data were generated using the Kuramoto model in which each anatomical region acts as a phase oscillator. Network topology was studied using graph theory in the empirical and simulated data. The difference (relative error) between graph theory measures derived from empirical and simulated data was then estimated. We found that simulated data can be used with confidence to model graph measures of global network organization at different dynamic states and highlight the sensitive dependence of the solutions obtained in simulated data on the specified connection densities. This study provides a method for the quantitative evaluation and external validation of graph theory metrics derived from simulated data that can be used to inform future study designs. Copyright © 2016 The Authors. Published by Elsevier Inc. All rights reserved.

Dynamical graph theory networks techniques for the analysis of sparse connectivity networks in dementia

NASA Astrophysics Data System (ADS)

Tahmassebi, Amirhessam; Pinker-Domenig, Katja; Wengert, Georg; Lobbes, Marc; Stadlbauer, Andreas; Romero, Francisco J.; Morales, Diego P.; Castillo, Encarnacion; Garcia, Antonio; Botella, Guillermo; Meyer-Bäse, Anke

2017-05-01

Graph network models in dementia have become an important computational technique in neuroscience to study fundamental organizational principles of brain structure and function of neurodegenerative diseases such as dementia. The graph connectivity is reflected in the connectome, the complete set of structural and functional connections of the graph network, which is mostly based on simple Pearson correlation links. In contrast to simple Pearson correlation networks, the partial correlations (PC) only identify direct correlations while indirect associations are eliminated. In addition to this, the state-of-the-art techniques in brain research are based on static graph theory, which is unable to capture the dynamic behavior of the brain connectivity, as it alters with disease evolution. We propose a new research avenue in neuroimaging connectomics based on combining dynamic graph network theory and modeling strategies at different time scales. We present the theoretical framework for area aggregation and time-scale modeling in brain networks as they pertain to disease evolution in dementia. This novel paradigm is extremely powerful, since we can derive both static parameters pertaining to node and area parameters, as well as dynamic parameters, such as system's eigenvalues. By implementing and analyzing dynamically both disease driven PC-networks and regular concentration networks, we reveal differences in the structure of these network that play an important role in the temporal evolution of this disease. The described research is key to advance biomedical research on novel disease prediction trajectories and dementia therapies.

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cheng, Shaobo; Zhang, Dong; Deng, Shiqing

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

New graph polynomials in parametric QED Feynman integrals

NASA Astrophysics Data System (ADS)

Golz, Marcel

2017-10-01

In recent years enormous progress has been made in perturbative quantum field theory by applying methods of algebraic geometry to parametric Feynman integrals for scalar theories. The transition to gauge theories is complicated not only by the fact that their parametric integrand is much larger and more involved. It is, moreover, only implicitly given as the result of certain differential operators applied to the scalar integrand exp(-ΦΓ /ΨΓ) , where ΨΓ and ΦΓ are the Kirchhoff and Symanzik polynomials of the Feynman graph Γ. In the case of quantum electrodynamics we find that the full parametric integrand inherits a rich combinatorial structure from ΨΓ and ΦΓ. In the end, it can be expressed explicitly as a sum over products of new types of graph polynomials which have a combinatoric interpretation via simple cycle subgraphs of Γ.

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

DOE PAGES

Cheng, Shaobo; Zhang, Dong; Deng, Shiqing; ...

2018-04-19

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

Analysis of graphical representation among freshmen in undergraduate physics laboratory

NASA Astrophysics Data System (ADS)

Adam, A. S.; Anggrayni, S.; Kholiq, A.; Putri, N. P.; Suprapto, N.

2018-03-01

Physics concept understanding is the importance of the physics laboratory among freshmen in the undergraduate program. These include the ability to interpret the meaning of the graph to make an appropriate conclusion. This particular study analyses the graphical representation among freshmen in an undergraduate physics laboratory. This study uses empirical study with quantitative approach. The graphical representation covers 3 physics topics: velocity of sound, simple pendulum and spring system. The result of this study shows most of the freshmen (90% of the sample) make a graph based on the data from physics laboratory. It means the transferring process of raw data which illustrated in the table to physics graph can be categorised. Most of the Freshmen use the proportional principle of the variable in graph analysis. However, Freshmen can't make the graph in an appropriate variable to gain more information and can't analyse the graph to obtain the useful information from the slope.

Information-theoretic indices usage for the prediction and calculation of octanol-water partition coefficient.

PubMed

Persona, Marek; Kutarov, Vladimir V; Kats, Boris M; Persona, Andrzej; Marczewska, Barbara

2007-01-01

The paper describes the new prediction method of octanol-water partition coefficient, which is based on molecular graph theory. The results obtained using the new method are well correlated with experimental values. These results were compared with the ones obtained by use of ten other structure correlated methods. The comparison shows that graph theory can be very useful in structure correlation research.

Graph theory network function in Parkinson's disease assessed with electroencephalography.

PubMed

Utianski, Rene L; Caviness, John N; van Straaten, Elisabeth C W; Beach, Thomas G; Dugger, Brittany N; Shill, Holly A; Driver-Dunckley, Erika D; Sabbagh, Marwan N; Mehta, Shyamal; Adler, Charles H; Hentz, Joseph G

2016-05-01

To determine what differences exist in graph theory network measures derived from electroencephalography (EEG), between Parkinson's disease (PD) patients who are cognitively normal (PD-CN) and matched healthy controls; and between PD-CN and PD dementia (PD-D). EEG recordings were analyzed via graph theory network analysis to quantify changes in global efficiency and local integration. This included minimal spanning tree analysis. T-tests and correlations were used to assess differences between groups and assess the relationship with cognitive performance. Network measures showed increased local integration across all frequency bands between control and PD-CN; in contrast, decreased local integration occurred in PD-D when compared to PD-CN in the alpha1 frequency band. Differences found in PD-MCI mirrored PD-D. Correlations were found between network measures and assessments of global cognitive performance in PD. Our results reveal distinct patterns of band and network measure type alteration and breakdown for PD, as well as with cognitive decline in PD. These patterns suggest specific ways that interaction between cortical areas becomes abnormal and contributes to PD symptoms at various stages. Graph theory analysis by EEG suggests that network alteration and breakdown are robust attributes of PD cortical dysfunction pathophysiology. Copyright © 2016 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved.

Topological Characterization of Carbon Graphite and Crystal Cubic Carbon Structures.

PubMed

Siddiqui, Wei Gao Muhammad Kamran; Naeem, Muhammad; Rehman, Najma Abdul

2017-09-07

Graph theory is used for modeling, designing, analysis and understanding chemical structures or chemical networks and their properties. The molecular graph is a graph consisting of atoms called vertices and the chemical bond between atoms called edges. In this article, we study the chemical graphs of carbon graphite and crystal structure of cubic carbon. Moreover, we compute and give closed formulas of degree based additive topological indices, namely hyper-Zagreb index, first multiple and second multiple Zagreb indices, and first and second Zagreb polynomials.

Using Sorting by Reversal: Breakpoint Graph for Gene Assembly in Ciliates

NASA Astrophysics Data System (ADS)

Brijder, Robert; Jan Hoogeboom, Hendrik

2007-09-01

The theory of gene assembly in ciliates has much in common with the theory of sorting by reversal. Both model processes that are based on splicing, and have a fixed begin and end product. The main difference is the type of splicing operations used to obtain the end product from the begin product. In this overview paper we show that the concept of breakpoint graph, known from the theory of sorting by reversal, has many uses in the theory of gene assembly. Our aim is to present the material in an intuitive and informal manner to allow for an efficient introduction into the subject.

The Effects of Describing Antecedent Stimuli and Performance Criteria in Task Analysis Instruction for Graphing

ERIC Educational Resources Information Center

Tyner, Bryan C.; Fienup, Daniel M.

2016-01-01

Task analyses are ubiquitous to applied behavior analysis interventions, yet little is known about the factors that make them effective. Numerous task analyses have been published in behavior analytic journals for constructing single-subject design graphs; however, learner outcomes using these task analyses may fall short of what could be…

Postbuckling analysis of shear deformable composite flat panels taking into account geometrical imperfections

NASA Technical Reports Server (NTRS)

Librescu, L.; Stein, M.

1990-01-01

The effects of initial geometrical imperfections on the postbuckling response of flat laminated composite panels to uniaxial and biaxial compressive loading are investigated analytically. The derivation of the mathematical model on the basis of first-order transverse shear deformation theory is outlined, and numerical results for perfect and imperfect, single-layer and three-layer square plates with free-free, clamped-clamped, or free-clamped edges are presented in graphs and briefly characterized. The present approach is shown to be more accurate than analyses based on the classical Kirchhoff plate model.

Sequential visibility-graph motifs

NASA Astrophysics Data System (ADS)

Iacovacci, Jacopo; Lacasa, Lucas

2016-04-01

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

Test-retest reliability of fMRI-based graph theoretical properties during working memory, emotion processing, and resting state.

PubMed

Cao, Hengyi; Plichta, Michael M; Schäfer, Axel; Haddad, Leila; Grimm, Oliver; Schneider, Michael; Esslinger, Christine; Kirsch, Peter; Meyer-Lindenberg, Andreas; Tost, Heike

2014-01-01

The investigation of the brain connectome with functional magnetic resonance imaging (fMRI) and graph theory analyses has recently gained much popularity, but little is known about the robustness of these properties, in particular those derived from active fMRI tasks. Here, we studied the test-retest reliability of brain graphs calculated from 26 healthy participants with three established fMRI experiments (n-back working memory, emotional face-matching, resting state) and two parcellation schemes for node definition (AAL atlas, functional atlas proposed by Power et al.). We compared the intra-class correlation coefficients (ICCs) of five different data processing strategies and demonstrated a superior reliability of task-regression methods with condition-specific regressors. The between-task comparison revealed significantly higher ICCs for resting state relative to the active tasks, and a superiority of the n-back task relative to the face-matching task for global and local network properties. While the mean ICCs were typically lower for the active tasks, overall fair to good reliabilities were detected for global and local connectivity properties, and for the n-back task with both atlases, smallworldness. For all three tasks and atlases, low mean ICCs were seen for the local network properties. However, node-specific good reliabilities were detected for node degree in regions known to be critical for the challenged functions (resting-state: default-mode network nodes, n-back: fronto-parietal nodes, face-matching: limbic nodes). Between-atlas comparison demonstrated significantly higher reliabilities for the functional parcellations for global and local network properties. Our findings can inform the choice of processing strategies, brain atlases and outcome properties for fMRI studies using active tasks, graph theory methods, and within-subject designs, in particular future pharmaco-fMRI studies. © 2013 Elsevier Inc. All rights reserved.

Determination system for solar cell layout in traffic light network using dominating set

NASA Astrophysics Data System (ADS)

Eka Yulia Retnani, Windi; Fambudi, Brelyanes Z.; Slamin

2018-04-01

Graph Theory is one of the fields in Mathematics that solves discrete problems. In daily life, the applications of Graph Theory are used to solve various problems. One of the topics in the Graph Theory that is used to solve the problem is the dominating set. The concept of dominating set is used, for example, to locate some objects systematically. In this study, the dominating set are used to determine the dominating points for solar panels, where the vertex represents the traffic light point and the edge represents the connection between the points of the traffic light. To search the dominating points for solar panels using the greedy algorithm. This algorithm is used to determine the location of solar panel. This research produced applications that can determine the location of solar panels with optimal results, that is, the minimum dominating points.

Graph Theory at the Service of Electroencephalograms.

PubMed

Iakovidou, Nantia D

2017-04-01

The brain is one of the largest and most complex organs in the human body and EEG is a noninvasive electrophysiological monitoring method that is used to record the electrical activity of the brain. Lately, the functional connectivity in human brain has been regarded and studied as a complex network using EEG signals. This means that the brain is studied as a connected system where nodes, or units, represent different specialized brain regions and links, or connections, represent communication pathways between the nodes. Graph theory and theory of complex networks provide a variety of measures, methods, and tools that can be useful to efficiently model, analyze, and study EEG networks. This article is addressed to computer scientists who wish to be acquainted and deal with the study of EEG data and also to neuroscientists who would like to become familiar with graph theoretic approaches and tools to analyze EEG data.

Efficient Algorithmic Frameworks via Structural Graph Theory

DTIC Science & Technology

2016-10-28

centrally planned solution. Policy recommendation: Given a socioeconomic game among multiple parties (countries, armies, political parties, terrorist...etc.). 2 Graph Structure of Network Creation Games We completed the final versions of two of our papers about the graph structure inherent in...network creation games ”, which appeared in the following venues: Erik D. Demaine, MohammadTaghi Hajiaghayi, Hamid Mahini, and Morteza Zadi- moghaddam, “The

Energy Minimization of Discrete Protein Titration State Models Using Graph Theory.

PubMed

Purvine, Emilie; Monson, Kyle; Jurrus, Elizabeth; Star, Keith; Baker, Nathan A

2016-08-25

There are several applications in computational biophysics that require the optimization of discrete interacting states, for example, amino acid titration states, ligand oxidation states, or discrete rotamer angles. Such optimization can be very time-consuming as it scales exponentially in the number of sites to be optimized. In this paper, we describe a new polynomial time algorithm for optimization of discrete states in macromolecular systems. This algorithm was adapted from image processing and uses techniques from discrete mathematics and graph theory to restate the optimization problem in terms of "maximum flow-minimum cut" graph analysis. The interaction energy graph, a graph in which vertices (amino acids) and edges (interactions) are weighted with their respective energies, is transformed into a flow network in which the value of the minimum cut in the network equals the minimum free energy of the protein and the cut itself encodes the state that achieves the minimum free energy. Because of its deterministic nature and polynomial time performance, this algorithm has the potential to allow for the ionization state of larger proteins to be discovered.

Energy Minimization of Discrete Protein Titration State Models Using Graph Theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Purvine, Emilie AH; Monson, Kyle E.; Jurrus, Elizabeth R.

There are several applications in computational biophysics which require the optimization of discrete interacting states; e.g., amino acid titration states, ligand oxidation states, or discrete rotamer angles. Such optimization can be very time-consuming as it scales exponentially in the number of sites to be optimized. In this paper, we describe a new polynomial-time algorithm for optimization of discrete states in macromolecular systems. This algorithm was adapted from image processing and uses techniques from discrete mathematics and graph theory to restate the optimization problem in terms of maximum flow-minimum cut graph analysis. The interaction energy graph, a graph in which verticesmore » (amino acids) and edges (interactions) are weighted with their respective energies, is transformed into a flow network in which the value of the minimum cut in the network equals the minimum free energy of the protein, and the cut itself encodes the state that achieves the minimum free energy. Because of its deterministic nature and polynomial-time performance, this algorithm has the potential to allow for the ionization state of larger proteins to be discovered.« less

Energy Minimization of Discrete Protein Titration State Models Using Graph Theory

PubMed Central

Purvine, Emilie; Monson, Kyle; Jurrus, Elizabeth; Star, Keith; Baker, Nathan A.

2016-01-01

There are several applications in computational biophysics which require the optimization of discrete interacting states; e.g., amino acid titration states, ligand oxidation states, or discrete rotamer angles. Such optimization can be very time-consuming as it scales exponentially in the number of sites to be optimized. In this paper, we describe a new polynomial-time algorithm for optimization of discrete states in macromolecular systems. This algorithm was adapted from image processing and uses techniques from discrete mathematics and graph theory to restate the optimization problem in terms of “maximum flow-minimum cut” graph analysis. The interaction energy graph, a graph in which vertices (amino acids) and edges (interactions) are weighted with their respective energies, is transformed into a flow network in which the value of the minimum cut in the network equals the minimum free energy of the protein, and the cut itself encodes the state that achieves the minimum free energy. Because of its deterministic nature and polynomial-time performance, this algorithm has the potential to allow for the ionization state of larger proteins to be discovered. PMID:27089174

Counterbalancing for serial order carryover effects in experimental condition orders.

PubMed

Brooks, Joseph L

2012-12-01

Reactions of neural, psychological, and social systems are rarely, if ever, independent of previous inputs and states. The potential for serial order carryover effects from one condition to the next in a sequence of experimental trials makes counterbalancing of condition order an essential part of experimental design. Here, a method is proposed for generating counterbalanced sequences for repeated-measures designs including those with multiple observations of each condition on one participant and self-adjacencies of conditions. Condition ordering is reframed as a graph theory problem. Experimental conditions are represented as vertices in a graph and directed edges between them represent temporal relationships between conditions. A counterbalanced trial order results from traversing an Euler circuit through such a graph in which each edge is traversed exactly once. This method can be generalized to counterbalance for higher order serial order carryover effects as well as to create intentional serial order biases. Modern graph theory provides tools for finding other types of paths through such graph representations, providing a tool for generating experimental condition sequences with useful properties. PsycINFO Database Record (c) 2013 APA, all rights reserved.

Characterizing networks formed by P. polycephalum

NASA Astrophysics Data System (ADS)

Dirnberger, M.; Mehlhorn, K.

2017-06-01

We present a systematic study of the characteristic vein networks formed by the slime mold P. polycephalum. Our study is based on an extensive set of graph representations of slime mold networks. We analyze a total of 1998 graphs capturing growth and network formation of P. polycephalum as observed in 36 independent, identical, wet-lab experiments. Relying on concepts from graph theory such as face cycles and cuts as well as ideas from percolation theory, we establish a broad collection of individual observables taking into account various complementary aspects of P. polycephalum networks. As a whole, the collection is intended to serve as a specialized knowledge-base providing a comprehensive characterization of P. polycephalum networks. To this end, it contains individual as well as cumulative results for all investigated observables across all available data series, down to the level of single P. polycephalum graphs. Furthermore we include the raw numerical data as well as various plotting and analysis tools to ensure reproducibility and increase the usefulness of the collection. All our results are publicly available in an organized fashion in the slime mold graph repository (Smgr).

Dynamical Graph Theory Networks Methods for the Analysis of Sparse Functional Connectivity Networks and for Determining Pinning Observability in Brain Networks

PubMed Central

Meyer-Bäse, Anke; Roberts, Rodney G.; Illan, Ignacio A.; Meyer-Bäse, Uwe; Lobbes, Marc; Stadlbauer, Andreas; Pinker-Domenig, Katja

2017-01-01

Neuroimaging in combination with graph theory has been successful in analyzing the functional connectome. However almost all analysis are performed based on static graph theory. The derived quantitative graph measures can only describe a snap shot of the disease over time. Neurodegenerative disease evolution is poorly understood and treatment strategies are consequently only of limited efficiency. Fusing modern dynamic graph network theory techniques and modeling strategies at different time scales with pinning observability of complex brain networks will lay the foundation for a transformational paradigm in neurodegnerative diseases research regarding disease evolution at the patient level, treatment response evaluation and revealing some central mechanism in a network that drives alterations in these diseases. We model and analyze brain networks as two-time scale sparse dynamic graph networks with hubs (clusters) representing the fast sub-system and the interconnections between hubs the slow sub-system. Alterations in brain function as seen in dementia can be dynamically modeled by determining the clusters in which disturbance inputs have entered and the impact they have on the large-scale dementia dynamic system. Observing a small fraction of specific nodes in dementia networks such that the others can be recovered is accomplished by the novel concept of pinning observability. In addition, how to control this complex network seems to be crucial in understanding the progressive abnormal neural circuits in many neurodegenerative diseases. Detecting the controlling regions in the networks, which serve as key nodes to control the aberrant dynamics of the networks to a desired state and thus influence the progressive abnormal behavior, will have a huge impact in understanding and developing therapeutic solutions and also will provide useful information about the trajectory of the disease. In this paper, we present the theoretical framework and derive the necessary conditions for (1) area aggregation and time-scale modeling in brain networks and for (2) pinning observability of nodes in dynamic graph networks. Simulation examples are given to illustrate the theoretical concepts. PMID:29051730

Dynamical Graph Theory Networks Methods for the Analysis of Sparse Functional Connectivity Networks and for Determining Pinning Observability in Brain Networks.

PubMed

Meyer-Bäse, Anke; Roberts, Rodney G; Illan, Ignacio A; Meyer-Bäse, Uwe; Lobbes, Marc; Stadlbauer, Andreas; Pinker-Domenig, Katja

2017-01-01

Neuroimaging in combination with graph theory has been successful in analyzing the functional connectome. However almost all analysis are performed based on static graph theory. The derived quantitative graph measures can only describe a snap shot of the disease over time. Neurodegenerative disease evolution is poorly understood and treatment strategies are consequently only of limited efficiency. Fusing modern dynamic graph network theory techniques and modeling strategies at different time scales with pinning observability of complex brain networks will lay the foundation for a transformational paradigm in neurodegnerative diseases research regarding disease evolution at the patient level, treatment response evaluation and revealing some central mechanism in a network that drives alterations in these diseases. We model and analyze brain networks as two-time scale sparse dynamic graph networks with hubs (clusters) representing the fast sub-system and the interconnections between hubs the slow sub-system. Alterations in brain function as seen in dementia can be dynamically modeled by determining the clusters in which disturbance inputs have entered and the impact they have on the large-scale dementia dynamic system. Observing a small fraction of specific nodes in dementia networks such that the others can be recovered is accomplished by the novel concept of pinning observability. In addition, how to control this complex network seems to be crucial in understanding the progressive abnormal neural circuits in many neurodegenerative diseases. Detecting the controlling regions in the networks, which serve as key nodes to control the aberrant dynamics of the networks to a desired state and thus influence the progressive abnormal behavior, will have a huge impact in understanding and developing therapeutic solutions and also will provide useful information about the trajectory of the disease. In this paper, we present the theoretical framework and derive the necessary conditions for (1) area aggregation and time-scale modeling in brain networks and for (2) pinning observability of nodes in dynamic graph networks. Simulation examples are given to illustrate the theoretical concepts.

Extracting Knowledge from Graph Data in Adversarial Settings

NASA Astrophysics Data System (ADS)

Skillicorn, David

Graph data captures connections and relationships among individuals, and between individuals and objects, places, and times. Because many of the properties f graphs are emergent, they are resistant to manipulation by adversaries. This robustness comes at the expense of more-complex analysis algorithms. We describe several approaches to analysing graph data, illustrating with examples from the relationships within al Qaeda.

Spectral and scattering theory for Schrödinger operators on perturbed topological crystals

NASA Astrophysics Data System (ADS)

Parra, D.; Richard, S.

In this paper, we investigate the spectral and the scattering theory of Schrödinger operators acting on perturbed periodic discrete graphs. The perturbations considered are of two types: either a multiplication operator by a short-range or a long-range function, or a short-range type modification of the measure defined on the vertices and on the edges of the graph. Mourre theory is used for describing the nature of the spectrum of the underlying operators. For short-range perturbations, existence and asymptotic completeness of local wave operators are also proved.

Cytoscape.js: a graph theory library for visualisation and analysis.

PubMed

Franz, Max; Lopes, Christian T; Huck, Gerardo; Dong, Yue; Sumer, Onur; Bader, Gary D

2016-01-15

Cytoscape.js is an open-source JavaScript-based graph library. Its most common use case is as a visualization software component, so it can be used to render interactive graphs in a web browser. It also can be used in a headless manner, useful for graph operations on a server, such as Node.js. Cytoscape.js is implemented in JavaScript. Documentation, downloads and source code are available at http://js.cytoscape.org. gary.bader@utoronto.ca. © The Author 2015. Published by Oxford University Press.

Graph Theory and Cognition: An Alternative Avenue for Examining Neuropsychological Status in Epilepsy

PubMed Central

Garcia-Ramos, Camille; Lin, Jack J; Kellermann, Tanja S; Bonilha, Leonardo; Prabhakaran, Vivek; Hermann, Bruce P

2016-01-01

The recent revision of the classification of the epilepsies released by the ILAE Commission on Classification and Terminology (2005–2009) has been a major development in the field. Papers in this section of the special issue were charged with examining the relevance of other techniques and approaches to examining, categorizing and classifying cognitive and behavioral comorbidities. In that light, we investigate the applicability of graph theory to understand the impact of epilepsy on cognition compared to controls, and then the patterns of cognitive development in normally developing children which would set the stage for prospective comparisons of children with epilepsy and controls. The overall goal is to examine the potential utility of other analytic tools and approaches to conceptualize the cognitive comorbidities in epilepsy. Given that the major cognitive domains representing cognitive function are interdependent, the associations between the neuropsychological abilities underlying these domains can be referred to as a cognitive network. Therefore, the architecture of this cognitive network can be quantified and assessed using graph theory methods, rendering a novel approach to the characterization of cognitive status. In this article we provide fundamental information about graph theory procedures, followed by application of these techniques to cross-sectional analysis of neuropsychological data in children with epilepsy compared to controls, finalizing with prospective analysis of neuropsychological development in younger and older healthy controls. PMID:27017326

Alterations in Anatomical Covariance in the Prematurely Born.

PubMed

Scheinost, Dustin; Kwon, Soo Hyun; Lacadie, Cheryl; Vohr, Betty R; Schneider, Karen C; Papademetris, Xenophon; Constable, R Todd; Ment, Laura R

2017-01-01

Preterm (PT) birth results in long-term alterations in functional and structural connectivity, but the related changes in anatomical covariance are just beginning to be explored. To test the hypothesis that PT birth alters patterns of anatomical covariance, we investigated brain volumes of 25 PTs and 22 terms at young adulthood using magnetic resonance imaging. Using regional volumetrics, seed-based analyses, and whole brain graphs, we show that PT birth is associated with reduced volume in bilateral temporal and inferior frontal lobes, left caudate, left fusiform, and posterior cingulate for prematurely born subjects at young adulthood. Seed-based analyses demonstrate altered patterns of anatomical covariance for PTs compared with terms. PTs exhibit reduced covariance with R Brodmann area (BA) 47, Broca's area, and L BA 21, Wernicke's area, and white matter volume in the left prefrontal lobe, but increased covariance with R BA 47 and left cerebellum. Graph theory analyses demonstrate that measures of network complexity are significantly less robust in PTs compared with term controls. Volumes in regions showing group differences are significantly correlated with phonological awareness, the fundamental basis for reading acquisition, for the PTs. These data suggest both long-lasting and clinically significant alterations in the covariance in the PTs at young adulthood. © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

Toughness and Matching Extension in Graphs,

DTIC Science & Technology

1986-05-01

New York, 1977. V. CHVATAL 1973a. Tough graphs and Hamiltonian circuits, Discrete Math . 5, 1973, 215- 228. 1973b. New directions in Hamiltonian...PLUMMER 1986. Matching Theory, Ann. Discrete Math ., North-Holland, Amsterdam, 1986 (to appear). M. D. PLUMMER 1980. On n-extendable graphs, Discrete ... Math . 31, 1980, 201-210. 1985. A theorem on matchings in the plane, Conference in memory of Gabriel Dirac, Ann. Discrete Math ., North-Holland, Amsterdam

The Full Ward-Takahashi Identity for Colored Tensor Models

NASA Astrophysics Data System (ADS)

Pérez-Sánchez, Carlos I.

2018-03-01

Colored tensor models (CTM) is a random geometrical approach to quantum gravity. We scrutinize the structure of the connected correlation functions of general CTM-interactions and organize them by boundaries of Feynman graphs. For rank- D interactions including, but not restricted to, all melonic φ^4 -vertices—to wit, solely those quartic vertices that can lead to dominant spherical contributions in the large- N expansion—the aforementioned boundary graphs are shown to be precisely all (possibly disconnected) vertex-bipartite regularly edge- D-colored graphs. The concept of CTM-compatible boundary-graph automorphism is introduced and an auxiliary graph calculus is developed. With the aid of these constructs, certain U (∞)-invariance of the path integral measure is fully exploited in order to derive a strong Ward-Takahashi Identity for CTMs with a symmetry-breaking kinetic term. For the rank-3 φ^4 -theory, we get the exact integral-like equation for the 2-point function. Similarly, exact equations for higher multipoint functions can be readily obtained departing from this full Ward-Takahashi identity. Our results hold for some Group Field Theories as well. Altogether, our non-perturbative approach trades some graph theoretical methods for analytical ones. We believe that these tools can be extended to tensorial SYK-models.

Graph Metrics of Structural Brain Networks in Individuals with Schizophrenia and Healthy Controls: Group Differences, Relationships with Intelligence, and Genetics.

PubMed

Yeo, Ronald A; Ryman, Sephira G; van den Heuvel, Martijn P; de Reus, Marcel A; Jung, Rex E; Pommy, Jessica; Mayer, Andrew R; Ehrlich, Stefan; Schulz, S Charles; Morrow, Eric M; Manoach, Dara; Ho, Beng-Choon; Sponheim, Scott R; Calhoun, Vince D

2016-02-01

One of the most prominent features of schizophrenia is relatively lower general cognitive ability (GCA). An emerging approach to understanding the roots of variation in GCA relies on network properties of the brain. In this multi-center study, we determined global characteristics of brain networks using graph theory and related these to GCA in healthy controls and individuals with schizophrenia. Participants (N=116 controls, 80 patients with schizophrenia) were recruited from four sites. GCA was represented by the first principal component of a large battery of neurocognitive tests. Graph metrics were derived from diffusion-weighted imaging. The global metrics of longer characteristic path length and reduced overall connectivity predicted lower GCA across groups, and group differences were noted for both variables. Measures of clustering, efficiency, and modularity did not differ across groups or predict GCA. Follow-up analyses investigated three topological types of connectivity--connections among high degree "rich club" nodes, "feeder" connections to these rich club nodes, and "local" connections not involving the rich club. Rich club and local connectivity predicted performance across groups. In a subsample (N=101 controls, 56 patients), a genetic measure reflecting mutation load, based on rare copy number deletions, was associated with longer characteristic path length. Results highlight the importance of characteristic path lengths and rich club connectivity for GCA and provide no evidence for group differences in the relationships between graph metrics and GCA.

Real World Graph Connectivity

ERIC Educational Resources Information Center

Lind, Joy; Narayan, Darren

2009-01-01

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

Some theoretical issues on computer simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Barrett, C.L.; Reidys, C.M.

1998-02-01

The subject of this paper is the development of mathematical foundations for a theory of simulation. Sequentially updated cellular automata (sCA) over arbitrary graphs are employed as a paradigmatic framework. In the development of the theory, the authors focus on the properties of causal dependencies among local mappings in a simulation. The main object of and study is the mapping between a graph representing the dependencies among entities of a simulation and a representing the equivalence classes of systems obtained by all possible updates.

Matching and Vertex Packing: How Hard Are They?

DTIC Science & Technology

1991-01-01

Theory, 29, Ann. Discrete Math ., North-Holland, Amsterdam, 1986. [2] M.D. Plummer, Matching theory - a sampler: from D~nes K~nig to the present...Ser. B, 28, 1980, 284-304. [20i N. Sbihi, Algorithme de recherche d’un stable de cardinalit6 maximum dans un graphe sans 6toile, Discrete Math ., 29...cliques and by finite families of graphs, Discrete Math ., 49, 1984, 45-59. [92] G. Cornu~jols, D. Hartvigsen and W.R. Pulleyblank, Packing subgraphs in

Application of Theodorsen's Theory to Propeller Design

NASA Technical Reports Server (NTRS)

Crigler, John L

1948-01-01

A theoretical analysis is presented for obtaining by use of Theodorsen's propeller theory the load distribution along a propeller radius to give the optimum propeller efficiency for any design condition.The efficiencies realized by designing for the optimum load distribution are given in graphs, and the optimum efficiency for any design condition may be read directly from the graph without any laborious calculations. Examples are included to illustrate the method of obtaining the optimum load distributions for both single-rotating and dual-rotating propellers.

Application of Theodorsen's theory to propeller design

NASA Technical Reports Server (NTRS)

Crigler, John L

1949-01-01

A theoretical analysis is presented for obtaining, by use of Theodorsen's propeller theory, the load distribution along a propeller radius to give the optimum propeller efficiency for any design condition. The efficiencies realized by designing for the optimum load distribution are given in graphs, and the optimum efficiency for any design condition may be read directly from the graph without any laborious calculations. Examples are included to illustrate the method of obtaining the optimum load distributions for both single-rotating and dual-rotating propellers.

AN EDUCATIONAL THEORY MODEL--(SIGGS), AN INTEGRATION OF SET THEORY, INFORMATION THEORY, AND GRAPH THEORY WITH GENERAL SYSTEMS THEORY.

ERIC Educational Resources Information Center

MACCIA, ELIZABETH S.; AND OTHERS

AN ANNOTATED BIBLIOGRAPHY OF 20 ITEMS AND A DISCUSSION OF ITS SIGNIFICANCE WAS PRESENTED TO DESCRIBE CURRENT UTILIZATION OF SUBJECT THEORIES IN THE CONSTRUCTION OF AN EDUCATIONAL THEORY. ALSO, A THEORY MODEL WAS USED TO DEMONSTRATE CONSTRUCTION OF A SCIENTIFIC EDUCATIONAL THEORY. THE THEORY MODEL INCORPORATED SET THEORY (S), INFORMATION THEORY…

Extending Matchings in Planar Graphs 4

DTIC Science & Technology

1989-01-01

Discrete Math ., 18, 1977, 213-216. [31 B. Grfianbaum, Convex Polytopes, Interscience Publishers, John Wiley & Sons, Lon- don, 1967. [4] D.A. Holton and...Kalamazoo, 1988), John Wiley & Sons, (to appear). [6] D.A. Holton, D. Lou and M.D. Plummer, On the 2-extendability of planar graphs, preprint, Discrete Math ., (to...81 L. Lovasz and M.D. Plummer, Matching Theory, Ann. Discrete Math . 29, North- Holland, Amsterdam, 1986. [9] M.D. Plummer, On n-extendable graphs

Cryptographic Boolean Functions with Biased Inputs

DTIC Science & Technology

2015-07-31

theory of random graphs developed by Erdős and Rényi [2]. The graph properties in a random graph expressed as such Boolean functions are used by...distributed Bernoulli variates with the parameter p. Since our scope is within the area of cryptography , we initiate an analysis of cryptographic...Boolean functions with biased inputs, which we refer to as µp-Boolean functions, is a common generalization of Boolean functions which stems from the

Connections between the Sznajd model with general confidence rules and graph theory

NASA Astrophysics Data System (ADS)

Timpanaro, André M.; Prado, Carmen P. C.

2012-10-01

The Sznajd model is a sociophysics model that is used to model opinion propagation and consensus formation in societies. Its main feature is that its rules favor bigger groups of agreeing people. In a previous work, we generalized the bounded confidence rule in order to model biases and prejudices in discrete opinion models. In that work, we applied this modification to the Sznajd model and presented some preliminary results. The present work extends what we did in that paper. We present results linking many of the properties of the mean-field fixed points, with only a few qualitative aspects of the confidence rule (the biases and prejudices modeled), finding an interesting connection with graph theory problems. More precisely, we link the existence of fixed points with the notion of strongly connected graphs and the stability of fixed points with the problem of finding the maximal independent sets of a graph. We state these results and present comparisons between the mean field and simulations in Barabási-Albert networks, followed by the main mathematical ideas and appendices with the rigorous proofs of our claims and some graph theory concepts, together with examples. We also show that there is no qualitative difference in the mean-field results if we require that a group of size q>2, instead of a pair, of agreeing agents be formed before they attempt to convince other sites (for the mean field, this would coincide with the q-voter model).

Nonlinear complexity of random visibility graph and Lempel-Ziv on multitype range-intensity interacting financial dynamics

NASA Astrophysics Data System (ADS)

Zhang, Yali; Wang, Jun

2017-09-01

In an attempt to investigate the nonlinear complex evolution of financial dynamics, a new financial price model - the multitype range-intensity contact (MRIC) financial model, is developed based on the multitype range-intensity interacting contact system, in which the interaction and transmission of different types of investment attitudes in a stock market are simulated by viruses spreading. Two new random visibility graph (VG) based analyses and Lempel-Ziv complexity (LZC) are applied to study the complex behaviors of return time series and the corresponding random sorted series. The VG method is the complex network theory, and the LZC is a non-parametric measure of complexity reflecting the rate of new pattern generation of a series. In this work, the real stock market indices are considered to be comparatively studied with the simulation data of the proposed model. Further, the numerical empirical study shows the similar complexity behaviors between the model and the real markets, the research confirms that the financial model is reasonable to some extent.

ELUCIDATING BRAIN CONNECTIVITY NETWORKS IN MAJOR DEPRESSIVE DISORDER USING CLASSIFICATION-BASED SCORING.

PubMed

Sacchet, Matthew D; Prasad, Gautam; Foland-Ross, Lara C; Thompson, Paul M; Gotlib, Ian H

2014-04-01

Graph theory is increasingly used in the field of neuroscience to understand the large-scale network structure of the human brain. There is also considerable interest in applying machine learning techniques in clinical settings, for example, to make diagnoses or predict treatment outcomes. Here we used support-vector machines (SVMs), in conjunction with whole-brain tractography, to identify graph metrics that best differentiate individuals with Major Depressive Disorder (MDD) from nondepressed controls. To do this, we applied a novel feature-scoring procedure that incorporates iterative classifier performance to assess feature robustness. We found that small-worldness , a measure of the balance between global integration and local specialization, most reliably differentiated MDD from nondepressed individuals. Post-hoc regional analyses suggested that heightened connectivity of the subcallosal cingulate gyrus (SCG) in MDDs contributes to these differences. The current study provides a novel way to assess the robustness of classification features and reveals anomalies in large-scale neural networks in MDD.

An Out-of-Math Experience: Einstein, Relativity, and the Developmental Mathematics Student.

ERIC Educational Resources Information Center

Fiore, Greg

2000-01-01

Discusses Einstein's special relativity theory and some of the developmental mathematics involved. Presents motivational classroom materials used in discussing relative-motion problems, evaluating a radical expression, graphing with asymptotes, interpreting a graph, studying variation, and solving literal and radical equations. (KHR)

New Methods of Spectral-Density Based Graph Construction and Their Application to Hyperspectral Image Analysis

NASA Astrophysics Data System (ADS)

Stevens, Jeffrey

The past decade has seen the emergence of many hyperspectral image (HSI) analysis algorithms based on graph theory and derived manifold-coordinates. Yet, despite the growing number of algorithms, there has been limited study of the graphs constructed from spectral data themselves. Which graphs are appropriate for various HSI analyses--and why? This research aims to begin addressing these questions as the performance of graph-based techniques is inextricably tied to the graphical model constructed from the spectral data. We begin with a literature review providing a survey of spectral graph construction techniques currently used by the hyperspectral community, starting with simple constructs demonstrating basic concepts and then incrementally adding components to derive more complex approaches. Throughout this development, we discuss algorithm advantages and disadvantages for different types of hyperspectral analysis. A focus is provided on techniques influenced by spectral density through which the concept of community structure arises. Through the use of simulated and real HSI data, we demonstrate density-based edge allocation produces more uniform nearest neighbor lists than non-density based techniques through increasing the number of intracluster edges, facilitating higher k-nearest neighbor (k-NN) classification performance. Imposing the common mutuality constraint to symmetrify adjacency matrices is demonstrated to be beneficial in most circumstances, especially in rural (less cluttered) scenes. Many complex adaptive edge-reweighting techniques are shown to slightly degrade nearest-neighbor list characteristics. Analysis suggests this condition is possibly attributable to the validity of characterizing spectral density by a single variable representing data scale for each pixel. Additionally, it is shown that imposing mutuality hurts the performance of adaptive edge-allocation techniques or any technique that aims to assign a low number of edges (<10) to any pixel. A simple k bias addresses this problem. Many of the adaptive edge-reweighting techniques are based on the concept of codensity, so we explore codensity properties as they relate to density-based edge reweighting. We find that codensity may not be the best estimator of local scale due to variations in cluster density, so we introduce and compare two inherently density-weighted graph construction techniques from the data mining literature: shared nearest neighbors (SNN) and mutual proximity (MP). MP and SNN are not reliant upon a codensity measure, hence are not susceptible to its shortcomings. Neither has been used for hyperspectral analyses, so this presents the first study of these techniques on HSI data. We demonstrate MP and SNN can offer better performance, but in general none of the reweighting techniques improve the quality of these spectral graphs in our neighborhood structure tests. As such, these complex adaptive edge-reweighting techniques may need to be modified to increase their effectiveness. During this investigation, we probe deeper into properties of high-dimensional data and introduce the concept of concentration of measure (CoM)--the degradation in the efficacy of many common distance measures with increasing dimensionality--as it relates to spectral graph construction. CoM exists in pairwise distances between HSI pixels, but not to the degree experienced in random data of the same extrinsic dimension; a characteristic we demonstrate is due to the rich correlation and cluster structure present in HSI data. CoM can lead to hubness--a condition wherein some nodes have short distances (high similarities) to an exceptionally large number of nodes. We study hub presence in 49 HSI datasets of varying resolutions, altitudes, and spectral bands to demonstrate hubness effects are negligible in a k-NN classification example (generalized counting scenarios), but we note its impact on methods that use edge weights to derive manifold coordinates or splitting clusters based on spectral graph theory requires more investigation. Many of these new graph-related quantities can be exploited to demonstrate new techniques for HSI classification and anomaly detection. We present an initial exploration into this relatively new and exciting field based on an enhanced Schroedinger Eigenmap classification example and compare results to the current state-of-the-art approach. We produce equivalent results, but demonstrate different types of misclassifications, opening the door to combine the best of both approaches to achieve truly superior performance. A separate less mature hubness-assisted anomaly detector (HAAD) is also presented.

SPECTRAL GRAPH THEORY AND GRAPH ENERGY METRICS SHOW EVIDENCE FOR THE ALZHEIMER’S DISEASE DISCONNECTION SYNDROME IN APOE-4 RISK GENE CARRIERS

PubMed Central

Daianu, Madelaine; Mezher, Adam; Jahanshad, Neda; Hibar, Derrek P.; Nir, Talia M.; Jack, Clifford R.; Weiner, Michael W.; Bernstein, Matt A.; Thompson, Paul M.

2015-01-01

Our understanding of network breakdown in Alzheimer’s disease (AD) is likely to be enhanced through advanced mathematical descriptors. Here, we applied spectral graph theory to provide novel metrics of structural connectivity based on 3-Tesla diffusion weighted images in 42 AD patients and 50 healthy controls. We reconstructed connectivity networks using whole-brain tractography and examined, for the first time here, cortical disconnection based on the graph energy and spectrum. We further assessed supporting metrics - link density and nodal strength - to better interpret our results. Metrics were analyzed in relation to the well-known APOE-4 genetic risk factor for late-onset AD. The number of disconnected cortical regions increased with the number of copies of the APOE-4 risk gene in people with AD. Each additional copy of the APOE-4 risk gene may lead to more dysfunctional networks with weakened or abnormal connections, providing evidence for the previously hypothesized “disconnection syndrome”. PMID:26413205

SPECTRAL GRAPH THEORY AND GRAPH ENERGY METRICS SHOW EVIDENCE FOR THE ALZHEIMER'S DISEASE DISCONNECTION SYNDROME IN APOE-4 RISK GENE CARRIERS.

PubMed

Daianu, Madelaine; Mezher, Adam; Jahanshad, Neda; Hibar, Derrek P; Nir, Talia M; Jack, Clifford R; Weiner, Michael W; Bernstein, Matt A; Thompson, Paul M

2015-04-01

Our understanding of network breakdown in Alzheimer's disease (AD) is likely to be enhanced through advanced mathematical descriptors. Here, we applied spectral graph theory to provide novel metrics of structural connectivity based on 3-Tesla diffusion weighted images in 42 AD patients and 50 healthy controls. We reconstructed connectivity networks using whole-brain tractography and examined, for the first time here, cortical disconnection based on the graph energy and spectrum. We further assessed supporting metrics - link density and nodal strength - to better interpret our results. Metrics were analyzed in relation to the well-known APOE -4 genetic risk factor for late-onset AD. The number of disconnected cortical regions increased with the number of copies of the APOE -4 risk gene in people with AD. Each additional copy of the APOE -4 risk gene may lead to more dysfunctional networks with weakened or abnormal connections, providing evidence for the previously hypothesized "disconnection syndrome".

Melonic Phase Transition in Group Field Theory

NASA Astrophysics Data System (ADS)

Baratin, Aristide; Carrozza, Sylvain; Oriti, Daniele; Ryan, James; Smerlak, Matteo

2014-08-01

Group field theories have recently been shown to admit a 1/N expansion dominated by so-called `melonic graphs', dual to triangulated spheres. In this note, we deepen the analysis of this melonic sector. We obtain a combinatorial formula for the melonic amplitudes in terms of a graph polynomial related to a higher-dimensional generalization of the Kirchhoff tree-matrix theorem. Simple bounds on these amplitudes show the existence of a phase transition driven by melonic interaction processes. We restrict our study to the Boulatov-Ooguri models, which describe topological BF theories and are the basis for the construction of 4-dimensional models of quantum gravity.

On a programming language for graph algorithms

NASA Technical Reports Server (NTRS)

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

1971-01-01

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

Quantum Experiments and Graphs: Multiparty States as Coherent Superpositions of Perfect Matchings

NASA Astrophysics Data System (ADS)

Krenn, Mario; Gu, Xuemei; Zeilinger, Anton

2017-12-01

We show a surprising link between experimental setups to realize high-dimensional multipartite quantum states and graph theory. In these setups, the paths of photons are identified such that the photon-source information is never created. We find that each of these setups corresponds to an undirected graph, and every undirected graph corresponds to an experimental setup. Every term in the emerging quantum superposition corresponds to a perfect matching in the graph. Calculating the final quantum state is in the #P-complete complexity class, thus it cannot be done efficiently. To strengthen the link further, theorems from graph theory—such as Hall's marriage problem—are rephrased in the language of pair creation in quantum experiments. We show explicitly how this link allows one to answer questions about quantum experiments (such as which classes of entangled states can be created) with graph theoretical methods, and how to potentially simulate properties of graphs and networks with quantum experiments (such as critical exponents and phase transitions).

Counting surface-kernel epimorphisms from a co-compact Fuchsian group to a cyclic group with motivations from string theory and QFT

NASA Astrophysics Data System (ADS)

Bibak, Khodakhast; Kapron, Bruce M.; Srinivasan, Venkatesh

2016-09-01

Graphs embedded into surfaces have many important applications, in particular, in combinatorics, geometry, and physics. For example, ribbon graphs and their counting is of great interest in string theory and quantum field theory (QFT). Recently, Koch et al. (2013) [12] gave a refined formula for counting ribbon graphs and discussed its applications to several physics problems. An important factor in this formula is the number of surface-kernel epimorphisms from a co-compact Fuchsian group to a cyclic group. The aim of this paper is to give an explicit and practical formula for the number of such epimorphisms. As a consequence, we obtain an 'equivalent' form of Harvey's famous theorem on the cyclic groups of automorphisms of compact Riemann surfaces. Our main tool is an explicit formula for the number of solutions of restricted linear congruence recently proved by Bibak et al. using properties of Ramanujan sums and of the finite Fourier transform of arithmetic functions.

Detectable states, cycle fluxes, and motility scaling of molecular motor kinesin: An integrative kinetic graph theory analysis

NASA Astrophysics Data System (ADS)

Ren, Jie

2017-12-01

The process by which a kinesin motor couples its ATPase activity with concerted mechanical hand-over-hand steps is a foremost topic of molecular motor physics. Two major routes toward elucidating kinesin mechanisms are the motility performance characterization of velocity and run length, and single-molecular state detection experiments. However, these two sets of experimental approaches are largely uncoupled to date. Here, we introduce an integrative motility state analysis based on a theorized kinetic graph theory for kinesin, which, on one hand, is validated by a wealth of accumulated motility data, and, on the other hand, allows for rigorous quantification of state occurrences and chemomechanical cycling probabilities. An interesting linear scaling for kinesin motility performance across species is discussed as well. An integrative kinetic graph theory analysis provides a powerful tool to bridge motility and state characterization experiments, so as to forge a unified effort for the elucidation of the working mechanisms of molecular motors.

Analysis of spontaneous EEG activity in Alzheimer's disease using cross-sample entropy and graph theory.

PubMed

Gomez, Carlos; Poza, Jesus; Gomez-Pilar, Javier; Bachiller, Alejandro; Juan-Cruz, Celia; Tola-Arribas, Miguel A; Carreres, Alicia; Cano, Monica; Hornero, Roberto

2016-08-01

The aim of this pilot study was to analyze spontaneous electroencephalography (EEG) activity in Alzheimer's disease (AD) by means of Cross-Sample Entropy (Cross-SampEn) and two local measures derived from graph theory: clustering coefficient (CC) and characteristic path length (PL). Five minutes of EEG activity were recorded from 37 patients with dementia due to AD and 29 elderly controls. Our results showed that Cross-SampEn values were lower in the AD group than in the control one for all the interactions among EEG channels. This finding indicates that EEG activity in AD is characterized by a lower statistical dissimilarity among channels. Significant differences were found mainly for fronto-central interactions (p <; 0.01, permutation test). Additionally, the application of graph theory measures revealed diverse neural network changes, i.e. lower CC and higher PL values in AD group, leading to a less efficient brain organization. This study suggests the usefulness of our approach to provide further insights into the underlying brain dynamics associated with AD.

Examining Graphing Calculator Affordances in Learning Pre-Calculus among Undergraduate Students

ERIC Educational Resources Information Center

Nzuki, Francis

2016-01-01

This study examines graphing calculator affordances in learning mathematics among college precalculus students. The study draws from the Cognitive Load Theory (CLT) and the "Intelligent Technology" theoretical framework proposed by Salomon, Perkins, and Globerson (1991). From these perspectives the effects "with" the graphing…

Fibonacci Identities, Matrices, and Graphs

ERIC Educational Resources Information Center

Huang, Danrun

2005-01-01

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

Random sequential renormalization and agglomerative percolation in networks: application to Erdös-Rényi and scale-free graphs.

PubMed

Bizhani, Golnoosh; Grassberger, Peter; Paczuski, Maya

2011-12-01

We study the statistical behavior under random sequential renormalization (RSR) of several network models including Erdös-Rényi (ER) graphs, scale-free networks, and an annealed model related to ER graphs. In RSR the network is locally coarse grained by choosing at each renormalization step a node at random and joining it to all its neighbors. Compared to previous (quasi-)parallel renormalization methods [Song et al., Nature (London) 433, 392 (2005)], RSR allows a more fine-grained analysis of the renormalization group (RG) flow and unravels new features that were not discussed in the previous analyses. In particular, we find that all networks exhibit a second-order transition in their RG flow. This phase transition is associated with the emergence of a giant hub and can be viewed as a new variant of percolation, called agglomerative percolation. We claim that this transition exists also in previous graph renormalization schemes and explains some of the scaling behavior seen there. For critical trees it happens as N/N(0) → 0 in the limit of large systems (where N(0) is the initial size of the graph and N its size at a given RSR step). In contrast, it happens at finite N/N(0) in sparse ER graphs and in the annealed model, while it happens for N/N(0) → 1 on scale-free networks. Critical exponents seem to depend on the type of the graph but not on the average degree and obey usual scaling relations for percolation phenomena. For the annealed model they agree with the exponents obtained from a mean-field theory. At late times, the networks exhibit a starlike structure in agreement with the results of Radicchi et al. [Phys. Rev. Lett. 101, 148701 (2008)]. While degree distributions are of main interest when regarding the scheme as network renormalization, mass distributions (which are more relevant when considering "supernodes" as clusters) are much easier to study using the fast Newman-Ziff algorithm for percolation, allowing us to obtain very high statistics.

Quantum walk on a chimera graph

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Pinching parameters for open (super) strings

NASA Astrophysics Data System (ADS)

Playle, Sam; Sciuto, Stefano

2018-02-01

We present an approach to the parametrization of (super) Schottky space obtained by sewing together three-punctured discs with strips. Different cubic ribbon graphs classify distinct sets of pinching parameters; we show how they are mapped onto each other. The parametrization is particularly well-suited to describing the region within (super) moduli space where open bosonic or Neveu-Schwarz string propagators become very long and thin, which dominates the IR behaviour of string theories. We show how worldsheet objects such as the Green's function converge to graph theoretic objects such as the Symanzik polynomials in the α ' → 0 limit, allowing us to see how string theory reproduces the sum over Feynman graphs. The (super) string measure takes on a simple and elegant form when expressed in terms of these parameters.

Using graph theory to analyze biological networks

PubMed Central

2011-01-01

Understanding complex systems often requires a bottom-up analysis towards a systems biology approach. The need to investigate a system, not only as individual components but as a whole, emerges. This can be done by examining the elementary constituents individually and then how these are connected. The myriad components of a system and their interactions are best characterized as networks and they are mainly represented as graphs where thousands of nodes are connected with thousands of vertices. In this article we demonstrate approaches, models and methods from the graph theory universe and we discuss ways in which they can be used to reveal hidden properties and features of a network. This network profiling combined with knowledge extraction will help us to better understand the biological significance of the system. PMID:21527005

Evolutionary dynamics on graphs

NASA Astrophysics Data System (ADS)

Lieberman, Erez; Hauert, Christoph; Nowak, Martin A.

2005-01-01

Evolutionary dynamics have been traditionally studied in the context of homogeneous or spatially extended populations. Here we generalize population structure by arranging individuals on a graph. Each vertex represents an individual. The weighted edges denote reproductive rates which govern how often individuals place offspring into adjacent vertices. The homogeneous population, described by the Moran process, is the special case of a fully connected graph with evenly weighted edges. Spatial structures are described by graphs where vertices are connected with their nearest neighbours. We also explore evolution on random and scale-free networks. We determine the fixation probability of mutants, and characterize those graphs for which fixation behaviour is identical to that of a homogeneous population. Furthermore, some graphs act as suppressors and others as amplifiers of selection. It is even possible to find graphs that guarantee the fixation of any advantageous mutant. We also study frequency-dependent selection and show that the outcome of evolutionary games can depend entirely on the structure of the underlying graph. Evolutionary graph theory has many fascinating applications ranging from ecology to multi-cellular organization and economics.

Graph theory and cognition: A complementary avenue for examining neuropsychological status in epilepsy.

PubMed

Garcia-Ramos, Camille; Lin, Jack J; Kellermann, Tanja S; Bonilha, Leonardo; Prabhakaran, Vivek; Hermann, Bruce P

2016-11-01

The recent revision of the classification of the epilepsies released by the ILAE Commission on Classification and Terminology (2005-2009) has been a major development in the field. Papers in this section of the special issue explore the relevance of other techniques to examine, categorize, and classify cognitive and behavioral comorbidities in epilepsy. In this review, we investigate the applicability of graph theory to understand the impact of epilepsy on cognition compared with controls and, then, the patterns of cognitive development in normally developing children which would set the stage for prospective comparisons of children with epilepsy and controls. The overall goal is to examine the potential utility of this analytic tool and approach to conceptualize the cognitive comorbidities in epilepsy. Given that the major cognitive domains representing cognitive function are interdependent, the associations between neuropsychological abilities underlying these domains can be referred to as a cognitive network. Therefore, the architecture of this cognitive network can be quantified and assessed using graph theory methods, rendering a novel approach to the characterization of cognitive status. We first provide fundamental information about graph theory procedures, followed by application of these techniques to cross-sectional analysis of neuropsychological data in children with epilepsy compared with that of controls, concluding with prospective analysis of neuropsychological development in younger and older healthy controls. This article is part of a Special Issue entitled "The new approach to classification: Rethinking cognition and behavior in epilepsy". Copyright © 2016 Elsevier Inc. All rights reserved.

Evolutionary graph theory: breaking the symmetry between interaction and replacement

PubMed Central

Ohtsuki, Hisashi; Pacheco, Jorge M.; Nowak, Martin A.

2008-01-01

We study evolutionary dynamics in a population whose structure is given by two graphs: the interaction graph determines who plays with whom in an evolutionary game; the replacement graph specifies the geometry of evolutionary competition and updating. First, we calculate the fixation probabilities of frequency dependent selection between two strategies or phenotypes. We consider three different update mechanisms: birth-death, death-birth and imitation. Then, as a particular example, we explore the evolution of cooperation. Suppose the interaction graph is a regular graph of degree h, the replacement graph is a regular graph of degree g and the overlap between the two graphs is a regular graph of degree l. We show that cooperation is favored by natural selection if b/c > hg/l. Here, b and c denote the benefit and cost of the altruistic act. This result holds for death-birth updating, weak selection and large population size. Note that the optimum population structure for cooperators is given by maximum overlap between the interaction and the replacement graph (g = h = l), which means that the two graphs are identical. We also prove that a modified replicator equation can describe how the expected values of the frequencies of an arbitrary number of strategies change on replacement and interaction graphs: the two graphs induce a transformation of the payoff matrix. PMID:17350049

Phase-change lines, scale breaks, and trend lines using Excel 2013.

PubMed

Deochand, Neil; Costello, Mack S; Fuqua, R Wayne

2015-01-01

The development of graphing skills for behavior analysts is an ongoing process. Specialized graphing software is often expensive, is not widely disseminated, and may require specific training. Dixon et al. (2009) provided an updated task analysis for graph making in the widely used platform Excel 2007. Vanselow and Bourret (2012) provided online tutorials that outline some alternate methods also using Office 2007. This article serves as an update to those task analyses and includes some alternative and underutilized methods in Excel 2013. To examine the utility of our recommendations, 12 psychology graduate students were presented with the task analyses, and the experimenters evaluated their performance and noted feedback. The task analyses were rated favorably. © Society for the Experimental Analysis of Behavior.

Analyses of Crime Patterns in NIBRS Data Based on a Novel Graph Theory Clustering Method: Virginia as a Case Study

PubMed Central

Nolan, Jim

2014-01-01

This paper suggests a novel clustering method for analyzing the National Incident-Based Reporting System (NIBRS) data, which include the determination of correlation of different crime types, the development of a likelihood index for crimes to occur in a jurisdiction, and the clustering of jurisdictions based on crime type. The method was tested by using the 2005 assault data from 121 jurisdictions in Virginia as a test case. The analyses of these data show that some different crime types are correlated and some different crime parameters are correlated with different crime types. The analyses also show that certain jurisdictions within Virginia share certain crime patterns. This information assists with constructing a pattern for a specific crime type and can be used to determine whether a jurisdiction may be more likely to see this type of crime occur in their area. PMID:24778585

Graph Theoretic and Motif Analyses of the Hippocampal Neuron Type Potential Connectome.

PubMed

Rees, Christopher L; Wheeler, Diek W; Hamilton, David J; White, Charise M; Komendantov, Alexander O; Ascoli, Giorgio A

2016-01-01

We computed the potential connectivity map of all known neuron types in the rodent hippocampal formation by supplementing scantly available synaptic data with spatial distributions of axons and dendrites from the open-access knowledge base Hippocampome.org. The network that results from this endeavor, the broadest and most complete for a mammalian cortical region at the neuron-type level to date, contains more than 3200 connections among 122 neuron types across six subregions. Analyses of these data using graph theory metrics unveil the fundamental architectural principles of the hippocampal circuit. Globally, we identify a highly specialized topology minimizing communication cost; a modular structure underscoring the prominence of the trisynaptic loop; a core set of neuron types serving as information-processing hubs as well as a distinct group of particular antihub neurons; a nested, two-tier rich club managing much of the network traffic; and an innate resilience to random perturbations. At the local level, we uncover the basic building blocks, or connectivity patterns, that combine to produce complex global functionality, and we benchmark their utilization in the circuit relative to random networks. Taken together, these results provide a comprehensive connectivity profile of the hippocampus, yielding novel insights on its functional operations at the computationally crucial level of neuron types.

Discovering Authorities and Hubs in Different Topological Web Graph Structures.

ERIC Educational Resources Information Center

Meghabghab, George

2002-01-01

Discussion of citation analysis on the Web considers Web hyperlinks as a source to analyze citations. Topics include basic graph theory applied to Web pages, including matrices, linear algebra, and Web topology; and hubs and authorities, including a search technique called HITS (Hyperlink Induced Topic Search). (Author/LRW)

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

PubMed

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

2013-02-01

Bootstrap methods have recently been introduced to diffusion-weighted magnetic resonance imaging to estimate the measurement uncertainty of ensuing diffusion parameters directly from the acquired data without the necessity to assume a noise model. These methods have been previously combined with deterministic streamline tractography algorithms to allow for the assessment of connection probabilities in the human brain. Thereby, the local noise induced disturbance in the diffusion data is accumulated additively due to the incremental progression of streamline tractography algorithms. Graph based approaches have been proposed to overcome this drawback of streamline techniques. For this reason, the bootstrap method is in the present work incorporated into a graph setup to derive a new probabilistic fiber tractography method, called BootGraph. The acquired data set is thereby converted into a weighted, undirected graph by defining a vertex in each voxel and edges between adjacent vertices. By means of the cone of uncertainty, which is derived using the wild bootstrap, a weight is thereafter assigned to each edge. Two path finding algorithms are subsequently applied to derive connection probabilities. While the first algorithm is based on the shortest path approach, the second algorithm takes all existing paths between two vertices into consideration. Tracking results are compared to an established algorithm based on the bootstrap method in combination with streamline fiber tractography and to another graph based algorithm. The BootGraph shows a very good performance in crossing situations with respect to false negatives and permits incorporating additional constraints, such as a curvature threshold. By inheriting the advantages of the bootstrap method and graph theory, the BootGraph method provides a computationally efficient and flexible probabilistic tractography setup to compute connection probability maps and virtual fiber pathways without the drawbacks of streamline tractography algorithms or the assumption of a noise distribution. Moreover, the BootGraph can be applied to common DTI data sets without further modifications and shows a high repeatability. Thus, it is very well suited for longitudinal studies and meta-studies based on DTI. Copyright © 2012 Elsevier Inc. All rights reserved.

Integrability of conformal fishnet theory

NASA Astrophysics Data System (ADS)

Gromov, Nikolay; Kazakov, Vladimir; Korchemsky, Gregory; Negro, Stefano; Sizov, Grigory

2018-01-01

We study integrability of fishnet-type Feynman graphs arising in planar four-dimensional bi-scalar chiral theory recently proposed in arXiv:1512.06704 as a special double scaling limit of gamma-deformed N = 4 SYM theory. We show that the transfer matrix "building" the fishnet graphs emerges from the R-matrix of non-compact conformal SU(2 , 2) Heisenberg spin chain with spins belonging to principal series representations of the four-dimensional conformal group. We demonstrate explicitly a relationship between this integrable spin chain and the Quantum Spectral Curve (QSC) of N = 4 SYM. Using QSC and spin chain methods, we construct Baxter equation for Q-functions of the conformal spin chain needed for computation of the anomalous dimensions of operators of the type tr( ϕ 1 J ) where ϕ 1 is one of the two scalars of the theory. For J = 3 we derive from QSC a quantization condition that fixes the relevant solution of Baxter equation. The scaling dimensions of the operators only receive contributions from wheel-like graphs. We develop integrability techniques to compute the divergent part of these graphs and use it to present the weak coupling expansion of dimensions to very high orders. Then we apply our exact equations to calculate the anomalous dimensions with J = 3 to practically unlimited precision at any coupling. These equations also describe an infinite tower of local conformal operators all carrying the same charge J = 3. The method should be applicable for any J and, in principle, to any local operators of bi-scalar theory. We show that at strong coupling the scaling dimensions can be derived from semiclassical quantization of finite gap solutions describing an integrable system of noncompact SU(2 , 2) spins. This bears similarities with the classical strings arising in the strongly coupled limit of N = 4 SYM.

Geographic information modeling of Econet of Northwestern Federal District territory on graph theory basis

NASA Astrophysics Data System (ADS)

Kopylova, N. S.; Bykova, A. A.; Beregovoy, D. N.

2018-05-01

Based on the landscape-geographical approach, a structural and logical scheme for the Northwestern Federal District Econet has been developed, which can be integrated into the federal and world ecological network in order to improve the environmental infrastructure of the region. The method of Northwestern Federal District Econet organization on the basis of graph theory by means of the Quantum GIS geographic information system is proposed as an effective mean of preserving and recreating the unique biodiversity of landscapes, regulation of the sphere of environmental protection.

On Connected Diagrams and Cumulants of Erdős-Rényi Matrix Models

NASA Astrophysics Data System (ADS)

Khorunzhiy, O.

2008-08-01

Regarding the adjacency matrices of n-vertex graphs and related graph Laplacian we introduce two families of discrete matrix models constructed both with the help of the Erdős-Rényi ensemble of random graphs. Corresponding matrix sums represent the characteristic functions of the average number of walks and closed walks over the random graph. These sums can be considered as discrete analogues of the matrix integrals of random matrix theory. We study the diagram structure of the cumulant expansions of logarithms of these matrix sums and analyze the limiting expressions as n → ∞ in the cases of constant and vanishing edge probabilities.

Bond graph modelling of multibody dynamics and its symbolic scheme

NASA Astrophysics Data System (ADS)

Kawase, Takehiko; Yoshimura, Hiroaki

A bond graph method of modeling multibody dynamics is demonstrated. Specifically, a symbolic generation scheme which fully utilizes the bond graph information is presented. It is also demonstrated that structural understanding and representation in bond graph theory is quite powerful for the modeling of such large scale systems, and that the nonenergic multiport of junction structure, which is a multiport expression of the system structure, plays an important role, as first suggested by Paynter. The principal part of the proposed symbolic scheme, that is, the elimination of excess variables, is done through tearing and interconnection in the sense of Kron using newly defined causal and causal coefficient arrays.

Summing Feynman graphs by Monte Carlo: Planar ϕ3-theory and dynamically triangulated random surfaces

NASA Astrophysics Data System (ADS)

Boulatov, D. V.; Kazakov, V. A.

1988-12-01

New combinatorial identities are suggested relating the ratio of (n - 1)th and nth orders of (planar) perturbation expansion for any quantity to some average over the ensemble of all planar graphs of the nth order. These identities are used for Monte Carlo calculation of critical exponents γstr (string susceptibility) in planar ϕ3-theory and in the dynamically triangulated random surface (DTRS) model near the convergence circle for various dimensions. In the solvable case D = 1 the exact critical properties of the theory are reproduced numerically. After August 3, 1988 the address will be: Cybernetics Council, Academy of Science, ul. Vavilova 40, 117333 Moscow, USSR.

The entropic boundary law in BF theory

NASA Astrophysics Data System (ADS)

Livine, Etera R.; Terno, Daniel R.

2009-01-01

We compute the entropy of a closed bounded region of space for pure 3d Riemannian gravity formulated as a topological BF theory for the gauge group SU(2) and show its holographic behavior. More precisely, we consider a fixed graph embedded in space and study the flat connection spin network state without and with particle-like topological defects. We regularize and compute exactly the entanglement for a bipartite splitting of the graph and show it scales at leading order with the number of vertices on the boundary (or equivalently with the number of loops crossing the boundary). More generally these results apply to BF theory with any compact gauge group in any space-time dimension.

Solving Multi-variate Polynomial Equations in a Finite Field

DTIC Science & Technology

2013-06-01

Algebraic Background In this section, some algebraic definitions and basics are discussed as they pertain to this re- search. For a more detailed...definitions and basics are discussed as they pertain to this research. For a more detailed treatment, consult a graph theory text such as [10]. A graph G...graph if V(G) can be partitioned into k subsets V1,V2, ...,Vk such that uv is only an edge of G if u and v belong to different partite sets. If, in

Group field theories for all loop quantum gravity

NASA Astrophysics Data System (ADS)

Oriti, Daniele; Ryan, James P.; Thürigen, Johannes

2015-02-01

Group field theories represent a second quantized reformulation of the loop quantum gravity state space and a completion of the spin foam formalism. States of the canonical theory, in the traditional continuum setting, have support on graphs of arbitrary valence. On the other hand, group field theories have usually been defined in a simplicial context, thus dealing with a restricted set of graphs. In this paper, we generalize the combinatorics of group field theories to cover all the loop quantum gravity state space. As an explicit example, we describe the group field theory formulation of the KKL spin foam model, as well as a particular modified version. We show that the use of tensor model tools allows for the most effective construction. In order to clarify the mathematical basis of our construction and of the formalisms with which we deal, we also give an exhaustive description of the combinatorial structures entering spin foam models and group field theories, both at the level of the boundary states and of the quantum amplitudes.

An algorithm for automatic reduction of complex signal flow graphs

NASA Technical Reports Server (NTRS)

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

1976-01-01

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

Improving the Pedagogy of Capital Structure Theory: An Excel Application

ERIC Educational Resources Information Center

Baltazar, Ramon; Maybee, Bryan; Santos, Michael R.

2012-01-01

This paper uses Excel to enhance the pedagogy of capital structure theory for corporate finance instructors and students. We provide a lesson plan that utilizes Excel spreadsheets and graphs to develop understanding of the theory. The theory is introduced in three scenarios that utilize Modigliani & Miller's Propositions and…

Experimental Study of Quantum Graphs with Microwave Networks

NASA Astrophysics Data System (ADS)

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

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

Disease management research using event graphs.

PubMed

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.

An Adiabatic Quantum Algorithm for Determining Gracefulness of a Graph

NASA Astrophysics Data System (ADS)

Hosseini, Sayed Mohammad; Davoudi Darareh, Mahdi; Janbaz, Shahrooz; Zaghian, Ali

2017-07-01

Graph labelling is one of the noticed contexts in combinatorics and graph theory. Graceful labelling for a graph G with e edges, is to label the vertices of G with 0, 1, ℒ, e such that, if we specify to each edge the difference value between its two ends, then any of 1, 2, ℒ, e appears exactly once as an edge label. For a given graph, there are still few efficient classical algorithms that determine either it is graceful or not, even for trees - as a well-known class of graphs. In this paper, we introduce an adiabatic quantum algorithm, which for a graceful graph G finds a graceful labelling. Also, this algorithm can determine if G is not graceful. Numerical simulations of the algorithm reveal that its time complexity has a polynomial behaviour with the problem size up to the range of 15 qubits. A general sufficient condition for a combinatorial optimization problem to have a satisfying adiabatic solution is also derived.

Decentralised consensus-based formation tracking of multiple differential drive robots

NASA Astrophysics Data System (ADS)

Chu, Xing; Peng, Zhaoxia; Wen, Guoguang; Rahmani, Ahmed

2017-11-01

This article investigates the control problem for formation tracking of multiple nonholonomic robots under distributed manner which means each robot only needs local information exchange. A class of general state and input transform is introduced to convert the formation-tracking issue of multi-robot systems into the consensus-like problem with time-varying reference. The distributed observer-based protocol with nonlinear dynamics is developed for each robot to achieve the consensus tracking of the new system, which namely means a group of nonholonomic mobile robots can form the desired formation configuration with its centroid moving along the predefined reference trajectory. The finite-time stability of observer and control law is analysed rigorously by using the Lyapunov direct method, algebraic graph theory and matrix analysis. Numerical examples are finally provided to illustrate the effectiveness of the theory results proposed in this paper.

Distributed Cooperative Optimal Control for Multiagent Systems on Directed Graphs: An Inverse Optimal Approach.

PubMed

Zhang, Huaguang; Feng, Tao; Yang, Guang-Hong; Liang, Hongjing

2015-07-01

In this paper, the inverse optimal approach is employed to design distributed consensus protocols that guarantee consensus and global optimality with respect to some quadratic performance indexes for identical linear systems on a directed graph. The inverse optimal theory is developed by introducing the notion of partial stability. As a result, the necessary and sufficient conditions for inverse optimality are proposed. By means of the developed inverse optimal theory, the necessary and sufficient conditions are established for globally optimal cooperative control problems on directed graphs. Basic optimal cooperative design procedures are given based on asymptotic properties of the resulting optimal distributed consensus protocols, and the multiagent systems can reach desired consensus performance (convergence rate and damping rate) asymptotically. Finally, two examples are given to illustrate the effectiveness of the proposed methods.

Multi-parametric centrality method for graph network models

NASA Astrophysics Data System (ADS)

Ivanov, Sergei Evgenievich; Gorlushkina, Natalia Nikolaevna; Ivanova, Lubov Nikolaevna

2018-04-01

The graph model networks are investigated to determine centrality, weights and the significance of vertices. For centrality analysis appliesa typical method that includesany one of the properties of graph vertices. In graph theory, methods of analyzing centrality are used: in terms by degree, closeness, betweenness, radiality, eccentricity, page-rank, status, Katz and eigenvector. We have proposed a new method of multi-parametric centrality, which includes a number of basic properties of the network member. The mathematical model of multi-parametric centrality method is developed. Comparison of results for the presented method with the centrality methods is carried out. For evaluate the results for the multi-parametric centrality methodthe graph model with hundreds of vertices is analyzed. The comparative analysis showed the accuracy of presented method, includes simultaneously a number of basic properties of vertices.

Conclusiveness of natural languages and recognition of images

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wojcik, Z.M.

1983-01-01

The conclusiveness is investigated using recognition processes and one-one correspondence between expressions of a natural language and graphs representing events. The graphs, as conceived in psycholinguistics, are obtained as a result of perception processes. It is possible to generate and process the graphs automatically, using computers and then to convert the resulting graphs into expressions of a natural language. Correctness and conclusiveness of the graphs and sentences are investigated using the fundamental condition for events representation processes. Some consequences of the conclusiveness are discussed, e.g. undecidability of arithmetic, human brain assymetry, correctness of statistical calculations and operations research. It ismore » suggested that the group theory should be imposed on mathematical models of any real system. Proof of the fundamental condition is also presented. 14 references.« less

Structural Analysis of Treatment Cycles Representing Transitions between Nursing Organizational Units Inferred from Diabetes

PubMed Central

Dehmer, Matthias; Kurt, Zeyneb; Emmert-Streib, Frank; Them, Christa; Schulc, Eva; Hofer, Sabine

2015-01-01

In this paper, we investigate treatment cycles inferred from diabetes data by means of graph theory. We define the term treatment cycles graph-theoretically and perform a descriptive as well as quantitative analysis thereof. Also, we interpret our findings in terms of nursing and clinical management. PMID:26030296

An Automated Method to Identify Mesoscale Convective Complexes (MCCs) Implementing Graph Theory

NASA Astrophysics Data System (ADS)

Whitehall, K. D.; Mattmann, C. A.; Jenkins, G. S.; Waliser, D. E.; Rwebangira, R.; Demoz, B.; Kim, J.; Goodale, C. E.; Hart, A. F.; Ramirez, P.; Joyce, M. J.; Loikith, P.; Lee, H.; Khudikyan, S.; Boustani, M.; Goodman, A.; Zimdars, P. A.; Whittell, J.

2013-12-01

Mesoscale convective complexes (MCCs) are convectively-driven weather systems with a duration of ~10 - 12 hours and contributions of large amounts to the rainfall daily and monthly totals. More than 400 MCCs occur annually over various locations on the globe. In West Africa, ~170 MCCs occur annually during the 180 days representing the summer months (June - November), and contribute ~75% of the annual wet season rainfall. The main objective of this study is to improve automatic identification of MCC over West Africa. The spatial expanse of MCCs and the spatio-temporal variability in their convective characteristics make them difficult to characterize even in dense networks of radars and/or surface gauges. As such there exist criteria for identifying MCCs with satellite images - mostly using infrared (IR) data. Automated MCC identification methods are based on forward and/or backward in time spatial-temporal analysis of the IR satellite data and characteristically incorporate a manual component as these algorithms routinely falter with merging and splitting cloud systems between satellite images. However, these algorithms are not readily transferable to voluminous data or other satellite-derived datasets (e.g. TRMM), thus hindering comprehensive studies of these features both at weather and climate timescales. Recognizing the existing limitations of automated methods, this study explores the applicability of graph theory to creating a fully automated method for deriving a West African MCC dataset from hourly infrared satellite images between 2001- 2012. Graph theory, though not heavily implemented in the atmospheric sciences, has been used for the predicting (nowcasting) of thunderstorms from radar and satellite data by considering the relationship between atmospheric variables at a given time, or for the spatial-temporal analysis of cloud volumes. From these few studies, graph theory appears to be innately applicable to the complexity, non-linearity and inherent chaos of the atmospheric system. Our preliminary results show that the use of graph theory improves data management thus allowing for longer periods to be studied, and creates a transferable method that allows for other data to be utilized.

Which causal structures might support a quantum-classical gap?

NASA Astrophysics Data System (ADS)

Pienaar, Jacques

2017-04-01

A causal scenario is a graph that describes the cause and effect relationships between all relevant variables in an experiment. A scenario is deemed ‘not interesting’ if there is no device-independent way to distinguish the predictions of classical physics from any generalised probabilistic theory (including quantum mechanics). Conversely, an interesting scenario is one in which there exists a gap between the predictions of different operational probabilistic theories, as occurs for example in Bell-type experiments. Henson, Lal and Pusey (HLP) recently proposed a sufficient condition for a causal scenario to not be interesting. In this paper we supplement their analysis with some new techniques and results. We first show that existing graphical techniques due to Evans can be used to confirm by inspection that many graphs are interesting without having to explicitly search for inequality violations. For three exceptional cases—the graphs numbered \\#15,16,20 in HLP—we show that there exist non-Shannon type entropic inequalities that imply these graphs are interesting. In doing so, we find that existing methods of entropic inequalities can be greatly enhanced by conditioning on the specific values of certain variables.

Functional connectivity and graph theory in preclinical Alzheimer's disease.

PubMed

Brier, Matthew R; Thomas, Jewell B; Fagan, Anne M; Hassenstab, Jason; Holtzman, David M; Benzinger, Tammie L; Morris, John C; Ances, Beau M

2014-04-01

Alzheimer's disease (AD) has a long preclinical phase in which amyloid and tau cerebral pathology accumulate without producing cognitive symptoms. Resting state functional connectivity magnetic resonance imaging has demonstrated that brain networks degrade during symptomatic AD. It is unclear to what extent these degradations exist before symptomatic onset. In this study, we investigated graph theory metrics of functional integration (path length), functional segregation (clustering coefficient), and functional distinctness (modularity) as a function of disease severity. Further, we assessed whether these graph metrics were affected in cognitively normal participants with cerebrospinal fluid evidence of preclinical AD. Clustering coefficient and modularity, but not path length, were reduced in AD. Cognitively normal participants who harbored AD biomarker pathology also showed reduced values in these graph measures, demonstrating brain changes similar to, but smaller than, symptomatic AD. Only modularity was significantly affected by age. We also demonstrate that AD has a particular effect on hub-like regions in the brain. We conclude that AD causes large-scale disconnection that is present before onset of symptoms. Copyright © 2014 Elsevier Inc. All rights reserved.

A Graph Theory Practice on Transformed Image: A Random Image Steganography

PubMed Central

Thanikaiselvan, V.; Arulmozhivarman, P.; Subashanthini, S.; Amirtharajan, Rengarajan

2013-01-01

Modern day information age is enriched with the advanced network communication expertise but unfortunately at the same time encounters infinite security issues when dealing with secret and/or private information. The storage and transmission of the secret information become highly essential and have led to a deluge of research in this field. In this paper, an optimistic effort has been taken to combine graceful graph along with integer wavelet transform (IWT) to implement random image steganography for secure communication. The implementation part begins with the conversion of cover image into wavelet coefficients through IWT and is followed by embedding secret image in the randomly selected coefficients through graph theory. Finally stegoimage is obtained by applying inverse IWT. This method provides a maximum of 44 dB peak signal to noise ratio (PSNR) for 266646 bits. Thus, the proposed method gives high imperceptibility through high PSNR value and high embedding capacity in the cover image due to adaptive embedding scheme and high robustness against blind attack through graph theoretic random selection of coefficients. PMID:24453857

Complementary Network-Based Approaches for Exploring Genetic Structure and Functional Connectivity in Two Vulnerable, Endemic Ground Squirrels

PubMed Central

Zero, Victoria H.; Barocas, Adi; Jochimsen, Denim M.; Pelletier, Agnès; Giroux-Bougard, Xavier; Trumbo, Daryl R.; Castillo, Jessica A.; Evans Mack, Diane; Linnell, Mark A.; Pigg, Rachel M.; Hoisington-Lopez, Jessica; Spear, Stephen F.; Murphy, Melanie A.; Waits, Lisette P.

2017-01-01

The persistence of small populations is influenced by genetic structure and functional connectivity. We used two network-based approaches to understand the persistence of the northern Idaho ground squirrel (Urocitellus brunneus) and the southern Idaho ground squirrel (U. endemicus), two congeners of conservation concern. These graph theoretic approaches are conventionally applied to social or transportation networks, but here are used to study population persistence and connectivity. Population graph analyses revealed that local extinction rapidly reduced connectivity for the southern species, while connectivity for the northern species could be maintained following local extinction. Results from gravity models complemented those of population graph analyses, and indicated that potential vegetation productivity and topography drove connectivity in the northern species. For the southern species, development (roads) and small-scale topography reduced connectivity, while greater potential vegetation productivity increased connectivity. Taken together, the results of the two network-based methods (population graph analyses and gravity models) suggest the need for increased conservation action for the southern species, and that management efforts have been effective at maintaining habitat quality throughout the current range of the northern species. To prevent further declines, we encourage the continuation of management efforts for the northern species, whereas conservation of the southern species requires active management and additional measures to curtail habitat fragmentation. Our combination of population graph analyses and gravity models can inform conservation strategies of other species exhibiting patchy distributions. PMID:28659969

Complementary Network-Based Approaches for Exploring Genetic Structure and Functional Connectivity in Two Vulnerable, Endemic Ground Squirrels.

PubMed

Zero, Victoria H; Barocas, Adi; Jochimsen, Denim M; Pelletier, Agnès; Giroux-Bougard, Xavier; Trumbo, Daryl R; Castillo, Jessica A; Evans Mack, Diane; Linnell, Mark A; Pigg, Rachel M; Hoisington-Lopez, Jessica; Spear, Stephen F; Murphy, Melanie A; Waits, Lisette P

2017-01-01

The persistence of small populations is influenced by genetic structure and functional connectivity. We used two network-based approaches to understand the persistence of the northern Idaho ground squirrel ( Urocitellus brunneus) and the southern Idaho ground squirrel ( U. endemicus ), two congeners of conservation concern. These graph theoretic approaches are conventionally applied to social or transportation networks, but here are used to study population persistence and connectivity. Population graph analyses revealed that local extinction rapidly reduced connectivity for the southern species, while connectivity for the northern species could be maintained following local extinction. Results from gravity models complemented those of population graph analyses, and indicated that potential vegetation productivity and topography drove connectivity in the northern species. For the southern species, development (roads) and small-scale topography reduced connectivity, while greater potential vegetation productivity increased connectivity. Taken together, the results of the two network-based methods (population graph analyses and gravity models) suggest the need for increased conservation action for the southern species, and that management efforts have been effective at maintaining habitat quality throughout the current range of the northern species. To prevent further declines, we encourage the continuation of management efforts for the northern species, whereas conservation of the southern species requires active management and additional measures to curtail habitat fragmentation. Our combination of population graph analyses and gravity models can inform conservation strategies of other species exhibiting patchy distributions.

Edge connectivity and the spectral gap of combinatorial and quantum graphs

NASA Astrophysics Data System (ADS)

Berkolaiko, Gregory; Kennedy, James B.; Kurasov, Pavel; Mugnolo, Delio

2017-09-01

We derive a number of upper and lower bounds for the first nontrivial eigenvalue of Laplacians on combinatorial and quantum graph in terms of the edge connectivity, i.e. the minimal number of edges which need to be removed to make the graph disconnected. On combinatorial graphs, one of the bounds corresponds to a well-known inequality of Fiedler, of which we give a new variational proof. On quantum graphs, the corresponding bound generalizes a recent result of Band and Lévy. All proofs are general enough to yield corresponding estimates for the p-Laplacian and allow us to identify the minimizers. Based on the Betti number of the graph, we also derive upper and lower bounds on all eigenvalues which are ‘asymptotically correct’, i.e. agree with the Weyl asymptotics for the eigenvalues of the quantum graph. In particular, the lower bounds improve the bounds of Friedlander on any given graph for all but finitely many eigenvalues, while the upper bounds improve recent results of Ariturk. Our estimates are also used to derive bounds on the eigenvalues of the normalized Laplacian matrix that improve known bounds of spectral graph theory.

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

PubMed

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

2017-09-26

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

Exploring biomedical ontology mappings with graph theory methods.

PubMed

Kocbek, Simon; Kim, Jin-Dong

2017-01-01

In the era of semantic web, life science ontologies play an important role in tasks such as annotating biological objects, linking relevant data pieces, and verifying data consistency. Understanding ontology structures and overlapping ontologies is essential for tasks such as ontology reuse and development. We present an exploratory study where we examine structure and look for patterns in BioPortal, a comprehensive publicly available repository of live science ontologies. We report an analysis of biomedical ontology mapping data over time. We apply graph theory methods such as Modularity Analysis and Betweenness Centrality to analyse data gathered at five different time points. We identify communities, i.e., sets of overlapping ontologies, and define similar and closest communities. We demonstrate evolution of identified communities over time and identify core ontologies of the closest communities. We use BioPortal project and category data to measure community coherence. We also validate identified communities with their mutual mentions in scientific literature. With comparing mapping data gathered at five different time points, we identified similar and closest communities of overlapping ontologies, and demonstrated evolution of communities over time. Results showed that anatomy and health ontologies tend to form more isolated communities compared to other categories. We also showed that communities contain all or the majority of ontologies being used in narrower projects. In addition, we identified major changes in mapping data after migration to BioPortal Version 4.

On the degree distribution of horizontal visibility graphs associated with Markov processes and dynamical systems: diagrammatic and variational approaches

NASA Astrophysics Data System (ADS)

Lacasa, Lucas

2014-09-01

Dynamical processes can be transformed into graphs through a family of mappings called visibility algorithms, enabling the possibility of (i) making empirical time series analysis and signal processing and (ii) characterizing classes of dynamical systems and stochastic processes using the tools of graph theory. Recent works show that the degree distribution of these graphs encapsulates much information on the signals' variability, and therefore constitutes a fundamental feature for statistical learning purposes. However, exact solutions for the degree distributions are only known in a few cases, such as for uncorrelated random processes. Here we analytically explore these distributions in a list of situations. We present a diagrammatic formalism which computes for all degrees their corresponding probability as a series expansion in a coupling constant which is the number of hidden variables. We offer a constructive solution for general Markovian stochastic processes and deterministic maps. As case tests we focus on Ornstein-Uhlenbeck processes, fully chaotic and quasiperiodic maps. Whereas only for certain degree probabilities can all diagrams be summed exactly, in the general case we show that the perturbation theory converges. In a second part, we make use of a variational technique to predict the complete degree distribution for special classes of Markovian dynamics with fast-decaying correlations. In every case we compare the theory with numerical experiments.

Graphing evolutionary pattern and process: a history of techniques in archaeology and paleobiology.

PubMed

Lyman, R Lee

2009-02-01

Graphs displaying evolutionary patterns are common in paleontology and in United States archaeology. Both disciplines subscribed to a transformational theory of evolution and graphed evolution as a sequence of archetypes in the late nineteenth and early twentieth centuries. U.S. archaeologists in the second decade of the twentieth century, and paleontologists shortly thereafter, developed distinct graphic styles that reflected the Darwinian variational model of evolution. Paleobiologists adopted the view of a species as a set of phenotypically variant individuals and graphed those variations either as central tendencies or as histograms of frequencies of variants. Archaeologists presumed their artifact types reflected cultural norms of prehistoric artisans and the frequency of specimens in each type reflected human choice and type popularity. They graphed cultural evolution as shifts in frequencies of specimens representing each of several artifact types. Confusion of pattern and process is exemplified by a paleobiologist misinterpreting the process illustrated by an archaeological graph, and an archaeologist misinterpreting the process illustrated by a paleobiological graph. Each style of graph displays particular evolutionary patterns and implies particular evolutionary processes. Graphs of a multistratum collection of prehistoric mammal remains and a multistratum collection of artifacts demonstrate that many graph styles can be used for both kinds of collections.

Model-Based Fault Diagnosis: Performing Root Cause and Impact Analyses in Real Time

NASA Technical Reports Server (NTRS)

Figueroa, Jorge F.; Walker, Mark G.; Kapadia, Ravi; Morris, Jonathan

2012-01-01

Generic, object-oriented fault models, built according to causal-directed graph theory, have been integrated into an overall software architecture dedicated to monitoring and predicting the health of mission- critical systems. Processing over the generic fault models is triggered by event detection logic that is defined according to the specific functional requirements of the system and its components. Once triggered, the fault models provide an automated way for performing both upstream root cause analysis (RCA), and for predicting downstream effects or impact analysis. The methodology has been applied to integrated system health management (ISHM) implementations at NASA SSC's Rocket Engine Test Stands (RETS).

Homology groups for particles on one-connected graphs

NASA Astrophysics Data System (ADS)

MaciÄ Żek, Tomasz; Sawicki, Adam

2017-06-01

We present a mathematical framework for describing the topology of configuration spaces for particles on one-connected graphs. In particular, we compute the homology groups over integers for different classes of one-connected graphs. Our approach is based on some fundamental combinatorial properties of the configuration spaces, Mayer-Vietoris sequences for different parts of configuration spaces, and some limited use of discrete Morse theory. As one of the results, we derive the closed-form formulae for ranks of the homology groups for indistinguishable particles on tree graphs. We also give a detailed discussion of the second homology group of the configuration space of both distinguishable and indistinguishable particles. Our motivation is the search for new kinds of quantum statistics.

Identifying patients with Alzheimer's disease using resting-state fMRI and graph theory.

PubMed

Khazaee, Ali; Ebrahimzadeh, Ata; Babajani-Feremi, Abbas

2015-11-01

Study of brain network on the basis of resting-state functional magnetic resonance imaging (fMRI) has provided promising results to investigate changes in connectivity among different brain regions because of diseases. Graph theory can efficiently characterize different aspects of the brain network by calculating measures of integration and segregation. In this study, we combine graph theoretical approaches with advanced machine learning methods to study functional brain network alteration in patients with Alzheimer's disease (AD). Support vector machine (SVM) was used to explore the ability of graph measures in diagnosis of AD. We applied our method on the resting-state fMRI data of twenty patients with AD and twenty age and gender matched healthy subjects. The data were preprocessed and each subject's graph was constructed by parcellation of the whole brain into 90 distinct regions using the automated anatomical labeling (AAL) atlas. The graph measures were then calculated and used as the discriminating features. Extracted network-based features were fed to different feature selection algorithms to choose most significant features. In addition to the machine learning approach, statistical analysis was performed on connectivity matrices to find altered connectivity patterns in patients with AD. Using the selected features, we were able to accurately classify patients with AD from healthy subjects with accuracy of 100%. Results of this study show that pattern recognition and graph of brain network, on the basis of the resting state fMRI data, can efficiently assist in the diagnosis of AD. Classification based on the resting-state fMRI can be used as a non-invasive and automatic tool to diagnosis of Alzheimer's disease. Copyright © 2015 International Federation of Clinical Neurophysiology. All rights reserved.

Graph Theory and Ion and Molecular Aggregation in Aqueous Solutions.

PubMed

Choi, Jun-Ho; Lee, Hochan; Choi, Hyung Ran; Cho, Minhaeng

2018-04-20

In molecular and cellular biology, dissolved ions and molecules have decisive effects on chemical and biological reactions, conformational stabilities, and functions of small to large biomolecules. Despite major efforts, the current state of understanding of the effects of specific ions, osmolytes, and bioprotecting sugars on the structure and dynamics of water H-bonding networks and proteins is not yet satisfactory. Recently, to gain deeper insight into this subject, we studied various aggregation processes of ions and molecules in high-concentration salt, osmolyte, and sugar solutions with time-resolved vibrational spectroscopy and molecular dynamics simulation methods. It turns out that ions (or solute molecules) have a strong propensity to self-assemble into large and polydisperse aggregates that affect both local and long-range water H-bonding structures. In particular, we have shown that graph-theoretical approaches can be used to elucidate morphological characteristics of large aggregates in various aqueous salt, osmolyte, and sugar solutions. When ion and molecular aggregates in such aqueous solutions are treated as graphs, a variety of graph-theoretical properties, such as graph spectrum, degree distribution, clustering coefficient, minimum path length, and graph entropy, can be directly calculated by considering an ensemble of configurations taken from molecular dynamics trajectories. Here we show percolating behavior exhibited by ion and molecular aggregates upon increase in solute concentration in high solute concentrations and discuss compelling evidence of the isomorphic relation between percolation transitions of ion and molecular aggregates and water H-bonding networks. We anticipate that the combination of graph theory and molecular dynamics simulation methods will be of exceptional use in achieving a deeper understanding of the fundamental physical chemistry of dissolution and in describing the interplay between the self-aggregation of solute molecules and the structure and dynamics of water.

Graph Theory and Ion and Molecular Aggregation in Aqueous Solutions

NASA Astrophysics Data System (ADS)

Choi, Jun-Ho; Lee, Hochan; Choi, Hyung Ran; Cho, Minhaeng

2018-04-01

In molecular and cellular biology, dissolved ions and molecules have decisive effects on chemical and biological reactions, conformational stabilities, and functions of small to large biomolecules. Despite major efforts, the current state of understanding of the effects of specific ions, osmolytes, and bioprotecting sugars on the structure and dynamics of water H-bonding networks and proteins is not yet satisfactory. Recently, to gain deeper insight into this subject, we studied various aggregation processes of ions and molecules in high-concentration salt, osmolyte, and sugar solutions with time-resolved vibrational spectroscopy and molecular dynamics simulation methods. It turns out that ions (or solute molecules) have a strong propensity to self-assemble into large and polydisperse aggregates that affect both local and long-range water H-bonding structures. In particular, we have shown that graph-theoretical approaches can be used to elucidate morphological characteristics of large aggregates in various aqueous salt, osmolyte, and sugar solutions. When ion and molecular aggregates in such aqueous solutions are treated as graphs, a variety of graph-theoretical properties, such as graph spectrum, degree distribution, clustering coefficient, minimum path length, and graph entropy, can be directly calculated by considering an ensemble of configurations taken from molecular dynamics trajectories. Here we show percolating behavior exhibited by ion and molecular aggregates upon increase in solute concentration in high solute concentrations and discuss compelling evidence of the isomorphic relation between percolation transitions of ion and molecular aggregates and water H-bonding networks. We anticipate that the combination of graph theory and molecular dynamics simulation methods will be of exceptional use in achieving a deeper understanding of the fundamental physical chemistry of dissolution and in describing the interplay between the self-aggregation of solute molecules and the structure and dynamics of water.

Self-complementary circular codes in coding theory.

PubMed

Fimmel, Elena; Michel, Christian J; Starman, Martin; Strüngmann, Lutz

2018-04-01

Self-complementary circular codes are involved in pairing genetic processes. A maximal [Formula: see text] self-complementary circular code X of trinucleotides was identified in genes of bacteria, archaea, eukaryotes, plasmids and viruses (Michel in Life 7(20):1-16 2017, J Theor Biol 380:156-177, 2015; Arquès and Michel in J Theor Biol 182:45-58 1996). In this paper, self-complementary circular codes are investigated using the graph theory approach recently formulated in Fimmel et al. (Philos Trans R Soc A 374:20150058, 2016). A directed graph [Formula: see text] associated with any code X mirrors the properties of the code. In the present paper, we demonstrate a necessary condition for the self-complementarity of an arbitrary code X in terms of the graph theory. The same condition has been proven to be sufficient for codes which are circular and of large size [Formula: see text] trinucleotides, in particular for maximal circular codes ([Formula: see text] trinucleotides). For codes of small-size [Formula: see text] trinucleotides, some very rare counterexamples have been constructed. Furthermore, the length and the structure of the longest paths in the graphs associated with the self-complementary circular codes are investigated. It has been proven that the longest paths in such graphs determine the reading frame for the self-complementary circular codes. By applying this result, the reading frame in any arbitrary sequence of trinucleotides is retrieved after at most 15 nucleotides, i.e., 5 consecutive trinucleotides, from the circular code X identified in genes. Thus, an X motif of a length of at least 15 nucleotides in an arbitrary sequence of trinucleotides (not necessarily all of them belonging to X) uniquely defines the reading (correct) frame, an important criterion for analyzing the X motifs in genes in the future.

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

ERIC Educational Resources Information Center

Barton, Erin E.; Reichow, Brian

2012-01-01

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

Topics on data transmission problem in software definition network

NASA Astrophysics Data System (ADS)

Gao, Wei; Liang, Li; Xu, Tianwei; Gan, Jianhou

2017-08-01

In normal computer networks, the data transmission between two sites go through the shortest path between two corresponding vertices. However, in the setting of software definition network (SDN), it should monitor the network traffic flow in each site and channel timely, and the data transmission path between two sites in SDN should consider the congestion in current networks. Hence, the difference of available data transmission theory between normal computer network and software definition network is that we should consider the prohibit graph structures in SDN, and these forbidden subgraphs represent the sites and channels in which data can't be passed by the serious congestion. Inspired by theoretical analysis of an available data transmission in SDN, we consider some computational problems from the perspective of the graph theory. Several results determined in the paper imply the sufficient conditions of data transmission in SDN in the various graph settings.

The ergodicity landscape of quantum theories

NASA Astrophysics Data System (ADS)

Ho, Wen Wei; Radičević, Đorđe

2018-02-01

This paper is a physicist’s review of the major conceptual issues concerning the problem of spectral universality in quantum systems. Here, we present a unified, graph-based view of all archetypical models of such universality (billiards, particles in random media, interacting spin or fermion systems). We find phenomenological relations between the onset of ergodicity (Gaussian-random delocalization of eigenstates) and the structure of the appropriate graphs, and we construct a heuristic picture of summing trajectories on graphs that describes why a generic interacting system should be ergodic. We also provide an operator-based discussion of quantum chaos and propose criteria to distinguish bases that can usefully diagnose ergodicity. The result of this analysis is a rough but systematic outline of how ergodicity changes across the space of all theories with a given Hilbert space dimension. As a particular example, we study the SYK model and report on the transition from maximal to partial ergodicity as the disorder strength is decreased.

The geometry of on-shell diagrams

NASA Astrophysics Data System (ADS)

Franco, Sebastián; Galloni, Daniele; Mariotti, Alberto

2014-08-01

The fundamental role of on-shell diagrams in quantum field theory has been recently recognized. On-shell diagrams, or equivalently bipartite graphs, provide a natural bridge connecting gauge theory to powerful mathematical structures such as the Grassmannian. We perform a detailed investigation of the combinatorial and geometric objects associated to these graphs. We mainly focus on their relation to polytopes and toric geometry, the Grassmannian and its stratification. Our work extends the current understanding of these connections along several important fronts, most notably eliminating restrictions imposed by planarity, positivity, reducibility and edge removability. We illustrate our ideas with several explicit examples and introduce concrete methods that considerably simplify computations. We consider it highly likely that the structures unveiled in this article will arise in the on-shell study of scattering amplitudes beyond the planar limit. Our results can be conversely regarded as an expansion in the understanding of the Grassmannian in terms of bipartite graphs.

Efficient quantum walk on a quantum processor

PubMed Central

Qiang, Xiaogang; Loke, Thomas; Montanaro, Ashley; Aungskunsiri, Kanin; Zhou, Xiaoqi; O'Brien, Jeremy L.; Wang, Jingbo B.; Matthews, Jonathan C. F.

2016-01-01

The random walk formalism is used across a wide range of applications, from modelling share prices to predicting population genetics. Likewise, quantum walks have shown much potential as a framework for developing new quantum algorithms. Here we present explicit efficient quantum circuits for implementing continuous-time quantum walks on the circulant class of graphs. These circuits allow us to sample from the output probability distributions of quantum walks on circulant graphs efficiently. We also show that solving the same sampling problem for arbitrary circulant quantum circuits is intractable for a classical computer, assuming conjectures from computational complexity theory. This is a new link between continuous-time quantum walks and computational complexity theory and it indicates a family of tasks that could ultimately demonstrate quantum supremacy over classical computers. As a proof of principle, we experimentally implement the proposed quantum circuit on an example circulant graph using a two-qubit photonics quantum processor. PMID:27146471

Stochastic generation of complex crystal structures combining group and graph theory with application to carbon

NASA Astrophysics Data System (ADS)

Shi, Xizhi; He, Chaoyu; Pickard, Chris J.; Tang, Chao; Zhong, Jianxin

2018-01-01

A method is introduced to stochastically generate crystal structures with defined structural characteristics. Reasonable quotient graphs for symmetric crystals are constructed using a random strategy combined with space group and graph theory. Our algorithm enables the search for large-size and complex crystal structures with a specified connectivity, such as threefold sp2 carbons, fourfold sp3 carbons, as well as mixed sp2-sp3 carbons. To demonstrate the method, we randomly construct initial structures adhering to space groups from 75 to 230 and a range of lattice constants, and we identify 281 new sp3 carbon crystals. First-principles optimization of these structures show that most of them are dynamically and mechanically stable and are energetically comparable to those previously proposed. Some of the new structures can be considered as candidates to explain the experimental cold compression of graphite.

Fiber tracking of brain white matter based on graph theory.

PubMed

Lu, Meng

2015-01-01

Brain white matter tractography is reconstructed via diffusion-weighted magnetic resonance images. Due to the complex structure of brain white matter fiber bundles, fiber crossing and fiber branching are abundant in human brain. And regular methods with diffusion tensor imaging (DTI) can't accurately handle this problem. the biggest problems of the brain tractography. Therefore, this paper presented a novel brain white matter tractography method based on graph theory, so the fiber tracking between two voxels is transformed into locating the shortest path in a graph. Besides, the presented method uses Q-ball imaging (QBI) as the source data instead of DTI, because QBI can provide accurate information about multiple fiber crossing and branching in one voxel using orientation distribution function (ODF). Experiments showed that the presented method can accurately handle the problem of brain white matter fiber crossing and branching, and reconstruct brain tractograhpy both in phantom data and real brain data.

Graph theory for feature extraction and classification: a migraine pathology case study.

PubMed

Jorge-Hernandez, Fernando; Garcia Chimeno, Yolanda; Garcia-Zapirain, Begonya; Cabrera Zubizarreta, Alberto; Gomez Beldarrain, Maria Angeles; Fernandez-Ruanova, Begonya

2014-01-01

Graph theory is also widely used as a representational form and characterization of brain connectivity network, as is machine learning for classifying groups depending on the features extracted from images. Many of these studies use different techniques, such as preprocessing, correlations, features or algorithms. This paper proposes an automatic tool to perform a standard process using images of the Magnetic Resonance Imaging (MRI) machine. The process includes pre-processing, building the graph per subject with different correlations, atlas, relevant feature extraction according to the literature, and finally providing a set of machine learning algorithms which can produce analyzable results for physicians or specialists. In order to verify the process, a set of images from prescription drug abusers and patients with migraine have been used. In this way, the proper functioning of the tool has been proved, providing results of 87% and 92% of success depending on the classifier used.

Efficient Inference for Trees and Alignments: Modeling Monolingual and Bilingual Syntax with Hard and Soft Constraints and Latent Variables

ERIC Educational Resources Information Center

Smith, David Arthur

2010-01-01

Much recent work in natural language processing treats linguistic analysis as an inference problem over graphs. This development opens up useful connections between machine learning, graph theory, and linguistics. The first part of this dissertation formulates syntactic dependency parsing as a dynamic Markov random field with the novel…

Dropout Rates, Student Momentum, and Course Walls: A New Tool for Distance Education Designers

ERIC Educational Resources Information Center

Christensen, Steven S.; Spackman, Jonathan S.

2017-01-01

This paper explores a new tool for instructional designers. By calculating and graphing the Student Momentum Indicator (M) for 196 university-level online courses and by employing the constant comparative method within the grounded theory framework, eight distinct graph shapes emerged as meaningful categories of dropout behavior. Several of the…

Multiscale connectivity and graph theory highlight critical areas for conservation under climate change.

PubMed

Dilt, Thomas E; Weisberg, Peter J; Leitner, Philip; Matocq, Marjorie D; Inman, Richard D; Nussear, Kenneth E; Esque, Todd C

2016-06-01

Conservation planning and biodiversity management require information on landscape connectivity across a range of spatial scales from individual home ranges to large regions. Reduction in landscape connectivity due changes in land use or development is expected to act synergistically with alterations to habitat mosaic configuration arising from climate change. We illustrate a multiscale connectivity framework to aid habitat conservation prioritization in the context of changing land use and climate. Our approach, which builds upon the strengths of multiple landscape connectivity methods, including graph theory, circuit theory, and least-cost path analysis, is here applied to the conservation planning requirements of the Mohave ground squirrel. The distribution of this threatened Californian species, as for numerous other desert species, overlaps with the proposed placement of several utility-scale renewable energy developments in the American southwest. Our approach uses information derived at three spatial scales to forecast potential changes in habitat connectivity under various scenarios of energy development and climate change. By disentangling the potential effects of habitat loss and fragmentation across multiple scales, we identify priority conservation areas for both core habitat and critical corridor or stepping stone habitats. This approach is a first step toward applying graph theory to analyze habitat connectivity for species with continuously distributed habitat and should be applicable across a broad range of taxa.

Statistical Inference for Cultural Consensus Theory

DTIC Science & Technology

2014-02-24

Social Network Conference XXXII , Redondo Beach, California, March 2012. Agrawal, K. (Presenter), and Batchelder, W. H. Cultural Consensus Theory...Aggregating Complete Signed Graphs Under a Balance Constraint -- Part 2. International Sunbelt Social Network Conference XXXII , Redondo Beach

Evaluation of the User Strategy on 2d and 3d City Maps Based on Novel Scanpath Comparison Method and Graph Visualization

NASA Astrophysics Data System (ADS)

Dolezalova, J.; Popelka, S.

2016-06-01

The paper is dealing with scanpath comparison of eye-tracking data recorded during case study focused on the evaluation of 2D and 3D city maps. The experiment contained screenshots from three map portals. Two types of maps were used - standard map and 3D visualization. Respondents' task was to find particular point symbol on the map as fast as possible. Scanpath comparison is one group of the eye-tracking data analyses methods used for revealing the strategy of the respondents. In cartographic studies, the most commonly used application for scanpath comparison is eyePatterns that output is hierarchical clustering and a tree graph representing the relationships between analysed sequences. During an analysis of the algorithm generating a tree graph, it was found that the outputs do not correspond to the reality. We proceeded to the creation of a new tool called ScanGraph. This tool uses visualization of cliques in simple graphs and is freely available at www.eyetracking.upol.cz/scangraph. Results of the study proved the functionality of the tool and its suitability for analyses of different strategies of map readers. Based on the results of the tool, similar scanpaths were selected, and groups of respondents with similar strategies were identified. With this knowledge, it is possible to analyse the relationship between belonging to the group with similar strategy and data gathered from the questionnaire (age, sex, cartographic knowledge, etc.) or type of stimuli (2D, 3D map).

Query optimization for graph analytics on linked data using SPARQL

DOE Office of Scientific and Technical Information (OSTI.GOV)

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

2015-07-01

Triplestores that support query languages such as SPARQL are emerging as the preferred and scalable solution to represent data and meta-data as massive heterogeneous graphs using Semantic Web standards. With increasing adoption, the desire to conduct graph-theoretic mining and exploratory analysis has also increased. Addressing that desire, this paper presents a solution that is the marriage of Graph Theory and the Semantic Web. We present software that can analyze Linked Data using graph operations such as counting triangles, finding eccentricity, testing connectedness, and computing PageRank directly on triple stores via the SPARQL interface. We describe the process of optimizing performancemore » of the SPARQL-based implementation of such popular graph algorithms by reducing the space-overhead, simplifying iterative complexity and removing redundant computations by understanding query plans. Our optimized approach shows significant performance gains on triplestores hosted on stand-alone workstations as well as hardware-optimized scalable supercomputers such as the Cray XMT.« less

Clarifying and Teaching Bohm-Bawerk's "Marginal Pairs."

ERIC Educational Resources Information Center

Egger, John B.

1998-01-01

Briefly defines and provides some background on Eugen von Bohm-Bawerk's "marginal pairs" theory of pricing. Asserts that Bohm-Bawerk's theory is a good introduction to the Austrian school of economics and illustrates the differences between this approach and neoclassical economic theory. Includes several graphs and tables of data. (MJP)

Chemical graphs, molecular matrices and topological indices in chemoinformatics and quantitative structure-activity relationships.

PubMed

Ivanciuc, Ovidiu

2013-06-01

Chemical and molecular graphs have fundamental applications in chemoinformatics, quantitative structureproperty relationships (QSPR), quantitative structure-activity relationships (QSAR), virtual screening of chemical libraries, and computational drug design. Chemoinformatics applications of graphs include chemical structure representation and coding, database search and retrieval, and physicochemical property prediction. QSPR, QSAR and virtual screening are based on the structure-property principle, which states that the physicochemical and biological properties of chemical compounds can be predicted from their chemical structure. Such structure-property correlations are usually developed from topological indices and fingerprints computed from the molecular graph and from molecular descriptors computed from the three-dimensional chemical structure. We present here a selection of the most important graph descriptors and topological indices, including molecular matrices, graph spectra, spectral moments, graph polynomials, and vertex topological indices. These graph descriptors are used to define several topological indices based on molecular connectivity, graph distance, reciprocal distance, distance-degree, distance-valency, spectra, polynomials, and information theory concepts. The molecular descriptors and topological indices can be developed with a more general approach, based on molecular graph operators, which define a family of graph indices related by a common formula. Graph descriptors and topological indices for molecules containing heteroatoms and multiple bonds are computed with weighting schemes based on atomic properties, such as the atomic number, covalent radius, or electronegativity. The correlation in QSPR and QSAR models can be improved by optimizing some parameters in the formula of topological indices, as demonstrated for structural descriptors based on atomic connectivity and graph distance.

Effect of Resting-State fNIRS Scanning Duration on Functional Brain Connectivity and Graph Theory Metrics of Brain Network.

PubMed

Geng, Shujie; Liu, Xiangyu; Biswal, Bharat B; Niu, Haijing

2017-01-01

As an emerging brain imaging technique, functional near infrared spectroscopy (fNIRS) has attracted widespread attention for advancing resting-state functional connectivity (FC) and graph theoretical analyses of brain networks. However, it remains largely unknown how the duration of the fNIRS signal scanning is related to stable and reproducible functional brain network features. To answer this question, we collected resting-state fNIRS signals (10-min duration, two runs) from 18 participants and then truncated the hemodynamic time series into 30-s time bins that ranged from 1 to 10 min. Measures of nodal efficiency, nodal betweenness, network local efficiency, global efficiency, and clustering coefficient were computed for each subject at each fNIRS signal acquisition duration. Analyses of the stability and between-run reproducibility were performed to identify optimal time length for each measure. We found that the FC, nodal efficiency and nodal betweenness stabilized and were reproducible after 1 min of fNIRS signal acquisition, whereas network clustering coefficient, local and global efficiencies stabilized after 1 min and were reproducible after 5 min of fNIRS signal acquisition for only local and global efficiencies. These quantitative results provide direct evidence regarding the choice of the resting-state fNIRS scanning duration for functional brain connectivity and topological metric stability of brain network connectivity.

Predicting conversion from MCI to AD using resting-state fMRI, graph theoretical approach and SVM.

PubMed

Hojjati, Seyed Hani; Ebrahimzadeh, Ata; Khazaee, Ali; Babajani-Feremi, Abbas

2017-04-15

We investigated identifying patients with mild cognitive impairment (MCI) who progress to Alzheimer's disease (AD), MCI converter (MCI-C), from those with MCI who do not progress to AD, MCI non-converter (MCI-NC), based on resting-state fMRI (rs-fMRI). Graph theory and machine learning approach were utilized to predict progress of patients with MCI to AD using rs-fMRI. Eighteen MCI converts (average age 73.6 years; 11 male) and 62 age-matched MCI non-converters (average age 73.0 years, 28 male) were included in this study. We trained and tested a support vector machine (SVM) to classify MCI-C from MCI-NC using features constructed based on the local and global graph measures. A novel feature selection algorithm was developed and utilized to select an optimal subset of features. Using subset of optimal features in SVM, we classified MCI-C from MCI-NC with an accuracy, sensitivity, specificity, and the area under the receiver operating characteristic (ROC) curve of 91.4%, 83.24%, 90.1%, and 0.95, respectively. Furthermore, results of our statistical analyses were used to identify the affected brain regions in AD. To the best of our knowledge, this is the first study that combines the graph measures (constructed based on rs-fMRI) with machine learning approach and accurately classify MCI-C from MCI-NC. Results of this study demonstrate potential of the proposed approach for early AD diagnosis and demonstrate capability of rs-fMRI to predict conversion from MCI to AD by identifying affected brain regions underlying this conversion. Copyright © 2017 Elsevier B.V. All rights reserved.

Network science and the human brain: Using graph theory to understand the brain and one of its hubs, the amygdala, in health and disease.

PubMed

Mears, David; Pollard, Harvey B

2016-06-01

Over the past 15 years, the emerging field of network science has revealed the key features of brain networks, which include small-world topology, the presence of highly connected hubs, and hierarchical modularity. The value of network studies of the brain is underscored by the range of network alterations that have been identified in neurological and psychiatric disorders, including epilepsy, depression, Alzheimer's disease, schizophrenia, and many others. Here we briefly summarize the concepts of graph theory that are used to quantify network properties and describe common experimental approaches for analysis of brain networks of structural and functional connectivity. These range from tract tracing to functional magnetic resonance imaging, diffusion tensor imaging, electroencephalography, and magnetoencephalography. We then summarize the major findings from the application of graph theory to nervous systems ranging from Caenorhabditis elegans to more complex primate brains, including man. Focusing, then, on studies involving the amygdala, a brain region that has attracted intense interest as a center for emotional processing, fear, and motivation, we discuss the features of the amygdala in brain networks for fear conditioning and emotional perception. Finally, to highlight the utility of graph theory for studying dysfunction of the amygdala in mental illness, we review data with regard to changes in the hub properties of the amygdala in brain networks of patients with depression. We suggest that network studies of the human brain may serve to focus attention on regions and connections that act as principal drivers and controllers of brain function in health and disease. Published 2016. This article is a U.S. Government work and is in the public domain in the USA.

Discovery of Empirical Components by Information Theory

DTIC Science & Technology

2016-08-10

AFRL-AFOSR-VA-TR-2016-0289 Discovery of Empirical Components by Information Theory Amit Singer TRUSTEES OF PRINCETON UNIVERSITY 1 NASSAU HALL...3. DATES COVERED (From - To) 15 Feb 2013 to 14 Feb 2016 5a. CONTRACT NUMBER Discovery of Empirical Components by Information Theory 5b. GRANT...they draw not only from traditional linear algebra based numerical analysis or approximation theory , but also from information theory , graph theory

Introduction to Statistics. Learning Packages in the Policy Sciences Series, PS-26. Revised Edition.

ERIC Educational Resources Information Center

Policy Studies Associates, Croton-on-Hudson, NY.

The primary objective of this booklet is to introduce students to basic statistical skills that are useful in the analysis of public policy data. A few, selected statistical methods are presented, and theory is not emphasized. Chapter 1 provides instruction for using tables, bar graphs, bar graphs with grouped data, trend lines, pie diagrams,…

Making Graphical Inferences: A Hierarchical Framework

DTIC Science & Technology

2004-08-01

from graphs is considered one of the more complex skills graph readers should possess. According to the National Council of Teachers of Mathematics ...understanding graphical perception. Human Computer Interaction, 8, 353-388. NCTM : Standards for Mathematics . (2003, 2003). Pinker, S. (1990). A theory... NCTM ) the simplest type of question involves the extraction or comparison of a few explicitly represented data points (read-offs) ( NCTM : Standards

Predicting activity approach based on new atoms similarity kernel function.

PubMed

Abu El-Atta, Ahmed H; Moussa, M I; Hassanien, Aboul Ella

2015-07-01

Drug design is a high cost and long term process. To reduce time and costs for drugs discoveries, new techniques are needed. Chemoinformatics field implements the informational techniques and computer science like machine learning and graph theory to discover the chemical compounds properties, such as toxicity or biological activity. This is done through analyzing their molecular structure (molecular graph). To overcome this problem there is an increasing need for algorithms to analyze and classify graph data to predict the activity of molecules. Kernels methods provide a powerful framework which combines machine learning with graph theory techniques. These kernels methods have led to impressive performance results in many several chemoinformatics problems like biological activity prediction. This paper presents a new approach based on kernel functions to solve activity prediction problem for chemical compounds. First we encode all atoms depending on their neighbors then we use these codes to find a relationship between those atoms each other. Then we use relation between different atoms to find similarity between chemical compounds. The proposed approach was compared with many other classification methods and the results show competitive accuracy with these methods. Copyright © 2015 Elsevier Inc. All rights reserved.

What can graph theory tell us about word learning and lexical retrieval?

PubMed

Vitevitch, Michael S

2008-04-01

Graph theory and the new science of networks provide a mathematically rigorous approach to examine the development and organization of complex systems. These tools were applied to the mental lexicon to examine the organization of words in the lexicon and to explore how that structure might influence the acquisition and retrieval of phonological word-forms. Pajek, a program for large network analysis and visualization (V. Batagelj & A. Mvrar, 1998), was used to examine several characteristics of a network derived from a computerized database of the adult lexicon. Nodes in the network represented words, and a link connected two nodes if the words were phonological neighbors. The average path length and clustering coefficient suggest that the phonological network exhibits small-world characteristics. The degree distribution was fit better by an exponential rather than a power-law function. Finally, the network exhibited assortative mixing by degree. Some of these structural characteristics were also found in graphs that were formed by 2 simple stochastic processes suggesting that similar processes might influence the development of the lexicon. The graph theoretic perspective may provide novel insights about the mental lexicon and lead to future studies that help us better understand language development and processing.

Does Guiding Toward Task-Relevant Information Help Improve Graph Processing and Graph Comprehension of Individuals with Low or High Numeracy? An Eye-Tracker Experiment.

PubMed

Keller, Carmen; Junghans, Alex

2017-11-01

Individuals with low numeracy have difficulties with understanding complex graphs. Combining the information-processing approach to numeracy with graph comprehension and information-reduction theories, we examined whether high numerates' better comprehension might be explained by their closer attention to task-relevant graphical elements, from which they would expect numerical information to understand the graph. Furthermore, we investigated whether participants could be trained in improving their attention to task-relevant information and graph comprehension. In an eye-tracker experiment ( N = 110) involving a sample from the general population, we presented participants with 2 hypothetical scenarios (stomach cancer, leukemia) showing survival curves for 2 treatments. In the training condition, participants received written instructions on how to read the graph. In the control condition, participants received another text. We tracked participants' eye movements while they answered 9 knowledge questions. The sum constituted graph comprehension. We analyzed visual attention to task-relevant graphical elements by using relative fixation durations and relative fixation counts. The mediation analysis revealed a significant ( P < 0.05) indirect effect of numeracy on graph comprehension through visual attention to task-relevant information, which did not differ between the 2 conditions. Training had a significant main effect on visual attention ( P < 0.05) but not on graph comprehension ( P < 0.07). Individuals with high numeracy have better graph comprehension due to their greater attention to task-relevant graphical elements than individuals with low numeracy. With appropriate instructions, both groups can be trained to improve their graph-processing efficiency. Future research should examine (e.g., motivational) mediators between visual attention and graph comprehension to develop appropriate instructions that also result in higher graph comprehension.

Projected power iteration for network alignment

NASA Astrophysics Data System (ADS)

Onaran, Efe; Villar, Soledad

2017-08-01

The network alignment problem asks for the best correspondence between two given graphs, so that the largest possible number of edges are matched. This problem appears in many scientific problems (like the study of protein-protein interactions) and it is very closely related to the quadratic assignment problem which has graph isomorphism, traveling salesman and minimum bisection problems as particular cases. The graph matching problem is NP-hard in general. However, under some restrictive models for the graphs, algorithms can approximate the alignment efficiently. In that spirit the recent work by Feizi and collaborators introduce EigenAlign, a fast spectral method with convergence guarantees for Erd-s-Renyí graphs. In this work we propose the algorithm Projected Power Alignment, which is a projected power iteration version of EigenAlign. We numerically show it improves the recovery rates of EigenAlign and we describe the theory that may be used to provide performance guarantees for Projected Power Alignment.

Exact and approximate graph matching using random walks.

PubMed

Gori, Marco; Maggini, Marco; Sarti, Lorenzo

2005-07-01

In this paper, we propose a general framework for graph matching which is suitable for different problems of pattern recognition. The pattern representation we assume is at the same time highly structured, like for classic syntactic and structural approaches, and of subsymbolic nature with real-valued features, like for connectionist and statistic approaches. We show that random walk based models, inspired by Google's PageRank, give rise to a spectral theory that nicely enhances the graph topological features at node level. As a straightforward consequence, we derive a polynomial algorithm for the classic graph isomorphism problem, under the restriction of dealing with Markovian spectrally distinguishable graphs (MSD), a class of graphs that does not seem to be easily reducible to others proposed in the literature. The experimental results that we found on different test-beds of the TC-15 graph database show that the defined MSD class "almost always" covers the database, and that the proposed algorithm is significantly more efficient than top scoring VF algorithm on the same data. Most interestingly, the proposed approach is very well-suited for dealing with partial and approximate graph matching problems, derived for instance from image retrieval tasks. We consider the objects of the COIL-100 visual collection and provide a graph-based representation, whose node's labels contain appropriate visual features. We show that the adoption of classic bipartite graph matching algorithms offers a straightforward generalization of the algorithm given for graph isomorphism and, finally, we report very promising experimental results on the COIL-100 visual collection.

Assessing dynamic brain graphs of time-varying connectivity in fMRI data: application to healthy controls and patients with schizophrenia

PubMed Central

Yu, Qingbao; Erhardt, Erik B.; Sui, Jing; Du, Yuhui; He, Hao; Hjelm, Devon; Cetin, Mustafa S.; Rachakonda, Srinivas; Miller, Robyn L.; Pearlson, Godfrey; Calhoun, Vince D.

2014-01-01

Graph theory-based analysis has been widely employed in brain imaging studies, and altered topological properties of brain connectivity have emerged as important features of mental diseases such as schizophrenia. However, most previous studies have focused on graph metrics of stationary brain graphs, ignoring that brain connectivity exhibits fluctuations over time. Here we develop a new framework for accessing dynamic graph properties of time-varying functional brain connectivity in resting state fMRI data and apply it to healthy controls (HCs) and patients with schizophrenia (SZs). Specifically, nodes of brain graphs are defined by intrinsic connectivity networks (ICNs) identified by group independent component analysis (ICA). Dynamic graph metrics of the time-varying brain connectivity estimated by the correlation of sliding time-windowed ICA time courses of ICNs are calculated. First- and second-level connectivity states are detected based on the correlation of nodal connectivity strength between time-varying brain graphs. Our results indicate that SZs show decreased variance in the dynamic graph metrics. Consistent with prior stationary functional brain connectivity works, graph measures of identified first-level connectivity states show lower values in SZs. In addition, more first-level connectivity states are disassociated with the second-level connectivity state which resembles the stationary connectivity pattern computed by the entire scan. Collectively, the findings provide new evidence about altered dynamic brain graphs in schizophrenia which may underscore the abnormal brain performance in this mental illness. PMID:25514514

Genetic algorithm and graph theory based matrix factorization method for online friend recommendation.

PubMed

Li, Qu; Yao, Min; Yang, Jianhua; Xu, Ning

2014-01-01

Online friend recommendation is a fast developing topic in web mining. In this paper, we used SVD matrix factorization to model user and item feature vector and used stochastic gradient descent to amend parameter and improve accuracy. To tackle cold start problem and data sparsity, we used KNN model to influence user feature vector. At the same time, we used graph theory to partition communities with fairly low time and space complexity. What is more, matrix factorization can combine online and offline recommendation. Experiments showed that the hybrid recommendation algorithm is able to recommend online friends with good accuracy.

Graph Structure Theory: Proceedings of a Joint Summer Research Conference on Graph Minors Held June 22 to July 5, 1991, at the University of Washington, Seattle. Contemporary Mathematics 147

DTIC Science & Technology

1991-01-01

aspects of classical field theory, 1992 131 L A. Bokut’, Yu. L Ershov, and A. I. Kostrikin, Editors, Proceedings of the International Conference on Algebra...should be addressed to the Manager of Editorial Services , American Mathematical Society, P.O. Box 6248, Providence, Rhode Island 02940-6248. The...dominant edges in T, and b(T) as the number of dominant edges not in T, for the fixed enumeration U. In [2] a(T) is called the " internal activity" and b(T

Graph theory in brain-to-brain connectivity: A simulation study and an application to an EEG hyperscanning experiment.

PubMed

Toppi, J; Ciaramidaro, A; Vogel, P; Mattia, D; Babiloni, F; Siniatchkin, M; Astolfi, L

2015-08-01

Hyperscanning consists in the simultaneous recording of hemodynamic or neuroelectrical signals from two or more subjects acting in a social context. Well-established methodologies for connectivity estimation have already been adapted to hyperscanning purposes. The extension of graph theory approach to multi-subjects case is still a challenging issue. In the present work we aim to test the ability of the currently used graph theory global indices in describing the properties of a network given by two interacting subjects. The testing was conducted first on surrogate brain-to-brain networks reproducing typical social scenarios and then on real EEG hyperscanning data recorded during a Joint Action task. The results of the simulation study highlighted the ability of all the investigated indexes in modulating their values according to the level of interaction between subjects. However, only global efficiency and path length indexes demonstrated to be sensitive to an asymmetry in the communication between the two subjects. Such results were, then, confirmed by the application on real EEG data. Global efficiency modulated, in fact, their values according to the inter-brain density, assuming higher values in the social condition with respect to the non-social condition.

Faster quantum walk search on a weighted graph

NASA Astrophysics Data System (ADS)

Wong, Thomas G.

2015-09-01

A randomly walking quantum particle evolving by Schrödinger's equation searches for a unique marked vertex on the "simplex of complete graphs" in time Θ (N3 /4) . We give a weighted version of this graph that preserves vertex transitivity, and we show that the time to search on it can be reduced to nearly Θ (√{N }) . To prove this, we introduce two extensions to degenerate perturbation theory: an adjustment that distinguishes the weights of the edges and a method to determine how precisely the jumping rate of the quantum walk must be chosen.

Quantum speedup of the traveling-salesman problem for bounded-degree graphs

NASA Astrophysics Data System (ADS)

Moylett, Dominic J.; Linden, Noah; Montanaro, Ashley

2017-03-01

The traveling-salesman problem is one of the most famous problems in graph theory. However, little is currently known about the extent to which quantum computers could speed up algorithms for the problem. In this paper, we prove a quadratic quantum speedup when the degree of each vertex is at most 3 by applying a quantum backtracking algorithm to a classical algorithm by Xiao and Nagamochi. We then use similar techniques to accelerate a classical algorithm for when the degree of each vertex is at most 4, before speeding up higher-degree graphs via reductions to these instances.

Graph C ∗-algebras and Z2-quotients of quantum spheres

NASA Astrophysics Data System (ADS)

Hajac, Piotr M.; Matthes, Rainer; Szymański, Wojciech

2003-06-01

We consider two Z2-actions on the Podleś generic quantum spheres. They yield, as noncommutative quotient spaces, the Klimek-Lesmewski q-disc and the quantum real projective space, respectively. The C ∗-algebas of all these quantum spaces are described as graph C ∗-algebras. The K-groups of the thus presented C ∗-algebras are then easily determined from the general theory of graph C ∗-algebas. For the quantum real projective space, we also recall the classification of the classes of irreducible ∗-representations of its algebra and give a linear basis for this algebra.

Advanced classical thermodynamics

NASA Astrophysics Data System (ADS)

Emanuel, George

The theoretical and mathematical foundations of thermodynamics are presented in an advanced text intended for graduate engineering students. Chapters are devoted to definitions and postulates, the fundamental equation, equilibrium, the application of Jacobian theory to thermodynamics, the Maxwell equations, stability, the theory of real gases, critical-point theory, and chemical thermodynamics. Diagrams, graphs, tables, and sample problems are provided.

Topics in Computational Learning Theory and Graph Algorithms.

ERIC Educational Resources Information Center

Board, Raymond Acton

This thesis addresses problems from two areas of theoretical computer science. The first area is that of computational learning theory, which is the study of the phenomenon of concept learning using formal mathematical models. The goal of computational learning theory is to investigate learning in a rigorous manner through the use of techniques…

On discrete field theory properties of the dimer and Ising models and their conformal field theory limits

NASA Astrophysics Data System (ADS)

Kriz, Igor; Loebl, Martin; Somberg, Petr

2013-05-01

We study various mathematical aspects of discrete models on graphs, specifically the Dimer and the Ising models. We focus on proving gluing formulas for individual summands of the partition function. We also obtain partial results regarding conjectured limits realized by fermions in rational conformal field theories.

RNA Graph Partitioning for the Discovery of RNA Modularity: A Novel Application of Graph Partition Algorithm to Biology

PubMed Central

Elmetwaly, Shereef; Schlick, Tamar

2014-01-01

Graph representations have been widely used to analyze and design various economic, social, military, political, and biological networks. In systems biology, networks of cells and organs are useful for understanding disease and medical treatments and, in structural biology, structures of molecules can be described, including RNA structures. In our RNA-As-Graphs (RAG) framework, we represent RNA structures as tree graphs by translating unpaired regions into vertices and helices into edges. Here we explore the modularity of RNA structures by applying graph partitioning known in graph theory to divide an RNA graph into subgraphs. To our knowledge, this is the first application of graph partitioning to biology, and the results suggest a systematic approach for modular design in general. The graph partitioning algorithms utilize mathematical properties of the Laplacian eigenvector (µ2) corresponding to the second eigenvalues (λ2) associated with the topology matrix defining the graph: λ2 describes the overall topology, and the sum of µ2′s components is zero. The three types of algorithms, termed median, sign, and gap cuts, divide a graph by determining nodes of cut by median, zero, and largest gap of µ2′s components, respectively. We apply these algorithms to 45 graphs corresponding to all solved RNA structures up through 11 vertices (∼220 nucleotides). While we observe that the median cut divides a graph into two similar-sized subgraphs, the sign and gap cuts partition a graph into two topologically-distinct subgraphs. We find that the gap cut produces the best biologically-relevant partitioning for RNA because it divides RNAs at less stable connections while maintaining junctions intact. The iterative gap cuts suggest basic modules and assembly protocols to design large RNA structures. Our graph substructuring thus suggests a systematic approach to explore the modularity of biological networks. In our applications to RNA structures, subgraphs also suggest design strategies for novel RNA motifs. PMID:25188578

The structure of gallery networks in the nests of termite Cubitermes spp. revealed by X-ray tomography

NASA Astrophysics Data System (ADS)

Perna, Andrea; Jost, Christian; Couturier, Etienne; Valverde, Sergi; Douady, Stéphane; Theraulaz, Guy

2008-09-01

Recent studies have introduced computer tomography (CT) as a tool for the visualisation and characterisation of insect architectures. Here, we use CT to map the three-dimensional networks of galleries inside Cubitermes nests in order to analyse them with tools from graph theory. The structure of these networks indicates that connections inside the nest are rearranged during the whole nest life. The functional analysis reveals that the final network topology represents an excellent compromise between efficient connectivity inside the nest and defence against attacking predators. We further discuss and illustrate the usefulness of CT to disentangle environmental and specific influences on nest architecture.

Multi-scale connectivity and graph theory highlight critical areas for conservation under climate change

USGS Publications Warehouse

Dilts, Thomas E.; Weisberg, Peter J.; Leitner, Phillip; Matocq, Marjorie D.; Inman, Richard D.; Nussear, Ken E.; Esque, Todd C.

2016-01-01

Conservation planning and biodiversity management require information on landscape connectivity across a range of spatial scales from individual home ranges to large regions. Reduction in landscape connectivity due changes in land-use or development is expected to act synergistically with alterations to habitat mosaic configuration arising from climate change. We illustrate a multi-scale connectivity framework to aid habitat conservation prioritization in the context of changing land use and climate. Our approach, which builds upon the strengths of multiple landscape connectivity methods including graph theory, circuit theory and least-cost path analysis, is here applied to the conservation planning requirements of the Mohave ground squirrel. The distribution of this California threatened species, as for numerous other desert species, overlaps with the proposed placement of several utility-scale renewable energy developments in the American Southwest. Our approach uses information derived at three spatial scales to forecast potential changes in habitat connectivity under various scenarios of energy development and climate change. By disentangling the potential effects of habitat loss and fragmentation across multiple scales, we identify priority conservation areas for both core habitat and critical corridor or stepping stone habitats. This approach is a first step toward applying graph theory to analyze habitat connectivity for species with continuously-distributed habitat, and should be applicable across a broad range of taxa.

Genome alignment with graph data structures: a comparison

PubMed Central

2014-01-01

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

Process and representation in graphical displays

NASA Technical Reports Server (NTRS)

Gillan, Douglas J.; Lewis, Robert; Rudisill, Marianne

1990-01-01

How people comprehend graphics is examined. Graphical comprehension involves the cognitive representation of information from a graphic display and the processing strategies that people apply to answer questions about graphics. Research on representation has examined both the features present in a graphic display and the cognitive representation of the graphic. The key features include the physical components of a graph, the relation between the figure and its axes, and the information in the graph. Tests of people's memory for graphs indicate that both the physical and informational aspect of a graph are important in the cognitive representation of a graph. However, the physical (or perceptual) features overshadow the information to a large degree. Processing strategies also involve a perception-information distinction. In order to answer simple questions (e.g., determining the value of a variable, comparing several variables, and determining the mean of a set of variables), people switch between two information processing strategies: (1) an arithmetic, look-up strategy in which they use a graph much like a table, looking up values and performing arithmetic calculations; and (2) a perceptual strategy in which they use the spatial characteristics of the graph to make comparisons and estimations. The user's choice of strategies depends on the task and the characteristics of the graph. A theory of graphic comprehension is presented.

Graph embedding and extensions: a general framework for dimensionality reduction.

PubMed

Yan, Shuicheng; Xu, Dong; Zhang, Benyu; Zhang, Hong-Jiang; Yang, Qiang; Lin, Stephen

2007-01-01

Over the past few decades, a large family of algorithms - supervised or unsupervised; stemming from statistics or geometry theory - has been designed to provide different solutions to the problem of dimensionality reduction. Despite the different motivations of these algorithms, we present in this paper a general formulation known as graph embedding to unify them within a common framework. In graph embedding, each algorithm can be considered as the direct graph embedding or its linear/kernel/tensor extension of a specific intrinsic graph that describes certain desired statistical or geometric properties of a data set, with constraints from scale normalization or a penalty graph that characterizes a statistical or geometric property that should be avoided. Furthermore, the graph embedding framework can be used as a general platform for developing new dimensionality reduction algorithms. By utilizing this framework as a tool, we propose a new supervised dimensionality reduction algorithm called Marginal Fisher Analysis in which the intrinsic graph characterizes the intraclass compactness and connects each data point with its neighboring points of the same class, while the penalty graph connects the marginal points and characterizes the interclass separability. We show that MFA effectively overcomes the limitations of the traditional Linear Discriminant Analysis algorithm due to data distribution assumptions and available projection directions. Real face recognition experiments show the superiority of our proposed MFA in comparison to LDA, also for corresponding kernel and tensor extensions.

The Replicator Equation on Graphs

PubMed Central

Ohtsuki, Hisashi; Nowak, Martin A.

2008-01-01

We study evolutionary games on graphs. Each player is represented by a vertex of the graph. The edges denote who meets whom. A player can use any one of n strategies. Players obtain a payoff from interaction with all their immediate neighbors. We consider three different update rules, called ‘birth-death’, ‘death-birth’ and ‘imitation’. A fourth update rule, ‘pairwise comparison’, is shown to be equivalent to birth-death updating in our model. We use pair-approximation to describe the evolutionary game dynamics on regular graphs of degree k. In the limit of weak selection, we can derive a differential equation which describes how the average frequency of each strategy on the graph changes over time. Remarkably, this equation is a replicator equation with a transformed payoff matrix. Therefore, moving a game from a well-mixed population (the complete graph) onto a regular graph simply results in a transformation of the payoff matrix. The new payoff matrix is the sum of the original payoff matrix plus another matrix, which describes the local competition of strategies. We discuss the application of our theory to four particular examples, the Prisoner’s Dilemma, the Snow-Drift game, a coordination game and the Rock-Scissors-Paper game. PMID:16860343

Efficient solution for finding Hamilton cycles in undirected graphs.

PubMed

Alhalabi, Wadee; Kitanneh, Omar; Alharbi, Amira; Balfakih, Zain; Sarirete, Akila

2016-01-01

The Hamilton cycle problem is closely related to a series of famous problems and puzzles (traveling salesman problem, Icosian game) and, due to the fact that it is NP-complete, it was extensively studied with different algorithms to solve it. The most efficient algorithm is not known. In this paper, a necessary condition for an arbitrary un-directed graph to have Hamilton cycle is proposed. Based on this condition, a mathematical solution for this problem is developed and several proofs and an algorithmic approach are introduced. The algorithm is successfully implemented on many Hamiltonian and non-Hamiltonian graphs. This provides a new effective approach to solve a problem that is fundamental in graph theory and can influence the manner in which the existing applications are used and improved.

Communication: Analysing kinetic transition networks for rare events.

PubMed

Stevenson, Jacob D; Wales, David J

2014-07-28

The graph transformation approach is a recently proposed method for computing mean first passage times, rates, and committor probabilities for kinetic transition networks. Here we compare the performance to existing linear algebra methods, focusing on large, sparse networks. We show that graph transformation provides a much more robust framework, succeeding when numerical precision issues cause the other methods to fail completely. These are precisely the situations that correspond to rare event dynamics for which the graph transformation was introduced.

Graph theory data for topological quantum chemistry.

PubMed

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

2017-08-01

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

EDENetworks: a user-friendly software to build and analyse networks in biogeography, ecology and population genetics.

PubMed

Kivelä, Mikko; Arnaud-Haond, Sophie; Saramäki, Jari

2015-01-01

The recent application of graph-based network theory analysis to biogeography, community ecology and population genetics has created a need for user-friendly software, which would allow a wider accessibility to and adaptation of these methods. EDENetworks aims to fill this void by providing an easy-to-use interface for the whole analysis pipeline of ecological and evolutionary networks starting from matrices of species distributions, genotypes, bacterial OTUs or populations characterized genetically. The user can choose between several different ecological distance metrics, such as Bray-Curtis or Sorensen distance, or population genetic metrics such as FST or Goldstein distances, to turn the raw data into a distance/dissimilarity matrix. This matrix is then transformed into a network by manual or automatic thresholding based on percolation theory or by building the minimum spanning tree. The networks can be visualized along with auxiliary data and analysed with various metrics such as degree, clustering coefficient, assortativity and betweenness centrality. The statistical significance of the results can be estimated either by resampling the original biological data or by null models based on permutations of the data. © 2014 John Wiley & Sons Ltd.

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

NASA Astrophysics Data System (ADS)

Wang, Na; Li, Dong; Wang, Qiwen

2012-12-01

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

Kirchhoff's rule for quantum wires

NASA Astrophysics Data System (ADS)

Kostrykin, V.; Schrader, R.

1999-01-01

We formulate and discuss one-particle quantum scattering theory on an arbitrary finite graph with n open ends and where we define the Hamiltonian to be (minus) the Laplace operator with general boundary conditions at the vertices. This results in a scattering theory with n channels. The corresponding on-shell S-matrix formed by the reflection and transmission amplitudes for incoming plane waves of energy E>0 is given explicitly in terms of the boundary conditions and the lengths of the internal lines. It is shown to be unitary, which may be viewed as the quantum version of Kirchhoff's law. We exhibit covariance and symmetry properties. It is symmetric if the boundary conditions are real. Also there is a duality transformation on the set of boundary conditions and the lengths of the internal lines such that the low-energy behaviour of one theory gives the high-energy behaviour of the transformed theory. Finally, we provide a composition rule by which the on-shell S-matrix of a graph is factorizable in terms of the S-matrices of its subgraphs. All proofs use only known facts from the theory of self-adjoint extensions, standard linear algebra, complex function theory and elementary arguments from the theory of Hermitian symplectic forms.

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

PubMed Central

Dye, Thomas S.

2014-01-01

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Minghai; Duan, Mojie; Fan, Jue

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 ofmore » 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.« less

Data mining the EXFOR database

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brown, David A.; Hirdt, John; Herman, Michal

2013-12-13

The EXFOR database contains the largest collection of experimental nuclear reaction data available as well as this data's bibliographic information and experimental details. We created an undirected graph from the EXFOR datasets with graph nodes representing single observables and graph links representing the connections of various types between these observables. This graph is an abstract representation of the connections in EXFOR, similar to graphs of social networks, authorship networks, etc. Analysing this abstract graph, we are able to address very specific questions such as 1) what observables are being used as reference measurements by the experimental community? 2) are thesemore » observables given the attention needed by various standards organisations? 3) are there classes of observables that are not connected to these reference measurements? In addressing these questions, we propose several (mostly cross section) observables that should be evaluated and made into reaction reference standards.« less

Network Simulation Models

DTIC Science & Technology

2008-12-01

1979; Wasserman and Faust, 1994). SNA thus relies heavily on graph theory to make predictions about network structure and thus social behavior...becomes a tool for increasing the specificity of theory , thinking through the theoretical implications, and generating testable predictions. In...to summarize Construct and its roots in constructural sociological theory . We discover that the (LPM) provides a mathematical bridge between

The Influence of Preprocessing Steps on Graph Theory Measures Derived from Resting State fMRI

PubMed Central

Gargouri, Fatma; Kallel, Fathi; Delphine, Sebastien; Ben Hamida, Ahmed; Lehéricy, Stéphane; Valabregue, Romain

2018-01-01

Resting state functional MRI (rs-fMRI) is an imaging technique that allows the spontaneous activity of the brain to be measured. Measures of functional connectivity highly depend on the quality of the BOLD signal data processing. In this study, our aim was to study the influence of preprocessing steps and their order of application on small-world topology and their efficiency in resting state fMRI data analysis using graph theory. We applied the most standard preprocessing steps: slice-timing, realign, smoothing, filtering, and the tCompCor method. In particular, we were interested in how preprocessing can retain the small-world economic properties and how to maximize the local and global efficiency of a network while minimizing the cost. Tests that we conducted in 54 healthy subjects showed that the choice and ordering of preprocessing steps impacted the graph measures. We found that the csr (where we applied realignment, smoothing, and tCompCor as a final step) and the scr (where we applied realignment, tCompCor and smoothing as a final step) strategies had the highest mean values of global efficiency (eg). Furthermore, we found that the fscr strategy (where we applied realignment, tCompCor, smoothing, and filtering as a final step), had the highest mean local efficiency (el) values. These results confirm that the graph theory measures of functional connectivity depend on the ordering of the processing steps, with the best results being obtained using smoothing and tCompCor as the final steps for global efficiency with additional filtering for local efficiency. PMID:29497372

The Influence of Preprocessing Steps on Graph Theory Measures Derived from Resting State fMRI.

PubMed

Gargouri, Fatma; Kallel, Fathi; Delphine, Sebastien; Ben Hamida, Ahmed; Lehéricy, Stéphane; Valabregue, Romain

2018-01-01

Resting state functional MRI (rs-fMRI) is an imaging technique that allows the spontaneous activity of the brain to be measured. Measures of functional connectivity highly depend on the quality of the BOLD signal data processing. In this study, our aim was to study the influence of preprocessing steps and their order of application on small-world topology and their efficiency in resting state fMRI data analysis using graph theory. We applied the most standard preprocessing steps: slice-timing, realign, smoothing, filtering, and the tCompCor method. In particular, we were interested in how preprocessing can retain the small-world economic properties and how to maximize the local and global efficiency of a network while minimizing the cost. Tests that we conducted in 54 healthy subjects showed that the choice and ordering of preprocessing steps impacted the graph measures. We found that the csr (where we applied realignment, smoothing, and tCompCor as a final step) and the scr (where we applied realignment, tCompCor and smoothing as a final step) strategies had the highest mean values of global efficiency (eg) . Furthermore, we found that the fscr strategy (where we applied realignment, tCompCor, smoothing, and filtering as a final step), had the highest mean local efficiency (el) values. These results confirm that the graph theory measures of functional connectivity depend on the ordering of the processing steps, with the best results being obtained using smoothing and tCompCor as the final steps for global efficiency with additional filtering for local efficiency.

Tools for Large Graph Mining

DTIC Science & Technology

2005-06-01

regarding criminals among many police departments. The criminal graph links suspects, crimes , locations, previous case histories, etc. These linkages...rebroadcast rate is high enough that dying out is not a concern. With the rise of sensor and peer to peer networks characterized by high churn, theory that...document groups (say, science fiction novels and thrillers ), based on the word groups that occur most frequently in them. A user who prefers one

What Can Graph Theory Tell Us About Word Learning and Lexical Retrieval?

PubMed Central

Vitevitch, Michael S.

2008-01-01

Purpose Graph theory and the new science of networks provide a mathematically rigorous approach to examine the development and organization of complex systems. These tools were applied to the mental lexicon to examine the organization of words in the lexicon and to explore how that structure might influence the acquisition and retrieval of phonological word-forms. Method Pajek, a program for large network analysis and visualization (V. Batagelj & A. Mvrar, 1998), was used to examine several characteristics of a network derived from a computerized database of the adult lexicon. Nodes in the network represented words, and a link connected two nodes if the words were phonological neighbors. Results The average path length and clustering coefficient suggest that the phonological network exhibits small-world characteristics. The degree distribution was fit better by an exponential rather than a power-law function. Finally, the network exhibited assortative mixing by degree. Some of these structural characteristics were also found in graphs that were formed by 2 simple stochastic processes suggesting that similar processes might influence the development of the lexicon. Conclusions The graph theoretic perspective may provide novel insights about the mental lexicon and lead to future studies that help us better understand language development and processing. PMID:18367686

Two's company, three (or more) is a simplex : Algebraic-topological tools for understanding higher-order structure in neural data.

PubMed

Giusti, Chad; Ghrist, Robert; Bassett, Danielle S

2016-08-01

The language of graph theory, or network science, has proven to be an exceptional tool for addressing myriad problems in neuroscience. Yet, the use of networks is predicated on a critical simplifying assumption: that the quintessential unit of interest in a brain is a dyad - two nodes (neurons or brain regions) connected by an edge. While rarely mentioned, this fundamental assumption inherently limits the types of neural structure and function that graphs can be used to model. Here, we describe a generalization of graphs that overcomes these limitations, thereby offering a broad range of new possibilities in terms of modeling and measuring neural phenomena. Specifically, we explore the use of simplicial complexes: a structure developed in the field of mathematics known as algebraic topology, of increasing applicability to real data due to a rapidly growing computational toolset. We review the underlying mathematical formalism as well as the budding literature applying simplicial complexes to neural data, from electrophysiological recordings in animal models to hemodynamic fluctuations in humans. Based on the exceptional flexibility of the tools and recent ground-breaking insights into neural function, we posit that this framework has the potential to eclipse graph theory in unraveling the fundamental mysteries of cognition.

Spectral-clustering approach to Lagrangian vortex detection.

PubMed

Hadjighasem, Alireza; Karrasch, Daniel; Teramoto, Hiroshi; Haller, George

2016-06-01

One of the ubiquitous features of real-life turbulent flows is the existence and persistence of coherent vortices. Here we show that such coherent vortices can be extracted as clusters of Lagrangian trajectories. We carry out the clustering on a weighted graph, with the weights measuring pairwise distances of fluid trajectories in the extended phase space of positions and time. We then extract coherent vortices from the graph using tools from spectral graph theory. Our method locates all coherent vortices in the flow simultaneously, thereby showing high potential for automated vortex tracking. We illustrate the performance of this technique by identifying coherent Lagrangian vortices in several two- and three-dimensional flows.

The Crossing Number of Graphs: Theory and Computation

NASA Astrophysics Data System (ADS)

Mutzel, Petra

This survey concentrates on selected theoretical and computational aspects of the crossing number of graphs. Starting with its introduction by Turán, we will discuss known results for complete and complete bipartite graphs. Then we will focus on some historical confusion on the crossing number that has been brought up by Pach and Tóth as well as Székely. A connection to computational geometry is made in the section on the geometric version, namely the rectilinear crossing number. We will also mention some applications of the crossing number to geometrical problems. This review ends with recent results on approximation and exact computations.

Eigenvalue asymptotics for the damped wave equation on metric graphs

NASA Astrophysics Data System (ADS)

Freitas, Pedro; Lipovský, Jiří

2017-09-01

We consider the linear damped wave equation on finite metric graphs and analyse its spectral properties with an emphasis on the asymptotic behaviour of eigenvalues. In the case of equilateral graphs and standard coupling conditions we show that there is only a finite number of high-frequency abscissas, whose location is solely determined by the averages of the damping terms on each edge. We further describe some of the possible behaviour when the edge lengths are no longer necessarily equal but remain commensurate.

The Legacy of Leonhard Euler--A Tricentennial Tribute

ERIC Educational Resources Information Center

Debnath, Lokenath

2009-01-01

This tricentennial tribute commemorates Euler's major contributions to mathematical and physical sciences. A brief biographical sketch is presented with his major contributions to certain selected areas of number theory, differential and integral calculus, differential equations, solid and fluid mechanics, topology and graph theory, infinite…

Connectomics and graph theory analyses: Novel insights into network abnormalities in epilepsy.

PubMed

Gleichgerrcht, Ezequiel; Kocher, Madison; Bonilha, Leonardo

2015-11-01

The assessment of neural networks in epilepsy has become increasingly relevant in the context of translational research, given that localized forms of epilepsy are more likely to be related to abnormal function within specific brain networks, as opposed to isolated focal brain pathology. It is notable that variability in clinical outcomes from epilepsy treatment may be a reflection of individual patterns of network abnormalities. As such, network endophenotypes may be important biomarkers for the diagnosis and treatment of epilepsy. Despite its exceptional potential, measuring abnormal networks in translational research has been thus far constrained by methodologic limitations. Fortunately, recent advancements in neuroscience, particularly in the field of connectomics, permit a detailed assessment of network organization, dynamics, and function at an individual level. Data from the personal connectome can be assessed using principled forms of network analyses based on graph theory, which may disclose patterns of organization that are prone to abnormal dynamics and epileptogenesis. Although the field of connectomics is relatively new, there is already a rapidly growing body of evidence to suggest that it can elucidate several important and fundamental aspects of abnormal networks to epilepsy. In this article, we provide a review of the emerging evidence from connectomics research regarding neural network architecture, dynamics, and function related to epilepsy. We discuss how connectomics may bring together pathophysiologic hypotheses from conceptual and basic models of epilepsy and in vivo biomarkers for clinical translational research. By providing neural network information unique to each individual, the field of connectomics may help to elucidate variability in clinical outcomes and open opportunities for personalized medicine approaches to epilepsy. Connectomics involves complex and rich data from each subject, thus collaborative efforts to enable the systematic and rigorous evaluation of this form of "big data" are paramount to leverage the full potential of this new approach. Wiley Periodicals, Inc. © 2015 International League Against Epilepsy.

A GRAPH PARTITIONING APPROACH TO PREDICTING PATTERNS IN LATERAL INHIBITION SYSTEMS

PubMed Central

RUFINO FERREIRA, ANA S.; ARCAK, MURAT

2017-01-01

We analyze spatial patterns on networks of cells where adjacent cells inhibit each other through contact signaling. We represent the network as a graph where each vertex represents the dynamics of identical individual cells and where graph edges represent cell-to-cell signaling. To predict steady-state patterns we find equitable partitions of the graph vertices and assign them into disjoint classes. We then use results from monotone systems theory to prove the existence of patterns that are structured in such a way that all the cells in the same class have the same final fate. To study the stability properties of these patterns, we rely on the graph partition to perform a block decomposition of the system. Then, to guarantee stability, we provide a small-gain type criterion that depends on the input-output properties of each cell in the reduced system. Finally, we discuss pattern formation in stochastic models. With the help of a modal decomposition we show that noise can enhance the parameter region where patterning occurs. PMID:29225552

The signed permutation group on Feynman graphs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Purkart, Julian, E-mail: purkart@physik.hu-berlin.de

2016-08-15

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

Decision-Making in National Security Affairs: Toward a Typology.

DTIC Science & Technology

1985-06-07

decisional model, and thus provide the necessary linkage between observation and application of theory in explaining and/or predicting policy decisions . r...examines theories and models of decision -making processes from an interdisciplinary perspective, with a view toward deriving means by which the behavior of...processes, game theory , linear programming, network and graph theory , time series analysis, and the like. The discipline of decision analysis is a relatively

A Composite Network Approach for Assessing Multi-Species Connectivity: An Application to Road Defragmentation Prioritisation

PubMed Central

Saura, Santiago; Rondinini, Carlo

2016-01-01

One of the biggest challenges in large-scale conservation is quantifying connectivity at broad geographic scales and for a large set of species. Because connectivity analyses can be computationally intensive, and the planning process quite complex when multiple taxa are involved, assessing connectivity at large spatial extents for many species turns to be often intractable. Such limitation results in that conducted assessments are often partial by focusing on a few key species only, or are generic by considering a range of dispersal distances and a fixed set of areas to connect that are not directly linked to the actual spatial distribution or mobility of particular species. By using a graph theory framework, here we propose an approach to reduce computational effort and effectively consider large assemblages of species in obtaining multi-species connectivity priorities. We demonstrate the potential of the approach by identifying defragmentation priorities in the Italian road network focusing on medium and large terrestrial mammals. We show that by combining probabilistic species graphs prior to conducting the network analysis (i) it is possible to analyse connectivity once for all species simultaneously, obtaining conservation or restoration priorities that apply for the entire species assemblage; and that (ii) those priorities are well aligned with the ones that would be obtained by aggregating the results of separate connectivity analysis for each of the individual species. This approach offers great opportunities to extend connectivity assessments to large assemblages of species and broad geographic scales. PMID:27768718

Edge length dynamics on graphs with applications to p-adic AdS/CFT

DOE PAGES

Gubser, Steven S.; Heydeman, Matthew; Jepsen, Christian; ...

2017-06-30

We formulate a Euclidean theory of edge length dynamics based on a notion of Ricci curvature on graphs with variable edge lengths. In order to write an explicit form for the discrete analog of the Einstein-Hilbert action, we require that the graph should either be a tree or that all its cycles should be sufficiently long. The infinite regular tree with all edge lengths equal is an example of a graph with constant negative curvature, providing a connection with p-adic AdS/CFT, where such a tree takes the place of anti-de Sitter space. Here, we compute simple correlators of the operatormore » holographically dual to edge length fluctuations. This operator has dimension equal to the dimension of the boundary, and it has some features in common with the stress tensor.« less

Edge length dynamics on graphs with applications to p-adic AdS/CFT

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gubser, Steven S.; Heydeman, Matthew; Jepsen, Christian

We formulate a Euclidean theory of edge length dynamics based on a notion of Ricci curvature on graphs with variable edge lengths. In order to write an explicit form for the discrete analog of the Einstein-Hilbert action, we require that the graph should either be a tree or that all its cycles should be sufficiently long. The infinite regular tree with all edge lengths equal is an example of a graph with constant negative curvature, providing a connection with p-adic AdS/CFT, where such a tree takes the place of anti-de Sitter space. Here, we compute simple correlators of the operatormore » holographically dual to edge length fluctuations. This operator has dimension equal to the dimension of the boundary, and it has some features in common with the stress tensor.« less

GenoLink: a graph-based querying and browsing system for investigating the function of genes and proteins.

PubMed

Durand, Patrick; Labarre, Laurent; Meil, Alain; Divo, Jean-Louis; Vandenbrouck, Yves; Viari, Alain; Wojcik, Jérôme

2006-01-17

A large variety of biological data can be represented by graphs. These graphs can be constructed from heterogeneous data coming from genomic and post-genomic technologies, but there is still need for tools aiming at exploring and analysing such graphs. This paper describes GenoLink, a software platform for the graphical querying and exploration of graphs. GenoLink provides a generic framework for representing and querying data graphs. This framework provides a graph data structure, a graph query engine, allowing to retrieve sub-graphs from the entire data graph, and several graphical interfaces to express such queries and to further explore their results. A query consists in a graph pattern with constraints attached to the vertices and edges. A query result is the set of all sub-graphs of the entire data graph that are isomorphic to the pattern and satisfy the constraints. The graph data structure does not rely upon any particular data model but can dynamically accommodate for any user-supplied data model. However, for genomic and post-genomic applications, we provide a default data model and several parsers for the most popular data sources. GenoLink does not require any programming skill since all operations on graphs and the analysis of the results can be carried out graphically through several dedicated graphical interfaces. GenoLink is a generic and interactive tool allowing biologists to graphically explore various sources of information. GenoLink is distributed either as a standalone application or as a component of the Genostar/Iogma platform. Both distributions are free for academic research and teaching purposes and can be requested at academy@genostar.com. A commercial licence form can be obtained for profit company at info@genostar.com. See also http://www.genostar.org.

GenoLink: a graph-based querying and browsing system for investigating the function of genes and proteins

PubMed Central

Durand, Patrick; Labarre, Laurent; Meil, Alain; Divo1, Jean-Louis; Vandenbrouck, Yves; Viari, Alain; Wojcik, Jérôme

2006-01-01

Background A large variety of biological data can be represented by graphs. These graphs can be constructed from heterogeneous data coming from genomic and post-genomic technologies, but there is still need for tools aiming at exploring and analysing such graphs. This paper describes GenoLink, a software platform for the graphical querying and exploration of graphs. Results GenoLink provides a generic framework for representing and querying data graphs. This framework provides a graph data structure, a graph query engine, allowing to retrieve sub-graphs from the entire data graph, and several graphical interfaces to express such queries and to further explore their results. A query consists in a graph pattern with constraints attached to the vertices and edges. A query result is the set of all sub-graphs of the entire data graph that are isomorphic to the pattern and satisfy the constraints. The graph data structure does not rely upon any particular data model but can dynamically accommodate for any user-supplied data model. However, for genomic and post-genomic applications, we provide a default data model and several parsers for the most popular data sources. GenoLink does not require any programming skill since all operations on graphs and the analysis of the results can be carried out graphically through several dedicated graphical interfaces. Conclusion GenoLink is a generic and interactive tool allowing biologists to graphically explore various sources of information. GenoLink is distributed either as a standalone application or as a component of the Genostar/Iogma platform. Both distributions are free for academic research and teaching purposes and can be requested at academy@genostar.com. A commercial licence form can be obtained for profit company at info@genostar.com. See also . PMID:16417636

Directed acyclic graphs (DAGs): an aid to assess confounding in dental research.

PubMed

Merchant, Anwar T; Pitiphat, Waranuch

2002-12-01

Confounding, a special type of bias, occurs when an extraneous factor is associated with the exposure and independently affects the outcome. In order to get an unbiased estimate of the exposure-outcome relationship, we need to identify potential confounders, collect information on them, design appropriate studies, and adjust for confounding in data analysis. However, it is not always clear which variables to collect information on and adjust for in the analyses. Inappropriate adjustment for confounding can even introduce bias where none existed. Directed acyclic graphs (DAGs) provide a method to select potential confounders and minimize bias in the design and analysis of epidemiological studies. DAGs have been used extensively in expert systems and robotics. Robins (1987) introduced the application of DAGs in epidemiology to overcome shortcomings of traditional methods to control for confounding, especially as they related to unmeasured confounding. DAGs provide a quick and visual way to assess confounding without making parametric assumptions. We introduce DAGs, starting with definitions and rules for basic manipulation, stressing more on applications than theory. We then demonstrate their application in the control of confounding through examples of observational and cross-sectional epidemiological studies.

Study of amyloid-β peptide functional brain networks in AD, MCI and HC.

PubMed

Jiang, Jiehui; Duan, Huoqiang; Huang, Zheming; Yu, Zhihua

2015-01-01

One medical challenge in studying the amyloid-β (Aβ) peptide mechanism for Alzheimer's disease (AD) is exploring the law of beta toxic oligomers' diffusion in human brains in vivo. One beneficial means of solving this problem is brain network analysis based on graph theory. In this study, the characteristics of Aβ functional brain networks of Healthy Control (HC), Mild Cognitive Impairment (MCI), and AD groups were compared by applying graph theoretical analyses to Carbon 11-labeled Pittsburgh compound B positron emission tomography (11C PiB-PET) data. 120 groups of PiB-PET images from the ADNI database were analyzed. The results showed that the small-world property of MCI and AD were lost as compared to HC. Furthermore, the local clustering of networks was higher in both MCI and AD as compared to HC, whereas the path length was similar among the three groups. The results also showed that there could be four potential Aβ toxic oligomer seeds: Frontal_Sup_Medial_L, Parietal_Inf_L, Frontal_Med_Orb_R, and Parietal_Inf_R. These four seeds are corresponding to Regions of Interests referred by physicians to clinically diagnose AD.

Information Graph Flow: A Geometric Approximation of Quantum and Statistical Systems

NASA Astrophysics Data System (ADS)

Vanchurin, Vitaly

2018-05-01

Given a quantum (or statistical) system with a very large number of degrees of freedom and a preferred tensor product factorization of the Hilbert space (or of a space of distributions) we describe how it can be approximated with a very low-dimensional field theory with geometric degrees of freedom. The geometric approximation procedure consists of three steps. The first step is to construct weighted graphs (we call information graphs) with vertices representing subsystems (e.g., qubits or random variables) and edges representing mutual information (or the flow of information) between subsystems. The second step is to deform the adjacency matrices of the information graphs to that of a (locally) low-dimensional lattice using the graph flow equations introduced in the paper. (Note that the graph flow produces very sparse adjacency matrices and thus might also be used, for example, in machine learning or network science where the task of graph sparsification is of a central importance.) The third step is to define an emergent metric and to derive an effective description of the metric and possibly other degrees of freedom. To illustrate the procedure we analyze (numerically and analytically) two information graph flows with geometric attractors (towards locally one- and two-dimensional lattices) and metric perturbations obeying a geometric flow equation. Our analysis also suggests a possible approach to (a non-perturbative) quantum gravity in which the geometry (a secondary object) emerges directly from a quantum state (a primary object) due to the flow of the information graphs.

Information Graph Flow: A Geometric Approximation of Quantum and Statistical Systems

NASA Astrophysics Data System (ADS)

Vanchurin, Vitaly

2018-06-01

Given a quantum (or statistical) system with a very large number of degrees of freedom and a preferred tensor product factorization of the Hilbert space (or of a space of distributions) we describe how it can be approximated with a very low-dimensional field theory with geometric degrees of freedom. The geometric approximation procedure consists of three steps. The first step is to construct weighted graphs (we call information graphs) with vertices representing subsystems (e.g., qubits or random variables) and edges representing mutual information (or the flow of information) between subsystems. The second step is to deform the adjacency matrices of the information graphs to that of a (locally) low-dimensional lattice using the graph flow equations introduced in the paper. (Note that the graph flow produces very sparse adjacency matrices and thus might also be used, for example, in machine learning or network science where the task of graph sparsification is of a central importance.) The third step is to define an emergent metric and to derive an effective description of the metric and possibly other degrees of freedom. To illustrate the procedure we analyze (numerically and analytically) two information graph flows with geometric attractors (towards locally one- and two-dimensional lattices) and metric perturbations obeying a geometric flow equation. Our analysis also suggests a possible approach to (a non-perturbative) quantum gravity in which the geometry (a secondary object) emerges directly from a quantum state (a primary object) due to the flow of the information graphs.

Association between abnormal brain functional connectivity in children and psychopathology: A study based on graph theory and machine learning.

PubMed

Sato, João Ricardo; Biazoli, Claudinei Eduardo; Salum, Giovanni Abrahão; Gadelha, Ary; Crossley, Nicolas; Vieira, Gilson; Zugman, André; Picon, Felipe Almeida; Pan, Pedro Mario; Hoexter, Marcelo Queiroz; Amaro, Edson; Anés, Mauricio; Moura, Luciana Monteiro; Del'Aquilla, Marco Antonio Gomes; Mcguire, Philip; Rohde, Luis Augusto; Miguel, Euripedes Constantino; Jackowski, Andrea Parolin; Bressan, Rodrigo Affonseca

2018-03-01

One of the major challenges facing psychiatry is how to incorporate biological measures in the classification of mental health disorders. Many of these disorders affect brain development and its connectivity. In this study, we propose a novel method for assessing brain networks based on the combination of a graph theory measure (eigenvector centrality) and a one-class support vector machine (OC-SVM). We applied this approach to resting-state fMRI data from 622 children and adolescents. Eigenvector centrality (EVC) of nodes from positive- and negative-task networks were extracted from each subject and used as input to an OC-SVM to label individual brain networks as typical or atypical. We hypothesised that classification of these subjects regarding the pattern of brain connectivity would predict the level of psychopathology. Subjects with atypical brain network organisation had higher levels of psychopathology (p < 0.001). There was a greater EVC in the typical group at the bilateral posterior cingulate and bilateral posterior temporal cortices; and significant decreases in EVC at left temporal pole. The combination of graph theory methods and an OC-SVM is a promising method to characterise neurodevelopment, and may be useful to understand the deviations leading to mental disorders.

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

PubMed Central

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

2016-01-01

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

A multicolour graph as a complete topological invariant for \\Omega-stable flows without periodic trajectories on surfaces

NASA Astrophysics Data System (ADS)

Kruglov, V. E.; Malyshev, D. S.; Pochinka, O. V.

2018-01-01

Studying the dynamics of a flow on surfaces by partitioning the phase space into cells with the same limit behaviour of trajectories within a cell goes back to the classical papers of Andronov, Pontryagin, Leontovich and Maier. The types of cells (the number of which is finite) and how the cells adjoin one another completely determine the topological equivalence class of a flow with finitely many special trajectories. If one trajectory is chosen in every cell of a rough flow without periodic orbits, then the cells are partitioned into so-called triangular regions of the same type. A combinatorial description of such a partition gives rise to the three-colour Oshemkov-Sharko graph, the vertices of which correspond to the triangular regions, and the edges to separatrices connecting them. Oshemkov and Sharko proved that such flows are topologically equivalent if and only if the three-colour graphs of the flows are isomorphic, and described an algorithm of distinguishing three-colour graphs. But their algorithm is not efficient with respect to graph theory. In the present paper, we describe the dynamics of Ω-stable flows without periodic trajectories on surfaces in the language of four-colour graphs, present an efficient algorithm for distinguishing such graphs, and develop a realization of a flow from some abstract graph. Bibliography: 17 titles.

Supervisory control based on minimal cuts and Petri net sub-controllers coordination

NASA Astrophysics Data System (ADS)

Rezig, Sadok; Achour, Zied; Rezg, Nidhal; Kammoun, Mohamed-Ali

2016-10-01

This paper addresses the synthesis of Petri net (PN) controller for the forbidden state transition problem with a new utilisation of the theory of regions. Moreover, as any method of control synthesis based on a reachability graph, the theory of regions suffers from the combinatorial explosion problem. The proposed work minimises the number of equations in the linear system of theory of regions and therefore one can reduce the computation time. In this paper, two different approaches are proposed to select minimal cuts in the reachability graph in order to synthesise a PN controller. Thanks to a switch from one cut to another, one can activate and deactivate the corresponding PNcontroller. An application is implemented in a flexible manufacturing system to illustrate the present method. Finally, comparison with previous works with experimental results in obtaining a maximally permissive controller is presented.

Discriminating micropathogen lineages and their reticulate evolution through graph theory-based network analysis: the case of Trypanosoma cruzi, the agent of Chagas disease.

PubMed

Arnaud-Haond, Sophie; Moalic, Yann; Barnabé, Christian; Ayala, Francisco José; Tibayrenc, Michel

2014-01-01

Micropathogens (viruses, bacteria, fungi, parasitic protozoa) share a common trait, which is partial clonality, with wide variance in the respective influence of clonality and sexual recombination on the dynamics and evolution of taxa. The discrimination of distinct lineages and the reconstruction of their phylogenetic history are key information to infer their biomedical properties. However, the phylogenetic picture is often clouded by occasional events of recombination across divergent lineages, limiting the relevance of classical phylogenetic analysis and dichotomic trees. We have applied a network analysis based on graph theory to illustrate the relationships among genotypes of Trypanosoma cruzi, the parasitic protozoan responsible for Chagas disease, to identify major lineages and to unravel their past history of divergence and possible recombination events. At the scale of T. cruzi subspecific diversity, graph theory-based networks applied to 22 isoenzyme loci (262 distinct Multi-Locus-Enzyme-Electrophoresis -MLEE) and 19 microsatellite loci (66 Multi-Locus-Genotypes -MLG) fully confirms the high clustering of genotypes into major lineages or "near-clades". The release of the dichotomic constraint associated with phylogenetic reconstruction usually applied to Multilocus data allows identifying putative hybrids and their parental lineages. Reticulate topology suggests a slightly different history for some of the main "near-clades", and a possibly more complex origin for the putative hybrids than hitherto proposed. Finally the sub-network of the near-clade T. cruzi I (28 MLG) shows a clustering subdivision into three differentiated lesser near-clades ("Russian doll pattern"), which confirms the hypothesis recently proposed by other investigators. The present study broadens and clarifies the hypotheses previously obtained from classical markers on the same sets of data, which demonstrates the added value of this approach. This underlines the potential of graph theory-based network analysis for describing the nature and relationships of major pathogens, thereby opening stimulating prospects to unravel the organization, dynamics and history of major micropathogen lineages.

Symposium on Chemical Applications of Topology and Graph Theory, April 18-22, 1983.

DTIC Science & Technology

1983-04-01

illustrated by application to the Lotka - Volterra oscillator. ELECTRICAL NETWORK REPRESENTATION OF n-DIMENSIONAL CHEMICAL MANIFOLDS L. Peusner P.O. Box 380...like molecules and others; the original formulas by Cayley were extended by Polya in a general enumeration theorem, simplified by Otter, and also studied...Gutman, leading to a joint paper which generalized it, using line graphs. Finally, electroneqativity consider- ations tell the strength of a chemical

Deep graphs-A general framework to represent and analyze heterogeneous complex systems across scales.

PubMed

Traxl, Dominik; Boers, Niklas; Kurths, Jürgen

2016-06-01

Network theory has proven to be a powerful tool in describing and analyzing systems by modelling the relations between their constituent objects. Particularly in recent years, a great progress has been made by augmenting "traditional" network theory in order to account for the multiplex nature of many networks, multiple types of connections between objects, the time-evolution of networks, networks of networks and other intricacies. However, existing network representations still lack crucial features in order to serve as a general data analysis tool. These include, most importantly, an explicit association of information with possibly heterogeneous types of objects and relations, and a conclusive representation of the properties of groups of nodes as well as the interactions between such groups on different scales. In this paper, we introduce a collection of definitions resulting in a framework that, on the one hand, entails and unifies existing network representations (e.g., network of networks and multilayer networks), and on the other hand, generalizes and extends them by incorporating the above features. To implement these features, we first specify the nodes and edges of a finite graph as sets of properties (which are permitted to be arbitrary mathematical objects). Second, the mathematical concept of partition lattices is transferred to the network theory in order to demonstrate how partitioning the node and edge set of a graph into supernodes and superedges allows us to aggregate, compute, and allocate information on and between arbitrary groups of nodes. The derived partition lattice of a graph, which we denote by deep graph, constitutes a concise, yet comprehensive representation that enables the expression and analysis of heterogeneous properties, relations, and interactions on all scales of a complex system in a self-contained manner. Furthermore, to be able to utilize existing network-based methods and models, we derive different representations of multilayer networks from our framework and demonstrate the advantages of our representation. On the basis of the formal framework described here, we provide a rich, fully scalable (and self-explanatory) software package that integrates into the PyData ecosystem and offers interfaces to popular network packages, making it a powerful, general-purpose data analysis toolkit. We exemplify an application of deep graphs using a real world dataset, comprising 16 years of satellite-derived global precipitation measurements. We deduce a deep graph representation of these measurements in order to track and investigate local formations of spatio-temporal clusters of extreme precipitation events.

A sediment graph model based on SCS-CN method

NASA Astrophysics Data System (ADS)

Singh, P. K.; Bhunya, P. K.; Mishra, S. K.; Chaube, U. C.

2008-01-01

SummaryThis paper proposes new conceptual sediment graph models based on coupling of popular and extensively used methods, viz., Nash model based instantaneous unit sediment graph (IUSG), soil conservation service curve number (SCS-CN) method, and Power law. These models vary in their complexity and this paper tests their performance using data of the Nagwan watershed (area = 92.46 km 2) (India). The sensitivity of total sediment yield and peak sediment flow rate computations to model parameterisation is analysed. The exponent of the Power law, β, is more sensitive than other model parameters. The models are found to have substantial potential for computing sediment graphs (temporal sediment flow rate distribution) as well as total sediment yield.

A graph algebra for scalable visual analytics.

PubMed

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

2012-01-01

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

A New Analysis of Resting State Connectivity and Graph Theory Reveals Distinctive Short-Term Modulations due to Whisker Stimulation in Rats.

PubMed

Kreitz, Silke; de Celis Alonso, Benito; Uder, Michael; Hess, Andreas

2018-01-01

Resting state (RS) connectivity has been increasingly studied in healthy and diseased brains in humans and animals. This paper presents a new method to analyze RS data from fMRI that combines multiple seed correlation analysis with graph-theory (MSRA). We characterize and evaluate this new method in relation to two other graph-theoretical methods and ICA. The graph-theoretical methods calculate cross-correlations of regional average time-courses, one using seed regions of the same size (SRCC) and the other using whole brain structure regions (RCCA). We evaluated the reproducibility, power, and capacity of these methods to characterize short-term RS modulation to unilateral physiological whisker stimulation in rats. Graph-theoretical networks found with the MSRA approach were highly reproducible, and their communities showed large overlaps with ICA components. Additionally, MSRA was the only one of all tested methods that had the power to detect significant RS modulations induced by whisker stimulation that are controlled by family-wise error rate (FWE). Compared to the reduced resting state network connectivity during task performance, these modulations implied decreased connectivity strength in the bilateral sensorimotor and entorhinal cortex. Additionally, the contralateral ventromedial thalamus (part of the barrel field related lemniscal pathway) and the hypothalamus showed reduced connectivity. Enhanced connectivity was observed in the amygdala, especially the contralateral basolateral amygdala (involved in emotional learning processes). In conclusion, MSRA is a powerful analytical approach that can reliably detect tiny modulations of RS connectivity. It shows a great promise as a method for studying RS dynamics in healthy and pathological conditions.

A New Analysis of Resting State Connectivity and Graph Theory Reveals Distinctive Short-Term Modulations due to Whisker Stimulation in Rats

PubMed Central

Kreitz, Silke; de Celis Alonso, Benito; Uder, Michael; Hess, Andreas

2018-01-01

Resting state (RS) connectivity has been increasingly studied in healthy and diseased brains in humans and animals. This paper presents a new method to analyze RS data from fMRI that combines multiple seed correlation analysis with graph-theory (MSRA). We characterize and evaluate this new method in relation to two other graph-theoretical methods and ICA. The graph-theoretical methods calculate cross-correlations of regional average time-courses, one using seed regions of the same size (SRCC) and the other using whole brain structure regions (RCCA). We evaluated the reproducibility, power, and capacity of these methods to characterize short-term RS modulation to unilateral physiological whisker stimulation in rats. Graph-theoretical networks found with the MSRA approach were highly reproducible, and their communities showed large overlaps with ICA components. Additionally, MSRA was the only one of all tested methods that had the power to detect significant RS modulations induced by whisker stimulation that are controlled by family-wise error rate (FWE). Compared to the reduced resting state network connectivity during task performance, these modulations implied decreased connectivity strength in the bilateral sensorimotor and entorhinal cortex. Additionally, the contralateral ventromedial thalamus (part of the barrel field related lemniscal pathway) and the hypothalamus showed reduced connectivity. Enhanced connectivity was observed in the amygdala, especially the contralateral basolateral amygdala (involved in emotional learning processes). In conclusion, MSRA is a powerful analytical approach that can reliably detect tiny modulations of RS connectivity. It shows a great promise as a method for studying RS dynamics in healthy and pathological conditions. PMID:29875622

Graph Theoretic Foundations of Multibody Dynamics Part I: Structural Properties

PubMed Central

Jain, Abhinandan

2011-01-01

This is the first part of two papers that use concepts from graph theory to obtain a deeper understanding of the mathematical foundations of multibody dynamics. The key contribution is the development of a unifying framework that shows that key analytical results and computational algorithms in multibody dynamics are a direct consequence of structural properties and require minimal assumptions about the specific nature of the underlying multibody system. This first part focuses on identifying the abstract graph theoretic structural properties of spatial operator techniques in multibody dynamics. The second part paper exploits these structural properties to develop a broad spectrum of analytical results and computational algorithms. Towards this, we begin with the notion of graph adjacency matrices and generalize it to define block-weighted adjacency (BWA) matrices and their 1-resolvents. Previously developed spatial operators are shown to be special cases of such BWA matrices and their 1-resolvents. These properties are shown to hold broadly for serial and tree topology multibody systems. Specializations of the BWA and 1-resolvent matrices are referred to as spatial kernel operators (SKO) and spatial propagation operators (SPO). These operators and their special properties provide the foundation for the analytical and algorithmic techniques developed in the companion paper. We also use the graph theory concepts to study the topology induced sparsity structure of these operators and the system mass matrix. Similarity transformations of these operators are also studied. While the detailed development is done for the case of rigid-link multibody systems, the extension of these techniques to a broader class of systems (e.g. deformable links) are illustrated. PMID:22102790

Review on Graph Clustering and Subgraph Similarity Based Analysis of Neurological Disorders

PubMed Central

Thomas, Jaya; Seo, Dongmin; Sael, Lee

2016-01-01

How can complex relationships among molecular or clinico-pathological entities of neurological disorders be represented and analyzed? Graphs seem to be the current answer to the question no matter the type of information: molecular data, brain images or neural signals. We review a wide spectrum of graph representation and graph analysis methods and their application in the study of both the genomic level and the phenotypic level of the neurological disorder. We find numerous research works that create, process and analyze graphs formed from one or a few data types to gain an understanding of specific aspects of the neurological disorders. Furthermore, with the increasing number of data of various types becoming available for neurological disorders, we find that integrative analysis approaches that combine several types of data are being recognized as a way to gain a global understanding of the diseases. Although there are still not many integrative analyses of graphs due to the complexity in analysis, multi-layer graph analysis is a promising framework that can incorporate various data types. We describe and discuss the benefits of the multi-layer graph framework for studies of neurological disease. PMID:27258269

Review on Graph Clustering and Subgraph Similarity Based Analysis of Neurological Disorders.

PubMed

Thomas, Jaya; Seo, Dongmin; Sael, Lee

2016-06-01

How can complex relationships among molecular or clinico-pathological entities of neurological disorders be represented and analyzed? Graphs seem to be the current answer to the question no matter the type of information: molecular data, brain images or neural signals. We review a wide spectrum of graph representation and graph analysis methods and their application in the study of both the genomic level and the phenotypic level of the neurological disorder. We find numerous research works that create, process and analyze graphs formed from one or a few data types to gain an understanding of specific aspects of the neurological disorders. Furthermore, with the increasing number of data of various types becoming available for neurological disorders, we find that integrative analysis approaches that combine several types of data are being recognized as a way to gain a global understanding of the diseases. Although there are still not many integrative analyses of graphs due to the complexity in analysis, multi-layer graph analysis is a promising framework that can incorporate various data types. We describe and discuss the benefits of the multi-layer graph framework for studies of neurological disease.

Network reconstruction via graph blending

NASA Astrophysics Data System (ADS)

Estrada, Rolando

2016-05-01

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

Flux control coefficients determined by inhibitor titration: the design and analysis of experiments to minimize errors.

PubMed Central

Small, J R

1993-01-01

This paper is a study into the effects of experimental error on the estimated values of flux control coefficients obtained using specific inhibitors. Two possible techniques for analysing the experimental data are compared: a simple extrapolation method (the so-called graph method) and a non-linear function fitting method. For these techniques, the sources of systematic errors are identified and the effects of systematic and random errors are quantified, using both statistical analysis and numerical computation. It is shown that the graph method is very sensitive to random errors and, under all conditions studied, that the fitting method, even under conditions where the assumptions underlying the fitted function do not hold, outperformed the graph method. Possible ways of designing experiments to minimize the effects of experimental errors are analysed and discussed. PMID:8257434

Analyzing and synthesizing phylogenies using tree alignment graphs.

PubMed

Smith, Stephen A; Brown, Joseph W; Hinchliff, Cody E

2013-01-01

Phylogenetic trees are used to analyze and visualize evolution. However, trees can be imperfect datatypes when summarizing multiple trees. This is especially problematic when accommodating for biological phenomena such as horizontal gene transfer, incomplete lineage sorting, and hybridization, as well as topological conflict between datasets. Additionally, researchers may want to combine information from sets of trees that have partially overlapping taxon sets. To address the problem of analyzing sets of trees with conflicting relationships and partially overlapping taxon sets, we introduce methods for aligning, synthesizing and analyzing rooted phylogenetic trees within a graph, called a tree alignment graph (TAG). The TAG can be queried and analyzed to explore uncertainty and conflict. It can also be synthesized to construct trees, presenting an alternative to supertrees approaches. We demonstrate these methods with two empirical datasets. In order to explore uncertainty, we constructed a TAG of the bootstrap trees from the Angiosperm Tree of Life project. Analysis of the resulting graph demonstrates that areas of the dataset that are unresolved in majority-rule consensus tree analyses can be understood in more detail within the context of a graph structure, using measures incorporating node degree and adjacency support. As an exercise in synthesis (i.e., summarization of a TAG constructed from the alignment trees), we also construct a TAG consisting of the taxonomy and source trees from a recent comprehensive bird study. We synthesized this graph into a tree that can be reconstructed in a repeatable fashion and where the underlying source information can be updated. The methods presented here are tractable for large scale analyses and serve as a basis for an alternative to consensus tree and supertree methods. Furthermore, the exploration of these graphs can expose structures and patterns within the dataset that are otherwise difficult to observe.

Analyzing and Synthesizing Phylogenies Using Tree Alignment Graphs

PubMed Central

Smith, Stephen A.; Brown, Joseph W.; Hinchliff, Cody E.

2013-01-01

Phylogenetic trees are used to analyze and visualize evolution. However, trees can be imperfect datatypes when summarizing multiple trees. This is especially problematic when accommodating for biological phenomena such as horizontal gene transfer, incomplete lineage sorting, and hybridization, as well as topological conflict between datasets. Additionally, researchers may want to combine information from sets of trees that have partially overlapping taxon sets. To address the problem of analyzing sets of trees with conflicting relationships and partially overlapping taxon sets, we introduce methods for aligning, synthesizing and analyzing rooted phylogenetic trees within a graph, called a tree alignment graph (TAG). The TAG can be queried and analyzed to explore uncertainty and conflict. It can also be synthesized to construct trees, presenting an alternative to supertrees approaches. We demonstrate these methods with two empirical datasets. In order to explore uncertainty, we constructed a TAG of the bootstrap trees from the Angiosperm Tree of Life project. Analysis of the resulting graph demonstrates that areas of the dataset that are unresolved in majority-rule consensus tree analyses can be understood in more detail within the context of a graph structure, using measures incorporating node degree and adjacency support. As an exercise in synthesis (i.e., summarization of a TAG constructed from the alignment trees), we also construct a TAG consisting of the taxonomy and source trees from a recent comprehensive bird study. We synthesized this graph into a tree that can be reconstructed in a repeatable fashion and where the underlying source information can be updated. The methods presented here are tractable for large scale analyses and serve as a basis for an alternative to consensus tree and supertree methods. Furthermore, the exploration of these graphs can expose structures and patterns within the dataset that are otherwise difficult to observe. PMID:24086118

Voxelwise Spectral Diffusional Connectivity and its Applications to Alzheimer’s Disease and Intelligence Prediction

PubMed Central

Li, Junning; Jin, Yan; Shi, Yonggang; Dinov, Ivo D.; Wang, Danny J.; Toga, Arthur W.; Thompson, Paul M.

2014-01-01

Human brain connectivity can be studied using graph theory. Many connectivity studies parcellate the brain into regions and count fibres extracted between them. The resulting network analyses require validation of the tractography, as well as region and parameter selection. Here we investigate whole brain connectivity from a different perspective. We propose a mathematical formulation based on studying the eigenvalues of the Laplacian matrix of the diffusion tensor field at the voxel level. This voxelwise matrix has over a million parameters, but we derive the Kirchhoff complexity and eigen-spectrum through elegant mathematical theorems, without heavy computation. We use these novel measures to accurately estimate the voxelwise connectivity in multiple biomedical applications such as Alzheimer’s disease and intelligence prediction. PMID:24505723

Imperial College near infrared spectroscopy neuroimaging analysis framework.

PubMed

Orihuela-Espina, Felipe; Leff, Daniel R; James, David R C; Darzi, Ara W; Yang, Guang-Zhong

2018-01-01

This paper describes the Imperial College near infrared spectroscopy neuroimaging analysis (ICNNA) software tool for functional near infrared spectroscopy neuroimaging data. ICNNA is a MATLAB-based object-oriented framework encompassing an application programming interface and a graphical user interface. ICNNA incorporates reconstruction based on the modified Beer-Lambert law and basic processing and data validation capabilities. Emphasis is placed on the full experiment rather than individual neuroimages as the central element of analysis. The software offers three types of analyses including classical statistical methods based on comparison of changes in relative concentrations of hemoglobin between the task and baseline periods, graph theory-based metrics of connectivity and, distinctively, an analysis approach based on manifold embedding. This paper presents the different capabilities of ICNNA in its current version.

n-Nucleotide circular codes in graph theory.

PubMed

Fimmel, Elena; Michel, Christian J; Strüngmann, Lutz

2016-03-13

The circular code theory proposes that genes are constituted of two trinucleotide codes: the classical genetic code with 61 trinucleotides for coding the 20 amino acids (except the three stop codons {TAA,TAG,TGA}) and a circular code based on 20 trinucleotides for retrieving, maintaining and synchronizing the reading frame. It relies on two main results: the identification of a maximal C(3) self-complementary trinucleotide circular code X in genes of bacteria, eukaryotes, plasmids and viruses (Michel 2015 J. Theor. Biol. 380, 156-177. (doi:10.1016/j.jtbi.2015.04.009); Arquès & Michel 1996 J. Theor. Biol. 182, 45-58. (doi:10.1006/jtbi.1996.0142)) and the finding of X circular code motifs in tRNAs and rRNAs, in particular in the ribosome decoding centre (Michel 2012 Comput. Biol. Chem. 37, 24-37. (doi:10.1016/j.compbiolchem.2011.10.002); El Soufi & Michel 2014 Comput. Biol. Chem. 52, 9-17. (doi:10.1016/j.compbiolchem.2014.08.001)). The univerally conserved nucleotides A1492 and A1493 and the conserved nucleotide G530 are included in X circular code motifs. Recently, dinucleotide circular codes were also investigated (Michel & Pirillo 2013 ISRN Biomath. 2013, 538631. (doi:10.1155/2013/538631); Fimmel et al. 2015 J. Theor. Biol. 386, 159-165. (doi:10.1016/j.jtbi.2015.08.034)). As the genetic motifs of different lengths are ubiquitous in genes and genomes, we introduce a new approach based on graph theory to study in full generality n-nucleotide circular codes X, i.e. of length 2 (dinucleotide), 3 (trinucleotide), 4 (tetranucleotide), etc. Indeed, we prove that an n-nucleotide code X is circular if and only if the corresponding graph [Formula: see text] is acyclic. Moreover, the maximal length of a path in [Formula: see text] corresponds to the window of nucleotides in a sequence for detecting the correct reading frame. Finally, the graph theory of tournaments is applied to the study of dinucleotide circular codes. It has full equivalence between the combinatorics theory (Michel & Pirillo 2013 ISRN Biomath. 2013, 538631. (doi:10.1155/2013/538631)) and the group theory (Fimmel et al. 2015 J. Theor. Biol. 386, 159-165. (doi:10.1016/j.jtbi.2015.08.034)) of dinucleotide circular codes while its mathematical approach is simpler. © 2016 The Author(s).

Graph theory analysis of cortical thickness networks in adolescents with d-transposition of the great arteries.

PubMed

Watson, Christopher G; Stopp, Christian; Newburger, Jane W; Rivkin, Michael J

2018-02-01

Adolescents with d-transposition of the great arteries (d-TGA) who had the arterial switch operation in infancy have been found to have structural brain differences compared to healthy controls. We used cortical thickness measurements obtained from structural brain MRI to determine group differences in global brain organization using a graph theoretical approach. Ninety-two d-TGA subjects and 49 controls were scanned using one of two identical 1.5-Tesla MRI systems. Mean cortical thickness was obtained from 34 regions per hemisphere using Freesurfer. A linear model was used for each brain region to adjust for subject age, sex, and scanning location. Structural connectivity for each group was inferred based on the presence of high inter-regional correlations of the linear model residuals, and binary connectivity matrices were created by thresholding over a range of correlation values for each group. Graph theory analysis was performed using packages in R. Permutation tests were performed to determine significance of between-group differences in global network measures. Within-group connectivity patterns were qualitatively different between groups. At lower network densities, controls had significantly more long-range connections. The location and number of hub regions differed between groups: controls had a greater number of hubs at most network densities. The control network had a significant rightward asymmetry compared to the d-TGA group at all network densities. Using graph theory analysis of cortical thickness correlations, we found differences in brain structural network organization among d-TGA adolescents compared to controls. These may be related to the white matter and gray matter differences previously found in this cohort, and in turn may be related to the cognitive deficits this cohort presents.

A simplifying feature of the heterotic one loop four graviton amplitude

NASA Astrophysics Data System (ADS)

Basu, Anirban

2018-01-01

We show that the weight four modular graph functions that contribute to the integrand of the t8t8D4R4 term at one loop in heterotic string theory do not require regularization, and hence the integrand is simple. This is unlike the graphs that contribute to the integrands of the other gravitational terms at this order in the low momentum expansion, and these integrands require regularization. This property persists for an infinite number of terms in the effective action, and their integrands do not require regularization. We find non-trivial relations between weight four graphs of distinct topologies that do not require regularization by performing trivial manipulations using auxiliary diagrams.

Information Measures of Degree Distributions with an Application to Labeled Graphs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Joslyn, Cliff A.; Purvine, Emilie AH

2016-01-11

The problem of describing the distribution of labels over a set of objects is relevant to many domains. For example: cyber security, social media, and protein interactions all care about the manner in which labels are distributed among different objects. In this paper we present three interacting statistical measures on label distributions, inspired by entropy and information theory. Labeled graphs are discussed as a specific case of labels distributed over a set of edges. We describe a use case in cyber security using a labeled directed multi-graph of IPFLOW. Finally we show how these measures respond when labels are updatedmore » in certain ways.« less

Non-planar one-loop Parke-Taylor factors in the CHY approach for quadratic propagators

NASA Astrophysics Data System (ADS)

Ahmadiniaz, Naser; Gomez, Humberto; Lopez-Arcos, Cristhiam

2018-05-01

In this work we have studied the Kleiss-Kuijf relations for the recently introduced Parke-Taylor factors at one-loop in the CHY approach, that reproduce quadratic Feynman propagators. By doing this, we were able to identify the non-planar one-loop Parke-Taylor factors. In order to check that, in fact, these new factors can describe non-planar amplitudes, we applied them to the bi-adjoint Φ3 theory. As a byproduct, we found a new type of graphs that we called the non-planar CHY-graphs. These graphs encode all the information for the subleading order at one-loop, and there is not an equivalent of these in the Feynman formalism.

Automatic segmentation of closed-contour features in ophthalmic images using graph theory and dynamic programming.

PubMed

Chiu, Stephanie J; Toth, Cynthia A; Bowes Rickman, Catherine; Izatt, Joseph A; Farsiu, Sina

2012-05-01

This paper presents a generalized framework for segmenting closed-contour anatomical and pathological features using graph theory and dynamic programming (GTDP). More specifically, the GTDP method previously developed for quantifying retinal and corneal layer thicknesses is extended to segment objects such as cells and cysts. The presented technique relies on a transform that maps closed-contour features in the Cartesian domain into lines in the quasi-polar domain. The features of interest are then segmented as layers via GTDP. Application of this method to segment closed-contour features in several ophthalmic image types is shown. Quantitative validation experiments for retinal pigmented epithelium cell segmentation in confocal fluorescence microscopy images attests to the accuracy of the presented technique.

Systems Engineering Design Via Experimental Operation Research: Complex Organizational Metric for Programmatic Risk Environments (COMPRE)

NASA Technical Reports Server (NTRS)

Mog, Robert A.

1999-01-01

Unique and innovative graph theory, neural network, organizational modeling, and genetic algorithms are applied to the design and evolution of programmatic and organizational architectures. Graph theory representations of programs and organizations increase modeling capabilities and flexibility, while illuminating preferable programmatic/organizational design features. Treating programs and organizations as neural networks results in better system synthesis, and more robust data modeling. Organizational modeling using covariance structures enhances the determination of organizational risk factors. Genetic algorithms improve programmatic evolution characteristics, while shedding light on rulebase requirements for achieving specified technological readiness levels, given budget and schedule resources. This program of research improves the robustness and verifiability of systems synthesis tools, including the Complex Organizational Metric for Programmatic Risk Environments (COMPRE).

Automatic segmentation of closed-contour features in ophthalmic images using graph theory and dynamic programming

PubMed Central

Chiu, Stephanie J.; Toth, Cynthia A.; Bowes Rickman, Catherine; Izatt, Joseph A.; Farsiu, Sina

2012-01-01

This paper presents a generalized framework for segmenting closed-contour anatomical and pathological features using graph theory and dynamic programming (GTDP). More specifically, the GTDP method previously developed for quantifying retinal and corneal layer thicknesses is extended to segment objects such as cells and cysts. The presented technique relies on a transform that maps closed-contour features in the Cartesian domain into lines in the quasi-polar domain. The features of interest are then segmented as layers via GTDP. Application of this method to segment closed-contour features in several ophthalmic image types is shown. Quantitative validation experiments for retinal pigmented epithelium cell segmentation in confocal fluorescence microscopy images attests to the accuracy of the presented technique. PMID:22567602

HBNG: Graph theory based visualization of hydrogen bond networks in protein structures.

PubMed

Tiwari, Abhishek; Tiwari, Vivek

2007-07-09

HBNG is a graph theory based tool for visualization of hydrogen bond network in 2D. Digraphs generated by HBNG facilitate visualization of cooperativity and anticooperativity chains and rings in protein structures. HBNG takes hydrogen bonds list files (output from HBAT, HBEXPLORE, HBPLUS and STRIDE) as input and generates a DOT language script and constructs digraphs using freeware AT and T Graphviz tool. HBNG is useful in the enumeration of favorable topologies of hydrogen bond networks in protein structures and determining the effect of cooperativity and anticooperativity on protein stability and folding. HBNG can be applied to protein structure comparison and in the identification of secondary structural regions in protein structures. Program is available from the authors for non-commercial purposes.

Numbers and functions in quantum field theory

NASA Astrophysics Data System (ADS)

Schnetz, Oliver

2018-04-01

We review recent results in the theory of numbers and single-valued functions on the complex plane which arise in quantum field theory. These results are the basis for a new approach to high-loop-order calculations. As concrete examples, we provide scheme-independent counterterms of primitive log-divergent graphs in ϕ4 theory up to eight loops and the renormalization functions β , γ , γm of dimensionally regularized ϕ4 theory in the minimal subtraction scheme up to seven loops.

Learning molecular energies using localized graph kernels.

PubMed

Ferré, Grégoire; Haut, Terry; Barros, Kipton

2017-03-21

Recent machine learning methods make it possible to model potential energy of atomic configurations with chemical-level accuracy (as calculated from ab initio calculations) and at speeds suitable for molecular dynamics simulation. Best performance is achieved when the known physical constraints are encoded in the machine learning models. For example, the atomic energy is invariant under global translations and rotations; it is also invariant to permutations of same-species atoms. Although simple to state, these symmetries are complicated to encode into machine learning algorithms. In this paper, we present a machine learning approach based on graph theory that naturally incorporates translation, rotation, and permutation symmetries. Specifically, we use a random walk graph kernel to measure the similarity of two adjacency matrices, each of which represents a local atomic environment. This Graph Approximated Energy (GRAPE) approach is flexible and admits many possible extensions. We benchmark a simple version of GRAPE by predicting atomization energies on a standard dataset of organic molecules.

Learning molecular energies using localized graph kernels

NASA Astrophysics Data System (ADS)

Ferré, Grégoire; Haut, Terry; Barros, Kipton

2017-03-01

Recent machine learning methods make it possible to model potential energy of atomic configurations with chemical-level accuracy (as calculated from ab initio calculations) and at speeds suitable for molecular dynamics simulation. Best performance is achieved when the known physical constraints are encoded in the machine learning models. For example, the atomic energy is invariant under global translations and rotations; it is also invariant to permutations of same-species atoms. Although simple to state, these symmetries are complicated to encode into machine learning algorithms. In this paper, we present a machine learning approach based on graph theory that naturally incorporates translation, rotation, and permutation symmetries. Specifically, we use a random walk graph kernel to measure the similarity of two adjacency matrices, each of which represents a local atomic environment. This Graph Approximated Energy (GRAPE) approach is flexible and admits many possible extensions. We benchmark a simple version of GRAPE by predicting atomization energies on a standard dataset of organic molecules.

Non-Markovian Infection Spread Dramatically Alters the Susceptible-Infected-Susceptible Epidemic Threshold in Networks

NASA Astrophysics Data System (ADS)

Van Mieghem, P.; van de Bovenkamp, R.

2013-03-01

Most studies on susceptible-infected-susceptible epidemics in networks implicitly assume Markovian behavior: the time to infect a direct neighbor is exponentially distributed. Much effort so far has been devoted to characterize and precisely compute the epidemic threshold in susceptible-infected-susceptible Markovian epidemics on networks. Here, we report the rather dramatic effect of a nonexponential infection time (while still assuming an exponential curing time) on the epidemic threshold by considering Weibullean infection times with the same mean, but different power exponent α. For three basic classes of graphs, the Erdős-Rényi random graph, scale-free graphs and lattices, the average steady-state fraction of infected nodes is simulated from which the epidemic threshold is deduced. For all graph classes, the epidemic threshold significantly increases with the power exponents α. Hence, real epidemics that violate the exponential or Markovian assumption can behave seriously differently than anticipated based on Markov theory.

Generalized monogamy of contextual inequalities from the no-disturbance principle.

PubMed

Ramanathan, Ravishankar; Soeda, Akihito; Kurzyński, Paweł; Kaszlikowski, Dagomir

2012-08-03

In this Letter, we demonstrate that the property of monogamy of Bell violations seen for no-signaling correlations in composite systems can be generalized to the monogamy of contextuality in single systems obeying the Gleason property of no disturbance. We show how one can construct monogamies for contextual inequalities by using the graph-theoretic technique of vertex decomposition of a graph representing a set of measurements into subgraphs of suitable independence numbers that themselves admit a joint probability distribution. After establishing that all the subgraphs that are chordal graphs admit a joint probability distribution, we formulate a precise graph-theoretic condition that gives rise to the monogamy of contextuality. We also show how such monogamies arise within quantum theory for a single four-dimensional system and interpret violation of these relations in terms of a violation of causality. These monogamies can be tested with current experimental techniques.

Poor textural image tie point matching via graph theory

NASA Astrophysics Data System (ADS)

Yuan, Xiuxiao; Chen, Shiyu; Yuan, Wei; Cai, Yang

2017-07-01

Feature matching aims to find corresponding points to serve as tie points between images. Robust matching is still a challenging task when input images are characterized by low contrast or contain repetitive patterns, occlusions, or homogeneous textures. In this paper, a novel feature matching algorithm based on graph theory is proposed. This algorithm integrates both geometric and radiometric constraints into an edge-weighted (EW) affinity tensor. Tie points are then obtained by high-order graph matching. Four pairs of poor textural images covering forests, deserts, bare lands, and urban areas are tested. For comparison, three state-of-the-art matching techniques, namely, scale-invariant feature transform (SIFT), speeded up robust features (SURF), and features from accelerated segment test (FAST), are also used. The experimental results show that the matching recall obtained by SIFT, SURF, and FAST varies from 0 to 35% in different types of poor textures. However, through the integration of both geometry and radiometry and the EW strategy, the recall obtained by the proposed algorithm is better than 50% in all four image pairs. The better matching recall improves the number of correct matches, dispersion, and positional accuracy.

A cDNA microarray gene expression data classifier for clinical diagnostics based on graph theory.

PubMed

Benso, Alfredo; Di Carlo, Stefano; Politano, Gianfranco

2011-01-01

Despite great advances in discovering cancer molecular profiles, the proper application of microarray technology to routine clinical diagnostics is still a challenge. Current practices in the classification of microarrays' data show two main limitations: the reliability of the training data sets used to build the classifiers, and the classifiers' performances, especially when the sample to be classified does not belong to any of the available classes. In this case, state-of-the-art algorithms usually produce a high rate of false positives that, in real diagnostic applications, are unacceptable. To address this problem, this paper presents a new cDNA microarray data classification algorithm based on graph theory and is able to overcome most of the limitations of known classification methodologies. The classifier works by analyzing gene expression data organized in an innovative data structure based on graphs, where vertices correspond to genes and edges to gene expression relationships. To demonstrate the novelty of the proposed approach, the authors present an experimental performance comparison between the proposed classifier and several state-of-the-art classification algorithms.

Quantum Graphical Models and Belief Propagation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Leifer, M.S.; Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo Ont., N2L 2Y5; Poulin, D.

Belief Propagation algorithms acting on Graphical Models of classical probability distributions, such as Markov Networks, Factor Graphs and Bayesian Networks, are amongst the most powerful known methods for deriving probabilistic inferences amongst large numbers of random variables. This paper presents a generalization of these concepts and methods to the quantum case, based on the idea that quantum theory can be thought of as a noncommutative, operator-valued, generalization of classical probability theory. Some novel characterizations of quantum conditional independence are derived, and definitions of Quantum n-Bifactor Networks, Markov Networks, Factor Graphs and Bayesian Networks are proposed. The structure of Quantum Markovmore » Networks is investigated and some partial characterization results are obtained, along the lines of the Hammersley-Clifford theorem. A Quantum Belief Propagation algorithm is presented and is shown to converge on 1-Bifactor Networks and Markov Networks when the underlying graph is a tree. The use of Quantum Belief Propagation as a heuristic algorithm in cases where it is not known to converge is discussed. Applications to decoding quantum error correcting codes and to the simulation of many-body quantum systems are described.« less

Graph Theoretical Framework of Brain Networks in Multiple Sclerosis: A Review of Concepts.

PubMed

Fleischer, Vinzenz; Radetz, Angela; Ciolac, Dumitru; Muthuraman, Muthuraman; Gonzalez-Escamilla, Gabriel; Zipp, Frauke; Groppa, Sergiu

2017-11-01

Network science provides powerful access to essential organizational principles of the human brain. It has been applied in combination with graph theory to characterize brain connectivity patterns. In multiple sclerosis (MS), analysis of the brain networks derived from either structural or functional imaging provides new insights into pathological processes within the gray and white matter. Beyond focal lesions and diffuse tissue damage, network connectivity patterns could be important for closely tracking and predicting the disease course. In this review, we describe concepts of graph theory, highlight novel issues of tissue reorganization in acute and chronic neuroinflammation and address pitfalls with regard to network analysis in MS patients. We further provide an outline of functional and structural connectivity patterns observed in MS, spanning from disconnection and disruption on one hand to adaptation and compensation on the other. Moreover, we link network changes and their relation to clinical disability based on the current literature. Finally, we discuss the perspective of network science in MS for future research and postulate its role in the clinical framework. Copyright © 2017 IBRO. Published by Elsevier Ltd. All rights reserved.

Network analysis for a network disorder: The emerging role of graph theory in the study of epilepsy.

PubMed

Bernhardt, Boris C; Bonilha, Leonardo; Gross, Donald W

2015-09-01

Recent years have witnessed a paradigm shift in the study and conceptualization of epilepsy, which is increasingly understood as a network-level disorder. An emblematic case is temporal lobe epilepsy (TLE), the most common drug-resistant epilepsy that is electroclinically defined as a focal epilepsy and pathologically associated with hippocampal sclerosis. In this review, we will summarize histopathological, electrophysiological, and neuroimaging evidence supporting the concept that the substrate of TLE is not limited to the hippocampus alone, but rather is broadly distributed across multiple brain regions and interconnecting white matter pathways. We will introduce basic concepts of graph theory, a formalism to quantify topological properties of complex systems that has recently been widely applied to study networks derived from brain imaging and electrophysiology. We will discuss converging graph theoretical evidence indicating that networks in TLE show marked shifts in their overall topology, providing insight into the neurobiology of TLE as a network-level disorder. Our review will conclude by discussing methodological challenges and future clinical applications of this powerful analytical approach. Copyright © 2015 Elsevier Inc. All rights reserved.

A Domain-Specific Language for Discrete Mathematics

NASA Astrophysics Data System (ADS)

Jha, Rohit; Samuel, Alfy; Pawar, Ashmee; Kiruthika, M.

2013-05-01

This paper discusses a Domain Specific Language (DSL) that has been developed to enable implementation of concepts of discrete mathematics. A library of data types and functions provides functionality which is frequently required by users. Covering the areas of Mathematical Logic, Set Theory, Functions, Graph Theory, Number Theory, Linear Algebra and Combinatorics, the language's syntax is close to the actual notation used in the specific fields.

Free Quantum Field Theory from Quantum Cellular Automata

NASA Astrophysics Data System (ADS)

Bisio, Alessandro; D'Ariano, Giacomo Mauro; Perinotti, Paolo; Tosini, Alessandro

2015-10-01

After leading to a new axiomatic derivation of quantum theory (see D'Ariano et al. in Found Phys, 2015), the new informational paradigm is entering the domain of quantum field theory, suggesting a quantum automata framework that can be regarded as an extension of quantum field theory to including an hypothetical Planck scale, and with the usual quantum field theory recovered in the relativistic limit of small wave-vectors. Being derived from simple principles (linearity, unitarity, locality, homogeneity, isotropy, and minimality of dimension), the automata theory is quantum ab-initio, and does not assume Lorentz covariance and mechanical notions. Being discrete it can describe localized states and measurements (unmanageable by quantum field theory), solving all the issues plaguing field theory originated from the continuum. These features make the theory an ideal framework for quantum gravity, with relativistic covariance and space-time emergent solely from the interactions, and not assumed a priori. The paper presents a synthetic derivation of the automata theory, showing how the principles lead to a description in terms of a quantum automaton over a Cayley graph of a group. Restricting to Abelian groups we show how the automata recover the Weyl, Dirac and Maxwell dynamics in the relativistic limit. We conclude with some new routes about the more general scenario of non-Abelian Cayley graphs. The phenomenology arising from the automata theory in the ultra-relativistic domain and the analysis of corresponding distorted Lorentz covariance is reviewed in Bisio et al. (Found Phys 2015, in this same issue).

SpectralNET – an application for spectral graph analysis and visualization

PubMed Central

Forman, Joshua J; Clemons, Paul A; Schreiber, Stuart L; Haggarty, Stephen J

2005-01-01

Background Graph theory provides a computational framework for modeling a variety of datasets including those emerging from genomics, proteomics, and chemical genetics. Networks of genes, proteins, small molecules, or other objects of study can be represented as graphs of nodes (vertices) and interactions (edges) that can carry different weights. SpectralNET is a flexible application for analyzing and visualizing these biological and chemical networks. Results Available both as a standalone .NET executable and as an ASP.NET web application, SpectralNET was designed specifically with the analysis of graph-theoretic metrics in mind, a computational task not easily accessible using currently available applications. Users can choose either to upload a network for analysis using a variety of input formats, or to have SpectralNET generate an idealized random network for comparison to a real-world dataset. Whichever graph-generation method is used, SpectralNET displays detailed information about each connected component of the graph, including graphs of degree distribution, clustering coefficient by degree, and average distance by degree. In addition, extensive information about the selected vertex is shown, including degree, clustering coefficient, various distance metrics, and the corresponding components of the adjacency, Laplacian, and normalized Laplacian eigenvectors. SpectralNET also displays several graph visualizations, including a linear dimensionality reduction for uploaded datasets (Principal Components Analysis) and a non-linear dimensionality reduction that provides an elegant view of global graph structure (Laplacian eigenvectors). Conclusion SpectralNET provides an easily accessible means of analyzing graph-theoretic metrics for data modeling and dimensionality reduction. SpectralNET is publicly available as both a .NET application and an ASP.NET web application from . Source code is available upon request. PMID:16236170

SpectralNET--an application for spectral graph analysis and visualization.

PubMed

Forman, Joshua J; Clemons, Paul A; Schreiber, Stuart L; Haggarty, Stephen J

2005-10-19

Graph theory provides a computational framework for modeling a variety of datasets including those emerging from genomics, proteomics, and chemical genetics. Networks of genes, proteins, small molecules, or other objects of study can be represented as graphs of nodes (vertices) and interactions (edges) that can carry different weights. SpectralNET is a flexible application for analyzing and visualizing these biological and chemical networks. Available both as a standalone .NET executable and as an ASP.NET web application, SpectralNET was designed specifically with the analysis of graph-theoretic metrics in mind, a computational task not easily accessible using currently available applications. Users can choose either to upload a network for analysis using a variety of input formats, or to have SpectralNET generate an idealized random network for comparison to a real-world dataset. Whichever graph-generation method is used, SpectralNET displays detailed information about each connected component of the graph, including graphs of degree distribution, clustering coefficient by degree, and average distance by degree. In addition, extensive information about the selected vertex is shown, including degree, clustering coefficient, various distance metrics, and the corresponding components of the adjacency, Laplacian, and normalized Laplacian eigenvectors. SpectralNET also displays several graph visualizations, including a linear dimensionality reduction for uploaded datasets (Principal Components Analysis) and a non-linear dimensionality reduction that provides an elegant view of global graph structure (Laplacian eigenvectors). SpectralNET provides an easily accessible means of analyzing graph-theoretic metrics for data modeling and dimensionality reduction. SpectralNET is publicly available as both a .NET application and an ASP.NET web application from http://chembank.broad.harvard.edu/resources/. Source code is available upon request.

Graph theoretical model of a sensorimotor connectome in zebrafish.

PubMed

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

2012-01-01

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

Mean Curvature, Threshold Dynamics, and Phase Field Theory on Finite Graphs

DTIC Science & Technology

2013-06-28

of the graph in a low dimensional space . Of course, the various definitions of curvature in the ... with a velocity depending on the mean curvature of the front. Recently, there has been an increasing interest in using ideas from continuum PDEs...functions V → R and E the space of all skew-symmetric4 functions E → R. Again to simplify notation, we extend each ϕ ∈ E to a function ϕ : V 2 → R

Detailing the equivalence between real equiangular tight frames and certain strongly regular graphs

NASA Astrophysics Data System (ADS)

Fickus, Matthew; Watson, Cody E.

2015-08-01

An equiangular tight frame (ETF) is a set of unit vectors whose coherence achieves the Welch bound, and so is as incoherent as possible. They arise in numerous applications. It is well known that real ETFs are equivalent to a certain subclass of strongly regular graphs. In this note, we give some alternative techniques for understanding this equivalence. In a later document, we will use these techniques to further generalize this theory.

Default mode network abnormalities in posttraumatic stress disorder: A novel network-restricted topology approach.

PubMed

Akiki, Teddy J; Averill, Christopher L; Wrocklage, Kristen M; Scott, J Cobb; Averill, Lynnette A; Schweinsburg, Brian; Alexander-Bloch, Aaron; Martini, Brenda; Southwick, Steven M; Krystal, John H; Abdallah, Chadi G

2018-08-01

Disruption in the default mode network (DMN) has been implicated in numerous neuropsychiatric disorders, including posttraumatic stress disorder (PTSD). However, studies have largely been limited to seed-based methods and involved inconsistent definitions of the DMN. Recent advances in neuroimaging and graph theory now permit the systematic exploration of intrinsic brain networks. In this study, we used resting-state functional magnetic resonance imaging (fMRI), diffusion MRI, and graph theoretical analyses to systematically examine the DMN connectivity and its relationship with PTSD symptom severity in a cohort of 65 combat-exposed US Veterans. We employed metrics that index overall connectivity strength, network integration (global efficiency), and network segregation (clustering coefficient). Then, we conducted a modularity and network-based statistical analysis to identify DMN regions of particular importance in PTSD. Finally, structural connectivity analyses were used to probe whether white matter abnormalities are associated with the identified functional DMN changes. We found decreased DMN functional connectivity strength to be associated with increased PTSD symptom severity. Further topological characterization suggests decreased functional integration and increased segregation in subjects with severe PTSD. Modularity analyses suggest a spared connectivity in the posterior DMN community (posterior cingulate, precuneus, angular gyrus) despite overall DMN weakened connections with increasing PTSD severity. Edge-wise network-based statistical analyses revealed a prefrontal dysconnectivity. Analysis of the diffusion networks revealed no alterations in overall strength or prefrontal structural connectivity. DMN abnormalities in patients with severe PTSD symptoms are characterized by decreased overall interconnections. On a finer scale, we found a pattern of prefrontal dysconnectivity, but increased cohesiveness in the posterior DMN community and relative sparing of connectivity in this region. The DMN measures established in this study may serve as a biomarker of disease severity and could have potential utility in developing circuit-based therapeutics. Published by Elsevier Inc.

A novel model for DNA sequence similarity analysis based on graph theory.

PubMed

Qi, Xingqin; Wu, Qin; Zhang, Yusen; Fuller, Eddie; Zhang, Cun-Quan

2011-01-01

Determination of sequence similarity is one of the major steps in computational phylogenetic studies. As we know, during evolutionary history, not only DNA mutations for individual nucleotide but also subsequent rearrangements occurred. It has been one of major tasks of computational biologists to develop novel mathematical descriptors for similarity analysis such that various mutation phenomena information would be involved simultaneously. In this paper, different from traditional methods (eg, nucleotide frequency, geometric representations) as bases for construction of mathematical descriptors, we construct novel mathematical descriptors based on graph theory. In particular, for each DNA sequence, we will set up a weighted directed graph. The adjacency matrix of the directed graph will be used to induce a representative vector for DNA sequence. This new approach measures similarity based on both ordering and frequency of nucleotides so that much more information is involved. As an application, the method is tested on a set of 0.9-kb mtDNA sequences of twelve different primate species. All output phylogenetic trees with various distance estimations have the same topology, and are generally consistent with the reported results from early studies, which proves the new method's efficiency; we also test the new method on a simulated data set, which shows our new method performs better than traditional global alignment method when subsequent rearrangements happen frequently during evolutionary history.

Go With the Flow, on Jupiter and Snow. Coherence from Model-Free Video Data Without Trajectories

NASA Astrophysics Data System (ADS)

AlMomani, Abd AlRahman R.; Bollt, Erik

2018-06-01

Viewing a data set such as the clouds of Jupiter, coherence is readily apparent to human observers, especially the Great Red Spot, but also other great storms and persistent structures. There are now many different definitions and perspectives mathematically describing coherent structures, but we will take an image processing perspective here. We describe an image processing perspective inference of coherent sets from a fluidic system directly from image data, without attempting to first model underlying flow fields, related to a concept in image processing called motion tracking. In contrast to standard spectral methods for image processing which are generally related to a symmetric affinity matrix, leading to standard spectral graph theory, we need a not symmetric affinity which arises naturally from the underlying arrow of time. We develop an anisotropic, directed diffusion operator corresponding to flow on a directed graph, from a directed affinity matrix developed with coherence in mind, and corresponding spectral graph theory from the graph Laplacian. Our methodology is not offered as more accurate than other traditional methods of finding coherent sets, but rather our approach works with alternative kinds of data sets, in the absence of vector field. Our examples will include partitioning the weather and cloud structures of Jupiter, and a local to Potsdam, NY, lake effect snow event on Earth, as well as the benchmark test double-gyre system.

The hypergraph regularity method and its applications

PubMed Central

Rödl, V.; Nagle, B.; Skokan, J.; Schacht, M.; Kohayakawa, Y.

2005-01-01

Szemerédi's regularity lemma asserts that every graph can be decomposed into relatively few random-like subgraphs. This random-like behavior enables one to find and enumerate subgraphs of a given isomorphism type, yielding the so-called counting lemma for graphs. The combined application of these two lemmas is known as the regularity method for graphs and has proved useful in graph theory, combinatorial geometry, combinatorial number theory, and theoretical computer science. Here, we report on recent advances in the regularity method for k-uniform hypergraphs, for arbitrary k ≥ 2. This method, purely combinatorial in nature, gives alternative proofs of density theorems originally due to E. Szemerédi, H. Furstenberg, and Y. Katznelson. Further results in extremal combinatorics also have been obtained with this approach. The two main components of the regularity method for k-uniform hypergraphs, the regularity lemma and the counting lemma, have been obtained recently: Rödl and Skokan (based on earlier work of Frankl and Rödl) generalized Szemerédi's regularity lemma to k-uniform hypergraphs, and Nagle, Rödl, and Schacht succeeded in proving a counting lemma accompanying the Rödl–Skokan hypergraph regularity lemma. The counting lemma is proved by reducing the counting problem to a simpler one previously investigated by Kohayakawa, Rödl, and Skokan. Similar results were obtained independently by W. T. Gowers, following a different approach. PMID:15919821

The Stability Analysis Method of the Cohesive Granular Slope on the Basis of Graph Theory.

PubMed

Guan, Yanpeng; Liu, Xiaoli; Wang, Enzhi; Wang, Sijing

2017-02-27

This paper attempted to provide a method to calculate progressive failure of the cohesivefrictional granular geomaterial and the spatial distribution of the stability of the cohesive granular slope. The methodology can be divided into two parts: the characterization method of macro-contact and the analysis of the slope stability. Based on the graph theory, the vertexes, the edges and the edge sequences are abstracted out to characterize the voids, the particle contact and the macro-contact, respectively, bridging the gap between the mesoscopic and macro scales of granular materials. This paper adopts this characterization method to extract a graph from a granular slope and characterize the macro sliding surface, then the weighted graph is analyzed to calculate the slope safety factor. Each edge has three weights representing the sliding moment, the anti-sliding moment and the braking index of contact-bond, respectively, . The safety factor of the slope is calculated by presupposing a certain number of sliding routes and reducing Weight repeatedly and counting the mesoscopic failure of the edge. It is a kind of slope analysis method from mesoscopic perspective so it can present more detail of the mesoscopic property of the granular slope. In the respect of macro scale, the spatial distribution of the stability of the granular slope is in agreement with the theoretical solution.

Metric learning with spectral graph convolutions on brain connectivity networks.

PubMed

Ktena, Sofia Ira; Parisot, Sarah; Ferrante, Enzo; Rajchl, Martin; Lee, Matthew; Glocker, Ben; Rueckert, Daniel

2018-04-01

Graph representations are often used to model structured data at an individual or population level and have numerous applications in pattern recognition problems. In the field of neuroscience, where such representations are commonly used to model structural or functional connectivity between a set of brain regions, graphs have proven to be of great importance. This is mainly due to the capability of revealing patterns related to brain development and disease, which were previously unknown. Evaluating similarity between these brain connectivity networks in a manner that accounts for the graph structure and is tailored for a particular application is, however, non-trivial. Most existing methods fail to accommodate the graph structure, discarding information that could be beneficial for further classification or regression analyses based on these similarities. We propose to learn a graph similarity metric using a siamese graph convolutional neural network (s-GCN) in a supervised setting. The proposed framework takes into consideration the graph structure for the evaluation of similarity between a pair of graphs, by employing spectral graph convolutions that allow the generalisation of traditional convolutions to irregular graphs and operates in the graph spectral domain. We apply the proposed model on two datasets: the challenging ABIDE database, which comprises functional MRI data of 403 patients with autism spectrum disorder (ASD) and 468 healthy controls aggregated from multiple acquisition sites, and a set of 2500 subjects from UK Biobank. We demonstrate the performance of the method for the tasks of classification between matching and non-matching graphs, as well as individual subject classification and manifold learning, showing that it leads to significantly improved results compared to traditional methods. Copyright © 2017 Elsevier Inc. All rights reserved.

Breaking of Ensemble Equivalence in Networks

NASA Astrophysics Data System (ADS)

Squartini, Tiziano; de Mol, Joey; den Hollander, Frank; Garlaschelli, Diego

2015-12-01

It is generally believed that, in the thermodynamic limit, the microcanonical description as a function of energy coincides with the canonical description as a function of temperature. However, various examples of systems for which the microcanonical and canonical ensembles are not equivalent have been identified. A complete theory of this intriguing phenomenon is still missing. Here we show that ensemble nonequivalence can manifest itself also in random graphs with topological constraints. We find that, while graphs with a given number of links are ensemble equivalent, graphs with a given degree sequence are not. This result holds irrespective of whether the energy is nonadditive (as in unipartite graphs) or additive (as in bipartite graphs). In contrast with previous expectations, our results show that (1) physically, nonequivalence can be induced by an extensive number of local constraints, and not necessarily by long-range interactions or nonadditivity, (2) mathematically, nonequivalence is determined by a different large-deviation behavior of microcanonical and canonical probabilities for a single microstate, and not necessarily for almost all microstates. The latter criterion, which is entirely local, is not restricted to networks and holds in general.

EIT Imaging Regularization Based on Spectral Graph Wavelets.

PubMed

Gong, Bo; Schullcke, Benjamin; Krueger-Ziolek, Sabine; Vauhkonen, Marko; Wolf, Gerhard; Mueller-Lisse, Ullrich; Moeller, Knut

2017-09-01

The objective of electrical impedance tomographic reconstruction is to identify the distribution of tissue conductivity from electrical boundary conditions. This is an ill-posed inverse problem usually solved under the finite-element method framework. In previous studies, standard sparse regularization was used for difference electrical impedance tomography to achieve a sparse solution. However, regarding elementwise sparsity, standard sparse regularization interferes with the smoothness of conductivity distribution between neighboring elements and is sensitive to noise. As an effect, the reconstructed images are spiky and depict a lack of smoothness. Such unexpected artifacts are not realistic and may lead to misinterpretation in clinical applications. To eliminate such artifacts, we present a novel sparse regularization method that uses spectral graph wavelet transforms. Single-scale or multiscale graph wavelet transforms are employed to introduce local smoothness on different scales into the reconstructed images. The proposed approach relies on viewing finite-element meshes as undirected graphs and applying wavelet transforms derived from spectral graph theory. Reconstruction results from simulations, a phantom experiment, and patient data suggest that our algorithm is more robust to noise and produces more reliable images.

Inspection of aeronautical mechanical parts with a pan-tilt-zoom camera: an approach guided by the computer-aided design model

NASA Astrophysics Data System (ADS)

Viana, Ilisio; Orteu, Jean-José; Cornille, Nicolas; Bugarin, Florian

2015-11-01

We focus on quality control of mechanical parts in aeronautical context using a single pan-tilt-zoom (PTZ) camera and a computer-aided design (CAD) model of the mechanical part. We use the CAD model to create a theoretical image of the element to be checked, which is further matched with the sensed image of the element to be inspected, using a graph theory-based approach. The matching is carried out in two stages. First, the two images are used to create two attributed graphs representing the primitives (ellipses and line segments) in the images. In the second stage, the graphs are matched using a similarity function built from the primitive parameters. The similarity scores of the matching are injected in the edges of a bipartite graph. A best-match-search procedure in the bipartite graph guarantees the uniqueness of the match solution. The method achieves promising performance in tests with synthetic data including missing elements, displaced elements, size changes, and combinations of these cases. The results open good prospects for using the method with realistic data.

Mean-field theory of spin-glasses with finite coordination number

NASA Technical Reports Server (NTRS)

Kanter, I.; Sompolinsky, H.

1987-01-01

The mean-field theory of dilute spin-glasses is studied in the limit where the average coordination number is finite. The zero-temperature phase diagram is calculated and the relationship between the spin-glass phase and the percolation transition is discussed. The present formalism is applicable also to graph optimization problems.

Latin and Magic Squares

ERIC Educational Resources Information Center

Emanouilidis, Emanuel

2005-01-01

Latin squares have existed for hundreds of years but it wasn't until rather recently that Latin squares were used in other areas such as statistics, graph theory, coding theory and the generation of random numbers as well as in the design and analysis of experiments. This note describes Latin and diagonal Latin squares, a method of constructing…

Latin and Cross Latin Squares

ERIC Educational Resources Information Center

Emanouilidis, Emanuel

2008-01-01

Latin squares were first introduced and studied by the famous mathematician Leonhard Euler in the 1700s. Through the years, Latin squares have been used in areas such as statistics, graph theory, coding theory, the generation of random numbers as well as in the design and analysis of experiments. Recently, with the international popularity of…

Paul Erdos

ERIC Educational Resources Information Center

Monroe, Helen; Scott, Paul

2004-01-01

This article presents a brief biography of Paul Erdos, who focused on problem-solving, particularly in the areas of number theory, combinatorics and graph theory. During his life he had no property, no family and no fixed address. He buttered his first piece of bread at age 21. He never cooked, nor ever drove a car. Another mathematician, Ron…

Graph pyramids as models of human problem solving

NASA Astrophysics Data System (ADS)

Pizlo, Zygmunt; Li, Zheng

2004-05-01

Prior theories have assumed that human problem solving involves estimating distances among states and performing search through the problem space. The role of mental representation in those theories was minimal. Results of our recent experiments suggest that humans are able to solve some difficult problems quickly and accurately. Specifically, in solving these problems humans do not seem to rely on distances or on search. It is quite clear that producing good solutions without performing search requires a very effective mental representation. In this paper we concentrate on studying the nature of this representation. Our theory takes the form of a graph pyramid. To verify the psychological plausibility of this theory we tested subjects in a Euclidean Traveling Salesman Problem in the presence of obstacles. The role of the number and size of obstacles was tested for problems with 6-50 cities. We analyzed the effect of experimental conditions on solution time per city and on solution error. The main result is that time per city is systematically affected only by the size of obstacles, but not by their number, or by the number of cities.

Infinities in Quantum Field Theory and in Classical Computing: Renormalization Program

NASA Astrophysics Data System (ADS)

Manin, Yuri I.

Introduction. The main observable quantities in Quantum Field Theory, correlation functions, are expressed by the celebrated Feynman path integrals. A mathematical definition of them involving a measure and actual integration is still lacking. Instead, it is replaced by a series of ad hoc but highly efficient and suggestive heuristic formulas such as perturbation formalism. The latter interprets such an integral as a formal series of finite-dimensional but divergent integrals, indexed by Feynman graphs, the list of which is determined by the Lagrangian of the theory. Renormalization is a prescription that allows one to systematically "subtract infinities" from these divergent terms producing an asymptotic series for quantum correlation functions. On the other hand, graphs treated as "flowcharts", also form a combinatorial skeleton of the abstract computation theory. Partial recursive functions that according to Church's thesis exhaust the universe of (semi)computable maps are generally not everywhere defined due to potentially infinite searches and loops. In this paper I argue that such infinities can be addressed in the same way as Feynman divergences. More details can be found in [9,10].

Topology in colored tensor models via crystallization theory

NASA Astrophysics Data System (ADS)

Casali, Maria Rita; Cristofori, Paola; Dartois, Stéphane; Grasselli, Luigi

2018-07-01

The aim of this paper is twofold. On the one hand, it provides a review of the links between random tensor models, seen as quantum gravity theories, and the PL-manifolds representation by means of edge-colored graphs (crystallization theory). On the other hand, the core of the paper is to establish results about the topological and geometrical properties of the Gurau-degree (or G-degree) of the represented manifolds, in relation with the motivations coming from physics. In fact, the G-degree appears naturally in higher dimensional tensor models as the quantity driving their 1 / N expansion, exactly as it happens for the genus of surfaces in the two-dimensional matrix model setting. In particular, the G-degree of PL-manifolds is proved to be finite-to-one in any dimension, while in dimension 3 and 4 a series of classification theorems are obtained for PL-manifolds represented by graphs with a fixed G-degree. All these properties have specific relevance in the tensor models framework, showing a direct fruitful interaction between tensor models and discrete geometry, via crystallization theory.

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

NASA Astrophysics Data System (ADS)

Sokolowski, Andrzej

2017-11-01

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

The Quantified Characterization Method of the Micro-Macro Contacts of Three-Dimensional Granular Materials on the Basis of Graph Theory.

PubMed

Guan, Yanpeng; Wang, Enzhi; Liu, Xiaoli; Wang, Sijing; Luan, Hebing

2017-08-03

We have attempted a multiscale and quantified characterization method of the contact in three-dimensional granular material made of spherical particles, particularly in cemented granular material. Particle contact is defined as a type of surface contact with voids in its surroundings, rather than a point contact. Macro contact is a particle contact set satisfying the restrictive condition of a two-dimensional manifold with a boundary. On the basis of graph theory, two dual geometrical systems are abstracted from the granular pack. The face and the face set, which satisfies the two-dimensional manifold with a boundary in the solid cell system, are extracted to characterize the particle contact and the macro contact, respectively. This characterization method is utilized to improve the post-processing in DEM (Discrete Element Method) from a micro perspective to describe the macro effect of the cemented granular material made of spherical particles. Since the crack has the same shape as its corresponding contact, this method is adopted to characterize the crack and realize its visualization. The integral failure route of the sample can be determined by a graph theory algorithm. The contact force is assigned to the weight value of the face characterizing the particle contact. Since the force vectors can be added, the macro contact force can be solved by adding the weight of its corresponding faces.

Analysis of the enzyme network involved in cattle milk production using graph theory.

PubMed

Ghorbani, Sholeh; Tahmoorespur, Mojtaba; Masoudi Nejad, Ali; Nasiri, Mohammad; Asgari, Yazdan

2015-06-01

Understanding cattle metabolism and its relationship with milk products is important in bovine breeding. A systemic view could lead to consequences that will result in a better understanding of existing concepts. Topological indices and quantitative characterizations mostly result from the application of graph theory on biological data. In the present work, the enzyme network involved in cattle milk production was reconstructed and analyzed based on available bovine genome information using several public datasets (NCBI, Uniprot, KEGG, and Brenda). The reconstructed network consisted of 3605 reactions named by KEGG compound numbers and 646 enzymes that catalyzed the corresponding reactions. The characteristics of the directed and undirected network were analyzed using Graph Theory. The mean path length was calculated to be4.39 and 5.41 for directed and undirected networks, respectively. The top 11 hub enzymes whose abnormality could harm bovine health and reduce milk production were determined. Therefore, the aim of constructing the enzyme centric network was twofold; first to find out whether such network followed the same properties of other biological networks, and second, to find the key enzymes. The results of the present study can improve our understanding of milk production in cattle. Also, analysis of the enzyme network can help improve the modeling and simulation of biological systems and help design desired phenotypes to increase milk production quality or quantity.

Differences in graph theory functional connectivity in left and right temporal lobe epilepsy.

PubMed

Chiang, Sharon; Stern, John M; Engel, Jerome; Levin, Harvey S; Haneef, Zulfi

2014-12-01

To investigate lateralized differences in limbic system functional connectivity between left and right temporal lobe epilepsy (TLE) using graph theory. Interictal resting state fMRI was performed in 14 left TLE patients, 11 right TLE patients, and 12 controls. Graph theory analysis of 10 bilateral limbic regions of interest was conducted. Changes in edgewise functional connectivity, network topology, and regional topology were quantified, and then left and right TLE were compared. Limbic edgewise functional connectivity was predominantly reduced in both left and right TLE. More regional connections were reduced in right TLE, most prominently involving reduced interhemispheric connectivity between the bilateral insula and bilateral hippocampi. A smaller number of limbic connections were increased in TLE, more so in left than in right TLE. Topologically, the most pronounced change was a reduction in average network betweenness centrality and concurrent increase in left hippocampal betweenness centrality in right TLE. In contrast, left TLE exhibited a weak trend toward increased right hippocampal betweenness centrality, with no change in average network betweenness centrality. Limbic functional connectivity is predominantly reduced in both left and right TLE, with more pronounced reductions in right TLE. In contrast, left TLE exhibits both edgewise and topological changes that suggest a tendency toward reorganization. Network changes in TLE and lateralized differences thereof may have important diagnostic and prognostic implications. Published by Elsevier B.V.

Large-scale DCMs for resting-state fMRI.

PubMed

Razi, Adeel; Seghier, Mohamed L; Zhou, Yuan; McColgan, Peter; Zeidman, Peter; Park, Hae-Jeong; Sporns, Olaf; Rees, Geraint; Friston, Karl J

2017-01-01

This paper considers the identification of large directed graphs for resting-state brain networks based on biophysical models of distributed neuronal activity, that is, effective connectivity . This identification can be contrasted with functional connectivity methods based on symmetric correlations that are ubiquitous in resting-state functional MRI (fMRI). We use spectral dynamic causal modeling (DCM) to invert large graphs comprising dozens of nodes or regions. The ensuing graphs are directed and weighted, hence providing a neurobiologically plausible characterization of connectivity in terms of excitatory and inhibitory coupling. Furthermore, we show that the use of to discover the most likely sparse graph (or model) from a parent (e.g., fully connected) graph eschews the arbitrary thresholding often applied to large symmetric (functional connectivity) graphs. Using empirical fMRI data, we show that spectral DCM furnishes connectivity estimates on large graphs that correlate strongly with the estimates provided by stochastic DCM. Furthermore, we increase the efficiency of model inversion using functional connectivity modes to place prior constraints on effective connectivity. In other words, we use a small number of modes to finesse the potentially redundant parameterization of large DCMs. We show that spectral DCM-with functional connectivity priors-is ideally suited for directed graph theoretic analyses of resting-state fMRI. We envision that directed graphs will prove useful in understanding the psychopathology and pathophysiology of neurodegenerative and neurodevelopmental disorders. We will demonstrate the utility of large directed graphs in clinical populations in subsequent reports, using the procedures described in this paper.

Weighted graph based ordering techniques for preconditioned conjugate gradient methods

NASA Technical Reports Server (NTRS)

Clift, Simon S.; Tang, Wei-Pai

1994-01-01

We describe the basis of a matrix ordering heuristic for improving the incomplete factorization used in preconditioned conjugate gradient techniques applied to anisotropic PDE's. Several new matrix ordering techniques, derived from well-known algorithms in combinatorial graph theory, which attempt to implement this heuristic, are described. These ordering techniques are tested against a number of matrices arising from linear anisotropic PDE's, and compared with other matrix ordering techniques. A variation of RCM is shown to generally improve the quality of incomplete factorization preconditioners.

Designer: A Knowledge-Based Graphic Design Assistant.

DTIC Science & Technology

1986-07-01

pro- pulsion. The system consists of a color graphics interface to a mathematical simulation. One can view and manipulate this simulation at a number of...valve vaive graph 50- mufi -plot graph 100 4 0 80 6.. 30 60 4 20 .... 40 2 10 V 20 0 2 4 6 8 10 0 20 40 60 80 100 FIGURE 4. Icon Sampler. This view...in Computing Systems. New York: ACM, 1983. 8306. Paul Smolensky. Harmony Theory: A Mathematical Framework for Stochastic Parallel Pro- cessing

Exponential stability of stochastic complex networks with multi-weights based on graph theory

NASA Astrophysics Data System (ADS)

Zhang, Chunmei; Chen, Tianrui

2018-04-01

In this paper, a novel approach to exponential stability of stochastic complex networks with multi-weights is investigated by means of the graph-theoretical method. New sufficient conditions are provided to ascertain the moment exponential stability and almost surely exponential stability of stochastic complex networks with multiple weights. It is noted that our stability results are closely related with multi-weights and the intensity of stochastic disturbance. Numerical simulations are also presented to substantiate the theoretical results.

Bilogy Machine Initiative: Developing Innovative Novel Methods to Improve Neuro-rehabilitation for Amputees and Treatment for Patients at Remote Sites with Acute Brain Injury

DTIC Science & Technology

2010-09-01

service to support the creation of both normative and pathological neuroinformatics databases. Project 3 Deliverable: The aim of this project is to...Gainesville, FL, 2010. D. Hammond, P. Vandergheynst, R. Gribonval, “ Wavelets on Graphs via Spectral Graph Theory,” Applied Computational and...the Phantom Experiments,” International Conference on Electrical Bioimpedance, April 4-8-, Gainesville, FL, 2010. 21 D. Hammond, “ Wavelets on

Graph distance for complex networks

NASA Astrophysics Data System (ADS)

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

2016-10-01

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

Graph-theoretic approach to quantum correlations.

PubMed

Cabello, Adán; Severini, Simone; Winter, Andreas

2014-01-31

Correlations in Bell and noncontextuality inequalities can be expressed as a positive linear combination of probabilities of events. Exclusive events can be represented as adjacent vertices of a graph, so correlations can be associated to a subgraph. We show that the maximum value of the correlations for classical, quantum, and more general theories is the independence number, the Lovász number, and the fractional packing number of this subgraph, respectively. We also show that, for any graph, there is always a correlation experiment such that the set of quantum probabilities is exactly the Grötschel-Lovász-Schrijver theta body. This identifies these combinatorial notions as fundamental physical objects and provides a method for singling out experiments with quantum correlations on demand.

Method of optimum channel switching in equipment of infocommunication network in conditions of cyber attacks to their telecommunication infrastructure.

NASA Astrophysics Data System (ADS)

Kochedykov, S. S.; Noev, A. N.; Dushkin, A. V.; Gubin, I. A.

2018-05-01

On the basis of the mathematical graph theory, the method of optimum switching of infocommunication networks in the conditions of cyber attacks is developed. The idea of representation of a set of possible ways on the graph in the form of the multilevel tree ordered by rules of algebra of a logic theory is the cornerstone of a method. As a criterion of optimization, the maximum of network transmission capacity to which assessment Ford- Falkerson's theorem is applied is used. The method is realized in the form of a numerical algorithm, which can be used not only for design, but also for operational management of infocommunication networks in conditions of violation of the functioning of their switching centers.

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

PubMed

Li, Zhigang; Shi, Zhongping; Li, Xin

2014-05-01

Several fermentations with consecutively feeding of acetate/butyrate were conducted in a 7 L fermentor and the results indicated that exogenous acetate/butyrate enhanced solvents productivities by 47.1% and 39.2% respectively, and changed butyrate/acetate ratios greatly. Then extracellular butyrate/acetate ratios were utilized for calculation of acids rates and the results revealed that acetate and butyrate formation pathways were almost blocked by corresponding acids feeding. In addition, models for acetate/butyrate feeding fermentations were constructed by graph theory based on calculation results and relevant reports. Solvents concentrations and butanol/acetone ratios of these fermentations were also calculated and the results of models calculation matched fermentation data accurately which demonstrated that models were constructed in a reasonable way. Copyright © 2014 Elsevier Ltd. All rights reserved.

Graph theory approach to the eigenvalue problem of large space structures

NASA Technical Reports Server (NTRS)

Reddy, A. S. S. R.; Bainum, P. M.

1981-01-01

Graph theory is used to obtain numerical solutions to eigenvalue problems of large space structures (LSS) characterized by a state vector of large dimensions. The LSS are considered as large, flexible systems requiring both orientation and surface shape control. Graphic interpretation of the determinant of a matrix is employed to reduce a higher dimensional matrix into combinations of smaller dimensional sub-matrices. The reduction is implemented by means of a Boolean equivalent of the original matrices formulated to obtain smaller dimensional equivalents of the original numerical matrix. Computation time becomes less and more accurate solutions are possible. An example is provided in the form of a free-free square plate. Linearized system equations and numerical values of a stiffness matrix are presented, featuring a state vector with 16 components.

Normalized Cut Algorithm for Automated Assignment of Protein Domains

NASA Technical Reports Server (NTRS)

Samanta, M. P.; Liang, S.; Zha, H.; Biegel, Bryan A. (Technical Monitor)

2002-01-01

We present a novel computational method for automatic assignment of protein domains from structural data. At the core of our algorithm lies a recently proposed clustering technique that has been very successful for image-partitioning applications. This grap.,l-theory based clustering method uses the notion of a normalized cut to partition. an undirected graph into its strongly-connected components. Computer implementation of our method tested on the standard comparison set of proteins from the literature shows a high success rate (84%), better than most existing alternative In addition, several other features of our algorithm, such as reliance on few adjustable parameters, linear run-time with respect to the size of the protein and reduced complexity compared to other graph-theory based algorithms, would make it an attractive tool for structural biologists.

Temporal networks

NASA Astrophysics Data System (ADS)

Holme, Petter; Saramäki, Jari

2012-10-01

A great variety of systems in nature, society and technology-from the web of sexual contacts to the Internet, from the nervous system to power grids-can be modeled as graphs of vertices coupled by edges. The network structure, describing how the graph is wired, helps us understand, predict and optimize the behavior of dynamical systems. In many cases, however, the edges are not continuously active. As an example, in networks of communication via e-mail, text messages, or phone calls, edges represent sequences of instantaneous or practically instantaneous contacts. In some cases, edges are active for non-negligible periods of time: e.g., the proximity patterns of inpatients at hospitals can be represented by a graph where an edge between two individuals is on throughout the time they are at the same ward. Like network topology, the temporal structure of edge activations can affect dynamics of systems interacting through the network, from disease contagion on the network of patients to information diffusion over an e-mail network. In this review, we present the emergent field of temporal networks, and discuss methods for analyzing topological and temporal structure and models for elucidating their relation to the behavior of dynamical systems. In the light of traditional network theory, one can see this framework as moving the information of when things happen from the dynamical system on the network, to the network itself. Since fundamental properties, such as the transitivity of edges, do not necessarily hold in temporal networks, many of these methods need to be quite different from those for static networks. The study of temporal networks is very interdisciplinary in nature. Reflecting this, even the object of study has many names-temporal graphs, evolving graphs, time-varying graphs, time-aggregated graphs, time-stamped graphs, dynamic networks, dynamic graphs, dynamical graphs, and so on. This review covers different fields where temporal graphs are considered, but does not attempt to unify related terminology-rather, we want to make papers readable across disciplines.

Using Social Network Graphs as Visualization Tools to Influence Peer Selection Decision-Making Strategies to Access Information about Complex Socioscientific Issues

ERIC Educational Resources Information Center

Yoon, Susan A.

2011-01-01

This study extends previous research that explores how visualization affordances that computational tools provide and social network analyses that account for individual- and group-level dynamic processes can work in conjunction to improve learning outcomes. The study's main hypothesis is that when social network graphs are used in instruction,…

Hydrodynamic modeling of hydrologic surface connectivity within a coastal river-floodplain system

NASA Astrophysics Data System (ADS)

Castillo, C. R.; Guneralp, I.

2017-12-01

Hydrologic surface connectivity (HSC) within river-floodplain environments is a useful indicator of the overall health of riparian habitats because it allows connections amongst components/landforms of the riverine landscape system to be quantified. Overbank flows have traditionally been the focus for analyses concerned with river-floodplain connectivity, but recent works have identified the large significance from sub-bankfull streamflows. Through the use of morphometric analysis and a digital elevation model that is relative to the river water surface, we previously determined that >50% of the floodplain for Mission River on the Coastal Bend of Texas becomes connected to the river at streamflows well-below bankfull conditions. Guided by streamflow records, field-based inundation data, and morphometric analysis; we develop a two-dimensional hydrodynamic model for lower portions of Mission River Floodplain system. This model not only allows us to analyze connections induced by surface water inundation, but also other aspects of the hydrologic connectivity concept such as exchanges of sediment and energy between the river and its floodplain. We also aggregate hydrodynamic model outputs to an object/landform level in order to analyze HSC and associated attributes using measures from graph/network theory. Combining physically-based hydrodynamic models with object-based and graph theoretical analyses allow river-floodplain connectivity to be quantified in a consistent manner with measures/indicators commonly used in landscape analysis. Analyzes similar to ours build towards the establishment of a formal framework for analyzing river-floodplain interaction that will ultimately serve to inform the management of riverine/floodplain environments.

Measuring the hierarchy of feedforward networks

NASA Astrophysics Data System (ADS)

Corominas-Murtra, Bernat; Rodríguez-Caso, Carlos; Goñi, Joaquín; Solé, Ricard

2011-03-01

In this paper we explore the concept of hierarchy as a quantifiable descriptor of ordered structures, departing from the definition of three conditions to be satisfied for a hierarchical structure: order, predictability, and pyramidal structure. According to these principles, we define a hierarchical index taking concepts from graph and information theory. This estimator allows to quantify the hierarchical character of any system susceptible to be abstracted in a feedforward causal graph, i.e., a directed acyclic graph defined in a single connected structure. Our hierarchical index is a balance between this predictability and pyramidal condition by the definition of two entropies: one attending the onward flow and the other for the backward reversion. We show how this index allows to identify hierarchical, antihierarchical, and nonhierarchical structures. Our formalism reveals that departing from the defined conditions for a hierarchical structure, feedforward trees and the inverted tree graphs emerge as the only causal structures of maximal hierarchical and antihierarchical systems respectively. Conversely, null values of the hierarchical index are attributed to a number of different configuration networks; from linear chains, due to their lack of pyramid structure, to full-connected feedforward graphs where the diversity of onward pathways is canceled by the uncertainty (lack of predictability) when going backward. Some illustrative examples are provided for the distinction among these three types of hierarchical causal graphs.

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

NASA Astrophysics Data System (ADS)

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

2016-04-01

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

Measurement and simulation of the relatively competitive advantages and weaknesses between economies based on bipartite graph theory.

PubMed

Guan, Jun; Xu, Xiaoyu; Wu, Shan; Xing, Lizhi

2018-01-01

The input-output table is very comprehensive and detailed in describing the national economic systems with abundant economic relationships, which contain supply and demand information among various industrial sectors. The complex network, a theory, and method for measuring the structure of a complex system can depict the structural characteristics of the internal structure of the researched object by measuring the structural indicators of the social and economic systems, revealing the complex relationships between the inner hierarchies and the external economic functions. In this paper, functions of industrial sectors on the global value chain are to be distinguished with bipartite graph theory, and inter-sector competitive relationships are to be extracted through resource allocation process. Furthermore, quantitative analysis indices will be proposed under the perspective of a complex network, which will be used to bring about simulations on the variation tendencies of economies' status in different situations of commercial intercourses. Finally, a new econophysics analytical framework of international trade is to be established.

Measurement and simulation of the relatively competitive advantages and weaknesses between economies based on bipartite graph theory

PubMed Central

Guan, Jun; Xu, Xiaoyu; Wu, Shan

2018-01-01

The input-output table is very comprehensive and detailed in describing the national economic systems with abundant economic relationships, which contain supply and demand information among various industrial sectors. The complex network, a theory, and method for measuring the structure of a complex system can depict the structural characteristics of the internal structure of the researched object by measuring the structural indicators of the social and economic systems, revealing the complex relationships between the inner hierarchies and the external economic functions. In this paper, functions of industrial sectors on the global value chain are to be distinguished with bipartite graph theory, and inter-sector competitive relationships are to be extracted through resource allocation process. Furthermore, quantitative analysis indices will be proposed under the perspective of a complex network, which will be used to bring about simulations on the variation tendencies of economies’ status in different situations of commercial intercourses. Finally, a new econophysics analytical framework of international trade is to be established. PMID:29813083

[Some comments on ecological field].

PubMed

Wang, D

2000-06-01

Based on the data of plant ecological field studies, this paper reviewed the conception of ecological field, field eigenfunctions, graphs of ecological field and its application of ecological field theory in explaining plant interactions. It is suggested that the basic character of ecological field is material, and based on the current research level, it is not sure whether ecological field is a kind of specific field different from general physical field. The author gave some comments on the formula and estimation of parameters of basic field function-ecological potential model on ecological field. Both models have their own characteristics and advantages in specific conditions. The author emphasized that ecological field had even more meaning of ecological methodology, and applying ecological field theory in describing the types and processes of plant interactions had three characteristics: quantitative, synthetic and intuitionistic. Field graphing might provide a new way to ecological studies, especially applying the ecological field theory might give an appropriate quantitative explanation for the dynamic process of plant populations (coexistence and interference competition).

Game Theory in Fleet Management

NASA Astrophysics Data System (ADS)

Dulai, Tibor; Jaskó, Szilárd; Muhi, Dániel

2008-11-01

In this survey we attempt to apply the results of cooperative game theory on fleet management problems. We deal with the aspect of a fleet where the members have their own goal, however the fleet has a common purpose too. These goals are to reach all destinations and get back to the center as quickly as possible. If we draw the map of the area-which contains the destination points and their environment-as a graph, we should determinate circles in it for each member of the fleet. Separating the nodes for each member, we should find Hamilton-circles of the sub-graphs. How to separate the destination points between the fleet members? How to route the members? What happens if there is an accident on a road which changes the way of a member? It may influence the other members' route too. What to communicate for getting the relevant information? How to change the routes in real time? We use cooperative game theory to find the solution.

Using graph approach for managing connectivity in integrative landscape modelling

NASA Astrophysics Data System (ADS)

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

2013-04-01

In cultivated landscapes, a lot of landscape elements such as field boundaries, ditches or banks strongly impact water flows, mass and energy fluxes. At the watershed scale, these impacts are strongly conditionned by the connectivity of these landscape elements. An accurate representation of these elements and of their complex spatial arrangements is therefore of great importance for modelling and predicting these impacts.We developped in the framework of the OpenFLUID platform (Software Environment for Modelling Fluxes in Landscapes) a digital landscape representation that takes into account the spatial variabilities and connectivities of diverse landscape elements through the application of the graph theory concepts. The proposed landscape representation consider spatial units connected together to represent the flux exchanges or any other information exchanges. Each spatial unit of the landscape is represented as a node of a graph and relations between units as graph connections. The connections are of two types - parent-child connection and up/downstream connection - which allows OpenFLUID to handle hierarchical graphs. Connections can also carry informations and graph evolution during simulation is possible (connections or elements modifications). This graph approach allows a better genericity on landscape representation, a management of complex connections and facilitate development of new landscape representation algorithms. Graph management is fully operational in OpenFLUID for developers or modelers ; and several graph tools are available such as graph traversal algorithms or graph displays. Graph representation can be managed i) manually by the user (for example in simple catchments) through XML-based files in easily editable and readable format or ii) by using methods of the OpenFLUID-landr library which is an OpenFLUID library relying on common open-source spatial libraries (ogr vector, geos topologic vector and gdal raster libraries). OpenFLUID-landr library has been developed in order i) to be used with no GIS expert skills needed (common gis formats can be read and simplified spatial management is provided), ii) to easily develop adapted rules of landscape discretization and graph creation to follow spatialized model requirements and iii) to allow model developers to manage dynamic and complex spatial topology. Graph management in OpenFLUID are shown with i) examples of hydrological modelizations on complex farmed landscapes and ii) the new implementation of Geo-MHYDAS tool based on the OpenFLUID-landr library, which allows to discretize a landscape and create graph structure for the MHYDAS model requirements.

Cognitive Maps as a Way of Presenting the Dimension of Comparison within the History of Psychology.

ERIC Educational Resources Information Center

Diekhoff, George M.

1982-01-01

Describes how cognitive maps can help to stimulate discussion of the structural inter-relationships of psychological theory in college-level history of psychology classes. The author describes a cognitive mapping activity in which students pair prominent theorists and theories, rate their degrees of similarity, and graph the relationships of their…

Disrupted topology of hippocampal connectivity is associated with short-term antidepressant response in major depressive disorder.

PubMed

Gong, Liang; Hou, Zhenghua; Wang, Zan; He, Cancan; Yin, Yingying; Yuan, Yonggui; Zhang, Haisan; Lv, Luxian; Zhang, Hongxing; Xie, Chunming; Zhang, Zhijun

2018-01-01

Graph theoretical analyses have identified disrupted functional topological organization across the brain in patients with major depressive disorder (MDD). However, the relationship between brain topology and short-term treatment responses in patients with MDD remains unknown. Sixty-eight patients with MDD and 63 cognitively normal (CN) subjects were recruited at baseline and underwent resting-state functional magnetic resonance imaging scans. Graph theory analysis was used to examine group differences in the whole-brain functional topological properties. The association between altered brain topology and the early antidepressant response was examined. Patients with MDD showed lower normalized clustering coefficients, lower small-worldness scalars and increased nodal efficiencies in the default mode network and decreased nodal efficiencies in basal ganglia and hippocampal networks. In addition, the decreased nodal efficiency in left hippocampus was negatively correlated with depressive severity at baseline and positively correlated with changes in the depressive scores after two weeks of antidepressant treatment. The patients in the present study received different medications. These findings indicated that the altered brain functional topological organization in patients with MDD is associated with the treatment response in the early phase of medication. Therefore, brain topology assessments might be considered a useful and convenient predictor of short-term antidepressant responses. Copyright © 2017 Elsevier B.V. All rights reserved.

Metabolic PathFinding: inferring relevant pathways in biochemical networks.

PubMed

Croes, Didier; Couche, Fabian; Wodak, Shoshana J; van Helden, Jacques

2005-07-01

Our knowledge of metabolism can be represented as a network comprising several thousands of nodes (compounds and reactions). Several groups applied graph theory to analyse the topological properties of this network and to infer metabolic pathways by path finding. This is, however, not straightforward, with a major problem caused by traversing irrelevant shortcuts through highly connected nodes, which correspond to pool metabolites and co-factors (e.g. H2O, NADP and H+). In this study, we present a web server implementing two simple approaches, which circumvent this problem, thereby improving the relevance of the inferred pathways. In the simplest approach, the shortest path is computed, while filtering out the selection of highly connected compounds. In the second approach, the shortest path is computed on the weighted metabolic graph where each compound is assigned a weight equal to its connectivity in the network. This approach significantly increases the accuracy of the inferred pathways, enabling the correct inference of relatively long pathways (e.g. with as many as eight intermediate reactions). Available options include the calculation of the k-shortest paths between two specified seed nodes (either compounds or reactions). Multiple requests can be submitted in a queue. Results are returned by email, in textual as well as graphical formats (available in http://www.scmbb.ulb.ac.be/pathfinding/).

Qualitative and Quantitative Pedigree Analysis: Graph Theory, Computer Software, and Case Studies.

ERIC Educational Resources Information Center

Jungck, John R.; Soderberg, Patti

1995-01-01

Presents a series of elementary mathematical tools for re-representing pedigrees, pedigree generators, pedigree-driven database management systems, and case studies for exploring genetic relationships. (MKR)

The Beta Cell in Its Cluster: Stochastic Graphs of Beta Cell Connectivity in the Islets of Langerhans

PubMed Central

Striegel, Deborah A.; Hara, Manami; Periwal, Vipul

2015-01-01

Pancreatic islets of Langerhans consist of endocrine cells, primarily α, β and δ cells, which secrete glucagon, insulin, and somatostatin, respectively, to regulate plasma glucose. β cells form irregular locally connected clusters within islets that act in concert to secrete insulin upon glucose stimulation. Due to the central functional significance of this local connectivity in the placement of β cells in an islet, it is important to characterize it quantitatively. However, quantification of the seemingly stochastic cytoarchitecture of β cells in an islet requires mathematical methods that can capture topological connectivity in the entire β-cell population in an islet. Graph theory provides such a framework. Using large-scale imaging data for thousands of islets containing hundreds of thousands of cells in human organ donor pancreata, we show that quantitative graph characteristics differ between control and type 2 diabetic islets. Further insight into the processes that shape and maintain this architecture is obtained by formulating a stochastic theory of β-cell rearrangement in whole islets, just as the normal equilibrium distribution of the Ornstein-Uhlenbeck process can be viewed as the result of the interplay between a random walk and a linear restoring force. Requiring that rearrangements maintain the observed quantitative topological graph characteristics strongly constrained possible processes. Our results suggest that β-cell rearrangement is dependent on its connectivity in order to maintain an optimal cluster size in both normal and T2D islets. PMID:26266953

The Beta Cell in Its Cluster: Stochastic Graphs of Beta Cell Connectivity in the Islets of Langerhans.

PubMed

Striegel, Deborah A; Hara, Manami; Periwal, Vipul

2015-08-01

Pancreatic islets of Langerhans consist of endocrine cells, primarily α, β and δ cells, which secrete glucagon, insulin, and somatostatin, respectively, to regulate plasma glucose. β cells form irregular locally connected clusters within islets that act in concert to secrete insulin upon glucose stimulation. Due to the central functional significance of this local connectivity in the placement of β cells in an islet, it is important to characterize it quantitatively. However, quantification of the seemingly stochastic cytoarchitecture of β cells in an islet requires mathematical methods that can capture topological connectivity in the entire β-cell population in an islet. Graph theory provides such a framework. Using large-scale imaging data for thousands of islets containing hundreds of thousands of cells in human organ donor pancreata, we show that quantitative graph characteristics differ between control and type 2 diabetic islets. Further insight into the processes that shape and maintain this architecture is obtained by formulating a stochastic theory of β-cell rearrangement in whole islets, just as the normal equilibrium distribution of the Ornstein-Uhlenbeck process can be viewed as the result of the interplay between a random walk and a linear restoring force. Requiring that rearrangements maintain the observed quantitative topological graph characteristics strongly constrained possible processes. Our results suggest that β-cell rearrangement is dependent on its connectivity in order to maintain an optimal cluster size in both normal and T2D islets.

The Stability Analysis Method of the Cohesive Granular Slope on the Basis of Graph Theory

PubMed Central

Guan, Yanpeng; Liu, Xiaoli; Wang, Enzhi; Wang, Sijing

2017-01-01

This paper attempted to provide a method to calculate progressive failure of the cohesive-frictional granular geomaterial and the spatial distribution of the stability of the cohesive granular slope. The methodology can be divided into two parts: the characterization method of macro-contact and the analysis of the slope stability. Based on the graph theory, the vertexes, the edges and the edge sequences are abstracted out to characterize the voids, the particle contact and the macro-contact, respectively, bridging the gap between the mesoscopic and macro scales of granular materials. This paper adopts this characterization method to extract a graph from a granular slope and characterize the macro sliding surface, then the weighted graph is analyzed to calculate the slope safety factor. Each edge has three weights representing the sliding moment, the anti-sliding moment and the braking index of contact-bond, respectively, E1E2E3E1E2E3. The safety factor of the slope is calculated by presupposing a certain number of sliding routes and reducing Weight E3 repeatedly and counting the mesoscopic failure of the edge. It is a kind of slope analysis method from mesoscopic perspective so it can present more detail of the mesoscopic property of the granular slope. In the respect of macro scale, the spatial distribution of the stability of the granular slope is in agreement with the theoretical solution. PMID:28772596

On Functional Module Detection in Metabolic Networks

PubMed Central

Koch, Ina; Ackermann, Jörg

2013-01-01

Functional modules of metabolic networks are essential for understanding the metabolism of an organism as a whole. With the vast amount of experimental data and the construction of complex and large-scale, often genome-wide, models, the computer-aided identification of functional modules becomes more and more important. Since steady states play a key role in biology, many methods have been developed in that context, for example, elementary flux modes, extreme pathways, transition invariants and place invariants. Metabolic networks can be studied also from the point of view of graph theory, and algorithms for graph decomposition have been applied for the identification of functional modules. A prominent and currently intensively discussed field of methods in graph theory addresses the Q-modularity. In this paper, we recall known concepts of module detection based on the steady-state assumption, focusing on transition-invariants (elementary modes) and their computation as minimal solutions of systems of Diophantine equations. We present the Fourier-Motzkin algorithm in detail. Afterwards, we introduce the Q-modularity as an example for a useful non-steady-state method and its application to metabolic networks. To illustrate and discuss the concepts of invariants and Q-modularity, we apply a part of the central carbon metabolism in potato tubers (Solanum tuberosum) as running example. The intention of the paper is to give a compact presentation of known steady-state concepts from a graph-theoretical viewpoint in the context of network decomposition and reduction and to introduce the application of Q-modularity to metabolic Petri net models. PMID:24958145

THE PEAKS AND GEOMETRY OF FITNESS LANDSCAPES

PubMed Central

CRONA, KRISTINA; GREENE, DEVIN; BARLOW, MIRIAM

2012-01-01

Fitness landscapes are central in the theory of adaptation. Recent work compares global and local properties of fitness landscapes. It has been shown that multi-peaked fitness landscapes have a local property called reciprocal sign epistasis interactions. The converse is not true. We show that no condition phrased in terms of reciprocal sign epistasis interactions only, implies multiple peaks. We give a sufficient condition for multiple peaks phrased in terms of two-way interactions. This result is surprising since it has been claimed that no sufficient local condition for multiple peaks exist. We show that our result cannot be generalized to sufficient conditions for three or more peaks. Our proof depends on fitness graphs, where nodes represent genotypes and where arrows point toward more fit genotypes. We also use fitness graphs in order to give a new brief proof of the equivalent characterizations of fitness landscapes lacking genetic constraints on accessible mutational trajectories. We compare a recent geometric classification of fitness landscape based on triangulations of polytopes with qualitative aspects of gene interactions. One observation is that fitness graphs provide information not contained in the geometric classification. We argue that a qualitative perspective may help relating theory of fitness landscapes and empirical observations. PMID:23036916

Learning molecular energies using localized graph kernels

DOE PAGES

Ferré, Grégoire; Haut, Terry Scot; Barros, Kipton Marcos

2017-03-21

We report that recent machine learning methods make it possible to model potential energy of atomic configurations with chemical-level accuracy (as calculated from ab initio calculations) and at speeds suitable for molecular dynamics simulation. Best performance is achieved when the known physical constraints are encoded in the machine learning models. For example, the atomic energy is invariant under global translations and rotations; it is also invariant to permutations of same-species atoms. Although simple to state, these symmetries are complicated to encode into machine learning algorithms. In this paper, we present a machine learning approach based on graph theory that naturallymore » incorporates translation, rotation, and permutation symmetries. Specifically, we use a random walk graph kernel to measure the similarity of two adjacency matrices, each of which represents a local atomic environment. This Graph Approximated Energy (GRAPE) approach is flexible and admits many possible extensions. Finally, we benchmark a simple version of GRAPE by predicting atomization energies on a standard dataset of organic molecules.« less

Cluster Tails for Critical Power-Law Inhomogeneous Random Graphs

NASA Astrophysics Data System (ADS)

van der Hofstad, Remco; Kliem, Sandra; van Leeuwaarden, Johan S. H.

2018-04-01

Recently, the scaling limit of cluster sizes for critical inhomogeneous random graphs of rank-1 type having finite variance but infinite third moment degrees was obtained in Bhamidi et al. (Ann Probab 40:2299-2361, 2012). It was proved that when the degrees obey a power law with exponent τ \\in (3,4), the sequence of clusters ordered in decreasing size and multiplied through by n^{-(τ -2)/(τ -1)} converges as n→ ∞ to a sequence of decreasing non-degenerate random variables. Here, we study the tails of the limit of the rescaled largest cluster, i.e., the probability that the scaling limit of the largest cluster takes a large value u, as a function of u. This extends a related result of Pittel (J Combin Theory Ser B 82(2):237-269, 2001) for the Erdős-Rényi random graph to the setting of rank-1 inhomogeneous random graphs with infinite third moment degrees. We make use of delicate large deviations and weak convergence arguments.

Adaptive tracking control of leader-following linear multi-agent systems with external disturbances

NASA Astrophysics Data System (ADS)

Lin, Hanquan; Wei, Qinglai; Liu, Derong; Ma, Hongwen

2016-10-01

In this paper, the consensus problem for leader-following linear multi-agent systems with external disturbances is investigated. Brownian motions are used to describe exogenous disturbances. A distributed tracking controller based on Riccati inequalities with an adaptive law for adjusting coupling weights between neighbouring agents is designed for leader-following multi-agent systems under fixed and switching topologies. In traditional distributed static controllers, the coupling weights depend on the communication graph. However, coupling weights associated with the feedback gain matrix in our method are updated by state errors between neighbouring agents. We further present the stability analysis of leader-following multi-agent systems with stochastic disturbances under switching topology. Most traditional literature requires the graph to be connected all the time, while the communication graph is only assumed to be jointly connected in this paper. The design technique is based on Riccati inequalities and algebraic graph theory. Finally, simulations are given to show the validity of our method.

Learning molecular energies using localized graph kernels

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ferré, Grégoire; Haut, Terry Scot; Barros, Kipton Marcos

We report that recent machine learning methods make it possible to model potential energy of atomic configurations with chemical-level accuracy (as calculated from ab initio calculations) and at speeds suitable for molecular dynamics simulation. Best performance is achieved when the known physical constraints are encoded in the machine learning models. For example, the atomic energy is invariant under global translations and rotations; it is also invariant to permutations of same-species atoms. Although simple to state, these symmetries are complicated to encode into machine learning algorithms. In this paper, we present a machine learning approach based on graph theory that naturallymore » incorporates translation, rotation, and permutation symmetries. Specifically, we use a random walk graph kernel to measure the similarity of two adjacency matrices, each of which represents a local atomic environment. This Graph Approximated Energy (GRAPE) approach is flexible and admits many possible extensions. Finally, we benchmark a simple version of GRAPE by predicting atomization energies on a standard dataset of organic molecules.« less

Classification of pregnancy and labor contractions using a graph theory based analysis.

PubMed

Nader, N; Hassan, M; Falou, W; Diab, A; Al-Omar, S; Khalil, M; Marque, C

2015-08-01

In this paper, we propose a new framework to characterize the electrohysterographic (EHG) signals recorded during pregnancy and labor. The approach is based on the analysis of the propagation of the uterine electrical activity. The processing pipeline includes i) the estimation of the statistical dependencies between the different recorded EHG signals, ii) the characterization of the obtained connectivity matrices using network measures and iii) the use of these measures in clinical application: the classification between pregnancy and labor. Due to its robustness to volume conductor, we used the imaginary part of coherence in order to produce the connectivity matrix which is then transformed into a graph. We evaluate the performance of several graph measures. We also compare the results with the parameter mostly used in the literature: the peak frequency combined with the propagation velocity (PV +PF). Our results show that the use of the network measures is a promising tool to classify labor and pregnancy contractions with a small superiority of the graph strength over PV+PF.

Network analysis for the visualization and analysis of qualitative data.

PubMed

Pokorny, Jennifer J; Norman, Alex; Zanesco, Anthony P; Bauer-Wu, Susan; Sahdra, Baljinder K; Saron, Clifford D

2018-03-01

We present a novel manner in which to visualize the coding of qualitative data that enables representation and analysis of connections between codes using graph theory and network analysis. Network graphs are created from codes applied to a transcript or audio file using the code names and their chronological location. The resulting network is a representation of the coding data that characterizes the interrelations of codes. This approach enables quantification of qualitative codes using network analysis and facilitates examination of associations of network indices with other quantitative variables using common statistical procedures. Here, as a proof of concept, we applied this method to a set of interview transcripts that had been coded in 2 different ways and the resultant network graphs were examined. The creation of network graphs allows researchers an opportunity to view and share their qualitative data in an innovative way that may provide new insights and enhance transparency of the analytical process by which they reach their conclusions. (PsycINFO Database Record (c) 2018 APA, all rights reserved).

Quantum cellular automata and free quantum field theory

NASA Astrophysics Data System (ADS)

D'Ariano, Giacomo Mauro; Perinotti, Paolo

2017-02-01

In a series of recent papers [1-4] it has been shown how free quantum field theory can be derived without using mechanical primitives (including space-time, special relativity, quantization rules, etc.), but only considering the easiest quantum algorithm encompassing a countable set of quantum systems whose network of interactions satisfies the simple principles of unitarity, homogeneity, locality, and isotropy. This has opened the route to extending the axiomatic information-theoretic derivation of the quantum theory of abstract systems [5, 6] to include quantum field theory. The inherent discrete nature of the informational axiomatization leads to an extension of quantum field theory to a quantum cellular automata theory, where the usual field theory is recovered in a regime where the discrete structure of the automata cannot be probed. A simple heuristic argument sets the scale of discreteness to the Planck scale, and the customary physical regime where discreteness is not visible is the relativistic one of small wavevectors. In this paper we provide a thorough derivation from principles that in the most general case the graph of the quantum cellular automaton is the Cayley graph of a finitely presented group, and showing how for the case corresponding to Euclidean emergent space (where the group resorts to an Abelian one) the automata leads to Weyl, Dirac and Maxwell field dynamics in the relativistic limit. We conclude with some perspectives towards the more general scenario of non-linear automata for interacting quantum field theory.

Graph Theory Roots of Spatial Operators for Kinematics and Dynamics

NASA Technical Reports Server (NTRS)

Jain, Abhinandan

2011-01-01

Spatial operators have been used to analyze the dynamics of robotic multibody systems and to develop novel computational dynamics algorithms. Mass matrix factorization, inversion, diagonalization, and linearization are among several new insights obtained using such operators. While initially developed for serial rigid body manipulators, the spatial operators and the related mathematical analysis have been shown to extend very broadly including to tree and closed topology systems, to systems with flexible joints, links, etc. This work uses concepts from graph theory to explore the mathematical foundations of spatial operators. The goal is to study and characterize the properties of the spatial operators at an abstract level so that they can be applied to a broader range of dynamics problems. The rich mathematical properties of the kinematics and dynamics of robotic multibody systems has been an area of strong research interest for several decades. These properties are important to understand the inherent physical behavior of systems, for stability and control analysis, for the development of computational algorithms, and for model development of faithful models. Recurring patterns in spatial operators leads one to ask the more abstract question about the properties and characteristics of spatial operators that make them so broadly applicable. The idea is to step back from the specific application systems, and understand more deeply the generic requirements and properties of spatial operators, so that the insights and techniques are readily available across different kinematics and dynamics problems. In this work, techniques from graph theory were used to explore the abstract basis for the spatial operators. The close relationship between the mathematical properties of adjacency matrices for graphs and those of spatial operators and their kernels were established. The connections hold across very basic requirements on the system topology, the nature of the component bodies, the indexing schemes, etc. The relationship of the underlying structure is intimately connected with efficient, recursive computational algorithms. The results provide the foundational groundwork for a much broader look at the key problems in kinematics and dynamics. The properties of general graphs and trees of nodes and edge were examined, as well as the properties of adjacency matrices that are used to describe graph connectivity. The nilpotency property of such matrices for directed trees was reviewed, and the adjacency matrices were generalized to the notion of block weighted adjacency matrices that support block matrix elements. This leads us to the development of the notion of Spatial Kernel Operator SKO kernels. These kernels provide the basis for the development of SKO resolvent operators.

Deep graphs—A general framework to represent and analyze heterogeneous complex systems across scales

NASA Astrophysics Data System (ADS)

Traxl, Dominik; Boers, Niklas; Kurths, Jürgen

2016-06-01

Network theory has proven to be a powerful tool in describing and analyzing systems by modelling the relations between their constituent objects. Particularly in recent years, a great progress has been made by augmenting "traditional" network theory in order to account for the multiplex nature of many networks, multiple types of connections between objects, the time-evolution of networks, networks of networks and other intricacies. However, existing network representations still lack crucial features in order to serve as a general data analysis tool. These include, most importantly, an explicit association of information with possibly heterogeneous types of objects and relations, and a conclusive representation of the properties of groups of nodes as well as the interactions between such groups on different scales. In this paper, we introduce a collection of definitions resulting in a framework that, on the one hand, entails and unifies existing network representations (e.g., network of networks and multilayer networks), and on the other hand, generalizes and extends them by incorporating the above features. To implement these features, we first specify the nodes and edges of a finite graph as sets of properties (which are permitted to be arbitrary mathematical objects). Second, the mathematical concept of partition lattices is transferred to the network theory in order to demonstrate how partitioning the node and edge set of a graph into supernodes and superedges allows us to aggregate, compute, and allocate information on and between arbitrary groups of nodes. The derived partition lattice of a graph, which we denote by deep graph, constitutes a concise, yet comprehensive representation that enables the expression and analysis of heterogeneous properties, relations, and interactions on all scales of a complex system in a self-contained manner. Furthermore, to be able to utilize existing network-based methods and models, we derive different representations of multilayer networks from our framework and demonstrate the advantages of our representation. On the basis of the formal framework described here, we provide a rich, fully scalable (and self-explanatory) software package that integrates into the PyData ecosystem and offers interfaces to popular network packages, making it a powerful, general-purpose data analysis toolkit. We exemplify an application of deep graphs using a real world dataset, comprising 16 years of satellite-derived global precipitation measurements. We deduce a deep graph representation of these measurements in order to track and investigate local formations of spatio-temporal clusters of extreme precipitation events.

GenomeGraphs: integrated genomic data visualization with R.

PubMed

Durinck, Steffen; Bullard, James; Spellman, Paul T; Dudoit, Sandrine

2009-01-06

Biological studies involve a growing number of distinct high-throughput experiments to characterize samples of interest. There is a lack of methods to visualize these different genomic datasets in a versatile manner. In addition, genomic data analysis requires integrated visualization of experimental data along with constantly changing genomic annotation and statistical analyses. We developed GenomeGraphs, as an add-on software package for the statistical programming environment R, to facilitate integrated visualization of genomic datasets. GenomeGraphs uses the biomaRt package to perform on-line annotation queries to Ensembl and translates these to gene/transcript structures in viewports of the grid graphics package. This allows genomic annotation to be plotted together with experimental data. GenomeGraphs can also be used to plot custom annotation tracks in combination with different experimental data types together in one plot using the same genomic coordinate system. GenomeGraphs is a flexible and extensible software package which can be used to visualize a multitude of genomic datasets within the statistical programming environment R.

Multi-View Multi-Instance Learning Based on Joint Sparse Representation and Multi-View Dictionary Learning.

PubMed

Li, Bing; Yuan, Chunfeng; Xiong, Weihua; Hu, Weiming; Peng, Houwen; Ding, Xinmiao; Maybank, Steve

2017-12-01

In multi-instance learning (MIL), the relations among instances in a bag convey important contextual information in many applications. Previous studies on MIL either ignore such relations or simply model them with a fixed graph structure so that the overall performance inevitably degrades in complex environments. To address this problem, this paper proposes a novel multi-view multi-instance learning algorithm (MIL) that combines multiple context structures in a bag into a unified framework. The novel aspects are: (i) we propose a sparse -graph model that can generate different graphs with different parameters to represent various context relations in a bag, (ii) we propose a multi-view joint sparse representation that integrates these graphs into a unified framework for bag classification, and (iii) we propose a multi-view dictionary learning algorithm to obtain a multi-view graph dictionary that considers cues from all views simultaneously to improve the discrimination of the MIL. Experiments and analyses in many practical applications prove the effectiveness of the M IL.

Network analysis reveals disrupted functional brain circuitry in drug-naive social anxiety disorder.

PubMed

Yang, Xun; Liu, Jin; Meng, Yajing; Xia, Mingrui; Cui, Zaixu; Wu, Xi; Hu, Xinyu; Zhang, Wei; Gong, Gaolang; Gong, Qiyong; Sweeney, John A; He, Yong

2017-12-07

Social anxiety disorder (SAD) is a common and disabling condition characterized by excessive fear and avoidance of public scrutiny. Psychoradiology studies have suggested that the emotional and behavior deficits in SAD are associated with abnormalities in regional brain function and functional connectivity. However, little is known about whether intrinsic functional brain networks in patients with SAD are topologically disrupted. Here, we collected resting-state fMRI data from 33 drug-naive patients with SAD and 32 healthy controls (HC), constructed functional networks with 34 predefined regions based on previous meta-analytic research with task-based fMRI in SAD, and performed network-based statistic and graph-theory analyses. The network-based statistic analysis revealed a single connected abnormal circuitry including the frontolimbic circuit (termed the "fear circuit", including the dorsolateral prefrontal cortex, ventral medial prefrontal cortex and insula) and posterior cingulate/occipital areas supporting perceptual processing. In this single altered network, patients with SAD had higher functional connectivity than HC. At the global level, graph-theory analysis revealed that the patients exhibited a lower normalized characteristic path length than HC, which suggests a disorder-related shift of network topology toward randomized configurations. SAD-related deficits in nodal degree, efficiency and participation coefficient were detected in the parahippocampal gyrus, posterior cingulate cortex, dorsolateral prefrontal cortex, insula and the calcarine sulcus. Aspects of abnormal connectivity were associated with anxiety symptoms. These findings highlight the aberrant topological organization of functional brain network organization in SAD, which provides insights into the neural mechanisms underlying excessive fear and avoidance of social interactions in patients with debilitating social anxiety. Copyright © 2017. Published by Elsevier Inc.

[Characterization of access to normal childbirth care in Bahia State, Brazil, based on graph theory].

PubMed

Sousa, Ludmilla Monfort Oliveira; Araújo, Edna Maria de; Miranda, José Garcia Vivas

2017-12-18

Origin-destination flow is a phenomenon that can be modeled as a network. Graph theory is a mathematical tool to characterize a network and thus allows studying the topological properties and temporal and spatial development of a set of related elements. The article aims to estimate the topological evolution of an inter-municipal network of normal deliveries. We selected the admissions for normal deliveries in the Hospital Information System of the Brazilian Unified National Health System, from 2008 to 2014, for women residing in Bahia State, Brazil. The following indices were applied: entry degree (from how many municipalities the women came for childbirth), exit degree (to how many municipalities they left), entry flow (how many women came), exit flow (how many women left), and the mean size of the exit edge (distance traveled). Analyses between macro-regions used the following indicators: proportion of normal deliveries performed outside the municipality of residence and mean size of the exit edge. The results indicate an increase in deliveries performed outside the municipality of residence, in addition to the persistence of concentration of deliveries in the hub municipalities in the Health Regions, and an increase in the distance between the municipality of residence and the municipality where the delivery took place. The organization of networks for normal childbirth poses an on-going challenge. It is important to analyze the flow of women for childbirth care in order to support the establishment of inter-municipal references to guarantee safe labor and childbirth. In conclusion, it is necessary to develop a regionalized network to meet the demand by pregnant women in the territory with universal and equitable coverage.

Probabilistic graphs as a conceptual and computational tool in hydrology and water management

NASA Astrophysics Data System (ADS)

Schoups, Gerrit

2014-05-01

Originally developed in the fields of machine learning and artificial intelligence, probabilistic graphs constitute a general framework for modeling complex systems in the presence of uncertainty. The framework consists of three components: 1. Representation of the model as a graph (or network), with nodes depicting random variables in the model (e.g. parameters, states, etc), which are joined together by factors. Factors are local probabilistic or deterministic relations between subsets of variables, which, when multiplied together, yield the joint distribution over all variables. 2. Consistent use of probability theory for quantifying uncertainty, relying on basic rules of probability for assimilating data into the model and expressing unknown variables as a function of observations (via the posterior distribution). 3. Efficient, distributed approximation of the posterior distribution using general-purpose algorithms that exploit model structure encoded in the graph. These attributes make probabilistic graphs potentially useful as a conceptual and computational tool in hydrology and water management (and beyond). Conceptually, they can provide a common framework for existing and new probabilistic modeling approaches (e.g. by drawing inspiration from other fields of application), while computationally they can make probabilistic inference feasible in larger hydrological models. The presentation explores, via examples, some of these benefits.

Dynamic extension of the Simulation Problem Analysis Kernel (SPANK)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sowell, E.F.; Buhl, W.F.

1988-07-15

The Simulation Problem Analysis Kernel (SPANK) is an object-oriented simulation environment for general simulation purposes. Among its unique features is use of the directed graph as the primary data structure, rather than the matrix. This allows straightforward use of graph algorithms for matching variables and equations, and reducing the problem graph for efficient numerical solution. The original prototype implementation demonstrated the principles for systems of algebraic equations, allowing simulation of steady-state, nonlinear systems (Sowell 1986). This paper describes how the same principles can be extended to include dynamic objects, allowing simulation of general dynamic systems. The theory is developed andmore » an implementation is described. An example is taken from the field of building energy system simulation. 2 refs., 9 figs.« less

Information jet: Handling noisy big data from weakly disconnected network

NASA Astrophysics Data System (ADS)

Aurongzeb, Deeder

Sudden aggregation (information jet) of large amount of data is ubiquitous around connected social networks, driven by sudden interacting and non-interacting events, network security threat attacks, online sales channel etc. Clustering of information jet based on time series analysis and graph theory is not new but little work is done to connect them with particle jet statistics. We show pre-clustering based on context can element soft network or network of information which is critical to minimize time to calculate results from noisy big data. We show difference between, stochastic gradient boosting and time series-graph clustering. For disconnected higher dimensional information jet, we use Kallenberg representation theorem (Kallenberg, 2005, arXiv:1401.1137) to identify and eliminate jet similarities from dense or sparse graph.

Investigating the effects of streamline-based fiber tractography on matrix scaling in brain connective network.

PubMed

Jan, Hengtai; Chao, Yi-Ping; Cho, Kuan-Hung; Kuo, Li-Wei

2013-01-01

Investigating the brain connective network using the modern graph theory has been widely applied in cognitive and clinical neuroscience research. In this study, we aimed to investigate the effects of streamline-based fiber tractography on the change of network properties and established a systematic framework to understand how an adequate network matrix scaling can be determined. The network properties, including degree, efficiency and betweenness centrality, show similar tendency in both left and right hemispheres. By employing the curve-fitting process with exponential law and measuring the residuals, the association between changes of network properties and threshold of track numbers is found and an adequate range of investigating the lateralization of brain network is suggested. The proposed approach can be further applied in clinical applications to improve the diagnostic sensitivity using network analysis with graph theory.

Graph theory analysis of complex brain networks: new concepts in brain mapping applied to neurosurgery.

PubMed

Hart, Michael G; Ypma, Rolf J F; Romero-Garcia, Rafael; Price, Stephen J; Suckling, John

2016-06-01

Neuroanatomy has entered a new era, culminating in the search for the connectome, otherwise known as the brain's wiring diagram. While this approach has led to landmark discoveries in neuroscience, potential neurosurgical applications and collaborations have been lagging. In this article, the authors describe the ideas and concepts behind the connectome and its analysis with graph theory. Following this they then describe how to form a connectome using resting state functional MRI data as an example. Next they highlight selected insights into healthy brain function that have been derived from connectome analysis and illustrate how studies into normal development, cognitive function, and the effects of synthetic lesioning can be relevant to neurosurgery. Finally, they provide a précis of early applications of the connectome and related techniques to traumatic brain injury, functional neurosurgery, and neurooncology.

Information fusion-based approach for studying influence on Twitter using belief theory.

PubMed

Azaza, Lobna; Kirgizov, Sergey; Savonnet, Marinette; Leclercq, Éric; Gastineau, Nicolas; Faiz, Rim

2016-01-01

Influence in Twitter has become recently a hot research topic, since this micro-blogging service is widely used to share and disseminate information. Some users are more able than others to influence and persuade peers. Thus, studying most influential users leads to reach a large-scale information diffusion area, something very useful in marketing or political campaigns. In this study, we propose a new approach for multi-level influence assessment on multi-relational networks, such as Twitter . We define a social graph to model the relationships between users as a multiplex graph where users are represented by nodes, and links model the different relations between them (e.g., retweets , mentions , and replies ). We explore how relations between nodes in this graph could reveal about the influence degree and propose a generic computational model to assess influence degree of a certain node. This is based on the conjunctive combination rule from the belief functions theory to combine different types of relations. We experiment the proposed method on a large amount of data gathered from Twitter during the European Elections 2014 and deduce top influential candidates. The results show that our model is flexible enough to to consider multiple interactions combination according to social scientists needs or requirements and that the numerical results of the belief theory are accurate. We also evaluate the approach over the CLEF RepLab 2014 data set and show that our approach leads to quite interesting results.

The scientific theory profile: A philosophy of science model for science teachers

NASA Astrophysics Data System (ADS)

Loving, Cathleen C.

A model called the Scientific Theory Profile was developed for use with preservice and inservice science teachers or with graduate students interested in the various ways scientific theories are perceived. Early indications - from a survey of institutions with science education programs and a survey of current science methods texts - are that too little emphasis is placed on what contemporary writings reveal about the nature and importance of scientific theories. This prompted the development of the Profile. The Profile consists of a grid, with the x-axis representing methods for judging theories (rational vs. natural), and the y-axis representing views on reigning scientific theories as being the Truth versus models of what works best (realism vs. anti-realism). Three well-known philosophers of science who were selected for detailed analysis and who form the keystone positions on the Profile are Thomas Kuhn, Carl Hempel, and Sir Karl Popper. The hypothesis was that an analysis of the writings of respected individuals in philosophy and history of science who have different perspectives on theories (as well as overarching areas of agreement) could be translated into relative coordinates on a graph; and that this visual model might be helpful to science teachers in developing a balanced philosophy of science and a deeper understanding of the power of reigning theories. Nine other contemporary philosophers, all influenced by the three originals, are included in brief analyses, with their positions on the grid being relative to the keystones. The Scientific Theory Profile then forms the basis for a course, now in the planning stages, in perspectives on the nature of science, primarily for science teachers, with some objectives and activities suggested.

Analysing the connectivity and communication of suicidal users on twitter

PubMed Central

Colombo, Gualtiero B.; Burnap, Pete; Hodorog, Andrei; Scourfield, Jonathan

2016-01-01

In this paper we aim to understand the connectivity and communication characteristics of Twitter users who post content subsequently classified by human annotators as containing possible suicidal intent or thinking, commonly referred to as suicidal ideation. We achieve this understanding by analysing the characteristics of their social networks. Starting from a set of human annotated Tweets we retrieved the authors’ followers and friends lists, and identified users who retweeted the suicidal content. We subsequently built the social network graphs. Our results show a high degree of reciprocal connectivity between the authors of suicidal content when compared to other studies of Twitter users, suggesting a tightly-coupled virtual community. In addition, an analysis of the retweet graph has identified bridge nodes and hub nodes connecting users posting suicidal ideation with users who were not, thus suggesting a potential for information cascade and risk of a possible contagion effect. This is particularly emphasised by considering the combined graph merging friendship and retweeting links. PMID:26973360

Coordination of fractional-order nonlinear multi-agent systems via distributed impulsive control

NASA Astrophysics Data System (ADS)

Ma, Tiedong; Li, Teng; Cui, Bing

2018-01-01

The coordination of fractional-order nonlinear multi-agent systems via distributed impulsive control method is studied in this paper. Based on the theory of impulsive differential equations, algebraic graph theory, Lyapunov stability theory and Mittag-Leffler function, two novel sufficient conditions for achieving the cooperative control of a class of fractional-order nonlinear multi-agent systems are derived. Finally, two numerical simulations are verified to illustrate the effectiveness and feasibility of the proposed method.

Reality-and-Desire in Ciliates

NASA Astrophysics Data System (ADS)

Brijder, Robert; Hoogeboom, Hendrik Jan

The theory of gene assembly in ciliates has a number of similarities with the theory of sorting by reversal. Both theories model processes that are based on splicing, and have a fixed begin and end product. The main difference is the type of splicing operations used to obtain the end product from the begin product. In this overview paper, we show how the concept of breakpoint graph, known from the theory of sorting by reversal, can be used in the theory of gene assembly. Our aim is to present the material in an intuitive and informal manner to allow for an efficient introduction into the subject.

Local adjacency metric dimension of sun graph and stacked book graph

NASA Astrophysics Data System (ADS)

Yulisda Badri, Alifiah; Darmaji

2018-03-01

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

Feasibility of using the linac real-time log data for VMAT treatment verification

NASA Astrophysics Data System (ADS)

Midi, N. S.; Zin, Hafiz M.

2017-05-01

This study investigates the feasibility of using the real-time log data from a linac to verify Volumetric Modulated Arc Therapy (VMAT) treatment. The treatment log data for an Elekta Synergy linac can be recorded at a sampling rate of 4 Hz using the service graphing tool on the linac control computer. A treatment plan that simulates a VMAT treatment was delivered from the linac and all the dynamic treatment parameters including monitor unit (MU), Multileaf Collimator (MLC) position, jaw position, gantry angle and collimator angle were recorded in real-time using the service graphing tool. The recorded raw data were extracted and analysed using algorithms written in Matlab (MathWorks, Natick, MA). The actual treatment parameters logged using the service graphing tool was compared to the prescription and the deviations were analysed. The MLC position errors travelling at the speed range from -3.25 to 5.92 cm/s were between -1.7 mm to 2.5 mm, well within the 3.5 mm tolerance value (AAPM TG-142). The discrepancies of other delivery parameters were also within the tolerance. The real-time linac parameters logged using the service graphing tool can be used as a supplementary data for patient specific VMAT pre-treatment quality assurance.

Implementing the Standards. Teaching Discrete Mathematics in Grades 7-12.

ERIC Educational Resources Information Center

Hart, Eric W.; And Others

1990-01-01

Discrete mathematics are defined briefly. A course in discrete mathematics for high school students and teaching discrete mathematics in grades 7 and 8 including finite differences, recursion, and graph theory are discussed. (CW)

Understanding Magnetic Anomalies and Their Significance.

ERIC Educational Resources Information Center

Shea, James H.

1988-01-01

Describes a laboratory exercise testing the Vine-Matthews-Morley hypothesis of plate tectonics. Includes 14 questions with explanations using graphs and charts. Provides a historical account of the current plate tectonic and magnetic anomaly theory. (MVL)

Recent developments in rotary-wing aerodynamic theory

NASA Technical Reports Server (NTRS)

Johnson, W.

1986-01-01

Current progress in the computational analysis of rotary-wing flowfields is surveyed, and some typical results are presented in graphs. Topics examined include potential theory, rotating coordinate systems, lifting-surface theory (moving singularity, fixed wing, and rotary wing), panel methods (surface singularity representations, integral equations, and compressible flows), transonic theory (the small-disturbance equation), wake analysis (hovering rotor-wake models and transonic blade-vortex interaction), limitations on computational aerodynamics, and viscous-flow methods (dynamic-stall theories and lifting-line theory). It is suggested that the present algorithms and advanced computers make it possible to begin working toward the ultimate goal of turbulent Navier-Stokes calculations for an entire rotorcraft.

Measurement issues in research on social support and health.

PubMed Central

Dean, K; Holst, E; Kreiner, S; Schoenborn, C; Wilson, R

1994-01-01

STUDY OBJECTIVE--The aims were: (1) to identify methodological problems that may explain the inconsistencies and contradictions in the research evidence on social support and health, and (2) to validate a frequently used measure of social support in order to determine whether or not it could be used in multivariate analyses of population data in research on social support and health. DESIGN AND METHODS--Secondary analysis of data collected in a cross sectional survey of a multistage cluster sample of the population of the United States, designed to study relationships in behavioural, social support and health variables. Statistical models based on item response theory and graph theory were used to validate the measure of social support to be used in subsequent analyses. PARTICIPANTS--Data on 1755 men and women aged 20 to 64 years were available for the scale validation. RESULTS--Massive evidence of item bias was found for all items of a group membership subscale. The most serious problems were found in relationship to an item measuring membership in work related groups. Using that item in the social network scale in multivariate analyses would distort findings on the statistical effects of education, employment status, and household income. Evidence of item bias was also found for a sociability subscale. When marital status was included to create what is called an intimate contacts subscale, the confounding grew worse. CONCLUSIONS--The composite measure of social network is not valid and would seriously distort the findings of analyses attempting to study relationships between the index and other variables. The findings show that valid measurement is a methodological issue that must be addressed in scientific research on population health. PMID:8189179

Network Theory: A Primer and Questions for Air Transportation Systems Applications

NASA Technical Reports Server (NTRS)

Holmes, Bruce J.

2004-01-01

A new understanding (with potential applications to air transportation systems) has emerged in the past five years in the scientific field of networks. This development emerges in large part because we now have a new laboratory for developing theories about complex networks: The Internet. The premise of this new understanding is that most complex networks of interest, both of nature and of human contrivance, exhibit a fundamentally different behavior than thought for over two hundred years under classical graph theory. Classical theory held that networks exhibited random behavior, characterized by normal, (e.g., Gaussian or Poisson) degree distributions of the connectivity between nodes by links. The new understanding turns this idea on its head: networks of interest exhibit scale-free (or small world) degree distributions of connectivity, characterized by power law distributions. The implications of scale-free behavior for air transportation systems include the potential that some behaviors of complex system architectures might be analyzed through relatively simple approximations of local elements of the system. For air transportation applications, this presentation proposes a framework for constructing topologies (architectures) that represent the relationships between mobility, flight operations, aircraft requirements, and airspace capacity, and the related externalities in airspace procedures and architectures. The proposed architectures or topologies may serve as a framework for posing comparative and combinative analyses of performance, cost, security, environmental, and related metrics.

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

PubMed Central

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

2015-01-01

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

Analysis of Resting-State fMRI Topological Graph Theory Properties in Methamphetamine Drug Users Applying Box-Counting Fractal Dimension.

PubMed

Siyah Mansoory, Meysam; Oghabian, Mohammad Ali; Jafari, Amir Homayoun; Shahbabaie, Alireza

2017-01-01

Graph theoretical analysis of functional Magnetic Resonance Imaging (fMRI) data has provided new measures of mapping human brain in vivo. Of all methods to measure the functional connectivity between regions, Linear Correlation (LC) calculation of activity time series of the brain regions as a linear measure is considered the most ubiquitous one. The strength of the dependence obligatory for graph construction and analysis is consistently underestimated by LC, because not all the bivariate distributions, but only the marginals are Gaussian. In a number of studies, Mutual Information (MI) has been employed, as a similarity measure between each two time series of the brain regions, a pure nonlinear measure. Owing to the complex fractal organization of the brain indicating self-similarity, more information on the brain can be revealed by fMRI Fractal Dimension (FD) analysis. In the present paper, Box-Counting Fractal Dimension (BCFD) is introduced for graph theoretical analysis of fMRI data in 17 methamphetamine drug users and 18 normal controls. Then, BCFD performance was evaluated compared to those of LC and MI methods. Moreover, the global topological graph properties of the brain networks inclusive of global efficiency, clustering coefficient and characteristic path length in addict subjects were investigated too. Compared to normal subjects by using statistical tests (P<0.05), topological graph properties were postulated to be disrupted significantly during the resting-state fMRI. Based on the results, analyzing the graph topological properties (representing the brain networks) based on BCFD is a more reliable method than LC and MI.

Changes in functional brain networks following sports-related concussion in adolescents.

PubMed

Virji-Babul, Naznin; Hilderman, Courtney G E; Makan, Nadia; Liu, Aiping; Smith-Forrester, Jenna; Franks, Chris; Wang, Z J

2014-12-01

Sports-related concussion is a major public health issue; however, little is known about the underlying changes in functional brain networks in adolescents following injury. Our aim was to use the tools from graph theory to evaluate the changes in brain network properties following concussion in adolescent athletes. We recorded resting state electroencephalography (EEG) in 33 healthy adolescent athletes and 9 adolescent athletes with a clinical diagnosis of subacute concussion. Graph theory analysis was applied to these data to evaluate changes in brain networks. Global and local metrics of the structural properties of the graph were calculated for each group and correlated with Immediate Post-Concussion Assessment and Cognitive Testing (ImPACT) scores. Brain networks of both groups showed small-world topology with no statistically significant differences in the global metrics; however, significant differences were found in the local metrics. Specifically, in the concussed group, we noted: 1) increased values of betweenness and degree in frontal electrode sites corresponding to the (R) dorsolateral prefrontal cortex and the (R) inferior frontal gyrus and 2) decreased values of degree in the region corresponding to the (R) frontopolar prefrontal cortex. In addition, there was significant negative correlation between degree and hub value, with total symptom score at the electrode site corresponding to the (R) prefrontal cortex. This preliminary report in adolescent athletes shows for the first time that resting-state EEG combined with graph theoretical analysis may provide an objective method of evaluating changes in brain networks following concussion. This approach may be useful in identifying individuals at risk for future injury.

An advanced method for classifying atmospheric circulation types based on prototypes connectivity graph

NASA Astrophysics Data System (ADS)

Zagouras, Athanassios; Argiriou, Athanassios A.; Flocas, Helena A.; Economou, George; Fotopoulos, Spiros

2012-11-01

Classification of weather maps at various isobaric levels as a methodological tool is used in several problems related to meteorology, climatology, atmospheric pollution and to other fields for many years. Initially the classification was performed manually. The criteria used by the person performing the classification are features of isobars or isopleths of geopotential height, depending on the type of maps to be classified. Although manual classifications integrate the perceptual experience and other unquantifiable qualities of the meteorology specialists involved, these are typically subjective and time consuming. Furthermore, during the last years different approaches of automated methods for atmospheric circulation classification have been proposed, which present automated and so-called objective classifications. In this paper a new method of atmospheric circulation classification of isobaric maps is presented. The method is based on graph theory. It starts with an intelligent prototype selection using an over-partitioning mode of fuzzy c-means (FCM) algorithm, proceeds to a graph formulation for the entire dataset and produces the clusters based on the contemporary dominant sets clustering method. Graph theory is a novel mathematical approach, allowing a more efficient representation of spatially correlated data, compared to the classical Euclidian space representation approaches, used in conventional classification methods. The method has been applied to the classification of 850 hPa atmospheric circulation over the Eastern Mediterranean. The evaluation of the automated methods is performed by statistical indexes; results indicate that the classification is adequately comparable with other state-of-the-art automated map classification methods, for a variable number of clusters.

Graph Theory Approach for Studying Food Webs

NASA Astrophysics Data System (ADS)

Longjas, A.; Tejedor, A.; Foufoula-Georgiou, E.

2017-12-01

Food webs are complex networks of feeding interactions among species in ecological communities. Metrics describing food web structure have been proposed to compare and classify food webs ranging from food chain length, connectance, degree distribution, centrality measures, to the presence of motifs (distinct compartments), among others. However, formal methodologies for studying both food web topology and the dynamic processes operating on them are still lacking. Here, we utilize a quantitative framework using graph theory within which a food web is represented by a directed graph, i.e., a collection of vertices (species or trophic species defined as sets of species sharing the same predators and prey) and directed edges (predation links). This framework allows us to identify apex (environmental "source" node) to outlet (top predators) subnetworks and compute the steady-state flux (e.g., carbon, nutrients, energy etc.) in the food web. We use this framework to (1) construct vulnerability maps that quantify the relative change of flux delivery to the top predators in response to perturbations in prey species (2) identify keystone species, whose loss would precipitate further species extinction, and (3) introduce a suite of graph-theoretic metrics to quantify the topologic (imposed by food web connectivity) and dynamic (dictated by the flux partitioning and distribution) components of a food web's complexity. By projecting food webs into a 2D Topodynamic Complexity Space whose coordinates are given by Number of alternative paths (topologic) and Leakage Index (dynamic), we show that this space provides a basis for food web comparison and provide physical insights into their dynamic behavior.

Free Vibration Study of Anti-Symmetric Angle-Ply Laminated Plates under Clamped Boundary Conditions

NASA Astrophysics Data System (ADS)

Viswanathan, K. K.; Karthik, K.; Sanyasiraju, Y. V. S. S.; Aziz, Z. A.

2016-11-01

Two type of numerical approach namely, Radial Basis Function and Spline approximation, used to analyse the free vibration of anti-symmetric angle-ply laminated plates under clamped boundary conditions. The equations of motion are derived using YNS theory under first order shear deformation. By assuming the solution in separable form, coupled differential equations obtained in term of mid-plane displacement and rotational functions. The coupled differential is then approximated using Spline function and radial basis function to obtain the generalize eigenvalue problem and parametric studies are made to investigate the effect of aspect ratio, length-to-thickness ratio, number of layers, fibre orientation and material properties with respect to the frequency parameter. Some results are compared with the existing literature and other new results are given in tables and graphs.

DebtRank a centrality measure for financial systems and beyond

NASA Astrophysics Data System (ADS)

Caldarelli, Guido; Battiston, Stefano; Puliga, Michelangelo; Kaushik, Rahul; Tasca, Paolo; Chair of System Design Collaboration; IMT Alti Studi Lucca Collaboration

2013-03-01

Use of network theory made possible to measure quantitatively many features of social and technological systems. In this spirit, inspired by traditional measures of centrality we introduce DebtRank a novel measure of systemic impact. We that we intend the risk of default of a large portion of the financial system, depends on the network of financial exposures among institutions. As an application, we analyse a new and unique dataset on the USD 1.2 trillion FED emergency loans program to global financial institutions during 2008-2010. We find that a group of 22 institutions, which received most of the funds, form a strongly connected graph where each of the nodes becomes systemically important at the peak of the crisis. Moreover, a systemic default could have been triggered even by small dispersed shocks. Other application to different systems are also presented.

Using minimal spanning trees to compare the reliability of network topologies

NASA Technical Reports Server (NTRS)

Leister, Karen J.; White, Allan L.; Hayhurst, Kelly J.

1990-01-01

Graph theoretic methods are applied to compute the reliability for several types of networks of moderate size. The graph theory methods used are minimal spanning trees for networks with bi-directional links and the related concept of strongly connected directed graphs for networks with uni-directional links. A comparison is conducted of ring networks and braided networks. The case is covered where just the links fail and the case where both links and nodes fail. Two different failure modes for the links are considered. For one failure mode, the link no longer carries messages. For the other failure mode, the link delivers incorrect messages. There is a description and comparison of link-redundancy versus path-redundancy as methods to achieve reliability. All the computations are carried out by means of a fault tree program.

How mutation affects evolutionary games on graphs

PubMed Central

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

2011-01-01

Evolutionary dynamics are affected by population structure, mutation rates and update rules. Spatial or network structure facilitates the clustering of strategies, which represents a mechanism for the evolution of cooperation. Mutation dilutes this effect. Here we analyze how mutation influences evolutionary clustering on graphs. We introduce new mathematical methods to evolutionary game theory, specifically the analysis of coalescing random walks via generating functions. These techniques allow us to derive exact identity-by-descent (IBD) probabilities, which characterize spatial assortment on lattices and Cayley trees. From these IBD probabilities we obtain exact conditions for the evolution of cooperation and other game strategies, showing the dual effects of graph topology and mutation rate. High mutation rates diminish the clustering of cooperators, hindering their evolutionary success. Our model can represent either genetic evolution with mutation, or social imitation processes with random strategy exploration. PMID:21473871

Controlling bi-partite entanglement in multi-qubit systems

NASA Astrophysics Data System (ADS)

Plesch, Martin; Novotný, Jaroslav; Dzuráková, Zuzana; Buzek, Vladimír

2004-02-01

Bi-partite entanglement in multi-qubit systems cannot be shared freely. The rules of quantum mechanics impose bounds on how multi-qubit systems can be correlated. In this paper, we utilize a concept of entangled graphs with weighted edges in order to analyse pure quantum states of multi-qubit systems. Here qubits are represented by vertexes of the graph, while the presence of bi-partite entanglement is represented by an edge between corresponding vertexes. The weight of each edge is defined to be the entanglement between the two qubits connected by the edge, as measured by the concurrence. We prove that each entangled graph with entanglement bounded by a specific value of the concurrence can be represented by a pure multi-qubit state. In addition, we present a logic network with O(N2) elementary gates that can be used for preparation of the weighted entangled graphs of N qubits.

From free fields to AdS space. II

NASA Astrophysics Data System (ADS)

Gopakumar, Rajesh

2004-07-01

We continue with the program of paper I [Phys. Rev. D 70, 025009 (2004)] to implement open-closed string duality on free gauge field theory (in the large-N limit). In this paper we consider correlators such as <∏ni=1TrΦJi(xi)>. The Schwinger parametrization of this n-point function exhibits a partial gluing up into a set of basic skeleton graphs. We argue that the moduli space of the planar skeleton graphs is exactly the same as the moduli space of genus zero Riemann surfaces with n holes. In other words, we can explicitly rewrite the n-point (planar) free-field correlator as an integral over the moduli space of a sphere with n holes. A preliminary study of the integrand also indicates compatibility with a string theory on AdS space. The details of our argument are quite insensitive to the specific form of the operators and generalize to diagrams of a higher genus as well. We take this as evidence of the field theory’s ability to reorganize itself into a string theory.

Challenges in Computational Social Modeling and Simulation for National Security Decision Making

DTIC Science & Technology

2011-06-01

This study is grounded within a system-activity theory , a logico-philosophical model of interdisciplinary research [13, 14], the concepts of social...often a difficult challenge. Ironically, social science research methods , such as ethnography , may be tremendously helpful in designing these...social sciences. Moreover, CSS projects draw on knowledge and methods from other fields of study , including graph theory , information visualization

Towards a theory of automated elliptic mesh generation

NASA Technical Reports Server (NTRS)

Cordova, J. Q.

1992-01-01

The theory of elliptic mesh generation is reviewed and the fundamental problem of constructing computational space is discussed. It is argued that the construction of computational space is an NP-Complete problem and therefore requires a nonstandard approach for its solution. This leads to the development of graph-theoretic, combinatorial optimization and integer programming algorithms. Methods for the construction of two dimensional computational space are presented.

Statistical Inference in Graphical Models

DTIC Science & Technology

2008-06-17

fuse probability theory and graph theory in such a way as to permit efficient rep- resentation and computation with probability distributions. They...message passing. 59 viii 1. INTRODUCTION In approaching real-world problems, we often need to deal with uncertainty. Probability and statis- tics provide a...dynamic programming methods. However, for many sensors of interest, the signal-to-noise ratio does not allow such a treatment. Another source of

Modeling spatial decisions with graph theory: logging roads and forest fragmentation in the Brazilian Amazon.

PubMed

Walker, Robert; Arima, Eugenio; Messina, Joe; Soares-Filho, Britaldo; Perz, Stephen; Vergara, Dante; Sales, Marcio; Pereira, Ritaumaria; Castro, Williams

2013-01-01

This article addresses the spatial decision-making of loggers and implications for forest fragmentation in the Amazon basin. It provides a behavioral explanation for fragmentation by modeling how loggers build road networks, typically abandoned upon removal of hardwoods. Logging road networks provide access to land, and the settlers who take advantage of them clear fields and pastures that accentuate their spatial signatures. In shaping agricultural activities, these networks organize emergent patterns of forest fragmentation, even though the loggers move elsewhere. The goal of the article is to explicate how loggers shape their road networks, in order to theoretically explain an important type of forest fragmentation found in the Amazon basin, particularly in Brazil. This is accomplished by adapting graph theory to represent the spatial decision-making of loggers, and by implementing computational algorithms that build graphs interpretable as logging road networks. The economic behavior of loggers is conceptualized as a profit maximization problem, and translated into spatial decision-making by establishing a formal correspondence between mathematical graphs and road networks. New computational approaches, adapted from operations research, are used to construct graphs and simulate spatial decision-making as a function of discount rates, land tenure, and topographic constraints. The algorithms employed bracket a range of behavioral settings appropriate for areas of terras de volutas, public lands that have not been set aside for environmental protection, indigenous peoples, or colonization. The simulation target sites are located in or near so-called Terra do Meio, once a major logging frontier in the lower Amazon Basin. Simulation networks are compared to empirical ones identified by remote sensing and then used to draw inferences about factors influencing the spatial behavior of loggers. Results overall suggest that Amazonia's logging road networks induce more fragmentation than necessary to access fixed quantities of wood. The paper concludes by considering implications of the approach and findings for Brazil's move to a system of concession logging.

Graph Theory-Based Analysis of the Lymph Node Fibroblastic Reticular Cell Network.

PubMed

Novkovic, Mario; Onder, Lucas; Bocharov, Gennady; Ludewig, Burkhard

2017-01-01

Secondary lymphoid organs have developed segregated niches that are able to initiate and maintain effective immune responses. Such global organization requires tight control of diverse cellular components, specifically those that regulate lymphocyte trafficking. Fibroblastic reticular cells (FRCs) form a densely interconnected network in lymph nodes and provide key factors necessary for T cell migration and retention, and foster subsequent interactions between T cells and dendritic cells. Development of integrative systems biology approaches has made it possible to elucidate this multilevel complexity of the immune system. Here, we present a graph theory-based analysis of the FRC network in murine lymph nodes, where generation of the network topology is performed using high-resolution confocal microscopy and 3D reconstruction. This approach facilitates the analysis of physical cell-to-cell connectivity, and estimation of topological robustness and global behavior of the network when it is subjected to perturbation in silico.

A prediction model for cognitive performance in health ageing using diffusion tensor imaging with graph theory.

PubMed

Yun, Ruijuan; Lin, Chung-Chih; Wu, Shuicai; Huang, Chu-Chung; Lin, Ching-Po; Chao, Yi-Ping

2013-01-01

In this study, we employed diffusion tensor imaging (DTI) to construct brain structural network and then derive the connection matrices from 96 healthy elderly subjects. The correlation analysis between these topological properties of network based on graph theory and the Cognitive Abilities Screening Instrument (CASI) index were processed to extract the significant network characteristics. These characteristics were then integrated to estimate the models by various machine-learning algorithms to predict user's cognitive performance. From the results, linear regression model and Gaussian processes model showed presented better abilities with lower mean absolute errors of 5.8120 and 6.25 to predict the cognitive performance respectively. Moreover, these extracted topological properties of brain structural network derived from DTI also could be regarded as the bio-signatures for further evaluation of brain degeneration in healthy aged and early diagnosis of mild cognitive impairment (MCI).

Fuzzy Edge Connectivity of Graphical Fuzzy State Space Model in Multi-connected System

NASA Astrophysics Data System (ADS)

Harish, Noor Ainy; Ismail, Razidah; Ahmad, Tahir

2010-11-01

Structured networks of interacting components illustrate complex structure in a direct or intuitive way. Graph theory provides a mathematical modeling for studying interconnection among elements in natural and man-made systems. On the other hand, directed graph is useful to define and interpret the interconnection structure underlying the dynamics of the interacting subsystem. Fuzzy theory provides important tools in dealing various aspects of complexity, imprecision and fuzziness of the network structure of a multi-connected system. Initial development for systems of Fuzzy State Space Model (FSSM) and a fuzzy algorithm approach were introduced with the purpose of solving the inverse problems in multivariable system. In this paper, fuzzy algorithm is adapted in order to determine the fuzzy edge connectivity between subsystems, in particular interconnected system of Graphical Representation of FSSM. This new approach will simplify the schematic diagram of interconnection of subsystems in a multi-connected system.

Fitting of Hadron Mass Spectra and Contributions to Perturbation Theory of Conformal Quantum Field Theory

NASA Astrophysics Data System (ADS)

Luna Acosta, German Aurelio

The masses of observed hadrons are fitted according to the kinematic predictions of Conformal Relativity. The hypothesis gives a remarkably good fit. The isospin SU(2) gauge invariant Lagrangian L(,(pi)NN)(x,(lamda)) is used in the calculation of d(sigma)/d(OMEGA) to 2nd-order Feynman graphs for simplified models of (pi)N(--->)(pi)N. The resulting infinite mass sums over the nucleon (Conformal) families are done via the Generalized-Sommerfeld-Watson Transform Theorem. Even though the models are too simple to be realistic, they indicate that if (DELTA)-internal lines were to be included, 2nd-order Feynman graphs may reproduce the experimental data qualitatively. The energy -dependence of the propagator and couplings in Conformal QFT is different from that of ordinary QFT. Suggestions for further work are made in the areas of ultra-violet divergences and OPEC calculations.

Connectivity modeling and graph theory analysis predict recolonization in transient populations

NASA Astrophysics Data System (ADS)

Rognstad, Rhiannon L.; Wethey, David S.; Oliver, Hilde; Hilbish, Thomas J.

2018-07-01

Population connectivity plays a major role in the ecology and evolution of marine organisms. In these systems, connectivity of many species occurs primarily during a larval stage, when larvae are frequently too small and numerous to track directly. To indirectly estimate larval dispersal, ocean circulation models have emerged as a popular technique. Here we use regional ocean circulation models to estimate dispersal of the intertidal barnacle Semibalanus balanoides at its local distribution limit in Southwest England. We incorporate historical and recent repatriation events to provide support for our modeled dispersal estimates, which predict a recolonization rate similar to that observed in two recolonization events. Using graph theory techniques to describe the dispersal landscape, we identify likely physical barriers to dispersal in the region. Our results demonstrate the use of recolonization data to support dispersal models and how these models can be used to describe population connectivity.

Using Tutte polynomials to analyze the structure of the benzodiazepines

NASA Astrophysics Data System (ADS)

Cadavid Muñoz, Juan José

2014-05-01

Graph theory in general and Tutte polynomials in particular, are implemented for analyzing the chemical structure of the benzodiazepines. Similarity analysis are used with the Tutte polynomials for finding other molecules that are similar to the benzodiazepines and therefore that might show similar psycho-active actions for medical purpose, in order to evade the drawbacks associated to the benzodiazepines based medicine. For each type of benzodiazepines, Tutte polynomials are computed and some numeric characteristics are obtained, such as the number of spanning trees and the number of spanning forests. Computations are done using the computer algebra Maple's GraphTheory package. The obtained analytical results are of great importance in pharmaceutical engineering. As a future research line, the usage of the chemistry computational program named Spartan, will be used to extent and compare it with the obtained results from the Tutte polynomials of benzodiazepines.

Data and graph interpretation practices among preservice science teachers

NASA Astrophysics Data System (ADS)

Bowen, G. Michael; Roth, Wolff-Michael

2005-12-01

The interpretation of data and construction and interpretation of graphs are central practices in science, which, according to recent reform documents, science and mathematics teachers are expected to foster in their classrooms. However, are (preservice) science teachers prepared to teach inquiry with the purpose of transforming and analyzing data, and interpreting graphical representations? That is, are preservice science teachers prepared to teach data analysis and graph interpretation practices that scientists use by default in their everyday work? The present study was designed to answer these and related questions. We investigated the responses of preservice elementary and secondary science teachers to data and graph interpretation tasks. Our investigation shows that, despite considerable preparation, and for many, despite bachelor of science degrees, preservice teachers do not enact the (authentic) practices that scientists routinely do when asked to interpret data or graphs. Detailed analyses are provided of what data and graph interpretation practices actually were enacted. We conclude that traditional schooling emphasizes particular beliefs in the mathematical nature of the universe that make it difficult for many individuals to deal with data possessing the random variation found in measurements of natural phenomena. The results suggest that preservice teachers need more experience in engaging in data and graph interpretation practices originating in activities that provide the degree of variation in and complexity of data present in realistic investigations.

Analysis Tools for Interconnected Boolean Networks With Biological Applications.

PubMed

Chaves, Madalena; Tournier, Laurent

2018-01-01

Boolean networks with asynchronous updates are a class of logical models particularly well adapted to describe the dynamics of biological networks with uncertain measures. The state space of these models can be described by an asynchronous state transition graph, which represents all the possible exits from every single state, and gives a global image of all the possible trajectories of the system. In addition, the asynchronous state transition graph can be associated with an absorbing Markov chain, further providing a semi-quantitative framework where it becomes possible to compute probabilities for the different trajectories. For large networks, however, such direct analyses become computationally untractable, given the exponential dimension of the graph. Exploiting the general modularity of biological systems, we have introduced the novel concept of asymptotic graph , computed as an interconnection of several asynchronous transition graphs and recovering all asymptotic behaviors of a large interconnected system from the behavior of its smaller modules. From a modeling point of view, the interconnection of networks is very useful to address for instance the interplay between known biological modules and to test different hypotheses on the nature of their mutual regulatory links. This paper develops two new features of this general methodology: a quantitative dimension is added to the asymptotic graph, through the computation of relative probabilities for each final attractor and a companion cross-graph is introduced to complement the method on a theoretical point of view.

Software for illustrative presentation of basic clinical characteristics of laboratory tests--GraphROC for Windows.

PubMed

Kairisto, V; Poola, A

1995-01-01

GraphROC for Windows is a program for clinical test evaluation. It was designed for the handling of large datasets obtained from clinical laboratory databases. In the user interface, graphical and numerical presentations are combined. For simplicity, numerical data is not shown unless requested. Relevant numbers can be "picked up" from the graph by simple mouse operations. Reference distributions can be displayed by using automatically optimized bin widths. Any percentile of the distribution with corresponding confidence limits can be chosen for display. In sensitivity-specificity analysis, both illness- and health-related distributions are shown in the same graph. The following data for any cutoff limit can be shown in a separate click window: clinical sensitivity and specificity with corresponding confidence limits, positive and negative likelihood ratios, positive and negative predictive values and efficiency. Predictive values and clinical efficiency of the cutoff limit can be updated for any prior probability of disease. Receiver Operating Characteristics (ROC) curves can be generated and combined into the same graph for comparison of several different tests. The area under the curve with corresponding confidence interval is calculated for each ROC curve. Numerical results of analyses and graphs can be printed or exported to other Microsoft Windows programs. GraphROC for Windows also employs a new method, developed by us, for the indirect estimation of health-related limits and change limits from mixed distributions of clinical laboratory data.

Frog: Asynchronous Graph Processing on GPU with Hybrid Coloring Model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shi, Xuanhua; Luo, Xuan; Liang, Junling

GPUs have been increasingly used to accelerate graph processing for complicated computational problems regarding graph theory. Many parallel graph algorithms adopt the asynchronous computing model to accelerate the iterative convergence. Unfortunately, the consistent asynchronous computing requires locking or atomic operations, leading to significant penalties/overheads when implemented on GPUs. As such, coloring algorithm is adopted to separate the vertices with potential updating conflicts, guaranteeing the consistency/correctness of the parallel processing. Common coloring algorithms, however, may suffer from low parallelism because of a large number of colors generally required for processing a large-scale graph with billions of vertices. We propose a light-weightmore » asynchronous processing framework called Frog with a preprocessing/hybrid coloring model. The fundamental idea is based on Pareto principle (or 80-20 rule) about coloring algorithms as we observed through masses of realworld graph coloring cases. We find that a majority of vertices (about 80%) are colored with only a few colors, such that they can be read and updated in a very high degree of parallelism without violating the sequential consistency. Accordingly, our solution separates the processing of the vertices based on the distribution of colors. In this work, we mainly answer three questions: (1) how to partition the vertices in a sparse graph with maximized parallelism, (2) how to process large-scale graphs that cannot fit into GPU memory, and (3) how to reduce the overhead of data transfers on PCIe while processing each partition. We conduct experiments on real-world data (Amazon, DBLP, YouTube, RoadNet-CA, WikiTalk and Twitter) to evaluate our approach and make comparisons with well-known non-preprocessed (such as Totem, Medusa, MapGraph and Gunrock) and preprocessed (Cusha) approaches, by testing four classical algorithms (BFS, PageRank, SSSP and CC). On all the tested applications and datasets, Frog is able to significantly outperform existing GPU-based graph processing systems except Gunrock and MapGraph. MapGraph gets better performance than Frog when running BFS on RoadNet-CA. The comparison between Gunrock and Frog is inconclusive. Frog can outperform Gunrock more than 1.04X when running PageRank and SSSP, while the advantage of Frog is not obvious when running BFS and CC on some datasets especially for RoadNet-CA.« less

A graph theory approach to identify resonant and non-resonant transmission paths in statistical modal energy distribution analysis

NASA Astrophysics Data System (ADS)

Aragonès, Àngels; Maxit, Laurent; Guasch, Oriol

2015-08-01

Statistical modal energy distribution analysis (SmEdA) extends classical statistical energy analysis (SEA) to the mid frequency range by establishing power balance equations between modes in different subsystems. This circumvents the SEA requirement of modal energy equipartition and enables applying SmEdA to the cases of low modal overlap, locally excited subsystems and to deal with complex heterogeneous subsystems as well. Yet, widening the range of application of SEA is done at a price with large models because the number of modes per subsystem can become considerable when the frequency increases. Therefore, it would be worthwhile to have at one's disposal tools for a quick identification and ranking of the resonant and non-resonant paths involved in modal energy transmission between subsystems. It will be shown that previously developed graph theory algorithms for transmission path analysis (TPA) in SEA can be adapted to SmEdA and prove useful for that purpose. The case of airborne transmission between two cavities separated apart by homogeneous and ribbed plates will be first addressed to illustrate the potential of the graph approach. A more complex case representing transmission between non-contiguous cavities in a shipbuilding structure will be also presented.

A Hybrid Parallel Strategy Based on String Graph Theory to Improve De Novo DNA Assembly on the TianHe-2 Supercomputer.

PubMed

Zhang, Feng; Liao, Xiangke; Peng, Shaoliang; Cui, Yingbo; Wang, Bingqiang; Zhu, Xiaoqian; Liu, Jie

2016-06-01

' The de novo assembly of DNA sequences is increasingly important for biological researches in the genomic era. After more than one decade since the Human Genome Project, some challenges still exist and new solutions are being explored to improve de novo assembly of genomes. String graph assembler (SGA), based on the string graph theory, is a new method/tool developed to address the challenges. In this paper, based on an in-depth analysis of SGA we prove that the SGA-based sequence de novo assembly is an NP-complete problem. According to our analysis, SGA outperforms other similar methods/tools in memory consumption, but costs much more time, of which 60-70 % is spent on the index construction. Upon this analysis, we introduce a hybrid parallel optimization algorithm and implement this algorithm in the TianHe-2's parallel framework. Simulations are performed with different datasets. For data of small size the optimized solution is 3.06 times faster than before, and for data of middle size it's 1.60 times. The results demonstrate an evident performance improvement, with the linear scalability for parallel FM-index construction. This results thus contribute significantly to improving the efficiency of de novo assembly of DNA sequences.

Insights into Intrinsic Brain Networks based on Graph Theory and PET in right- compared to left-sided Temporal Lobe Epilepsy.

PubMed

Vanicek, Thomas; Hahn, Andreas; Traub-Weidinger, Tatjana; Hilger, Eva; Spies, Marie; Wadsak, Wolfgang; Lanzenberger, Rupert; Pataraia, Ekaterina; Asenbaum-Nan, Susanne

2016-06-28

The human brain exhibits marked hemispheric differences, though it is not fully understood to what extent lateralization of the epileptic focus is relevant. Preoperative [(18)F]FDG-PET depicts lateralization of seizure focus in patients with temporal lobe epilepsy and reveals dysfunctional metabolic brain connectivity. The aim of the present study was to compare metabolic connectivity, inferred from inter-regional [(18)F]FDG PET uptake correlations, in right-sided (RTLE; n = 30) and left-sided TLE (LTLE; n = 32) with healthy controls (HC; n = 31) using graph theory based network analysis. Comparing LTLE and RTLE and patient groups separately to HC, we observed higher lobar connectivity weights in RTLE compared to LTLE for connections of the temporal and the parietal lobe of the contralateral hemisphere (CH). Moreover, especially in RTLE compared to LTLE higher local efficiency were found in the temporal cortices and other brain regions of the CH. The results of this investigation implicate altered metabolic networks in patients with TLE specific to the lateralization of seizure focus, and describe compensatory mechanisms especially in the CH of patients with RTLE. We propose that graph theoretical analysis of metabolic connectivity using [(18)F]FDG-PET offers an important additional modality to explore brain networks.

A simple rule for the evolution of cooperation on graphs and social networks.

PubMed

Ohtsuki, Hisashi; Hauert, Christoph; Lieberman, Erez; Nowak, Martin A

2006-05-25

A fundamental aspect of all biological systems is cooperation. Cooperative interactions are required for many levels of biological organization ranging from single cells to groups of animals. Human society is based to a large extent on mechanisms that promote cooperation. It is well known that in unstructured populations, natural selection favours defectors over cooperators. There is much current interest, however, in studying evolutionary games in structured populations and on graphs. These efforts recognize the fact that who-meets-whom is not random, but determined by spatial relationships or social networks. Here we describe a surprisingly simple rule that is a good approximation for all graphs that we have analysed, including cycles, spatial lattices, random regular graphs, random graphs and scale-free networks: natural selection favours cooperation, if the benefit of the altruistic act, b, divided by the cost, c, exceeds the average number of neighbours, k, which means b/c > k. In this case, cooperation can evolve as a consequence of 'social viscosity' even in the absence of reputation effects or strategic complexity.

Resource utilization model for the algorithm to architecture mapping model

NASA Technical Reports Server (NTRS)

Stoughton, John W.; Patel, Rakesh R.

1993-01-01

The analytical model for resource utilization and the variable node time and conditional node model for the enhanced ATAMM model for a real-time data flow architecture are presented in this research. The Algorithm To Architecture Mapping Model, ATAMM, is a Petri net based graph theoretic model developed at Old Dominion University, and is capable of modeling the execution of large-grained algorithms on a real-time data flow architecture. Using the resource utilization model, the resource envelope may be obtained directly from a given graph and, consequently, the maximum number of required resources may be evaluated. The node timing diagram for one iteration period may be obtained using the analytical resource envelope. The variable node time model, which describes the change in resource requirement for the execution of an algorithm under node time variation, is useful to expand the applicability of the ATAMM model to heterogeneous architectures. The model also describes a method of detecting the presence of resource limited mode and its subsequent prevention. Graphs with conditional nodes are shown to be reduced to equivalent graphs with time varying nodes and, subsequently, may be analyzed using the variable node time model to determine resource requirements. Case studies are performed on three graphs for the illustration of applicability of the analytical theories.

Resistance and relatedness on an evolutionary graph

PubMed Central

Maciejewski, Wes

2012-01-01

When investigating evolution in structured populations, it is often convenient to consider the population as an evolutionary graph—individuals as nodes, and whom they may act with as edges. There has, in recent years, been a surge of interest in evolutionary graphs, especially in the study of the evolution of social behaviours. An inclusive fitness framework is best suited for this type of study. A central requirement for an inclusive fitness analysis is an expression for the genetic similarity between individuals residing on the graph. This has been a major hindrance for work in this area as highly technical mathematics are often required. Here, I derive a result that links genetic relatedness between haploid individuals on an evolutionary graph to the resistance between vertices on a corresponding electrical network. An example that demonstrates the potential computational advantage of this result over contemporary approaches is provided. This result offers more, however, to the study of population genetics than strictly computationally efficient methods. By establishing a link between gene transfer and electric circuit theory, conceptualizations of the latter can enhance understanding of the former. PMID:21849384

Self-similarity analysis of eubacteria genome based on weighted graph.

PubMed

Qi, Zhao-Hui; Li, Ling; Zhang, Zhi-Meng; Qi, Xiao-Qin

2011-07-07

We introduce a weighted graph model to investigate the self-similarity characteristics of eubacteria genomes. The regular treating in similarity comparison about genome is to discover the evolution distance among different genomes. Few people focus their attention on the overall statistical characteristics of each gene compared with other genes in the same genome. In our model, each genome is attributed to a weighted graph, whose topology describes the similarity relationship among genes in the same genome. Based on the related weighted graph theory, we extract some quantified statistical variables from the topology, and give the distribution of some variables derived from the largest social structure in the topology. The 23 eubacteria recently studied by Sorimachi and Okayasu are markedly classified into two different groups by their double logarithmic point-plots describing the similarity relationship among genes of the largest social structure in genome. The results show that the proposed model may provide us with some new sights to understand the structures and evolution patterns determined from the complete genomes. Copyright © 2011 Elsevier Ltd. All rights reserved.

Delay-time distribution in the scattering of time-narrow wave packets (II)—quantum graphs

NASA Astrophysics Data System (ADS)

Smilansky, Uzy; Schanz, Holger

2018-02-01

We apply the framework developed in the preceding paper in this series (Smilansky 2017 J. Phys. A: Math. Theor. 50 215301) to compute the time-delay distribution in the scattering of ultra short radio frequency pulses on complex networks of transmission lines which are modeled by metric (quantum) graphs. We consider wave packets which are centered at high wave number and comprise many energy levels. In the limit of pulses of very short duration we compute upper and lower bounds to the actual time-delay distribution of the radiation emerging from the network using a simplified problem where time is replaced by the discrete count of vertex-scattering events. The classical limit of the time-delay distribution is also discussed and we show that for finite networks it decays exponentially, with a decay constant which depends on the graph connectivity and the distribution of its edge lengths. We illustrate and apply our theory to a simple model graph where an algebraic decay of the quantum time-delay distribution is established.

A Novel Clustering Methodology Based on Modularity Optimisation for Detecting Authorship Affinities in Shakespearean Era Plays

PubMed Central

Craig, Hugh; Berretta, Regina; Moscato, Pablo

2016-01-01

In this study we propose a novel, unsupervised clustering methodology for analyzing large datasets. This new, efficient methodology converts the general clustering problem into the community detection problem in graph by using the Jensen-Shannon distance, a dissimilarity measure originating in Information Theory. Moreover, we use graph theoretic concepts for the generation and analysis of proximity graphs. Our methodology is based on a newly proposed memetic algorithm (iMA-Net) for discovering clusters of data elements by maximizing the modularity function in proximity graphs of literary works. To test the effectiveness of this general methodology, we apply it to a text corpus dataset, which contains frequencies of approximately 55,114 unique words across all 168 written in the Shakespearean era (16th and 17th centuries), to analyze and detect clusters of similar plays. Experimental results and comparison with state-of-the-art clustering methods demonstrate the remarkable performance of our new method for identifying high quality clusters which reflect the commonalities in the literary style of the plays. PMID:27571416

The Laplacian spectrum of neural networks

PubMed Central

de Lange, Siemon C.; de Reus, Marcel A.; van den Heuvel, Martijn P.

2014-01-01

The brain is a complex network of neural interactions, both at the microscopic and macroscopic level. Graph theory is well suited to examine the global network architecture of these neural networks. Many popular graph metrics, however, encode average properties of individual network elements. Complementing these “conventional” graph metrics, the eigenvalue spectrum of the normalized Laplacian describes a network's structure directly at a systems level, without referring to individual nodes or connections. In this paper, the Laplacian spectra of the macroscopic anatomical neuronal networks of the macaque and cat, and the microscopic network of the Caenorhabditis elegans were examined. Consistent with conventional graph metrics, analysis of the Laplacian spectra revealed an integrative community structure in neural brain networks. Extending previous findings of overlap of network attributes across species, similarity of the Laplacian spectra across the cat, macaque and C. elegans neural networks suggests a certain level of consistency in the overall architecture of the anatomical neural networks of these species. Our results further suggest a specific network class for neural networks, distinct from conceptual small-world and scale-free models as well as several empirical networks. PMID:24454286

Tensor Spectral Clustering for Partitioning Higher-order Network Structures.

PubMed

Benson, Austin R; Gleich, David F; Leskovec, Jure

2015-01-01

Spectral graph theory-based methods represent an important class of tools for studying the structure of networks. Spectral methods are based on a first-order Markov chain derived from a random walk on the graph and thus they cannot take advantage of important higher-order network substructures such as triangles, cycles, and feed-forward loops. Here we propose a Tensor Spectral Clustering (TSC) algorithm that allows for modeling higher-order network structures in a graph partitioning framework. Our TSC algorithm allows the user to specify which higher-order network structures (cycles, feed-forward loops, etc.) should be preserved by the network clustering. Higher-order network structures of interest are represented using a tensor, which we then partition by developing a multilinear spectral method. Our framework can be applied to discovering layered flows in networks as well as graph anomaly detection, which we illustrate on synthetic networks. In directed networks, a higher-order structure of particular interest is the directed 3-cycle, which captures feedback loops in networks. We demonstrate that our TSC algorithm produces large partitions that cut fewer directed 3-cycles than standard spectral clustering algorithms.

Tensor Spectral Clustering for Partitioning Higher-order Network Structures

PubMed Central

Benson, Austin R.; Gleich, David F.; Leskovec, Jure

2016-01-01

Spectral graph theory-based methods represent an important class of tools for studying the structure of networks. Spectral methods are based on a first-order Markov chain derived from a random walk on the graph and thus they cannot take advantage of important higher-order network substructures such as triangles, cycles, and feed-forward loops. Here we propose a Tensor Spectral Clustering (TSC) algorithm that allows for modeling higher-order network structures in a graph partitioning framework. Our TSC algorithm allows the user to specify which higher-order network structures (cycles, feed-forward loops, etc.) should be preserved by the network clustering. Higher-order network structures of interest are represented using a tensor, which we then partition by developing a multilinear spectral method. Our framework can be applied to discovering layered flows in networks as well as graph anomaly detection, which we illustrate on synthetic networks. In directed networks, a higher-order structure of particular interest is the directed 3-cycle, which captures feedback loops in networks. We demonstrate that our TSC algorithm produces large partitions that cut fewer directed 3-cycles than standard spectral clustering algorithms. PMID:27812399

Contact tracing for the control of infectious disease epidemics: Chronic Wasting Disease in deer farms.

PubMed

Rorres, Chris; Romano, Maria; Miller, Jennifer A; Mossey, Jana M; Grubesic, Tony H; Zellner, David E; Smith, Gary

2018-06-01

Contact tracing is a crucial component of the control of many infectious diseases, but is an arduous and time consuming process. Procedures that increase the efficiency of contact tracing increase the chance that effective controls can be implemented sooner and thus reduce the magnitude of the epidemic. We illustrate a procedure using Graph Theory in the context of infectious disease epidemics of farmed animals in which the epidemics are driven mainly by the shipment of animals between farms. Specifically, we created a directed graph of the recorded shipments of deer between deer farms in Pennsylvania over a timeframe and asked how the properties of the graph could be exploited to make contact tracing more efficient should Chronic Wasting Disease (a prion disease of deer) be discovered in one of the farms. We show that the presence of a large strongly connected component in the graph has a significant impact on the number of contacts that can arise. Copyright © 2017 The Authors. Published by Elsevier B.V. All rights reserved.

Exciton-phonon system on a star graph: A perturbative approach.

PubMed

Yalouz, Saad; Pouthier, Vincent

2016-05-01

Based on the operatorial formulation of the perturbation theory, the properties of an exciton coupled with optical phonons on a star graph are investigated. Within this method, the dynamics is governed by an effective Hamiltonian, which accounts for exciton-phonon entanglement. The exciton is dressed by a virtual phonon cloud whereas the phonons are clothed by virtual excitonic transitions. In spite of the coupling with the phonons, it is shown that the energy spectrum of the dressed exciton resembles that of a bare exciton. The only differences originate in a polaronic mechanism that favors an energy shift and a decay of the exciton hopping constant. By contrast, the motion of the exciton allows the phonons to propagate over the graph so that the dressed normal modes drastically differ from the localized modes associated to bare phonons. They define extended vibrations whose properties depend on the state occupied by the exciton that accompanies the phonons. It is shown that the phonon frequencies, either red shifted or blue shifted, are very sensitive to the model parameter in general, and to the size of the graph in particular.

Exploratory Item Classification Via Spectral Graph Clustering

PubMed Central

Chen, Yunxiao; Li, Xiaoou; Liu, Jingchen; Xu, Gongjun; Ying, Zhiliang

2017-01-01

Large-scale assessments are supported by a large item pool. An important task in test development is to assign items into scales that measure different characteristics of individuals, and a popular approach is cluster analysis of items. Classical methods in cluster analysis, such as the hierarchical clustering, K-means method, and latent-class analysis, often induce a high computational overhead and have difficulty handling missing data, especially in the presence of high-dimensional responses. In this article, the authors propose a spectral clustering algorithm for exploratory item cluster analysis. The method is computationally efficient, effective for data with missing or incomplete responses, easy to implement, and often outperforms traditional clustering algorithms in the context of high dimensionality. The spectral clustering algorithm is based on graph theory, a branch of mathematics that studies the properties of graphs. The algorithm first constructs a graph of items, characterizing the similarity structure among items. It then extracts item clusters based on the graphical structure, grouping similar items together. The proposed method is evaluated through simulations and an application to the revised Eysenck Personality Questionnaire. PMID:29033476

Altered brain network measures in patients with primary writing tremor.

PubMed

Lenka, Abhishek; Jhunjhunwala, Ketan Ramakant; Panda, Rajanikant; Saini, Jitender; Bharath, Rose Dawn; Yadav, Ravi; Pal, Pramod Kumar

2017-10-01

Primary writing tremor (PWT) is a rare task-specific tremor, which occurs only while writing or while adopting the hand in the writing position. The basic pathophysiology of PWT has not been fully understood. The objective of this study is to explore the alterations in the resting state functional brain connectivity, if any, in patients with PWT using graph theory-based analysis. This prospective case-control study included 10 patients with PWT and 10 age and gender matched healthy controls. All subjects underwent MRI in a 3-Tesla scanner. Several parameters of small-world functional connectivity were compared between patients and healthy controls by using graph theory-based analysis. There were no significant differences in age, handedness (all right handed), gender distribution (all were males), and MMSE scores between the patients and controls. The mean age at presentation of tremor in the patient group was 51.7 ± 8.6 years, and the mean duration of tremor was 3.5 ± 1.9 years. Graph theory-based analysis revealed that patients with PWT had significantly lower clustering coefficient and higher path length compared to healthy controls suggesting alterations in small-world architecture of the brain. The clustering coefficients were lower in PWT patients in left and right medial cerebellum, right dorsolateral prefrontal cortex (DLPFC), and left posterior parietal cortex (PPC). Patients with PWT have significantly altered small-world brain connectivity in bilateral medial cerebellum, right DLPFC, and left PPC. Further studies with larger sample size are required to confirm our results.

Enhanced Visualization of Subtle Outer Retinal Pathology by En Face Optical Coherence Tomography and Correlation with Multi-Modal Imaging

PubMed Central

Chew, Avenell L.; Lamey, Tina; McLaren, Terri; De Roach, John

2016-01-01

Purpose To present en face optical coherence tomography (OCT) images generated by graph-search theory algorithm-based custom software and examine correlation with other imaging modalities. Methods En face OCT images derived from high density OCT volumetric scans of 3 healthy subjects and 4 patients using a custom algorithm (graph-search theory) and commercial software (Heidelberg Eye Explorer software (Heidelberg Engineering)) were compared and correlated with near infrared reflectance, fundus autofluorescence, adaptive optics flood-illumination ophthalmoscopy (AO-FIO) and microperimetry. Results Commercial software was unable to generate accurate en face OCT images in eyes with retinal pigment epithelium (RPE) pathology due to segmentation error at the level of Bruch’s membrane (BM). Accurate segmentation of the basal RPE and BM was achieved using custom software. The en face OCT images from eyes with isolated interdigitation or ellipsoid zone pathology were of similar quality between custom software and Heidelberg Eye Explorer software in the absence of any other significant outer retinal pathology. En face OCT images demonstrated angioid streaks, lesions of acute macular neuroretinopathy, hydroxychloroquine toxicity and Bietti crystalline deposits that correlated with other imaging modalities. Conclusions Graph-search theory algorithm helps to overcome the limitations of outer retinal segmentation inaccuracies in commercial software. En face OCT images can provide detailed topography of the reflectivity within a specific layer of the retina which correlates with other forms of fundus imaging. Our results highlight the need for standardization of image reflectivity to facilitate quantification of en face OCT images and longitudinal analysis. PMID:27959968

Applied spectrophotometry: analysis of a biochemical mixture.

PubMed

Trumbo, Toni A; Schultz, Emeric; Borland, Michael G; Pugh, Michael Eugene

2013-01-01

Spectrophotometric analysis is essential for determining biomolecule concentration of a solution and is employed ubiquitously in biochemistry and molecular biology. The application of the Beer-Lambert-Bouguer Lawis routinely used to determine the concentration of DNA, RNA or protein. There is however a significant difference in determining the concentration of a given species (RNA, DNA, protein) in isolation (a contrived circumstance) as opposed to determining that concentration in the presence of other species (a more realistic situation). To present the student with a more realistic laboratory experience and also to fill a hole that we believe exists in student experience prior to reaching a biochemistry course, we have devised a three week laboratory experience designed so that students learn to: connect laboratory practice with theory, apply the Beer-Lambert-Bougert Law to biochemical analyses, demonstrate the utility and limitations of example quantitative colorimetric assays, demonstrate the utility and limitations of UV analyses for biomolecules, develop strategies for analysis of a solution of unknown biomolecular composition, use digital micropipettors to make accurate and precise measurements, and apply graphing software. Copyright © 2013 Wiley Periodicals, Inc.

37 CFR 104.1 - Definitions.

Code of Federal Regulations, 2010 CFR

2010-07-01

..., maps, graphs, pamphlets, notes, charts, tabulations, analyses, statistical or informational... Office. Official business means the authorized business of the Office. General Counsel means the General...

Application of graph theory to the statistical thermodynamics of lattice polymers. I. Elements of theory and test for dimers

NASA Astrophysics Data System (ADS)

Brazhnik, Olga D.; Freed, Karl F.

1996-07-01

The lattice cluster theory (LCT) is extended to enable inclusion of longer range correlation contributions to the partition function of lattice model polymers in the athermal limit. A diagrammatic technique represents the expansion of the partition function in powers of the inverse lattice coordination number. Graph theory is applied to sort, classify, and evaluate the numerous diagrams appearing in higher orders. New general theorems are proven that provide a significant reduction in the computational labor required to evaluate the contributions from higher order correlations. The new algorithm efficiently generates the correction to the Flory mean field approximation from as many as eight sterically interacting bonds. While the new results contain the essential ingredients for treating a system of flexible chains with arbitrary lengths and concentrations, the complexity of our new algorithm motivates us to test the theory here for the simplest case of a system of lattice dimers by comparison to the dimer packing entropies from the work of Gaunt. This comparison demonstrates that the eight bond LCT is exact through order φ5 for dimers in one through three dimensions, where φ is the volume fraction of dimers. A subsequent work will use the contracted diagrams, derived and tested here, to treat the packing entropy for a system of flexible N-mers at a volume fraction of φ on hypercubic lattices.