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…

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.

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.

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.

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…

Some Applications of Graph Theory to Clustering

ERIC Educational Resources Information Center

Hubert, Lawrence J.

1974-01-01

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

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

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

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 as a proxy for spatially explicit population models in conservation planning.

PubMed

Minor, Emily S; Urban, Dean L

2007-09-01

Spatially explicit population models (SEPMs) are often considered the best way to predict and manage species distributions in spatially heterogeneous landscapes. However, they are computationally intensive and require extensive knowledge of species' biology and behavior, limiting their application in many cases. An alternative to SEPMs is graph theory, which has minimal data requirements and efficient algorithms. Although only recently introduced to landscape ecology, graph theory is well suited to ecological applications concerned with connectivity or movement. This paper compares the performance of graph theory to a SEPM in selecting important habitat patches for Wood Thrush (Hylocichla mustelina) conservation. We use both models to identify habitat patches that act as population sources and persistent patches and also use graph theory to identify patches that act as stepping stones for dispersal. Correlations of patch rankings were very high between the two models. In addition, graph theory offers the ability to identify patches that are very important to habitat connectivity and thus long-term population persistence across the landscape. We show that graph theory makes very similar predictions in most cases and in other cases offers insight not available from the SEPM, and we conclude that graph theory is a suitable and possibly preferable alternative to SEPMs for species conservation in heterogeneous landscapes.

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

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.

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.

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).

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.

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.

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.

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".

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.

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.

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.

Use of graph theory measures to identify errors in record linkage.

PubMed

Randall, Sean M; Boyd, James H; Ferrante, Anna M; Bauer, Jacqueline K; Semmens, James B

2014-07-01

Ensuring high linkage quality is important in many record linkage applications. Current methods for ensuring quality are manual and resource intensive. This paper seeks to determine the effectiveness of graph theory techniques in identifying record linkage errors. A range of graph theory techniques was applied to two linked datasets, with known truth sets. The ability of graph theory techniques to identify groups containing errors was compared to a widely used threshold setting technique. This methodology shows promise; however, further investigations into graph theory techniques are required. The development of more efficient and effective methods of improving linkage quality will result in higher quality datasets that can be delivered to researchers in shorter timeframes. Copyright © 2014 Elsevier Ireland Ltd. All rights reserved.

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

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.

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.

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

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

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.…

Time-dependence of graph theory metrics in functional connectivity analysis

PubMed Central

Chiang, Sharon; Cassese, Alberto; Guindani, Michele; Vannucci, Marina; Yeh, Hsiang J.; Haneef, Zulfi; Stern, John M.

2016-01-01

Brain graphs provide a useful way to computationally model the network structure of the connectome, and this has led to increasing interest in the use of graph theory to quantitate and investigate the topological characteristics of the healthy brain and brain disorders on the network level. The majority of graph theory investigations of functional connectivity have relied on the assumption of temporal stationarity. However, recent evidence increasingly suggests that functional connectivity fluctuates over the length of the scan. In this study, we investigate the stationarity of brain network topology using a Bayesian hidden Markov model (HMM) approach that estimates the dynamic structure of graph theoretical measures of whole-brain functional connectivity. In addition to extracting the stationary distribution and transition probabilities of commonly employed graph theory measures, we propose two estimators of temporal stationarity: the S-index and N-index. These indexes can be used to quantify different aspects of the temporal stationarity of graph theory measures. We apply the method and proposed estimators to resting-state functional MRI data from healthy controls and patients with temporal lobe epilepsy. Our analysis shows that several graph theory measures, including small-world index, global integration measures, and betweenness centrality, may exhibit greater stationarity over time and therefore be more robust. Additionally, we demonstrate that accounting for subject-level differences in the level of temporal stationarity of network topology may increase discriminatory power in discriminating between disease states. Our results confirm and extend findings from other studies regarding the dynamic nature of functional connectivity, and suggest that using statistical models which explicitly account for the dynamic nature of functional connectivity in graph theory analyses may improve the sensitivity of investigations and consistency across investigations. PMID:26518632

Time-dependence of graph theory metrics in functional connectivity analysis.

PubMed

Chiang, Sharon; Cassese, Alberto; Guindani, Michele; Vannucci, Marina; Yeh, Hsiang J; Haneef, Zulfi; Stern, John M

2016-01-15

Brain graphs provide a useful way to computationally model the network structure of the connectome, and this has led to increasing interest in the use of graph theory to quantitate and investigate the topological characteristics of the healthy brain and brain disorders on the network level. The majority of graph theory investigations of functional connectivity have relied on the assumption of temporal stationarity. However, recent evidence increasingly suggests that functional connectivity fluctuates over the length of the scan. In this study, we investigate the stationarity of brain network topology using a Bayesian hidden Markov model (HMM) approach that estimates the dynamic structure of graph theoretical measures of whole-brain functional connectivity. In addition to extracting the stationary distribution and transition probabilities of commonly employed graph theory measures, we propose two estimators of temporal stationarity: the S-index and N-index. These indexes can be used to quantify different aspects of the temporal stationarity of graph theory measures. We apply the method and proposed estimators to resting-state functional MRI data from healthy controls and patients with temporal lobe epilepsy. Our analysis shows that several graph theory measures, including small-world index, global integration measures, and betweenness centrality, may exhibit greater stationarity over time and therefore be more robust. Additionally, we demonstrate that accounting for subject-level differences in the level of temporal stationarity of network topology may increase discriminatory power in discriminating between disease states. Our results confirm and extend findings from other studies regarding the dynamic nature of functional connectivity, and suggest that using statistical models which explicitly account for the dynamic nature of functional connectivity in graph theory analyses may improve the sensitivity of investigations and consistency across investigations. Copyright © 2015 Elsevier Inc. 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.

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.

Renormalization in Quantum Field Theory and the Riemann-Hilbert Problem I: The Hopf Algebra Structure of Graphs and the Main Theorem

NASA Astrophysics Data System (ADS)

Connes, Alain; Kreimer, Dirk

This paper gives a complete selfcontained proof of our result announced in [6] showing that renormalization in quantum field theory is a special instance of a general mathematical procedure of extraction of finite values based on the Riemann-Hilbert problem. We shall first show that for any quantum field theory, the combinatorics of Feynman graphs gives rise to a Hopf algebra which is commutative as an algebra. It is the dual Hopf algebra of the enveloping algebra of a Lie algebra whose basis is labelled by the one particle irreducible Feynman graphs. The Lie bracket of two such graphs is computed from insertions of one graph in the other and vice versa. The corresponding Lie group G is the group of characters of . We shall then show that, using dimensional regularization, the bare (unrenormalized) theory gives rise to a loop where C is a small circle of complex dimensions around the integer dimension D of space-time. Our main result is that the renormalized theory is just the evaluation at z=D of the holomorphic part γ+ of the Birkhoff decomposition of γ. We begin to analyse the group G and show that it is a semi-direct product of an easily understood abelian group by a highly non-trivial group closely tied up with groups of diffeomorphisms. The analysis of this latter group as well as the interpretation of the renormalization group and of anomalous dimensions are the content of our second paper with the same overall title.

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…

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.

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…

From brain topography to brain topology: relevance of graph theory to functional neuroscience.

PubMed

Minati, Ludovico; Varotto, Giulia; D'Incerti, Ludovico; Panzica, Ferruccio; Chan, Dennis

2013-07-10

Although several brain regions show significant specialization, higher functions such as cross-modal information integration, abstract reasoning and conscious awareness are viewed as emerging from interactions across distributed functional networks. Analytical approaches capable of capturing the properties of such networks can therefore enhance our ability to make inferences from functional MRI, electroencephalography and magnetoencephalography data. Graph theory is a branch of mathematics that focuses on the formal modelling of networks and offers a wide range of theoretical tools to quantify specific features of network architecture (topology) that can provide information complementing the anatomical localization of areas responding to given stimuli or tasks (topography). Explicit modelling of the architecture of axonal connections and interactions among areas can furthermore reveal peculiar topological properties that are conserved across diverse biological networks, and highly sensitive to disease states. The field is evolving rapidly, partly fuelled by computational developments that enable the study of connectivity at fine anatomical detail and the simultaneous interactions among multiple regions. Recent publications in this area have shown that graph-based modelling can enhance our ability to draw causal inferences from functional MRI experiments, and support the early detection of disconnection and the modelling of pathology spread in neurodegenerative disease, particularly Alzheimer's disease. Furthermore, neurophysiological studies have shown that network topology has a profound link to epileptogenesis and that connectivity indices derived from graph models aid in modelling the onset and spread of seizures. Graph-based analyses may therefore significantly help understand the bases of a range of neurological conditions. This review is designed to provide an overview of graph-based analyses of brain connectivity and their relevance to disease aimed principally at general neuroscientists and clinicians.

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.

Graph theory enables drug repurposing--how a mathematical model can drive the discovery of hidden mechanisms of action.

PubMed

Gramatica, Ruggero; Di Matteo, T; Giorgetti, Stefano; Barbiani, Massimo; Bevec, Dorian; Aste, Tomaso

2014-01-01

We introduce a methodology to efficiently exploit natural-language expressed biomedical knowledge for repurposing existing drugs towards diseases for which they were not initially intended. Leveraging on developments in Computational Linguistics and Graph Theory, a methodology is defined to build a graph representation of knowledge, which is automatically analysed to discover hidden relations between any drug and any disease: these relations are specific paths among the biomedical entities of the graph, representing possible Modes of Action for any given pharmacological compound. We propose a measure for the likeliness of these paths based on a stochastic process on the graph. This measure depends on the abundance of indirect paths between a peptide and a disease, rather than solely on the strength of the shortest path connecting them. We provide real-world examples, showing how the method successfully retrieves known pathophysiological Mode of Action and finds new ones by meaningfully selecting and aggregating contributions from known bio-molecular interactions. Applications of this methodology are presented, and prove the efficacy of the method for selecting drugs as treatment options for rare diseases.

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.

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

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.

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

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.

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.

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.

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.

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.

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.

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

Brain network dynamics characterization in epileptic seizures. Joint directed graph and pairwise synchronization measures

NASA Astrophysics Data System (ADS)

Rodrigues, A. C.; Machado, B. S.; Florence, G.; Hamad, A. P.; Sakamoto, A. C.; Fujita, A.; Baccalá, L. A.; Amaro, E.; Sameshima, K.

2014-12-01

Here we propose and evaluate a new approach to analyse multichannel mesial temporal lobe epilepsy EEG data from eight patients through complex network and synchronization theories. The method employs a Granger causality test to infer the directed connectivity graphs and a wavelet transform based phase synchronization measure whose characteristics allow studying dynamical transitions during epileptic seizures. We present a new combined graph measure that quantifies the level of network hub formation, called network hub out-degree, which closely reflects the level of synchronization observed during the ictus.

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.

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.

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.

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.

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.

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…

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.

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.

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.

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.

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

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.

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.

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.

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.

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

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 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 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.

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.

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.

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.

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.

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.

Using graph theory to quantify coarse sediment connectivity in alpine geosystems

NASA Astrophysics Data System (ADS)

Heckmann, Tobias; Thiel, Markus; Schwanghart, Wolfgang; Haas, Florian; Becht, Michael

2010-05-01

Networks are a common object of study in various disciplines. Among others, informatics, sociology, transportation science, economics and ecology frequently deal with objects which are linked with other objects to form a network. Despite this wide thematic range, a coherent formal basis to represent, measure and model the relational structure of models exists. The mathematical model for networks of all kinds is a graph which can be analysed using the tools of mathematical graph theory. In a graph model of a generic system, system components are represented by graph nodes, and the linkages between them are formed by graph edges. The latter may represent all kinds of linkages, from matter or energy fluxes to functional relations. To some extent, graph theory has been used in geosciences and related disciplines; in hydrology and fluvial geomorphology, for example, river networks have been modeled and analysed as graphs. An important issue in hydrology is the hydrological connectivity which determines if runoff generated on some area reaches the channel network. In ecology, a number of graph-theoretical indices is applicable to describing the influence of habitat distribution and landscape fragmentation on population structure and species mobility. In these examples, the mobility of matter (water, sediment, animals) through a system is an important consequence of system structure, i.e. the location and topology of its components as well as of properties of linkages between them. In geomorphology, sediment connectivity relates to the potential of sediment particles to move through the catchment. As a system property, connectivity depends, for example, on the degree to which hillslopes within a catchment are coupled to the channel system (lateral coupling), and to which channel reaches are coupled to each other (longitudinal coupling). In the present study, numerical GIS-based models are used to investigate the coupling of geomorphic process units by delineating the process domains of important geomorphic processes in a high-mountain environment (rockfall, slope-type debris flows, slope aquatic and fluvial processes). The results are validated by field mapping; they show that only small parts of a catchment are actually coupled to its outlet with respect to coarse (bedload) sediment. The models not only generate maps of the spatial extent and geomorphic activity of the aforementioned processes, they also output so-called edge lists that can be converted to adjacency matrices and graphs. Graph theory is then employed to explore ‘local' (i.e. referring to single nodes or edges) and ‘global' (i.e. system-wide, referring to the whole graph) measures that can be used to quantify coarse sediment connectivity. Such a quantification will complement the mainly qualitative appraisal of coupling and connectivity; the effect of connectivity on catchment properties such as specific sediment yield and catchment sensitivity will then be studied on the basis of quantitative measures.

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)

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

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…

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.

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 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.

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.

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

[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).

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.

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.

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.

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…

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.

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.

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.

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.

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

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".

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.

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.

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.

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

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.

On the complex interplay between learning and dynamics in life sciences. Comment on the paper "Collective learning modeling based on the kinetic theory of active particles" by Burini et al.

NASA Astrophysics Data System (ADS)

Bellomo, Nicola; Elaiw, Ahmed; Alghamdi, Mohamed Ali

2016-03-01

The paper by Burini, De Lillo, and Gibelli [8] presents an overview and critical analysis of the literature on the modeling of learning dynamics. The first reference is the celebrated paper by Cucker and Smale [9]. Then, the authors also propose their own approach, based on suitable development of methods of the kinetic theory [6] and theoretical tools of evolutionary game theory [12,13], recently developed on graphs [2].

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.

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

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.

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…

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.

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.

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

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).

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.

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.

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.

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)

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.

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…

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.

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.

A novel conductivity mechanism of highly disordered carbon systems based on an investigation of graph zeta function

NASA Astrophysics Data System (ADS)

Matsutani, Shigeki; Sato, Iwao

2017-09-01

In the previous report (Matsutani and Suzuki, 2000 [21]), by proposing the mechanism under which electric conductivity is caused by the activational hopping conduction with the Wigner surmise of the level statistics, the temperature-dependent of electronic conductivity of a highly disordered carbon system was evaluated including apparent metal-insulator transition. Since the system consists of small pieces of graphite, it was assumed that the reason why the level statistics appears is due to the behavior of the quantum chaos in each granular graphite. In this article, we revise the assumption and show another origin of the Wigner surmise, which is more natural for the carbon system based on a recent investigation of graph zeta function in graph theory. Our method can be applied to the statistical treatment of the electronic properties of the randomized molecular system in general.

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.

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

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

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

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.

Using Graph Components Derived from an Associative Concept Dictionary to Predict fMRI Neural Activation Patterns that Represent the Meaning of Nouns.

PubMed

Akama, Hiroyuki; Miyake, Maki; Jung, Jaeyoung; Murphy, Brian

2015-01-01

In this study, we introduce an original distance definition for graphs, called the Markov-inverse-F measure (MiF). This measure enables the integration of classical graph theory indices with new knowledge pertaining to structural feature extraction from semantic networks. MiF improves the conventional Jaccard and/or Simpson indices, and reconciles both the geodesic information (random walk) and co-occurrence adjustment (degree balance and distribution). We measure the effectiveness of graph-based coefficients through the application of linguistic graph information for a neural activity recorded during conceptual processing in the human brain. Specifically, the MiF distance is computed between each of the nouns used in a previous neural experiment and each of the in-between words in a subgraph derived from the Edinburgh Word Association Thesaurus of English. From the MiF-based information matrix, a machine learning model can accurately obtain a scalar parameter that specifies the degree to which each voxel in (the MRI image of) the brain is activated by each word or each principal component of the intermediate semantic features. Furthermore, correlating the voxel information with the MiF-based principal components, a new computational neurolinguistics model with a network connectivity paradigm is created. This allows two dimensions of context space to be incorporated with both semantic and neural distributional representations.

PDB2Graph: A toolbox for identifying critical amino acids map in proteins based on graph theory.

PubMed

Niknam, Niloofar; Khakzad, Hamed; Arab, Seyed Shahriar; Naderi-Manesh, Hossein

2016-05-01

The integrative and cooperative nature of protein structure involves the assessment of topological and global features of constituent parts. Network concept takes complete advantage of both of these properties in the analysis concomitantly. High compatibility to structural concepts or physicochemical properties in addition to exploiting a remarkable simplification in the system has made network an ideal tool to explore biological systems. There are numerous examples in which different protein structural and functional characteristics have been clarified by the network approach. Here, we present an interactive and user-friendly Matlab-based toolbox, PDB2Graph, devoted to protein structure network construction, visualization, and analysis. Moreover, PDB2Graph is an appropriate tool for identifying critical nodes involved in protein structural robustness and function based on centrality indices. It maps critical amino acids in protein networks and can greatly aid structural biologists in selecting proper amino acid candidates for manipulating protein structures in a more reasonable and rational manner. To introduce the capability and efficiency of PDB2Graph in detail, the structural modification of Calmodulin through allosteric binding of Ca(2+) is considered. In addition, a mutational analysis for three well-identified model proteins including Phage T4 lysozyme, Barnase and Ribonuclease HI, was performed to inspect the influence of mutating important central residues on protein activity. Copyright © 2016 Elsevier Ltd. All rights reserved.

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.

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.

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…

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,∞).

Hemispheric asymmetry of electroencephalography-based functional brain networks.

PubMed

Jalili, Mahdi

2014-11-12

Electroencephalography (EEG)-based functional brain networks have been investigated frequently in health and disease. It has been shown that a number of graph theory metrics are disrupted in brain disorders. EEG-based brain networks are often studied in the whole-brain framework, where all the nodes are grouped into a single network. In this study, we studied the brain networks in two hemispheres and assessed whether there are any hemispheric-specific patterns in the properties of the networks. To this end, resting state closed-eyes EEGs from 44 healthy individuals were processed and the network structures were extracted separately for each hemisphere. We examined neurophysiologically meaningful graph theory metrics: global and local efficiency measures. The global efficiency did not show any hemispheric asymmetry, whereas the local connectivity showed rightward asymmetry for a range of intermediate density values for the constructed networks. Furthermore, the age of the participants showed significant direct correlations with the global efficiency of the left hemisphere, but only in the right hemisphere, with local connectivity. These results suggest that only local connectivity of EEG-based functional networks is associated with brain hemispheres.

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.

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.

Network-based machine learning and graph theory algorithms for precision oncology.

PubMed

Zhang, Wei; Chien, Jeremy; Yong, Jeongsik; Kuang, Rui

2017-01-01

Network-based analytics plays an increasingly important role in precision oncology. Growing evidence in recent studies suggests that cancer can be better understood through mutated or dysregulated pathways or networks rather than individual mutations and that the efficacy of repositioned drugs can be inferred from disease modules in molecular networks. This article reviews network-based machine learning and graph theory algorithms for integrative analysis of personal genomic data and biomedical knowledge bases to identify tumor-specific molecular mechanisms, candidate targets and repositioned drugs for personalized treatment. The review focuses on the algorithmic design and mathematical formulation of these methods to facilitate applications and implementations of network-based analysis in the practice of precision oncology. We review the methods applied in three scenarios to integrate genomic data and network models in different analysis pipelines, and we examine three categories of network-based approaches for repositioning drugs in drug-disease-gene networks. In addition, we perform a comprehensive subnetwork/pathway analysis of mutations in 31 cancer genome projects in the Cancer Genome Atlas and present a detailed case study on ovarian cancer. Finally, we discuss interesting observations, potential pitfalls and future directions in network-based precision oncology.

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.

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

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.

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.

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.

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.

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.

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)

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

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.

Historical contingency in fluviokarst landscape evolution

NASA Astrophysics Data System (ADS)

Phillips, Jonathan D.

2018-02-01

Lateral and vertical erosion at meander bends in the Kentucky River gorge area has created a series of strath terraces on the interior of incised meander bends. These represent a chronosequence of fluviokarst landscape evolution from the youngest valley side transition zone near the valley bottom to the oldest upland surface. This five-part chronosequence (not including the active river channel and floodplain) was analyzed in terms of the landforms that occur at each stage or surface. These include dolines, uvalas, karst valleys, pocket valleys, unincised channels, incised channels, and cliffs (smaller features such as swallets and shafts also occur). Landform coincidence analysis shows higher coincidence indices (CI) than would be expected based on an idealized chronosequence. CI values indicate genetic relationships (common causality) among some landforms and unexpected persistence of some features on older surfaces. The idealized and two observed chronosequences were also represented as graphs and analyzed using algebraic graph theory. The two field sites yielded graphs more complex and with less historical contingency than the idealized sequence. Indeed, some of the spectral graph measures for the field sites more closely approximate a purely hypothetical no-historical-contingency benchmark graph. The deviations of observations from the idealized expectations, and the high levels of graph complexity both point to potential transitions among landform types as being the dominant phenomenon, rather than canalization along a particular evolutionary pathway. As the base level of both the fluvial and karst landforms is lowered as the meanders expand, both fluvial and karst denudation are rejuvenated, and landform transitions remain active.

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.

Analytical transmissibility based transfer path analysis for multi-energy-domain systems using four-pole parameter theory

NASA Astrophysics Data System (ADS)

Mashayekhi, Mohammad Jalali; Behdinan, Kamran

2017-10-01

The increasing demand to minimize undesired vibration and noise levels in several high-tech industries has generated a renewed interest in vibration transfer path analysis. Analyzing vibration transfer paths within a system is of crucial importance in designing an effective vibration isolation strategy. Most of the existing vibration transfer path analysis techniques are empirical which are suitable for diagnosis and troubleshooting purpose. The lack of an analytical transfer path analysis to be used in the design stage is the main motivation behind this research. In this paper an analytical transfer path analysis based on the four-pole theory is proposed for multi-energy-domain systems. Bond graph modeling technique which is an effective approach to model multi-energy-domain systems is used to develop the system model. In this paper an electro-mechanical system is used as a benchmark example to elucidate the effectiveness of the proposed technique. An algorithm to obtain the equivalent four-pole representation of a dynamical systems based on the corresponding bond graph model is also presented in this paper.

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

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

Cartographic generalization of urban street networks based on gravitational field theory

NASA Astrophysics Data System (ADS)

Liu, Gang; Li, Yongshu; Li, Zheng; Guo, Jiawei

2014-05-01

The automatic generalization of urban street networks is a constant and important aspect of geographical information science. Previous studies show that the dual graph for street-street relationships more accurately reflects the overall morphological properties and importance of streets than do other methods. In this study, we construct a dual graph to represent street-street relationship and propose an approach to generalize street networks based on gravitational field theory. We retain the global structural properties and topological connectivity of an original street network and borrow from gravitational field theory to define the gravitational force between nodes. The concept of multi-order neighbors is introduced and the gravitational force is taken as the measure of the importance contribution between nodes. The importance of a node is defined as the result of the interaction between a given node and its multi-order neighbors. Degree distribution is used to evaluate the level of maintaining the global structure and topological characteristics of a street network and to illustrate the efficiency of the suggested method. Experimental results indicate that the proposed approach can be used in generalizing street networks and retaining their density characteristics, connectivity and global structure.

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)

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.

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.

Applying graph theory to protein structures: an atlas of coiled coils.

PubMed

Heal, Jack W; Bartlett, Gail J; Wood, Christopher W; Thomson, Andrew R; Woolfson, Derek N

2018-05-02

To understand protein structure, folding and function fully and to design proteins de novo reliably, we must learn from natural protein structures that have been characterised experimentally. The number of protein structures available is large and growing exponentially, which makes this task challenging. Indeed, computational resources are becoming increasingly important for classifying and analysing this resource. Here, we use tools from graph theory to define an atlas classification scheme for automatically categorising certain protein substructures. Focusing on the α-helical coiled coils, which are ubiquitous protein-structure and protein-protein interaction motifs, we present a suite of computational resources designed for analysing these assemblies. iSOCKET enables interactive analysis of side-chain packing within proteins to identify coiled coils automatically and with considerable user control. Applying a graph theory-based atlas classification scheme to structures identified by iSOCKET gives the Atlas of Coiled Coils, a fully automated, updated overview of extant coiled coils. The utility of this approach is illustrated with the first formal classification of an emerging subclass of coiled coils called α-helical barrels. Furthermore, in the Atlas, the known coiled-coil universe is presented alongside a partial enumeration of the 'dark matter' of coiled-coil structures; i.e., those coiled-coil architectures that are theoretically possible but have not been observed to date, and thus present defined targets for protein design. iSOCKET is available as part of the open-source GitHub repository associated with this work (https://github.com/woolfson-group/isocket). This repository also contains all the data generated when classifying the protein graphs. The Atlas of Coiled Coils is available at: http://coiledcoils.chm.bris.ac.uk/atlas/app.

Efficient Graph-Based Resource Allocation Scheme Using Maximal Independent Set for Randomly- Deployed Small Star Networks

PubMed Central

Zhou, Jian; Wang, Lusheng; Wang, Weidong; Zhou, Qingfeng

2017-01-01

In future scenarios of heterogeneous and dense networks, randomly-deployed small star networks (SSNs) become a key paradigm, whose system performance is restricted to inter-SSN interference and requires an efficient resource allocation scheme for interference coordination. Traditional resource allocation schemes do not specifically focus on this paradigm and are usually too time consuming in dense networks. In this article, a very efficient graph-based scheme is proposed, which applies the maximal independent set (MIS) concept in graph theory to help divide SSNs into almost interference-free groups. We first construct an interference graph for the system based on a derived distance threshold indicating for any pair of SSNs whether there is intolerable inter-SSN interference or not. Then, SSNs are divided into MISs, and the same resource can be repetitively used by all the SSNs in each MIS. Empirical parameters and equations are set in the scheme to guarantee high performance. Finally, extensive scenarios both dense and nondense are randomly generated and simulated to demonstrate the performance of our scheme, indicating that it outperforms the classical max K-cut-based scheme in terms of system capacity, utility and especially time cost. Its achieved system capacity, utility and fairness can be close to the near-optimal strategy obtained by a time-consuming simulated annealing search. PMID:29113109

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.

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

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

Quantification of three-dimensional cell-mediated collagen remodeling using graph theory.

PubMed

Bilgin, Cemal Cagatay; Lund, Amanda W; Can, Ali; Plopper, George E; Yener, Bülent

2010-09-30

Cell cooperation is a critical event during tissue development. We present the first precise metrics to quantify the interaction between mesenchymal stem cells (MSCs) and extra cellular matrix (ECM). In particular, we describe cooperative collagen alignment process with respect to the spatio-temporal organization and function of mesenchymal stem cells in three dimensions. We defined two precise metrics: Collagen Alignment Index and Cell Dissatisfaction Level, for quantitatively tracking type I collagen and fibrillogenesis remodeling by mesenchymal stem cells over time. Computation of these metrics was based on graph theory and vector calculus. The cells and their three dimensional type I collagen microenvironment were modeled by three dimensional cell-graphs and collagen fiber organization was calculated from gradient vectors. With the enhancement of mesenchymal stem cell differentiation, acceleration through different phases was quantitatively demonstrated. The phases were clustered in a statistically significant manner based on collagen organization, with late phases of remodeling by untreated cells clustering strongly with early phases of remodeling by differentiating cells. The experiments were repeated three times to conclude that the metrics could successfully identify critical phases of collagen remodeling that were dependent upon cooperativity within the cell population. Definition of early metrics that are able to predict long-term functionality by linking engineered tissue structure to function is an important step toward optimizing biomaterials for the purposes of regenerative medicine.

GDSCalc: A Web-Based Application for Evaluating Discrete Graph Dynamical Systems

PubMed Central

Elmeligy Abdelhamid, Sherif H.; Kuhlman, Chris J.; Marathe, Madhav V.; Mortveit, Henning S.; Ravi, S. S.

2015-01-01

Discrete dynamical systems are used to model various realistic systems in network science, from social unrest in human populations to regulation in biological networks. A common approach is to model the agents of a system as vertices of a graph, and the pairwise interactions between agents as edges. Agents are in one of a finite set of states at each discrete time step and are assigned functions that describe how their states change based on neighborhood relations. Full characterization of state transitions of one system can give insights into fundamental behaviors of other dynamical systems. In this paper, we describe a discrete graph dynamical systems (GDSs) application called GDSCalc for computing and characterizing system dynamics. It is an open access system that is used through a web interface. We provide an overview of GDS theory. This theory is the basis of the web application; i.e., an understanding of GDS provides an understanding of the software features, while abstracting away implementation details. We present a set of illustrative examples to demonstrate its use in education and research. Finally, we compare GDSCalc with other discrete dynamical system software tools. Our perspective is that no single software tool will perform all computations that may be required by all users; tools typically have particular features that are more suitable for some tasks. We situate GDSCalc within this space of software tools. PMID:26263006

GDSCalc: A Web-Based Application for Evaluating Discrete Graph Dynamical Systems.

PubMed

Elmeligy Abdelhamid, Sherif H; Kuhlman, Chris J; Marathe, Madhav V; Mortveit, Henning S; Ravi, S S

2015-01-01

Discrete dynamical systems are used to model various realistic systems in network science, from social unrest in human populations to regulation in biological networks. A common approach is to model the agents of a system as vertices of a graph, and the pairwise interactions between agents as edges. Agents are in one of a finite set of states at each discrete time step and are assigned functions that describe how their states change based on neighborhood relations. Full characterization of state transitions of one system can give insights into fundamental behaviors of other dynamical systems. In this paper, we describe a discrete graph dynamical systems (GDSs) application called GDSCalc for computing and characterizing system dynamics. It is an open access system that is used through a web interface. We provide an overview of GDS theory. This theory is the basis of the web application; i.e., an understanding of GDS provides an understanding of the software features, while abstracting away implementation details. We present a set of illustrative examples to demonstrate its use in education and research. Finally, we compare GDSCalc with other discrete dynamical system software tools. Our perspective is that no single software tool will perform all computations that may be required by all users; tools typically have particular features that are more suitable for some tasks. We situate GDSCalc within this space of software tools.

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.

Personal and Impersonal Stimuli Differentially Engage Brain Networks during Moral Reasoning

ERIC Educational Resources Information Center

Xue, Shao-Wei; Wang, Yan; Tang, Yi-Yuan

2013-01-01

Moral decision making has recently attracted considerable attention as a core feature of all human endeavors. Previous functional magnetic resonance imaging studies about moral judgment have identified brain areas associated with cognitive or emotional engagement. Here, we applied graph theory-based network analysis of event-related potentials…

Network reconstruction based on proteomic data and prior knowledge of protein connectivity using graph theory.

PubMed

Stavrakas, Vassilis; Melas, Ioannis N; Sakellaropoulos, Theodore; Alexopoulos, Leonidas G

2015-01-01

Modeling of signal transduction pathways is instrumental for understanding cells' function. People have been tackling modeling of signaling pathways in order to accurately represent the signaling events inside cells' biochemical microenvironment in a way meaningful for scientists in a biological field. In this article, we propose a method to interrogate such pathways in order to produce cell-specific signaling models. We integrate available prior knowledge of protein connectivity, in a form of a Prior Knowledge Network (PKN) with phosphoproteomic data to construct predictive models of the protein connectivity of the interrogated cell type. Several computational methodologies focusing on pathways' logic modeling using optimization formulations or machine learning algorithms have been published on this front over the past few years. Here, we introduce a light and fast approach that uses a breadth-first traversal of the graph to identify the shortest pathways and score proteins in the PKN, fitting the dependencies extracted from the experimental design. The pathways are then combined through a heuristic formulation to produce a final topology handling inconsistencies between the PKN and the experimental scenarios. Our results show that the algorithm we developed is efficient and accurate for the construction of medium and large scale signaling networks. We demonstrate the applicability of the proposed approach by interrogating a manually curated interaction graph model of EGF/TNFA stimulation against made up experimental data. To avoid the possibility of erroneous predictions, we performed a cross-validation analysis. Finally, we validate that the introduced approach generates predictive topologies, comparable to the ILP formulation. Overall, an efficient approach based on graph theory is presented herein to interrogate protein-protein interaction networks and to provide meaningful biological insights.

A Model-Based Method for Content Validation of Automatically Generated Test Items

ERIC Educational Resources Information Center

Zhang, Xinxin; Gierl, Mark

2016-01-01

The purpose of this study is to describe a methodology to recover the item model used to generate multiple-choice test items with a novel graph theory approach. Beginning with the generated test items and working backward to recover the original item model provides a model-based method for validating the content used to automatically generate test…

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).

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.

Distributed formation control of nonholonomic autonomous vehicle via RBF neural network

NASA Astrophysics Data System (ADS)

Yang, Shichun; Cao, Yaoguang; Peng, Zhaoxia; Wen, Guoguang; Guo, Konghui

2017-03-01

In this paper, RBF neural network consensus-based distributed control scheme is proposed for nonholonomic autonomous vehicles in a pre-defined formation along the specified reference trajectory. A variable transformation is first designed to convert the formation control problem into a state consensus problem. Then, the complete dynamics of the vehicles including inertia, Coriolis, friction model and unmodeled bounded disturbances are considered, which lead to the formation unstable when the distributed kinematic controllers are proposed based on the kinematics. RBF neural network torque controllers are derived to compensate for them. Some sufficient conditions are derived to accomplish the asymptotically stability of the systems based on algebraic graph theory, matrix theory, and Lyapunov theory. Finally, simulation examples illustrate the effectiveness of the proposed controllers.

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.

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.

Multisensory integration processing during olfactory-visual stimulation-An fMRI graph theoretical network analysis.

PubMed

Ripp, Isabelle; Zur Nieden, Anna-Nora; Blankenagel, Sonja; Franzmeier, Nicolai; Lundström, Johan N; Freiherr, Jessica

2018-05-07

In this study, we aimed to understand how whole-brain neural networks compute sensory information integration based on the olfactory and visual system. Task-related functional magnetic resonance imaging (fMRI) data was obtained during unimodal and bimodal sensory stimulation. Based on the identification of multisensory integration processing (MIP) specific hub-like network nodes analyzed with network-based statistics using region-of-interest based connectivity matrices, we conclude the following brain areas to be important for processing the presented bimodal sensory information: right precuneus connected contralaterally to the supramarginal gyrus for memory-related imagery and phonology retrieval, and the left middle occipital gyrus connected ipsilaterally to the inferior frontal gyrus via the inferior fronto-occipital fasciculus including functional aspects of working memory. Applied graph theory for quantification of the resulting complex network topologies indicates a significantly increased global efficiency and clustering coefficient in networks including aspects of MIP reflecting a simultaneous better integration and segregation. Graph theoretical analysis of positive and negative network correlations allowing for inferences about excitatory and inhibitory network architectures revealed-not significant, but very consistent-that MIP-specific neural networks are dominated by inhibitory relationships between brain regions involved in stimulus processing. © 2018 Wiley Periodicals, Inc.

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.

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.

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

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.

Combinatorial structures to modeling simple games and applications

NASA Astrophysics Data System (ADS)

Molinero, Xavier

2017-09-01

We connect three different topics: combinatorial structures, game theory and chemistry. In particular, we establish the bases to represent some simple games, defined as influence games, and molecules, defined from atoms, by using combinatorial structures. First, we characterize simple games as influence games using influence graphs. It let us to modeling simple games as combinatorial structures (from the viewpoint of structures or graphs). Second, we formally define molecules as combinations of atoms. It let us to modeling molecules as combinatorial structures (from the viewpoint of combinations). It is open to generate such combinatorial structures using some specific techniques as genetic algorithms, (meta-)heuristics algorithms and parallel programming, among others.

The Pt site reactivity of the molecular graphs of Au6Pt isomers

NASA Astrophysics Data System (ADS)

Xu, Tianlv; Jenkins, Samantha; Xiao, Chen-Xia; Maza, Julio R.; Kirk, Steven R.

2013-12-01

Within the framework of the theory of atoms in molecules (QTAIM), in an exploratory study we propose a new measure of site reactivity equivalent to the atomic coordination number based purely on the electronic structure. It was found that the number of ring critical points (NNRCPs) positioned on the boundary of the atomic basin of the dopant (Pt) nucleus correlated very well with the relative zero point energy (ZPE) corrected energies. A weaker condition (i.e. than the number of associated bond paths) for the association of the dopant Pt nucleus with the Au6Pt molecular graph is found for NNRCP = 0.

A vision-based approach for tramway rail extraction

NASA Astrophysics Data System (ADS)

Zwemer, Matthijs H.; van de Wouw, Dennis W. J. M.; Jaspers, Egbert; Zinger, Sveta; de With, Peter H. N.

2015-03-01

The growing traffic density in cities fuels the desire for collision assessment systems on public transportation. For this application, video analysis is broadly accepted as a cornerstone. For trams, the localization of tramway tracks is an essential ingredient of such a system, in order to estimate a safety margin for crossing traffic participants. Tramway-track detection is a challenging task due to the urban environment with clutter, sharp curves and occlusions of the track. In this paper, we present a novel and generic system to detect the tramway track in advance of the tram position. The system incorporates an inverse perspective mapping and a-priori geometry knowledge of the rails to find possible track segments. The contribution of this paper involves the creation of a new track reconstruction algorithm which is based on graph theory. To this end, we define track segments as vertices in a graph, in which edges represent feasible connections. This graph is then converted to a max-cost arborescence graph, and the best path is selected according to its location and additional temporal information based on a maximum a-posteriori estimate. The proposed system clearly outperforms a railway-track detector. Furthermore, the system performance is validated on 3,600 manually annotated frames. The obtained results are promising, where straight tracks are found in more than 90% of the images and complete curves are still detected in 35% of the cases.

Couple Graph Based Label Propagation Method for Hyperspectral Remote Sensing Data Classification

NASA Astrophysics Data System (ADS)

Wang, X. P.; Hu, Y.; Chen, J.

2018-04-01

Graph based semi-supervised classification method are widely used for hyperspectral image classification. We present a couple graph based label propagation method, which contains both the adjacency graph and the similar graph. We propose to construct the similar graph by using the similar probability, which utilize the label similarity among examples probably. The adjacency graph was utilized by a common manifold learning method, which has effective improve the classification accuracy of hyperspectral data. The experiments indicate that the couple graph Laplacian which unite both the adjacency graph and the similar graph, produce superior classification results than other manifold Learning based graph Laplacian and Sparse representation based graph Laplacian in label propagation framework.

An AI-based communication system for motor and speech disabled persons: design methodology and prototype testing.

PubMed

Sy, B K; Deller, J R

1989-05-01

An intelligent communication device is developed to assist the nonverbal, motor disabled in the generation of written and spoken messages. The device is centered on a knowledge base of the grammatical rules and message elements. A "belief" reasoning scheme based on both the information from external sources and the embedded knowledge is used to optimize the process of message search. The search for the message elements is conceptualized as a path search in the language graph, and a special frame architecture is used to construct and to partition the graph. Bayesian "belief" reasoning from the Dempster-Shafer theory of evidence is augmented to cope with time-varying evidence. An "information fusion" strategy is also introduced to integrate various forms of external information. Experimental testing of the prototype system is discussed.

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.

Carbon Nanotubes' Effect on Mitochondrial Oxygen Flux Dynamics: Polarography Experimental Study and Machine Learning Models using Star Graph Trace Invariants of Raman Spectra.

PubMed

González-Durruthy, Michael; Monserrat, Jose M; Rasulev, Bakhtiyor; Casañola-Martín, Gerardo M; Barreiro Sorrivas, José María; Paraíso-Medina, Sergio; Maojo, Víctor; González-Díaz, Humberto; Pazos, Alejandro; Munteanu, Cristian R

2017-11-11

This study presents the impact of carbon nanotubes (CNTs) on mitochondrial oxygen mass flux ( J m ) under three experimental conditions. New experimental results and a new methodology are reported for the first time and they are based on CNT Raman spectra star graph transform (spectral moments) and perturbation theory. The experimental measures of J m showed that no tested CNT family can inhibit the oxygen consumption profiles of mitochondria. The best model for the prediction of J m for other CNTs was provided by random forest using eight features, obtaining test R-squared ( R ²) of 0.863 and test root-mean-square error (RMSE) of 0.0461. The results demonstrate the capability of encoding CNT information into spectral moments of the Raman star graphs (SG) transform with a potential applicability as predictive tools in nanotechnology and material risk assessments.

Segmentation of touching handwritten Japanese characters using the graph theory method

NASA Astrophysics Data System (ADS)

Suwa, Misako

2000-12-01

Projection analysis methods have been widely used to segment Japanese character strings. However, if adjacent characters have overhanging strokes or a touching point doesn't correspond to the histogram minimum, the methods are prone to result in errors. In contrast, non-projection analysis methods being proposed for use on numerals or alphabet characters cannot be simply applied for Japanese characters because of the differences in the structure of the characters. Based on the oversegmenting strategy, a new pre-segmentation method is presented in this paper: touching patterns are represented as graphs and touching strokes are regarded as the elements of proper edge cutsets. By using the graph theoretical technique, the cutset martrix is calculated. Then, by applying pruning rules, potential touching strokes are determined and the patterns are over segmented. Moreover, this algorithm was confirmed to be valid for touching patterns with overhanging strokes and doubly connected patterns in simulations.

Brain white matter fiber estimation and tractography using Q-ball imaging and Bayesian MODEL.

PubMed

Lu, Meng

2015-01-01

Diffusion tensor imaging allows for the non-invasive in vivo mapping of the brain tractography. However, fiber bundles have complex structures such as fiber crossings, fiber branchings and fibers with large curvatures that tensor imaging (DTI) cannot accurately handle. This study presents a novel brain white matter tractography method using Q-ball imaging as the data source instead of DTI, because QBI can provide accurate information about multiple fiber crossings and branchings in a single voxel using an orientation distribution function (ODF). The presented method also uses graph theory to construct the Bayesian model-based graph, so that the fiber tracking between two voxels can be represented as the shortest path in a graph. Our experiment showed that our new method can accurately handle brain white matter fiber crossings and branchings, and reconstruct brain tractograhpy both in phantom data and real brain data.

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.

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.

Guidelines for a graph-theoretic implementation of structural equation modeling

USGS Publications Warehouse

Grace, James B.; Schoolmaster, Donald R.; Guntenspergen, Glenn R.; Little, Amanda M.; Mitchell, Brian R.; Miller, Kathryn M.; Schweiger, E. William

2012-01-01

Structural equation modeling (SEM) is increasingly being chosen by researchers as a framework for gaining scientific insights from the quantitative analyses of data. New ideas and methods emerging from the study of causality, influences from the field of graphical modeling, and advances in statistics are expanding the rigor, capability, and even purpose of SEM. Guidelines for implementing the expanded capabilities of SEM are currently lacking. In this paper we describe new developments in SEM that we believe constitute a third-generation of the methodology. Most characteristic of this new approach is the generalization of the structural equation model as a causal graph. In this generalization, analyses are based on graph theoretic principles rather than analyses of matrices. Also, new devices such as metamodels and causal diagrams, as well as an increased emphasis on queries and probabilistic reasoning, are now included. Estimation under a graph theory framework permits the use of Bayesian or likelihood methods. The guidelines presented start from a declaration of the goals of the analysis. We then discuss how theory frames the modeling process, requirements for causal interpretation, model specification choices, selection of estimation method, model evaluation options, and use of queries, both to summarize retrospective results and for prospective analyses. The illustrative example presented involves monitoring data from wetlands on Mount Desert Island, home of Acadia National Park. Our presentation walks through the decision process involved in developing and evaluating models, as well as drawing inferences from the resulting prediction equations. In addition to evaluating hypotheses about the connections between human activities and biotic responses, we illustrate how the structural equation (SE) model can be queried to understand how interventions might take advantage of an environmental threshold to limit Typha invasions. The guidelines presented provide for an updated definition of the SEM process that subsumes the historical matrix approach under a graph-theory implementation. The implementation is also designed to permit complex specifications and to be compatible with various estimation methods. Finally, they are meant to foster the use of probabilistic reasoning in both retrospective and prospective considerations of the quantitative implications of the results.

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

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.

Characterization of Combustion Dynamics, Detection, and Prevention of an Unstable Combustion State Based on a Complex-Network Theory

NASA Astrophysics Data System (ADS)

Gotoda, Hiroshi; Kinugawa, Hikaru; Tsujimoto, Ryosuke; Domen, Shohei; Okuno, Yuta

2017-04-01

Complex-network theory has attracted considerable attention for nearly a decade, and it enables us to encompass our understanding of nonlinear dynamics in complex systems in a wide range of fields, including applied physics and mechanical, chemical, and electrical engineering. We conduct an experimental study using a pragmatic online detection methodology based on complex-network theory to prevent a limiting unstable state such as blowout in a confined turbulent combustion system. This study introduces a modified version of the natural visibility algorithm based on the idea of a visibility limit to serve as a pragmatic online detector. The average degree of the modified version of the natural visibility graph allows us to detect the onset of blowout, resulting in online prevention.

Edge Pushing is Equivalent to Vertex Elimination for Computing Hessians

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

Wang, Mu; Pothen, Alex; Hovland, Paul

We prove the equivalence of two different Hessian evaluation algorithms in AD. The first is the Edge Pushing algorithm of Gower and Mello, which may be viewed as a second order Reverse mode algorithm for computing the Hessian. In earlier work, we have derived the Edge Pushing algorithm by exploiting a Reverse mode invariant based on the concept of live variables in compiler theory. The second algorithm is based on eliminating vertices in a computational graph of the gradient, in which intermediate variables are successively eliminated from the graph, and the weights of the edges are updated suitably. We provemore » that if the vertices are eliminated in a reverse topological order while preserving symmetry in the computational graph of the gradient, then the Vertex Elimination algorithm and the Edge Pushing algorithm perform identical computations. In this sense, the two algorithms are equivalent. This insight that unifies two seemingly disparate approaches to Hessian computations could lead to improved algorithms and implementations for computing Hessians. Read More: http://epubs.siam.org/doi/10.1137/1.9781611974690.ch11« less

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.

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).

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)

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.

Graph Theory-Based Brain Connectivity for Automatic Classification of Multiple Sclerosis Clinical Courses.

PubMed

Kocevar, Gabriel; Stamile, Claudio; Hannoun, Salem; Cotton, François; Vukusic, Sandra; Durand-Dubief, Françoise; Sappey-Marinier, Dominique

2016-01-01

Purpose: In this work, we introduce a method to classify Multiple Sclerosis (MS) patients into four clinical profiles using structural connectivity information. For the first time, we try to solve this question in a fully automated way using a computer-based method. The main goal is to show how the combination of graph-derived metrics with machine learning techniques constitutes a powerful tool for a better characterization and classification of MS clinical profiles. Materials and Methods: Sixty-four MS patients [12 Clinical Isolated Syndrome (CIS), 24 Relapsing Remitting (RR), 24 Secondary Progressive (SP), and 17 Primary Progressive (PP)] along with 26 healthy controls (HC) underwent MR examination. T1 and diffusion tensor imaging (DTI) were used to obtain structural connectivity matrices for each subject. Global graph metrics, such as density and modularity, were estimated and compared between subjects' groups. These metrics were further used to classify patients using tuned Support Vector Machine (SVM) combined with Radial Basic Function (RBF) kernel. Results: When comparing MS patients to HC subjects, a greater assortativity, transitivity, and characteristic path length as well as a lower global efficiency were found. Using all graph metrics, the best F -Measures (91.8, 91.8, 75.6, and 70.6%) were obtained for binary (HC-CIS, CIS-RR, RR-PP) and multi-class (CIS-RR-SP) classification tasks, respectively. When using only one graph metric, the best F -Measures (83.6, 88.9, and 70.7%) were achieved for modularity with previous binary classification tasks. Conclusion: Based on a simple DTI acquisition associated with structural brain connectivity analysis, this automatic method allowed an accurate classification of different MS patients' clinical profiles.

A Dynamic Intranet-Based Online-Portal Support for Computer Science Teaching

ERIC Educational Resources Information Center

Iyer, Viswanathan K.

2017-01-01

This paper addresses the issue of effective content-delivery of Computer Science subjects taking advantage of a university intranet. The proposal described herein for teaching a subject like Combinatorics and Graph Theory (CGT) is to supplement lectures with a moderated online forum against an associated intranet portal, which is referred to as a…

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

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.

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…

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.

A graph-theory framework for evaluating landscape connectivity and conservation planning.

PubMed

Minor, Emily S; Urban, Dean L

2008-04-01

Connectivity of habitat patches is thought to be important for movement of genes, individuals, populations, and species over multiple temporal and spatial scales. We used graph theory to characterize multiple aspects of landscape connectivity in a habitat network in the North Carolina Piedmont (U.S.A). We compared this landscape with simulated networks with known topology, resistance to disturbance, and rate of movement. We introduced graph measures such as compartmentalization and clustering, which can be used to identify locations on the landscape that may be especially resilient to human development or areas that may be most suitable for conservation. Our analyses indicated that for songbirds the Piedmont habitat network was well connected. Furthermore, the habitat network had commonalities with planar networks, which exhibit slow movement, and scale-free networks, which are resistant to random disturbances. These results suggest that connectivity in the habitat network was high enough to prevent the negative consequences of isolation but not so high as to allow rapid spread of disease. Our graph-theory framework provided insight into regional and emergent global network properties in an intuitive and visual way and allowed us to make inferences about rates and paths of species movements and vulnerability to disturbance. This approach can be applied easily to assessing habitat connectivity in any fragmented or patchy landscape.

Functional Organization of the Action Observation Network in Autism: A Graph Theory Approach.

PubMed

Alaerts, Kaat; Geerlings, Franca; Herremans, Lynn; Swinnen, Stephan P; Verhoeven, Judith; Sunaert, Stefan; Wenderoth, Nicole

2015-01-01

The ability to recognize, understand and interpret other's actions and emotions has been linked to the mirror system or action-observation-network (AON). Although variations in these abilities are prevalent in the neuro-typical population, persons diagnosed with autism spectrum disorders (ASD) have deficits in the social domain and exhibit alterations in this neural network. Here, we examined functional network properties of the AON using graph theory measures and region-to-region functional connectivity analyses of resting-state fMRI-data from adolescents and young adults with ASD and typical controls (TC). Overall, our graph theory analyses provided convergent evidence that the network integrity of the AON is altered in ASD, and that reductions in network efficiency relate to reductions in overall network density (i.e., decreased overall connection strength). Compared to TC, individuals with ASD showed significant reductions in network efficiency and increased shortest path lengths and centrality. Importantly, when adjusting for overall differences in network density between ASD and TC groups, participants with ASD continued to display reductions in network integrity, suggesting that also network-level organizational properties of the AON are altered in ASD. While differences in empirical connectivity contributed to reductions in network integrity, graph theoretical analyses provided indications that also changes in the high-level network organization reduced integrity of the AON.

A new method for sperm characterization for infertility treatment: hypothesis testing by using combination of watershed segmentation and graph theory.

PubMed

Shojaedini, Seyed Vahab; Heydari, Masoud

2014-10-01

Shape and movement features of sperms are important parameters for infertility study and treatment. In this article, a new method is introduced for characterization sperms in microscopic videos. In this method, first a hypothesis framework is defined to distinguish sperms from other particles in captured video. Then decision about each hypothesis is done in following steps: Selecting some primary regions as candidates for sperms by watershed-based segmentation, pruning of some false candidates during successive frames using graph theory concept and finally confirming correct sperms by using their movement trajectories. Performance of the proposed method is evaluated on real captured images belongs to semen with high density of sperms. The obtained results show the proposed method may detect 97% of sperms in presence of 5% false detections and track 91% of moving sperms. Furthermore, it can be shown that better characterization of sperms in proposed algorithm doesn't lead to extracting more false sperms compared to some present approaches.

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

Temperature distribution in the Cerro Prieto geothermal field

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

Castillo B, F.; Bermejo M, F.J.; Domiguez A, B.

1981-01-01

A series of temperature and pressure logs and flow rate measurements was compiled for each of the geothermal wells drilled to different reservoir depths between October 1979 and December 1980. Based on the valuable information obtained, a series of graphs showing the thermal characteristics of the reservoir were prepared. These graphs clearly show the temperature distribution resulting from the movement of fluids from the deep regions toward the higher zones of the reservoir, thus establishing more reliable parameters for locating new wells with better production zones. Updated information based on data from new deep wells drilled in the geothermal fieldmore » is presented here. This new information does not differ much from earlier estimates and theories. However, the influence of faulting and fracturing on the hydrothermal recharge of the geothermal reservoir is seen more clearly.« less

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

Altered Brain Network in Amyotrophic Lateral Sclerosis: A Resting Graph Theory-Based Network Study at Voxel-Wise Level.

PubMed

Zhou, Chaoyang; Hu, Xiaofei; Hu, Jun; Liang, Minglong; Yin, Xuntao; Chen, Lin; Zhang, Jiuquan; Wang, Jian

2016-01-01

Amyotrophic lateral sclerosis (ALS) is a rare degenerative disorder characterized by loss of upper and lower motor neurons. Neuroimaging has provided noticeable evidence that ALS is a complex disease, and shown that anatomical and functional lesions extend beyond precentral cortices and corticospinal tracts, to include the corpus callosum; frontal, sensory, and premotor cortices; thalamus; and midbrain. The aim of this study is to investigate graph theory-based functional network abnormalities at voxel-wise level in ALS patients on a whole brain scale. Forty-three ALS patients and 44 age- and sex-matched healthy volunteers were enrolled. The voxel-wise network degree centrality (DC), a commonly employed graph-based measure of network organization, was used to characterize the alteration of whole brain functional network. Compared with the controls, the ALS patients showed significant increase of DC in the left cerebellum posterior lobes, bilateral cerebellum crus, bilateral occipital poles, right orbital frontal lobe, and bilateral prefrontal lobes; significant decrease of DC in the bilateral primary motor cortex, bilateral sensory motor region, right prefrontal lobe, left bilateral precuneus, bilateral lateral temporal lobes, left cingulate cortex, and bilateral visual processing cortex. The DC's z-scores of right inferior occipital gyrus were significant negative correlated with the ALSFRS-r scores. Our findings confirm that the regions with abnormal network DC in ALS patients were located in multiple brain regions including primary motor, somatosensory and extra-motor areas, supporting the concept that ALS is a multisystem disorder. Specifically, our study found that DC in the visual areas was altered and ALS patients with higher DC in right inferior occipital gyrus have more severity of disease. The result demonstrated that the altered DC value in this region can probably be used to assess severity of ALS.

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)

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.

To the theory of non-local non-isothermal filtration in porous medium

NASA Astrophysics Data System (ADS)

Meilanov, R. R.; Akhmedov, E. N.; Beybalaev, V. D.; Magomedov, R. A.; Ragimkhanov, G. B.; Aliverdiev, A. A.

2018-01-01

A new approach to the theory of non-local and non-isothermal filtration based on the mathematical apparatus of fractional order derivatives is developing. A solution of the Cauchy problem for the system of equations of non-local non-isothermal filtration in fractional calculus is obtained. Some applications of the solutions obtained to the problems of underground hydrodynamics (fracturing and explosion) are considered. A computational experiment was carried out to analyze the solutions obtained. Graphs of pressure and temperature dependences are plotted against time.

Group consensus control for networked multi-agent systems with communication delays.

PubMed

An, Bao-Ran; Liu, Guo-Ping; Tan, Chong

2018-05-01

This paper investigates group consensus problems in networked multi-agent systems (NMAS) with communication delays. Based on the sed state prediction scheme, the group consensus control protocol is designed to compensate the communication delay actively. In light of algebraic graph theories and matrix theories, necessary and(or) sufficient conditions of group consensus with respect to a given admissible control set are obtained for the NMAS with communication delays under mild assumptions. Finally, simulations are performed to demonstrate the effectiveness of the theoretical results. Copyright © 2018 ISA. 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.

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.

The excitonic qubit coupled with a phonon bath on a star graph: anomalous decoherence and coherence revivals

NASA Astrophysics Data System (ADS)

Yalouz, S.; Falvo, C.; Pouthier, V.

2017-06-01

Based on the operatorial formulation of perturbation theory, the dynamical properties of a Frenkel exciton coupled with a thermal phonon bath on a star graph are studied. 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 dressed by virtual excitonic transitions. Special attention is paid to the description of the coherence of a qubit state initially located on the central node of the graph. Within the nonadiabatic weak coupling limit, it is shown that several timescales govern the coherence dynamics. In the short time limit, the coherence behaves as if the exciton was insensitive to the phonon bath. Then, quantum decoherence takes place, this decoherence being enhanced by the size of the graph and by temperature. However, the coherence does not vanish in the long time limit. Instead, it exhibits incomplete revivals that occur periodically at specific revival times and it shows almost exact recurrences that take place at particular super-revival times, a singular behavior that has been corroborated by performing exact quantum calculations.

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.

Graphs, matrices, and the GraphBLAS: Seven good reasons

DOE PAGES

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

2015-01-01

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

Prioritizing Urban Habitats for Connectivity Conservation: Integrating Centrality and Ecological Metrics.

PubMed

Poodat, Fatemeh; Arrowsmith, Colin; Fraser, David; Gordon, Ascelin

2015-09-01

Connectivity among fragmented areas of habitat has long been acknowledged as important for the viability of biological conservation, especially within highly modified landscapes. Identifying important habitat patches in ecological connectivity is a priority for many conservation strategies, and the application of 'graph theory' has been shown to provide useful information on connectivity. Despite the large number of metrics for connectivity derived from graph theory, only a small number have been compared in terms of the importance they assign to nodes in a network. This paper presents a study that aims to define a new set of metrics and compares these with traditional graph-based metrics, used in the prioritization of habitat patches for ecological connectivity. The metrics measured consist of "topological" metrics, "ecological metrics," and "integrated metrics," Integrated metrics are a combination of topological and ecological metrics. Eight metrics were applied to the habitat network for the fat-tailed dunnart within Greater Melbourne, Australia. A non-directional network was developed in which nodes were linked to adjacent nodes. These links were then weighted by the effective distance between patches. By applying each of the eight metrics for the study network, nodes were ranked according to their contribution to the overall network connectivity. The structured comparison revealed the similarity and differences in the way the habitat for the fat-tailed dunnart was ranked based on different classes of metrics. Due to the differences in the way the metrics operate, a suitable metric should be chosen that best meets the objectives established by the decision maker.

Combinatorial compatibility as habit-controlling factor in lysozyme crystallization I. Monomeric and tetrameric F faces derived graph-theoretically

NASA Astrophysics Data System (ADS)

Strom, C. S.; Bennema, P.

1997-03-01

A series of two articles discusses possible morphological evidence for oligomerization of growth units in the crystallization of tetragonal lysozyme, based on a rigorous graph-theoretic derivation of the F faces. In the first study (Part I), the growth layers are derived as valid networks satisfying the conditions of F slices in the context of the PBC theory using the graph-theoretic method implemented in program FFACE [C.S. Strom, Z. Krist. 172 (1985) 11]. The analysis is performed in monomeric and alternative tetrameric and octameric formulations of the unit cell, assuming tetramer formation according to the strongest bonds. F (flat) slices with thickness Rdhkl ( {1}/{2} < R ≤ 1 ) are predicted theoretically in the forms 1 1 0, 0 1 1, 1 1 1. The relevant energies are established in the broken bond model. The relation between possible oligomeric specifications of the unit cell and combinatorially feasible F slice compositions in these orientations is explored.

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.

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.

SAR-based change detection using hypothesis testing and Markov random field modelling

NASA Astrophysics Data System (ADS)

Cao, W.; Martinis, S.

2015-04-01

The objective of this study is to automatically detect changed areas caused by natural disasters from bi-temporal co-registered and calibrated TerraSAR-X data. The technique in this paper consists of two steps: Firstly, an automatic coarse detection step is applied based on a statistical hypothesis test for initializing the classification. The original analytical formula as proposed in the constant false alarm rate (CFAR) edge detector is reviewed and rewritten in a compact form of the incomplete beta function, which is a builtin routine in commercial scientific software such as MATLAB and IDL. Secondly, a post-classification step is introduced to optimize the noisy classification result in the previous step. Generally, an optimization problem can be formulated as a Markov random field (MRF) on which the quality of a classification is measured by an energy function. The optimal classification based on the MRF is related to the lowest energy value. Previous studies provide methods for the optimization problem using MRFs, such as the iterated conditional modes (ICM) algorithm. Recently, a novel algorithm was presented based on graph-cut theory. This method transforms a MRF to an equivalent graph and solves the optimization problem by a max-flow/min-cut algorithm on the graph. In this study this graph-cut algorithm is applied iteratively to improve the coarse classification. At each iteration the parameters of the energy function for the current classification are set by the logarithmic probability density function (PDF). The relevant parameters are estimated by the method of logarithmic cumulants (MoLC). Experiments are performed using two flood events in Germany and Australia in 2011 and a forest fire on La Palma in 2009 using pre- and post-event TerraSAR-X data. The results show convincing coarse classifications and considerable improvement by the graph-cut post-classification step.

Brain gray matter structural network in myotonic dystrophy type 1.

PubMed

Sugiyama, Atsuhiko; Sone, Daichi; Sato, Noriko; Kimura, Yukio; Ota, Miho; Maikusa, Norihide; Maekawa, Tomoko; Enokizono, Mikako; Mori-Yoshimura, Madoka; Ohya, Yasushi; Kuwabara, Satoshi; Matsuda, Hiroshi

2017-01-01

This study aimed to investigate abnormalities in structural covariance network constructed from gray matter volume in myotonic dystrophy type 1 (DM1) patients by using graph theoretical analysis for further clarification of the underlying mechanisms of central nervous system involvement. Twenty-eight DM1 patients (4 childhood onset, 10 juvenile onset, 14 adult onset), excluding three cases from 31 consecutive patients who underwent magnetic resonance imaging in a certain period, and 28 age- and sex- matched healthy control subjects were included in this study. The normalized gray matter images of both groups were subjected to voxel based morphometry (VBM) and Graph Analysis Toolbox for graph theoretical analysis. VBM revealed extensive gray matter atrophy in DM1 patients, including cortical and subcortical structures. On graph theoretical analysis, there were no significant differences between DM1 and control groups in terms of the global measures of connectivity. Betweenness centrality was increased in several regions including the left fusiform gyrus, whereas it was decreased in the right striatum. The absence of significant differences between the groups in global network measurements on graph theoretical analysis is consistent with the fact that the general cognitive function is preserved in DM1 patients. In DM1 patients, increased connectivity in the left fusiform gyrus and decreased connectivity in the right striatum might be associated with impairment in face perception and theory of mind, and schizotypal-paranoid personality traits, respectively.

GBS 1.0

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

2010-09-30

The Umbra gbs (Graph-Based Search) library provides implementations of graph-based search/planning algorithms that can be applied to legacy graph data structures. Unlike some other graph algorithm libraries, this one does not require your graph class to inherit from a specific base class. Implementations of Dijkstra's Algorithm and A-Star search are included and can be used with graphs that are lazily-constructed.

A Weight-Adaptive Laplacian Embedding for Graph-Based Clustering.

PubMed

Cheng, De; Nie, Feiping; Sun, Jiande; Gong, Yihong

2017-07-01

Graph-based clustering methods perform clustering on a fixed input data graph. Thus such clustering results are sensitive to the particular graph construction. If this initial construction is of low quality, the resulting clustering may also be of low quality. We address this drawback by allowing the data graph itself to be adaptively adjusted in the clustering procedure. In particular, our proposed weight adaptive Laplacian (WAL) method learns a new data similarity matrix that can adaptively adjust the initial graph according to the similarity weight in the input data graph. We develop three versions of these methods based on the L2-norm, fuzzy entropy regularizer, and another exponential-based weight strategy, that yield three new graph-based clustering objectives. We derive optimization algorithms to solve these objectives. Experimental results on synthetic data sets and real-world benchmark data sets exhibit the effectiveness of these new graph-based clustering 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

Experimental and theoretical distribution of electron density and thermopolimerization in crystals of Ph3Sb(O2CCH=CH2)2 complex

NASA Astrophysics Data System (ADS)

Fukin, Georgy K.; Samsonov, Maxim A.; Arapova, Alla V.; Mazur, Anton S.; Artamonova, Tatiana O.; Khodorkovskiy, Mikhail A.; Vasilyev, Aleksander V.

2017-10-01

In this paper we present the results of a high-resolution single crystal X-ray diffraction experiment of a triphenylantimony diacrylate (Ph3Sb(O2CCH=CH2)2 (1)) and a subsequent charge density study based on a topological analysis according to quantum theory of atoms in molecules (QTAIM) together with density functional theory (DFT) calculation of isolated molecule. The QTAIM was used to investigate nature of the chemical bonds and molecular graph of Ph3Sb(O2CCH=CH2)2 complex. The molecular graph shows that only in one acrylate group there is an evidence of bonding between antimony and carbonyl oxygen atom in terms of the presence of a bond path. Thus the molecular graph for this class of compounds does not provide a definitive picture of the chemical bonding and should be complemented with other descriptors, such as and a source function (SF), noncovalent interaction (NCI) index and delocalization index (DI). Moreover the realization of π…π interactions between double bonds of acrylate groups in adjacent molecules allowed us to carry out a thermopolimerization reaction in crystals of Ph3Sb(O2CCH=CH2)2 complex and to determine a probable structure of polymer by solid state CP/MAS 13C NMR.

A new measure based on degree distribution that links information theory and network graph analysis

PubMed Central

2012-01-01

Background Detailed connection maps of human and nonhuman brains are being generated with new technologies, and graph metrics have been instrumental in understanding the general organizational features of these structures. Neural networks appear to have small world properties: they have clustered regions, while maintaining integrative features such as short average pathlengths. Results We captured the structural characteristics of clustered networks with short average pathlengths through our own variable, System Difference (SD), which is computationally simple and calculable for larger graph systems. SD is a Jaccardian measure generated by averaging all of the differences in the connection patterns between any two nodes of a system. We calculated SD over large random samples of matrices and found that high SD matrices have a low average pathlength and a larger number of clustered structures. SD is a measure of degree distribution with high SD matrices maximizing entropic properties. Phi (Φ), an information theory metric that assesses a system’s capacity to integrate information, correlated well with SD - with SD explaining over 90% of the variance in systems above 11 nodes (tested for 4 to 13 nodes). However, newer versions of Φ do not correlate well with the SD metric. Conclusions The new network measure, SD, provides a link between high entropic structures and degree distributions as related to small world properties. PMID:22726594

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

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

Wasatch: An architecture-proof multiphysics development environment using a Domain Specific Language and graph theory

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

Saad, Tony; Sutherland, James C.

To address the coding and software challenges of modern hybrid architectures, we propose an approach to multiphysics code development for high-performance computing. This approach is based on using a Domain Specific Language (DSL) in tandem with a directed acyclic graph (DAG) representation of the problem to be solved that allows runtime algorithm generation. When coupled with a large-scale parallel framework, the result is a portable development framework capable of executing on hybrid platforms and handling the challenges of multiphysics applications. In addition, we share our experience developing a code in such an environment – an effort that spans an interdisciplinarymore » team of engineers and computer scientists.« less

Wasatch: An architecture-proof multiphysics development environment using a Domain Specific Language and graph theory

DOE PAGES

Saad, Tony; Sutherland, James C.

2016-05-04

To address the coding and software challenges of modern hybrid architectures, we propose an approach to multiphysics code development for high-performance computing. This approach is based on using a Domain Specific Language (DSL) in tandem with a directed acyclic graph (DAG) representation of the problem to be solved that allows runtime algorithm generation. When coupled with a large-scale parallel framework, the result is a portable development framework capable of executing on hybrid platforms and handling the challenges of multiphysics applications. In addition, we share our experience developing a code in such an environment – an effort that spans an interdisciplinarymore » team of engineers and computer scientists.« less

[Baseflow separation methods in hydrological process research: a review].

PubMed

Xu, Lei-Lei; Liu, Jing-Lin; Jin, Chang-Jie; Wang, An-Zhi; Guan, De-Xin; Wu, Jia-Bing; Yuan, Feng-Hui

2011-11-01

Baseflow separation research is regarded as one of the most important and difficult issues in hydrology and ecohydrology, but lacked of unified standards in the concepts and methods. This paper introduced the theories of baseflow separation based on the definitions of baseflow components, and analyzed the development course of different baseflow separation methods. Among the methods developed, graph separation method is simple and applicable but arbitrary, balance method accords with hydrological mechanism but is difficult in application, whereas time series separation method and isotopic method can overcome the subjective and arbitrary defects caused by graph separation method, and thus can obtain the baseflow procedure quickly and efficiently. In recent years, hydrological modeling, digital filtering, and isotopic method are the main methods used for baseflow separation.

Geographical influences of an emerging network of gang rivalries

NASA Astrophysics Data System (ADS)

Hegemann, Rachel A.; Smith, Laura M.; Barbaro, Alethea B. T.; Bertozzi, Andrea L.; Reid, Shannon E.; Tita, George E.

2011-10-01

We propose an agent-based model to simulate the creation of street gang rivalries. The movement dynamics of agents are coupled to an evolving network of gang rivalries, which is determined by previous interactions among agents in the system. Basic gang data, geographic information, and behavioral dynamics suggested by the criminology literature are integrated into the model. The major highways, rivers, and the locations of gangs’ centers of activity influence the agents’ motion. We use a policing division of the Los Angeles Police Department as a case study to test our model. We apply common metrics from graph theory to analyze our model, comparing networks produced by our simulations and an instance of a Geographical Threshold Graph to the existing network from the criminology literature.

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.

- and Graph-Based Point Cloud Segmentation of 3d Scenes Using Perceptual Grouping Laws

NASA Astrophysics Data System (ADS)

Xu, Y.; Hoegner, L.; Tuttas, S.; Stilla, U.

2017-05-01

Segmentation is the fundamental step for recognizing and extracting objects from point clouds of 3D scene. In this paper, we present a strategy for point cloud segmentation using voxel structure and graph-based clustering with perceptual grouping laws, which allows a learning-free and completely automatic but parametric solution for segmenting 3D point cloud. To speak precisely, two segmentation methods utilizing voxel and supervoxel structures are reported and tested. The voxel-based data structure can increase efficiency and robustness of the segmentation process, suppressing the negative effect of noise, outliers, and uneven points densities. The clustering of voxels and supervoxel is carried out using graph theory on the basis of the local contextual information, which commonly conducted utilizing merely pairwise information in conventional clustering algorithms. By the use of perceptual laws, our method conducts the segmentation in a pure geometric way avoiding the use of RGB color and intensity information, so that it can be applied to more general applications. Experiments using different datasets have demonstrated that our proposed methods can achieve good results, especially for complex scenes and nonplanar surfaces of objects. Quantitative comparisons between our methods and other representative segmentation methods also confirms the effectiveness and efficiency of our proposals.

Revised procedure for the measurement of particulate matter in Naval JP5 aviation turbine fuel (F44; AVCAT) using the contaminated fuel detector (CFD)

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

McVea, G.G.; Power, A.J.

1995-04-01

USA Military Specification MIL-D-22612 provides a procedure for measurement of particulate levels in Naval aviation gas turbine engine JP5 fuel (F44; RAN AVCAT) using the contaminated fuel detector (CFD). Evaluation of this procedure within the specification has revealed significant shortcomings in the application of the theoretical principles upon which the method is based. CFD measurements have been compared to gravimetric results from ASTM D2276, which provides accurate determination of concentrations of particulate matter in JP5. Inaccuracies evident in the CFD readings have been found to relate to the high sensitivity of the CFD to variations in fuel particulate extinction coefficientsmore » (ECs) (relating to fuel sediment colour) and to an error in the application of light transmittance theory in the recommended method. This report demonstrates that accurate CFD determination of JP5 particulate concentrations depends on spectrophotometric measurement of a narrow range of ECs of particulate matter. A range of fuel sediments derived from Australian naval ship and shore fuel storages was studied. It was observed that the CFD plot, which is in light transmittance mode, in theory provides a curved line graph against the gravimetric test results, whereas MIL-D-22612 describes a straight line graph. It was concluded that this must be an approximation. However, conversion of light transmittance data derived from the CFD into the reciprocal logarithm to give light absorbance data was shown to give a straight line graph which corresponded well with the gravimetric results. This relationship depended on construction of the graph on the basis of a narrow range of known particulate ECs. The conversion to absorbance gave improved correlation for JP5 particulate measurements with gravimetric procedures, using the CFD.« less

Protein-protein interaction network-based detection of functionally similar proteins within species.

PubMed

Song, Baoxing; Wang, Fen; Guo, Yang; Sang, Qing; Liu, Min; Li, Dengyun; Fang, Wei; Zhang, Deli

2012-07-01

Although functionally similar proteins across species have been widely studied, functionally similar proteins within species showing low sequence similarity have not been examined in detail. Identification of these proteins is of significant importance for understanding biological functions, evolution of protein families, progression of co-evolution, and convergent evolution and others which cannot be obtained by detection of functionally similar proteins across species. Here, we explored a method of detecting functionally similar proteins within species based on graph theory. After denoting protein-protein interaction networks using graphs, we split the graphs into subgraphs using the 1-hop method. Proteins with functional similarities in a species were detected using a method of modified shortest path to compare these subgraphs and to find the eligible optimal results. Using seven protein-protein interaction networks and this method, some functionally similar proteins with low sequence similarity that cannot detected by sequence alignment were identified. By analyzing the results, we found that, sometimes, it is difficult to separate homologous from convergent evolution. Evaluation of the performance of our method by gene ontology term overlap showed that the precision of our method was excellent. Copyright © 2012 Wiley Periodicals, Inc.

Electric field theory based approach to search-direction line definition in image segmentation: application to optimal femur-tibia cartilage segmentation in knee-joint 3-D MR

NASA Astrophysics Data System (ADS)

Yin, Y.; Sonka, M.

2010-03-01

A novel method is presented for definition of search lines in a variety of surface segmentation approaches. The method is inspired by properties of electric field direction lines and is applicable to general-purpose n-D shapebased image segmentation tasks. Its utility is demonstrated in graph construction and optimal segmentation of multiple mutually interacting objects. The properties of the electric field-based graph construction guarantee that inter-object graph connecting lines are non-intersecting and inherently covering the entire object-interaction space. When applied to inter-object cross-surface mapping, our approach generates one-to-one and all-to-all vertex correspondent pairs between the regions of mutual interaction. We demonstrate the benefits of the electric field approach in several examples ranging from relatively simple single-surface segmentation to complex multiobject multi-surface segmentation of femur-tibia cartilage. The performance of our approach is demonstrated in 60 MR images from the Osteoarthritis Initiative (OAI), in which our approach achieved a very good performance as judged by surface positioning errors (average of 0.29 and 0.59 mm for signed and unsigned cartilage positioning errors, respectively).

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.

Functional Organization of the Action Observation Network in Autism: A Graph Theory Approach

PubMed Central

Alaerts, Kaat; Geerlings, Franca; Herremans, Lynn; Swinnen, Stephan P.; Verhoeven, Judith; Sunaert, Stefan; Wenderoth, Nicole

2015-01-01

Background The ability to recognize, understand and interpret other’s actions and emotions has been linked to the mirror system or action-observation-network (AON). Although variations in these abilities are prevalent in the neuro-typical population, persons diagnosed with autism spectrum disorders (ASD) have deficits in the social domain and exhibit alterations in this neural network. Method Here, we examined functional network properties of the AON using graph theory measures and region-to-region functional connectivity analyses of resting-state fMRI-data from adolescents and young adults with ASD and typical controls (TC). Results Overall, our graph theory analyses provided convergent evidence that the network integrity of the AON is altered in ASD, and that reductions in network efficiency relate to reductions in overall network density (i.e., decreased overall connection strength). Compared to TC, individuals with ASD showed significant reductions in network efficiency and increased shortest path lengths and centrality. Importantly, when adjusting for overall differences in network density between ASD and TC groups, participants with ASD continued to display reductions in network integrity, suggesting that also network-level organizational properties of the AON are altered in ASD. Conclusion While differences in empirical connectivity contributed to reductions in network integrity, graph theoretical analyses provided indications that also changes in the high-level network organization reduced integrity of the AON. PMID:26317222

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.

Distributed Adaptive Fuzzy Control for Nonlinear Multiagent Systems Via Sliding Mode Observers.

PubMed

Shen, Qikun; Shi, Peng; Shi, Yan

2016-12-01

In this paper, the problem of distributed adaptive fuzzy control is investigated for high-order uncertain nonlinear multiagent systems on directed graph with a fixed topology. It is assumed that only the outputs of each follower and its neighbors are available in the design of its distributed controllers. Equivalent output injection sliding mode observers are proposed for each follower to estimate the states of itself and its neighbors, and an observer-based distributed adaptive controller is designed for each follower to guarantee that it asymptotically synchronizes to a leader with tracking errors being semi-globally uniform ultimate bounded, in which fuzzy logic systems are utilized to approximate unknown functions. Based on algebraic graph theory and Lyapunov function approach, using Filippov-framework, the closed-loop system stability analysis is conducted. Finally, numerical simulations are provided to illustrate the effectiveness and potential of the developed design techniques.

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.

Network Analysis of Intrinsic Functional Brain Connectivity in Male and Female Adult Smokers: A Preliminary Study.

PubMed

Moran-Santa Maria, Megan M; Vanderweyen, Davy C; Camp, Christopher C; Zhu, Xun; McKee, Sherry A; Cosgrove, Kelly P; Hartwell, Karen J; Brady, Kathleen T; Joseph, Jane E

2018-06-07

The goal of this study was to conduct a preliminary network analysis (using graph-theory measures) of intrinsic functional connectivity in adult smokers, with an exploration of sex differences in smokers. Twenty-seven adult smokers (13 males; mean age = 35) and 17 sex and age-matched controls (11 males; mean age = 35) completed a blood oxygen level-dependent resting state functional magnetic resonance imaging experiment. Data analysis involved preprocessing, creation of connectivity matrices using partial correlation, and computation of graph-theory measures using the Brain Connectivity Toolbox. Connector hubs and additional graph-theory measures were examined for differences between smokers and controls and correlations with nicotine dependence. Sex differences were examined in a priori regions of interest based on prior literature. Compared to nonsmokers, connector hubs in smokers emerged primarily in limbic (parahippocampus) and salience network (cingulate cortex) regions. In addition, global influence of the right insula and left nucleus accumbens was associated with higher nicotine dependence. These trends were present in male but not female smokers. Network communication was altered in smokers, primarily in limbic and salience network regions. Network topology was associated with nicotine dependence in male but not female smokers in regions associated with reinforcement (nucleus accumbens) and craving (insula), consistent with the idea that male smokers are more sensitive to the reinforcing aspects of nicotine than female smokers. Identifying alterations in brain network communication in male and female smokers can help tailor future behavioral and pharmacological smoking interventions. Male smokers showed alterations in brain networks associated with the reinforcing effects of nicotine more so than females, suggesting that pharmacotherapies targeting reinforcement and craving may be more efficacious in male smokers.

On finding bicliques in bipartite graphs: a novel algorithm and its application to the integration of diverse biological data types

PubMed Central

2014-01-01

Background Integrating and analyzing heterogeneous genome-scale data is a huge algorithmic challenge for modern systems biology. Bipartite graphs can be useful for representing relationships across pairs of disparate data types, with the interpretation of these relationships accomplished through an enumeration of maximal bicliques. Most previously-known techniques are generally ill-suited to this foundational task, because they are relatively inefficient and without effective scaling. In this paper, a powerful new algorithm is described that produces all maximal bicliques in a bipartite graph. Unlike most previous approaches, the new method neither places undue restrictions on its input nor inflates the problem size. Efficiency is achieved through an innovative exploitation of bipartite graph structure, and through computational reductions that rapidly eliminate non-maximal candidates from the search space. An iterative selection of vertices for consideration based on non-decreasing common neighborhood sizes boosts efficiency and leads to more balanced recursion trees. Results The new technique is implemented and compared to previously published approaches from graph theory and data mining. Formal time and space bounds are derived. Experiments are performed on both random graphs and graphs constructed from functional genomics data. It is shown that the new method substantially outperforms the best previous alternatives. Conclusions The new method is streamlined, efficient, and particularly well-suited to the study of huge and diverse biological data. A robust implementation has been incorporated into GeneWeaver, an online tool for integrating and analyzing functional genomics experiments, available at http://geneweaver.org. The enormous increase in scalability it provides empowers users to study complex and previously unassailable gene-set associations between genes and their biological functions in a hierarchical fashion and on a genome-wide scale. This practical computational resource is adaptable to almost any applications environment in which bipartite graphs can be used to model relationships between pairs of heterogeneous entities. PMID:24731198

A method for independent component graph analysis of resting-state fMRI.

PubMed

Ribeiro de Paula, Demetrius; Ziegler, Erik; Abeyasinghe, Pubuditha M; Das, Tushar K; Cavaliere, Carlo; Aiello, Marco; Heine, Lizette; di Perri, Carol; Demertzi, Athena; Noirhomme, Quentin; Charland-Verville, Vanessa; Vanhaudenhuyse, Audrey; Stender, Johan; Gomez, Francisco; Tshibanda, Jean-Flory L; Laureys, Steven; Owen, Adrian M; Soddu, Andrea

2017-03-01

Independent component analysis (ICA) has been extensively used for reducing task-free BOLD fMRI recordings into spatial maps and their associated time-courses. The spatially identified independent components can be considered as intrinsic connectivity networks (ICNs) of non-contiguous regions. To date, the spatial patterns of the networks have been analyzed with techniques developed for volumetric data. Here, we detail a graph building technique that allows these ICNs to be analyzed with graph theory. First, ICA was performed at the single-subject level in 15 healthy volunteers using a 3T MRI scanner. The identification of nine networks was performed by a multiple-template matching procedure and a subsequent component classification based on the network "neuronal" properties. Second, for each of the identified networks, the nodes were defined as 1,015 anatomically parcellated regions. Third, between-node functional connectivity was established by building edge weights for each networks. Group-level graph analysis was finally performed for each network and compared to the classical network. Network graph comparison between the classically constructed network and the nine networks showed significant differences in the auditory and visual medial networks with regard to the average degree and the number of edges, while the visual lateral network showed a significant difference in the small-worldness. This novel approach permits us to take advantage of the well-recognized power of ICA in BOLD signal decomposition and, at the same time, to make use of well-established graph measures to evaluate connectivity differences. Moreover, by providing a graph for each separate network, it can offer the possibility to extract graph measures in a specific way for each network. This increased specificity could be relevant for studying pathological brain activity or altered states of consciousness as induced by anesthesia or sleep, where specific networks are known to be altered in different strength.

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 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.

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…

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

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

Graph-based normalization and whitening for non-linear data analysis.

PubMed

Aaron, Catherine

2006-01-01

In this paper we construct a graph-based normalization algorithm for non-linear data analysis. The principle of this algorithm is to get a spherical average neighborhood with unit radius. First we present a class of global dispersion measures used for "global normalization"; we then adapt these measures using a weighted graph to build a local normalization called "graph-based" normalization. Then we give details of the graph-based normalization algorithm and illustrate some results. In the second part we present a graph-based whitening algorithm built by analogy between the "global" and the "local" problem.

The dorsal striatum and the dynamics of the consensus connectomes in the frontal lobe of the human brain.

PubMed

Kerepesi, Csaba; Varga, Bálint; Szalkai, Balázs; Grolmusz, Vince

2018-04-23

In the applications of the graph theory, it is unusual that one considers numerous, pairwise different graphs on the very same set of vertices. In the case of human braingraphs or connectomes, however, this is the standard situation: the nodes correspond to anatomically identified cerebral regions, and two vertices are connected by an edge if a diffusion MRI-based workflow identifies a fiber of axons, running between the two regions, corresponding to the two vertices. Therefore, if we examine the braingraphs of n subjects, then we have n graphs on the very same, anatomically identified vertex set. It is a natural idea to describe the k-frequently appearing edges in these graphs: the edges that are present between the same two vertices in at least k out of the n graphs. Based on the NIH-funded large Human Connectome Project's public data release, we have reported the construction of the Budapest Reference Connectome Server http://www.connectome.pitgroup.org that generates and visualizes these k-frequently appearing edges. We call the graphs of the k-frequently appearing edges "k-consensus connectomes" since an edge could be included only if it is present in at least k graphs out of n. Considering the whole human brain, we have reported a surprising property of these consensus connectomes earlier. In the present work we are focusing on the frontal lobe of the brain, and we report here a similarly surprising dynamical property of the consensus connectomes when k is gradually changed from k = n to k = 1: the connections between the nodes of the frontal lobe are seemingly emanating from those nodes that were connected to sub-cortical structures of the dorsal striatum: the caudate nucleus, and the putamen. We hypothesize that this dynamic behavior copies the axonal fiber development of the frontal lobe. An animation of the phenomenon is presented at https://youtu.be/wBciB2eW6_8. Copyright © 2018 Elsevier B.V. All rights reserved.

Rule-based graph theory to enable exploration of the space system architecture design space

NASA Astrophysics Data System (ADS)

Arney, Dale Curtis

The primary goal of this research is to improve upon system architecture modeling in order to enable the exploration of design space options. A system architecture is the description of the functional and physical allocation of elements and the relationships, interactions, and interfaces between those elements necessary to satisfy a set of constraints and requirements. The functional allocation defines the functions that each system (element) performs, and the physical allocation defines the systems required to meet those functions. Trading the functionality between systems leads to the architecture-level design space that is available to the system architect. The research presents a methodology that enables the modeling of complex space system architectures using a mathematical framework. To accomplish the goal of improved architecture modeling, the framework meets five goals: technical credibility, adaptability, flexibility, intuitiveness, and exhaustiveness. The framework is technically credible, in that it produces an accurate and complete representation of the system architecture under consideration. The framework is adaptable, in that it provides the ability to create user-specified locations, steady states, and functions. The framework is flexible, in that it allows the user to model system architectures to multiple destinations without changing the underlying framework. The framework is intuitive for user input while still creating a comprehensive mathematical representation that maintains the necessary information to completely model complex system architectures. Finally, the framework is exhaustive, in that it provides the ability to explore the entire system architecture design space. After an extensive search of the literature, graph theory presents a valuable mechanism for representing the flow of information or vehicles within a simple mathematical framework. Graph theory has been used in developing mathematical models of many transportation and network flow problems in the past, where nodes represent physical locations and edges represent the means by which information or vehicles travel between those locations. In space system architecting, expressing the physical locations (low-Earth orbit, low-lunar orbit, etc.) and steady states (interplanetary trajectory) as nodes and the different means of moving between the nodes (propulsive maneuvers, etc.) as edges formulates a mathematical representation of this design space. The selection of a given system architecture using graph theory entails defining the paths that the systems take through the space system architecture graph. A path through the graph is defined as a list of edges that are traversed, which in turn defines functions performed by the system. A structure to compactly represent this information is a matrix, called the system map, in which the column indices are associated with the systems that exist and row indices are associated with the edges, or functions, to which each system has access. Several contributions have been added to the state of the art in space system architecture analysis. The framework adds the capability to rapidly explore the design space without the need to limit trade options or the need for user interaction during the exploration process. The unique mathematical representation of a system architecture, through the use of the adjacency, incidence, and system map matrices, enables automated design space exploration using stochastic optimization processes. The innovative rule-based graph traversal algorithm ensures functional feasibility of each system architecture that is analyzed, and the automatic generation of the system hierarchy eliminates the need for the user to manually determine the relationships between systems during or before the design space exploration process. Finally, the rapid evaluation of system architectures for various mission types enables analysis of the system architecture design space for multiple destinations within an evolutionary exploration program. (Abstract shortened by UMI.).

Traffic Patrol Service Platform Scheduling and Containment Optimization Strategy

NASA Astrophysics Data System (ADS)

Wang, Tiane; Niu, Taiyang; Wan, Baocheng; Li, Jian

This article is based on the traffic and patrol police service platform settings and scheduling, in order to achieve the main purpose of rapid containment for the suspect in an emergency event. Proposing new boundary definition based on graph theory, using 0-1 programming, Dijkstra algorithm, the shortest path tree (SPT) and some of the related knowledge establish a containment model. Finally, making a combination with a city-specific data and using this model obtain the best containment plan.

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

Framework based on communicability and flow to analyze complex network dynamics

NASA Astrophysics Data System (ADS)

Gilson, M.; Kouvaris, N. E.; Deco, G.; Zamora-López, G.

2018-05-01

Graph theory constitutes a widely used and established field providing powerful tools for the characterization of complex networks. The intricate topology of networks can also be investigated by means of the collective dynamics observed in the interactions of self-sustained oscillations (synchronization patterns) or propagationlike processes such as random walks. However, networks are often inferred from real-data-forming dynamic systems, which are different from those employed to reveal their topological characteristics. This stresses the necessity for a theoretical framework dedicated to the mutual relationship between the structure and dynamics in complex networks, as the two sides of the same coin. Here we propose a rigorous framework based on the network response over time (i.e., Green function) to study interactions between nodes across time. For this purpose we define the flow that describes the interplay between the network connectivity and external inputs. This multivariate measure relates to the concepts of graph communicability and the map equation. We illustrate our theory using the multivariate Ornstein-Uhlenbeck process, which describes stable and non-conservative dynamics, but the formalism can be adapted to other local dynamics for which the Green function is known. We provide applications to classical network examples, such as small-world ring and hierarchical networks. Our theory defines a comprehensive framework that is canonically related to directed and weighted networks, thus paving a way to revise the standards for network analysis, from the pairwise interactions between nodes to the global properties of networks including community detection.

Applying the expectancy disconfirmation and regret theories to online consumer behavior.

PubMed

Liao, Chechen; Liu, Chuang-Chun; Liu, Yu-Ping; To, Pui-Lai; Lin, Hong-Nan

2011-04-01

This study synthesizes the expectancy disconfirmation theory with empirical theories pertaining to customer regret in an e-commerce environment. The study begins by examining the roles that information quality (IQ), system quality (SYQ), and service quality (SEQ) play in determining customer regret and satisfaction. Then the consequences of regret and satisfaction on reuse intention are examined. Survey data collected from 445 respondents are analyzed using structural equation modeling with partial least squares (PLS-Graph 3.0) to provide support for the hypothesized links. Results show that IQ disconfirmation, SYQ disconfirmation and SEQ disconfirmation are related to regret and satisfaction. Both regret and satisfaction are related to reuse intention. In addition, satisfaction mediates the effect of regret on reuse intention. Based on these results, implications for theory and practice are discussed.

Preserving Differential Privacy in Degree-Correlation based Graph Generation

PubMed Central

Wang, Yue; Wu, Xintao

2014-01-01

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

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)

Network meta-analysis, electrical networks and graph theory.

PubMed

Rücker, Gerta

2012-12-01

Network meta-analysis is an active field of research in clinical biostatistics. It aims to combine information from all randomized comparisons among a set of treatments for a given medical condition. We show how graph-theoretical methods can be applied to network meta-analysis. A meta-analytic graph consists of vertices (treatments) and edges (randomized comparisons). We illustrate the correspondence between meta-analytic networks and electrical networks, where variance corresponds to resistance, treatment effects to voltage, and weighted treatment effects to current flows. Based thereon, we then show that graph-theoretical methods that have been routinely applied to electrical networks also work well in network meta-analysis. In more detail, the resulting consistent treatment effects induced in the edges can be estimated via the Moore-Penrose pseudoinverse of the Laplacian matrix. Moreover, the variances of the treatment effects are estimated in analogy to electrical effective resistances. It is shown that this method, being computationally simple, leads to the usual fixed effect model estimate when applied to pairwise meta-analysis and is consistent with published results when applied to network meta-analysis examples from the literature. Moreover, problems of heterogeneity and inconsistency, random effects modeling and including multi-armed trials are addressed. Copyright © 2012 John Wiley & Sons, Ltd. Copyright © 2012 John Wiley & Sons, Ltd.

Phase-Space Detection of Cyber Events

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

Hernandez Jimenez, Jarilyn M; Ferber, Aaron E; Prowell, Stacy J

Energy Delivery Systems (EDS) are a network of processes that produce, transfer and distribute energy. EDS are increasingly dependent on networked computing assets, as are many Industrial Control Systems. Consequently, cyber-attacks pose a real and pertinent threat, as evidenced by Stuxnet, Shamoon and Dragonfly. Hence, there is a critical need for novel methods to detect, prevent, and mitigate effects of such attacks. To detect cyber-attacks in EDS, we developed a framework for gathering and analyzing timing data that involves establishing a baseline execution profile and then capturing the effect of perturbations in the state from injecting various malware. The datamore » analysis was based on nonlinear dynamics and graph theory to improve detection of anomalous events in cyber applications. The goal was the extraction of changing dynamics or anomalous activity in the underlying computer system. Takens' theorem in nonlinear dynamics allows reconstruction of topologically invariant, time-delay-embedding states from the computer data in a sufficiently high-dimensional space. The resultant dynamical states were nodes, and the state-to-state transitions were links in a mathematical graph. Alternatively, sequential tabulation of executing instructions provides the nodes with corresponding instruction-to-instruction links. Graph theorems guarantee graph-invariant measures to quantify the dynamical changes in the running applications. Results showed a successful detection of cyber events.« less

Information visualisation based on graph models

NASA Astrophysics Data System (ADS)

Kasyanov, V. N.; Kasyanova, E. V.

2013-05-01

Information visualisation is a key component of support tools for many applications in science and engineering. A graph is an abstract structure that is widely used to model information for its visualisation. In this paper, we consider practical and general graph formalism called hierarchical graphs and present the Higres and Visual Graph systems aimed at supporting information visualisation on the base of hierarchical graph models.

Determining the Basis of Homodesmotic Reactions of Cyclic Organic Compounds by Means of Graph Theory

NASA Astrophysics Data System (ADS)

Khursan, S. L.; Ismagilova, A. S.; Akhmetyanova, A. I.

2018-07-01

Comparative calculations based on the use of a homodesmotic reaction (HDR)—an isodesmic process with the additional requirement for group balance—is used to analyze the thermochemical characteristics of cyclic organic compounds exemplified by bicyclo[2.1.0]pentene-2. To avoid confusion in selecting HDRs, an algorithm is developed for determining the HDR basis, i.e., the set of all possible independent homodesmotic reactions. The algorithm for constructing the set of HDRs is based on an analysis and transformations of the bond graph of groups for the investigated chemical compound. The use of graph theory allows us to automate the procedure for deriving the basis of homodesmotic reactions, and to obtain a visual geometric interpretation of the basis, which is important for subsequent physicochemical analysis. The energetics of bicyclo[2.1.0]pentene-2 is investigated using the proposed approach, and the independent basis of HDRs is found to include 19 formal transformations. Standard enthalpies for the test compound and the participants of homodesmotic reactions are calculated using the G3 composite approach. Thermochemical analysis of the obtained data allows us to determine the standard enthalpy of formation of the bicycle (Δf H° = 336.4 kJ/mol) and value Δf H° of a number of cyclic and acyclic alkenes and alkadienes that are products of theoretical decomposition of the test compound. The proposed method is shown to be extremely effective in analyzing the effects of nonbonded interactions in the structure of organic molecules. The ring strain energy of the bicycle is calculated or the test compound: E S = 295.2± 2.2 kJ/mol.

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.

Molecular graph convolutions: moving beyond fingerprints.

PubMed

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

2016-08-01

Molecular "fingerprints" encoding structural information are the workhorse of cheminformatics and machine learning in drug discovery applications. However, fingerprint representations necessarily emphasize particular aspects of the molecular structure while ignoring others, rather than allowing the model to make data-driven decisions. We describe molecular graph convolutions, a machine learning architecture for learning from undirected graphs, specifically small molecules. Graph convolutions use a simple encoding of the molecular graph-atoms, bonds, distances, etc.-which allows the model to take greater advantage of information in the graph structure. Although graph convolutions do not outperform all fingerprint-based methods, they (along with other graph-based methods) represent a new paradigm in ligand-based virtual screening with exciting opportunities for future improvement.

Modeling of a bimetallic eccentric cylindrical plasma waveguide based on a transmission line for TEM-mode

NASA Astrophysics Data System (ADS)

Golharani, Saeedeh; Jazi, Bahram; Jahanbakht, Sajad; Moeini-Nashalji, Azam

2018-07-01

In this paper, a plasma waveguide made of two eccentric cylindrical metallic walls have been studied according to the theory of transmission lines. The inductance per unit length L, the capacitance per unit length C, the resistance per unit length R and the shunt conductance per unit length G are obtained. The graphs of variations of the mentioned parameters vs. geometrical dimensions of waveguide are investigated. This investigations have been done for two different types of plasma waveguide. At first stage, plasma region will be considered in cold and collisional approximation and in second stage, a drift plasma in cold collisionless approximation will be considered. Also, graphs of phase velocity variation vs. the main parameters of the waveguide are presented.

A new formation control of multiple underactuated surface vessels

NASA Astrophysics Data System (ADS)

Xie, Wenjing; Ma, Baoli; Fernando, Tyrone; Iu, Herbert Ho-Ching

2018-05-01

This work investigates a new formation control problem of multiple underactuated surface vessels. The controller design is based on input-output linearisation technique, graph theory, consensus idea and some nonlinear tools. The proposed smooth time-varying distributed control law guarantees that the multiple underactuated surface vessels globally exponentially converge to some desired geometric shape, which is especially centred at the initial average position of vessels. Furthermore, the stability analysis of zero dynamics proves that the orientations of vessels tend to some constants that are dependent on the initial values of vessels, and the velocities and control inputs of the vessels decay to zero. All the results are obtained under the communication scenarios of static directed balanced graph with a spanning tree. Effectiveness of the proposed distributed control scheme is demonstrated using a simulation example.

Multi-Centrality Graph Spectral Decompositions and Their Application to Cyber Intrusion Detection

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

Chen, Pin-Yu; Choudhury, Sutanay; Hero, Alfred

Many modern datasets can be represented as graphs and hence spectral decompositions such as graph principal component analysis (PCA) can be useful. Distinct from previous graph decomposition approaches based on subspace projection of a single topological feature, e.g., the centered graph adjacency matrix (graph Laplacian), we propose spectral decomposition approaches to graph PCA and graph dictionary learning that integrate multiple features, including graph walk statistics, centrality measures and graph distances to reference nodes. In this paper we propose a new PCA method for single graph analysis, called multi-centrality graph PCA (MC-GPCA), and a new dictionary learning method for ensembles ofmore » graphs, called multi-centrality graph dictionary learning (MC-GDL), both based on spectral decomposition of multi-centrality matrices. As an application to cyber intrusion detection, MC-GPCA can be an effective indicator of anomalous connectivity pattern and MC-GDL can provide discriminative basis for attack classification.« less

Topological Filtering of Dynamic Functional Brain Networks Unfolds Informative Chronnectomics: A Novel Data-Driven Thresholding Scheme Based on Orthogonal Minimal Spanning Trees (OMSTs)

PubMed Central

Dimitriadis, Stavros I.; Salis, Christos; Tarnanas, Ioannis; Linden, David E.

2017-01-01

The human brain is a large-scale system of functionally connected brain regions. This system can be modeled as a network, or graph, by dividing the brain into a set of regions, or “nodes,” and quantifying the strength of the connections between nodes, or “edges,” as the temporal correlation in their patterns of activity. Network analysis, a part of graph theory, provides a set of summary statistics that can be used to describe complex brain networks in a meaningful way. The large-scale organization of the brain has features of complex networks that can be quantified using network measures from graph theory. The adaptation of both bivariate (mutual information) and multivariate (Granger causality) connectivity estimators to quantify the synchronization between multichannel recordings yields a fully connected, weighted, (a)symmetric functional connectivity graph (FCG), representing the associations among all brain areas. The aforementioned procedure leads to an extremely dense network of tens up to a few hundreds of weights. Therefore, this FCG must be filtered out so that the “true” connectivity pattern can emerge. Here, we compared a large number of well-known topological thresholding techniques with the novel proposed data-driven scheme based on orthogonal minimal spanning trees (OMSTs). OMSTs filter brain connectivity networks based on the optimization between the global efficiency of the network and the cost preserving its wiring. We demonstrated the proposed method in a large EEG database (N = 101 subjects) with eyes-open (EO) and eyes-closed (EC) tasks by adopting a time-varying approach with the main goal to extract features that can totally distinguish each subject from the rest of the set. Additionally, the reliability of the proposed scheme was estimated in a second case study of fMRI resting-state activity with multiple scans. Our results demonstrated clearly that the proposed thresholding scheme outperformed a large list of thresholding schemes based on the recognition accuracy of each subject compared to the rest of the cohort (EEG). Additionally, the reliability of the network metrics based on the fMRI static networks was improved based on the proposed topological filtering scheme. Overall, the proposed algorithm could be used across neuroimaging and multimodal studies as a common computationally efficient standardized tool for a great number of neuroscientists and physicists working on numerous of projects. PMID:28491032

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

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.

Missile aerodynamics

NASA Technical Reports Server (NTRS)

Nielsen, Jack N.

1988-01-01

The fundamental aerodynamics of slender bodies is examined in the reprint edition of an introductory textbook originally published in 1960. Chapters are devoted to the formulas commonly used in missile aerodynamics; slender-body theory at supersonic and subsonic speeds; vortices in viscid and inviscid flow; wing-body interference; downwash, sidewash, and the wake; wing-tail interference; aerodynamic controls; pressure foredrag, base drag, and skin friction; and stability derivatives. Diagrams, graphs, tables of terms and formulas are provided.

Graph theoretical analysis of EEG functional network during multi-workload flight simulation experiment in virtual reality environment.

PubMed

Shengqian Zhang; Yuan Zhang; Yu Sun; Thakor, Nitish; Bezerianos, Anastasios

2017-07-01

The research field of mental workload has attracted abundant researchers as mental workload plays a crucial role in real-life performance and safety. While previous studies have examined the neural correlates of mental workload in 2D scenarios (i.e., presenting stimuli on a computer screen (CS) environment using univariate methods (e.g., EEG channel power), it is still unclear of the findings of one that uses multivariate approach using graphical theory and the effects of a 3D environment (i.e., presenting stimuli on a Virtual Reality (VR)). In this study, twenty subjects undergo flight simulation in both CS and VR environment with three stages each. After preprocessing, the Electroencephalogram (EEG) signals were a connectivity matrix based on Phase Lag Index (PLI) will be constructed. Graph theory analysis then will be applied based on their global efficiency, local efficiency and nodal efficiency on both alpha and theta band. For global efficiency and local efficiency, VR values are generally lower than CS in both bands. For nodal efficiency, the regions that show at least marginally significant decreases are very different for CS and VR. These findings suggest that 3D simulation effects a higher mental workload than 2D simulation and that they each involved a different brain region.

Graph-theoretical analysis of resting-state fMRI in pediatric obsessive-compulsive disorder

PubMed Central

Armstrong, Casey C.; Moody, Teena D.; Feusner, Jamie D.; McCracken, James T.; Chang, Susanna; Levitt, Jennifer G.; Piacentini, John C.; O'Neill, Joseph

2018-01-01

Background fMRI graph theory reveals resting-state brain networks, but has never been used in pediatric OCD. Methods Whole-brain resting-state fMRI was acquired at 3 T from 21 children with OCD and 20 age-matched healthy controls. BOLD connectivity was analyzed yielding global and local graph-theory metrics across 100 child-based functional nodes. We also compared local metrics between groups in frontopolar, supplementary motor, and sensorimotor cortices, regions implicated in recent neuroimaging and/or brain stimulation treatment studies in OCD. Results As in adults, the global metric small-worldness was significantly (P<0.05) lower in patients than controls, by 13.5% (%mean difference = 100%×(OCD mean – control mean)/control mean). This suggests less efficient information transfer in patients. In addition, modularity was lower in OCD (15.1%, P<0.01), suggesting less granular-- or differently organized-- functional brain parcellation. Higher clustering coefficients (23.9-32.4%, P<0.05) were observed in patients in frontopolar, supplementary motor, sensorimotor, and cortices with lower betweenness centrality (-63.6%, P<0.01) at one frontopolar site. These findings are consistent with more locally intensive connectivity or less interaction with other brain regions at these sites. Limitations Relatively large node size; relatively small sample size, comorbidities in some patients. Conclusions Pediatric OCD patients demonstrate aberrant global and local resting-state network connectivity topologies compared to healthy children. Local results accord with recent views of OCD as a disorder with sensorimotor component. PMID:26773910

Sparse cliques trump scale-free networks in coordination and competition

PubMed Central

Gianetto, David A.; Heydari, Babak

2016-01-01

Cooperative behavior, a natural, pervasive and yet puzzling phenomenon, can be significantly enhanced by networks. Many studies have shown how global network characteristics affect cooperation; however, it is difficult to understand how this occurs based on global factors alone, low-level network building blocks, or motifs are necessary. In this work, we systematically alter the structure of scale-free and clique networks and show, through a stochastic evolutionary game theory model, that cooperation on cliques increases linearly with community motif count. We further show that, for reactive stochastic strategies, network modularity improves cooperation in the anti-coordination Snowdrift game and the Prisoner’s Dilemma game but not in the Stag Hunt coordination game. We also confirm the negative effect of the scale-free graph on cooperation when effective payoffs are used. On the flip side, clique graphs are highly cooperative across social environments. Adding cycles to the acyclic scale-free graph increases cooperation when multiple games are considered; however, cycles have the opposite effect on how forgiving agents are when playing the Prisoner’s Dilemma game. PMID:26899456

Sparse cliques trump scale-free networks in coordination and competition

NASA Astrophysics Data System (ADS)

Gianetto, David A.; Heydari, Babak

2016-02-01

Cooperative behavior, a natural, pervasive and yet puzzling phenomenon, can be significantly enhanced by networks. Many studies have shown how global network characteristics affect cooperation; however, it is difficult to understand how this occurs based on global factors alone, low-level network building blocks, or motifs are necessary. In this work, we systematically alter the structure of scale-free and clique networks and show, through a stochastic evolutionary game theory model, that cooperation on cliques increases linearly with community motif count. We further show that, for reactive stochastic strategies, network modularity improves cooperation in the anti-coordination Snowdrift game and the Prisoner’s Dilemma game but not in the Stag Hunt coordination game. We also confirm the negative effect of the scale-free graph on cooperation when effective payoffs are used. On the flip side, clique graphs are highly cooperative across social environments. Adding cycles to the acyclic scale-free graph increases cooperation when multiple games are considered; however, cycles have the opposite effect on how forgiving agents are when playing the Prisoner’s Dilemma game.

Automatic Assignment of Methyl-NMR Spectra of Supramolecular Machines Using Graph Theory.

PubMed

Pritišanac, Iva; Degiacomi, Matteo T; Alderson, T Reid; Carneiro, Marta G; Ab, Eiso; Siegal, Gregg; Baldwin, Andrew J

2017-07-19

Methyl groups are powerful probes for the analysis of structure, dynamics and function of supramolecular assemblies, using both solution- and solid-state NMR. Widespread application of the methodology has been limited due to the challenges associated with assigning spectral resonances to specific locations within a biomolecule. Here, we present Methyl Assignment by Graph Matching (MAGMA), for the automatic assignment of methyl resonances. A graph matching protocol examines all possibilities for each resonance in order to determine an exact assignment that includes a complete description of any ambiguity. MAGMA gives 100% accuracy in confident assignments when tested against both synthetic data, and 9 cross-validated examples using both solution- and solid-state NMR data. We show that this remarkable accuracy enables a user to distinguish between alternative protein structures. In a drug discovery application on HSP90, we show the method can rapidly and efficiently distinguish between possible ligand binding modes. By providing an exact and robust solution to methyl resonance assignment, MAGMA can facilitate significantly accelerated studies of supramolecular machines using methyl-based NMR spectroscopy.

Network representation of protein interactions: Theory of graph description and analysis.

PubMed

Kurzbach, Dennis

2016-09-01

A methodological framework is presented for the graph theoretical interpretation of NMR data of protein interactions. The proposed analysis generalizes the idea of network representations of protein structures by expanding it to protein interactions. This approach is based on regularization of residue-resolved NMR relaxation times and chemical shift data and subsequent construction of an adjacency matrix that represents the underlying protein interaction as a graph or network. The network nodes represent protein residues. Two nodes are connected if two residues are functionally correlated during the protein interaction event. The analysis of the resulting network enables the quantification of the importance of each amino acid of a protein for its interactions. Furthermore, the determination of the pattern of correlations between residues yields insights into the functional architecture of an interaction. This is of special interest for intrinsically disordered proteins, since the structural (three-dimensional) architecture of these proteins and their complexes is difficult to determine. The power of the proposed methodology is demonstrated at the example of the interaction between the intrinsically disordered protein osteopontin and its natural ligand heparin. © 2016 The Protein Society.

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

A Graph Based Interface for Representing Volume Visualization Results

NASA Technical Reports Server (NTRS)

Patten, James M.; Ma, Kwan-Liu

1998-01-01

This paper discusses a graph based user interface for representing the results of the volume visualization process. As images are rendered, they are connected to other images in a graph based on their rendering parameters. The user can take advantage of the information in this graph to understand how certain rendering parameter changes affect a dataset, making the visualization process more efficient. Because the graph contains more information than is contained in an unstructured history of images, the image graph is also helpful for collaborative visualization and animation.

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.

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.

A Geometrical Approach to Bell's Theorem

NASA Technical Reports Server (NTRS)

Rubincam, David Parry

2000-01-01

Bell's theorem can be proved through simple geometrical reasoning, without the need for the Psi function, probability distributions, or calculus. The proof is based on N. David Mermin's explication of the Einstein-Podolsky-Rosen-Bohm experiment, which involves Stern-Gerlach detectors which flash red or green lights when detecting spin-up or spin-down. The statistics of local hidden variable theories for this experiment can be arranged in colored strips from which simple inequalities can be deduced. These inequalities lead to a demonstration of Bell's theorem. Moreover, all local hidden variable theories can be graphed in such a way as to enclose their statistics in a pyramid, with the quantum-mechanical result lying a finite distance beneath the base of the pyramid.

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.

Analyzing locomotion synthesis with feature-based motion graphs.

PubMed

Mahmudi, Mentar; Kallmann, Marcelo

2013-05-01

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

Ontology Design of Influential People Identification Using Centrality

NASA Astrophysics Data System (ADS)

Maulana Awangga, Rolly; Yusril, Muhammad; Setyawan, Helmi

2018-04-01

Identifying influential people as a node in a graph theory commonly calculated by social network analysis. The social network data has the user as node and edge as relation forming a friend relation graph. This research is conducting different meaning of every nodes relation in the social network. Ontology was perfect match science to describe the social network data as conceptual and domain. Ontology gives essential relationship in a social network more than a current graph. Ontology proposed as a standard for knowledge representation for the semantic web by World Wide Web Consortium. The formal data representation use Resource Description Framework (RDF) and Web Ontology Language (OWL) which is strategic for Open Knowledge-Based website data. Ontology used in the semantic description for a relationship in the social network, it is open to developing semantic based relationship ontology by adding and modifying various and different relationship to have influential people as a conclusion. This research proposes a model using OWL and RDF for influential people identification in the social network. The study use degree centrality, between ness centrality, and closeness centrality measurement for data validation. As a conclusion, influential people identification in Facebook can use proposed Ontology model in the Group, Photos, Photo Tag, Friends, Events and Works data.

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

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

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

Sengupta, Dipanjan; Song, Shuaiwen; Agarwal, Kapil

2015-11-15

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

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.

Molecular graph convolutions: moving beyond fingerprints

NASA Astrophysics Data System (ADS)

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

2016-08-01

Molecular "fingerprints" encoding structural information are the workhorse of cheminformatics and machine learning in drug discovery applications. However, fingerprint representations necessarily emphasize particular aspects of the molecular structure while ignoring others, rather than allowing the model to make data-driven decisions. We describe molecular graph convolutions, a machine learning architecture for learning from undirected graphs, specifically small molecules. Graph convolutions use a simple encoding of the molecular graph—atoms, bonds, distances, etc.—which allows the model to take greater advantage of information in the graph structure. Although graph convolutions do not outperform all fingerprint-based methods, they (along with other graph-based methods) represent a new paradigm in ligand-based virtual screening with exciting opportunities for future improvement.

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

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.

Mathematical biodescriptors of proteomics maps: background and applications.

PubMed

Basak, Subhash C; Gute, Brian D

2008-05-01

This article reviews recent developments in the formulation and application of biodescriptors to characterize proteomics maps. Such biodescriptors can be derived by applying techniques from discrete mathematics (graph theory, linear algebra and information theory). This review focuses on the development of biodescriptors for proteomics maps derived from 2D gel electrophoresis. Preliminary results demonstrated that such descriptors have a reasonable ability to differentiate between proteomics patterns that result from exposure to closely related individual chemicals and complex mixtures, such as the jet fuel JP-8. Further research is required to evaluate the utility of these proteomics-based biodescriptors for drug discovery and predictive toxicology.

Investigation of Zero Knowledge Proof Approaches Based on Graph Theory

DTIC Science & Technology

2011-02-01

that appears frequently in the literature is a metaheuristic algorithm called the Pilot Method. The Pilot Method improves upon another heuristic...Annual ACM-SIAM Symposium on Discrete Algorithms . Miami: ACM, 2006. 1-10. Voß, S., and C. Duin. "Look Ahead Features in Metaheuristics ." MIC2003...The Fifth Metaheuristics International Conference, 2003: 79-1 - 79-7. Woeginger, G.J. "Exact Algorithms for NP-Hard Problems: A Survey." Lecture

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

Text categorization of biomedical data sets using graph kernels and a controlled vocabulary.

PubMed

Bleik, Said; Mishra, Meenakshi; Huan, Jun; Song, Min

2013-01-01

Recently, graph representations of text have been showing improved performance over conventional bag-of-words representations in text categorization applications. In this paper, we present a graph-based representation for biomedical articles and use graph kernels to classify those articles into high-level categories. In our representation, common biomedical concepts and semantic relationships are identified with the help of an existing ontology and are used to build a rich graph structure that provides a consistent feature set and preserves additional semantic information that could improve a classifier's performance. We attempt to classify the graphs using both a set-based graph kernel that is capable of dealing with the disconnected nature of the graphs and a simple linear kernel. Finally, we report the results comparing the classification performance of the kernel classifiers to common text-based classifiers.

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

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

Sengupta, Dipanjan; Agarwal, Kapil; Song, Shuaiwen

2015-09-30

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

Molecular graph convolutions: moving beyond fingerprints

PubMed Central

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

2016-01-01

Molecular “fingerprints” encoding structural information are the workhorse of cheminformatics and machine learning in drug discovery applications. However, fingerprint representations necessarily emphasize particular aspects of the molecular structure while ignoring others, rather than allowing the model to make data-driven decisions. We describe molecular graph convolutions, a machine learning architecture for learning from undirected graphs, specifically small molecules. Graph convolutions use a simple encoding of the molecular graph—atoms, bonds, distances, etc.—which allows the model to take greater advantage of information in the graph structure. Although graph convolutions do not outperform all fingerprint-based methods, they (along with other graph-based methods) represent a new paradigm in ligand-based virtual screening with exciting opportunities for future improvement. PMID:27558503

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.

Infrared and visible image fusion with spectral graph wavelet transform.

PubMed

Yan, Xiang; Qin, Hanlin; Li, Jia; Zhou, Huixin; Zong, Jing-guo

2015-09-01

Infrared and visible image fusion technique is a popular topic in image analysis because it can integrate complementary information and obtain reliable and accurate description of scenes. Multiscale transform theory as a signal representation method is widely used in image fusion. In this paper, a novel infrared and visible image fusion method is proposed based on spectral graph wavelet transform (SGWT) and bilateral filter. The main novelty of this study is that SGWT is used for image fusion. On the one hand, source images are decomposed by SGWT in its transform domain. The proposed approach not only effectively preserves the details of different source images, but also excellently represents the irregular areas of the source images. On the other hand, a novel weighted average method based on bilateral filter is proposed to fuse low- and high-frequency subbands by taking advantage of spatial consistency of natural images. Experimental results demonstrate that the proposed method outperforms seven recently proposed image fusion methods in terms of both visual effect and objective evaluation metrics.

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

Mathematical foundations of the GraphBLAS

DOE PAGES

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

2016-12-01

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

New methods for analyzing semantic graph based assessments in science education

NASA Astrophysics Data System (ADS)

Vikaros, Lance Steven

This research investigated how the scoring of semantic graphs (known by many as concept maps) could be improved and automated in order to address issues of inter-rater reliability and scalability. As part of the NSF funded SENSE-IT project to introduce secondary school science students to sensor networks (NSF Grant No. 0833440), semantic graphs illustrating how temperature change affects water ecology were collected from 221 students across 16 schools. The graphing task did not constrain students' use of terms, as is often done with semantic graph based assessment due to coding and scoring concerns. The graphing software used provided real-time feedback to help students learn how to construct graphs, stay on topic and effectively communicate ideas. The collected graphs were scored by human raters using assessment methods expected to boost reliability, which included adaptations of traditional holistic and propositional scoring methods, use of expert raters, topical rubrics, and criterion graphs. High levels of inter-rater reliability were achieved, demonstrating that vocabulary constraints may not be necessary after all. To investigate a new approach to automating the scoring of graphs, thirty-two different graph features characterizing graphs' structure, semantics, configuration and process of construction were then used to predict human raters' scoring of graphs in order to identify feature patterns correlated to raters' evaluations of graphs' topical accuracy and complexity. Results led to the development of a regression model able to predict raters' scoring with 77% accuracy, with 46% accuracy expected when used to score new sets of graphs, as estimated via cross-validation tests. Although such performance is comparable to other graph and essay based scoring systems, cross-context testing of the model and methods used to develop it would be needed before it could be recommended for widespread use. Still, the findings suggest techniques for improving the reliability and scalability of semantic graph based assessments without requiring constraint of how ideas are expressed.

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.

xQuake: A Modern Approach to Seismic Network Analytics

NASA Astrophysics Data System (ADS)

Johnson, C. E.; Aikin, K. E.

2017-12-01

While seismic networks have expanded over the past few decades, and social needs for accurate and timely information has increased dramatically, approaches to the operational needs of both global and regional seismic observatories have been slow to adopt new technologies. This presentation presents the xQuake system that provides a fresh approach to seismic network analytics based on complexity theory and an adaptive architecture of streaming connected microservices as diverse data (picks, beams, and other data) flow into a final, curated catalog of events. The foundation for xQuake is the xGraph (executable graph) framework that is essentially a self-organizing graph database. An xGraph instance provides both the analytics as well as the data storage capabilities at the same time. Much of the analytics, such as synthetic annealing in the detection process and an evolutionary programing approach for event evolution, draws from the recent GLASS 3.0 seismic associator developed by and for the USGS National Earthquake Information Center (NEIC). In some respects xQuake is reminiscent of the Earthworm system, in that it comprises processes interacting through store and forward rings; not surprising as the first author was the lead architect of the original Earthworm project when it was known as "Rings and Things". While Earthworm components can easily be integrated into the xGraph processing framework, the architecture and analytics are more current (e.g. using a Kafka Broker for store and forward rings). The xQuake system is being released under an unrestricted open source license to encourage and enable sthe eismic community support in further development of its capabilities.

Transforming graph states using single-qubit operations.

PubMed

Dahlberg, Axel; Wehner, Stephanie

2018-07-13

Stabilizer states form an important class of states in quantum information, and are of central importance in quantum error correction. Here, we provide an algorithm for deciding whether one stabilizer (target) state can be obtained from another stabilizer (source) state by single-qubit Clifford operations (LC), single-qubit Pauli measurements (LPM) and classical communication (CC) between sites holding the individual qubits. What is more, we provide a recipe to obtain the sequence of LC+LPM+CC operations which prepare the desired target state from the source state, and show how these operations can be applied in parallel to reach the target state in constant time. Our algorithm has applications in quantum networks, quantum computing, and can also serve as a design tool-for example, to find transformations between quantum error correcting codes. We provide a software implementation of our algorithm that makes this tool easier to apply. A key insight leading to our algorithm is to show that the problem is equivalent to one in graph theory, which is to decide whether some graph G ' is a vertex-minor of another graph G The vertex-minor problem is, in general, [Formula: see text]-Complete, but can be solved efficiently on graphs which are not too complex. A measure of the complexity of a graph is the rank-width which equals the Schmidt-rank width of a subclass of stabilizer states called graph states, and thus intuitively is a measure of entanglement. Here, we show that the vertex-minor problem can be solved in time O (| G | 3 ), where | G | is the size of the graph G , whenever the rank-width of G and the size of G ' are bounded. Our algorithm is based on techniques by Courcelle for solving fixed parameter tractable problems, where here the relevant fixed parameter is the rank width. The second half of this paper serves as an accessible but far from exhausting introduction to these concepts, that could be useful for many other problems in quantum information.This article is part of a discussion meeting issue 'Foundations of quantum mechanics and their impact on contemporary society'. © 2018 The Author(s).

Graph Kernels for Molecular Similarity.

PubMed

Rupp, Matthias; Schneider, Gisbert

2010-04-12

Molecular similarity measures are important for many cheminformatics applications like ligand-based virtual screening and quantitative structure-property relationships. Graph kernels are formal similarity measures defined directly on graphs, such as the (annotated) molecular structure graph. Graph kernels are positive semi-definite functions, i.e., they correspond to inner products. This property makes them suitable for use with kernel-based machine learning algorithms such as support vector machines and Gaussian processes. We review the major types of kernels between graphs (based on random walks, subgraphs, and optimal assignments, respectively), and discuss their advantages, limitations, and successful applications in cheminformatics. Copyright © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

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.

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

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.

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…

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

Multiparametric MRI characterization and prediction in autism spectrum disorder using graph theory and machine learning.

PubMed

Zhou, Yongxia; Yu, Fang; Duong, Timothy

2014-01-01

This study employed graph theory and machine learning analysis of multiparametric MRI data to improve characterization and prediction in autism spectrum disorders (ASD). Data from 127 children with ASD (13.5±6.0 years) and 153 age- and gender-matched typically developing children (14.5±5.7 years) were selected from the multi-center Functional Connectome Project. Regional gray matter volume and cortical thickness increased, whereas white matter volume decreased in ASD compared to controls. Small-world network analysis of quantitative MRI data demonstrated decreased global efficiency based on gray matter cortical thickness but not with functional connectivity MRI (fcMRI) or volumetry. An integrative model of 22 quantitative imaging features was used for classification and prediction of phenotypic features that included the autism diagnostic observation schedule, the revised autism diagnostic interview, and intelligence quotient scores. Among the 22 imaging features, four (caudate volume, caudate-cortical functional connectivity and inferior frontal gyrus functional connectivity) were found to be highly informative, markedly improving classification and prediction accuracy when compared with the single imaging features. This approach could potentially serve as a biomarker in prognosis, diagnosis, and monitoring disease progression.

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

GrouseFlocks: steerable exploration of graph hierarchy space.

PubMed

Archambault, Daniel; Munzner, Tamara; Auber, David

2008-01-01

Several previous systems allow users to interactively explore a large input graph through cuts of a superimposed hierarchy. This hierarchy is often created using clustering algorithms or topological features present in the graph. However, many graphs have domain-specific attributes associated with the nodes and edges, which could be used to create many possible hierarchies providing unique views of the input graph. GrouseFlocks is a system for the exploration of this graph hierarchy space. By allowing users to see several different possible hierarchies on the same graph, the system helps users investigate graph hierarchy space instead of a single fixed hierarchy. GrouseFlocks provides a simple set of operations so that users can create and modify their graph hierarchies based on selections. These selections can be made manually or based on patterns in the attribute data provided with the graph. It provides feedback to the user within seconds, allowing interactive exploration of this space.

Yangian symmetry for bi-scalar loop amplitudes

NASA Astrophysics Data System (ADS)

Chicherin, Dmitry; Kazakov, Vladimir; Loebbert, Florian; Müller, Dennis; Zhong, De-liang

2018-05-01

We establish an all-loop conformal Yangian symmetry for the full set of planar amplitudes in the recently proposed integrable bi-scalar field theory in four dimensions. This chiral theory is a particular double scaling limit of γ-twisted weakly coupled N=4 SYM theory. Each amplitude with a certain order of scalar particles is given by a single fishnet Feynman graph of disc topology cut out of a regular square lattice. The Yangian can be realized by the action of a product of Lax operators with a specific sequence of inhomogeneity parameters on the boundary of the disc. Based on this observation, the Yangian generators of level one for generic bi-scalar amplitudes are explicitly constructed. Finally, we comment on the relation to the dual conformal symmetry of these scattering amplitudes.

Holography as deep learning

NASA Astrophysics Data System (ADS)

Gan, Wen-Cong; Shu, Fu-Wen

Quantum many-body problem with exponentially large degrees of freedom can be reduced to a tractable computational form by neural network method [G. Carleo and M. Troyer, Science 355 (2017) 602, arXiv:1606.02318.] The power of deep neural network (DNN) based on deep learning is clarified by mapping it to renormalization group (RG), which may shed lights on holographic principle by identifying a sequence of RG transformations to the AdS geometry. In this paper, we show that any network which reflects RG process has intrinsic hyperbolic geometry, and discuss the structure of entanglement encoded in the graph of DNN. We find the entanglement structure of DNN is of Ryu-Takayanagi form. Based on these facts, we argue that the emergence of holographic gravitational theory is related to deep learning process of the quantum-field theory.

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.

A study of the spreading scheme for viral marketing based on a complex network model

NASA Astrophysics Data System (ADS)

Yang, Jianmei; Yao, Canzhong; Ma, Weicheng; Chen, Guanrong

2010-02-01

Buzzword-based viral marketing, known also as digital word-of-mouth marketing, is a marketing mode attached to some carriers on the Internet, which can rapidly copy marketing information at a low cost. Viral marketing actually uses a pre-existing social network where, however, the scale of the pre-existing network is believed to be so large and so random, so that its theoretical analysis is intractable and unmanageable. There are very few reports in the literature on how to design a spreading scheme for viral marketing on real social networks according to the traditional marketing theory or the relatively new network marketing theory. Complex network theory provides a new model for the study of large-scale complex systems, using the latest developments of graph theory and computing techniques. From this perspective, the present paper extends the complex network theory and modeling into the research of general viral marketing and develops a specific spreading scheme for viral marking and an approach to design the scheme based on a real complex network on the QQ instant messaging system. This approach is shown to be rather universal and can be further extended to the design of various spreading schemes for viral marketing based on different instant messaging systems.

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.

Safety models incorporating graph theory based transit indicators.

PubMed

Quintero, Liliana; Sayed, Tarek; Wahba, Mohamed M

2013-01-01

There is a considerable need for tools to enable the evaluation of the safety of transit networks at the planning stage. One interesting approach for the planning of public transportation systems is the study of networks. Network techniques involve the analysis of systems by viewing them as a graph composed of a set of vertices (nodes) and edges (links). Once the transport system is visualized as a graph, various network properties can be evaluated based on the relationships between the network elements. Several indicators can be calculated including connectivity, coverage, directness and complexity, among others. The main objective of this study is to investigate the relationship between network-based transit indicators and safety. The study develops macro-level collision prediction models that explicitly incorporate transit physical and operational elements and transit network indicators as explanatory variables. Several macro-level (zonal) collision prediction models were developed using a generalized linear regression technique, assuming a negative binomial error structure. The models were grouped into four main themes: transit infrastructure, transit network topology, transit route design, and transit performance and operations. The safety models showed that collisions were significantly associated with transit network properties such as: connectivity, coverage, overlapping degree and the Local Index of Transit Availability. As well, the models showed a significant relationship between collisions and some transit physical and operational attributes such as the number of routes, frequency of routes, bus density, length of bus and 3+ priority lanes. Copyright © 2012 Elsevier Ltd. All rights reserved.

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.

Presurgery resting-state local graph-theory measures predict neurocognitive outcomes after brain surgery in temporal lobe epilepsy.

PubMed

Doucet, Gaelle E; Rider, Robert; Taylor, Nathan; Skidmore, Christopher; Sharan, Ashwini; Sperling, Michael; Tracy, Joseph I

2015-04-01

This study determined the ability of resting-state functional connectivity (rsFC) graph-theory measures to predict neurocognitive status postsurgery in patients with temporal lobe epilepsy (TLE) who underwent anterior temporal lobectomy (ATL). A presurgical resting-state functional magnetic resonance imaging (fMRI) condition was collected in 16 left and 16 right TLE patients who underwent ATL. In addition, patients received neuropsychological testing pre- and postsurgery in verbal and nonverbal episodic memory, language, working memory, and attention domains. Regarding the functional data, we investigated three graph-theory properties (local efficiency, distance, and participation), measuring segregation, integration and centrality, respectively. These measures were only computed in regions of functional relevance to the ictal pathology, or the cognitive domain. Linear regression analyses were computed to predict the change in each neurocognitive domain. Our analyses revealed that cognitive outcome was successfully predicted with at least 68% of the variance explained in each model, for both TLE groups. The only model not significantly predictive involved nonverbal episodic memory outcome in right TLE. Measures involving the healthy hippocampus were the most common among the predictors, suggesting that enhanced integration of this structure with the rest of the brain may improve cognitive outcomes. Regardless of TLE group, left inferior frontal regions were the best predictors of language outcome. Working memory outcome was predicted mostly by right-sided regions, in both groups. Overall, the results indicated our integration measure was the most predictive of neurocognitive outcome. In contrast, our segregation measure was the least predictive. This study provides evidence that presurgery rsFC measures may help determine neurocognitive outcomes following ATL. The results have implications for refining our understanding of compensatory reorganization and predicting cognitive outcome after ATL. The results are encouraging with regard to the clinical relevance of using graph-theory measures in presurgical algorithms in the setting of TLE. Wiley Periodicals, Inc. © 2015 International League Against Epilepsy.

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

ERIC Educational Resources Information Center

Deniz, Hasan; Dulger, Mehmet F.

2012-01-01

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

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

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

A framework for graph-based synthesis, analysis, and visualization of HPC cluster job data.

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

Mayo, Jackson R.; Kegelmeyer, W. Philip, Jr.; Wong, Matthew H.

The monitoring and system analysis of high performance computing (HPC) clusters is of increasing importance to the HPC community. Analysis of HPC job data can be used to characterize system usage and diagnose and examine failure modes and their effects. This analysis is not straightforward, however, due to the complex relationships that exist between jobs. These relationships are based on a number of factors, including shared compute nodes between jobs, proximity of jobs in time, etc. Graph-based techniques represent an approach that is particularly well suited to this problem, and provide an effective technique for discovering important relationships in jobmore » queuing and execution data. The efficacy of these techniques is rooted in the use of a semantic graph as a knowledge representation tool. In a semantic graph job data, represented in a combination of numerical and textual forms, can be flexibly processed into edges, with corresponding weights, expressing relationships between jobs, nodes, users, and other relevant entities. This graph-based representation permits formal manipulation by a number of analysis algorithms. This report presents a methodology and software implementation that leverages semantic graph-based techniques for the system-level monitoring and analysis of HPC clusters based on job queuing and execution data. Ontology development and graph synthesis is discussed with respect to the domain of HPC job data. The framework developed automates the synthesis of graphs from a database of job information. It also provides a front end, enabling visualization of the synthesized graphs. Additionally, an analysis engine is incorporated that provides performance analysis, graph-based clustering, and failure prediction capabilities for HPC systems.« less

A Ranking Approach on Large-Scale Graph With Multidimensional Heterogeneous Information.

PubMed

Wei, Wei; Gao, Bin; Liu, Tie-Yan; Wang, Taifeng; Li, Guohui; Li, Hang

2016-04-01

Graph-based ranking has been extensively studied and frequently applied in many applications, such as webpage ranking. It aims at mining potentially valuable information from the raw graph-structured data. Recently, with the proliferation of rich heterogeneous information (e.g., node/edge features and prior knowledge) available in many real-world graphs, how to effectively and efficiently leverage all information to improve the ranking performance becomes a new challenging problem. Previous methods only utilize part of such information and attempt to rank graph nodes according to link-based methods, of which the ranking performances are severely affected by several well-known issues, e.g., over-fitting or high computational complexity, especially when the scale of graph is very large. In this paper, we address the large-scale graph-based ranking problem and focus on how to effectively exploit rich heterogeneous information of the graph to improve the ranking performance. Specifically, we propose an innovative and effective semi-supervised PageRank (SSP) approach to parameterize the derived information within a unified semi-supervised learning framework (SSLF-GR), then simultaneously optimize the parameters and the ranking scores of graph nodes. Experiments on the real-world large-scale graphs demonstrate that our method significantly outperforms the algorithms that consider such graph information only partially.

Coordinates and intervals in graph-based reference genomes.

PubMed

Rand, Knut D; Grytten, Ivar; Nederbragt, Alexander J; Storvik, Geir O; Glad, Ingrid K; Sandve, Geir K

2017-05-18

It has been proposed that future reference genomes should be graph structures in order to better represent the sequence diversity present in a species. However, there is currently no standard method to represent genomic intervals, such as the positions of genes or transcription factor binding sites, on graph-based reference genomes. We formalize offset-based coordinate systems on graph-based reference genomes and introduce methods for representing intervals on these reference structures. We show the advantage of our methods by representing genes on a graph-based representation of the newest assembly of the human genome (GRCh38) and its alternative loci for regions that are highly variable. More complex reference genomes, containing alternative loci, require methods to represent genomic data on these structures. Our proposed notation for genomic intervals makes it possible to fully utilize the alternative loci of the GRCh38 assembly and potential future graph-based reference genomes. We have made a Python package for representing such intervals on offset-based coordinate systems, available at https://github.com/uio-cels/offsetbasedgraph . An interactive web-tool using this Python package to visualize genes on a graph created from GRCh38 is available at https://github.com/uio-cels/genomicgraphcoords .

Managing changes in distributed biomedical ontologies using hierarchical distributed graph transformation.

PubMed

Shaban-Nejad, Arash; Haarslev, Volker

2015-01-01

The issue of ontology evolution and change management is inadequately addressed by available tools and algorithms, mostly due to the lack of suitable knowledge representation formalisms to deal with temporal abstract notations and the overreliance on human factors. Also most of the current approaches have been focused on changes within the internal structure of ontologies and interactions with other existing ontologies have been widely neglected. In our research, after revealing and classifying some of the common alterations in a number of popular biomedical ontologies, we present a novel agent-based framework, Represent, Legitimate and Reproduce (RLR), to semi-automatically manage the evolution of bio-ontologies, with emphasis on the FungalWeb Ontology, with minimal human intervention. RLR assists and guides ontology engineers through the change management process in general and aids in tracking and representing the changes, particularly through the use of category theory and hierarchical graph transformation.

On a phase diagram for random neural networks with embedded spike timing dependent plasticity.

PubMed

Turova, Tatyana S; Villa, Alessandro E P

2007-01-01

This paper presents an original mathematical framework based on graph theory which is a first attempt to investigate the dynamics of a model of neural networks with embedded spike timing dependent plasticity. The neurons correspond to integrate-and-fire units located at the vertices of a finite subset of 2D lattice. There are two types of vertices, corresponding to the inhibitory and the excitatory neurons. The edges are directed and labelled by the discrete values of the synaptic strength. We assume that there is an initial firing pattern corresponding to a subset of units that generate a spike. The number of activated externally vertices is a small fraction of the entire network. The model presented here describes how such pattern propagates throughout the network as a random walk on graph. Several results are compared with computational simulations and new data are presented for identifying critical parameters of the model.

Topological analysis of metabolic control.

PubMed

Sen, A K

1990-12-01

A topological approach is presented for the analysis of control and regulation in metabolic pathways. In this approach, the control structure of a metabolic pathway is represented by a weighted directed graph. From an inspection of the topology of the graph, the control coefficients of the enzymes are evaluated in a heuristic manner in terms of the enzyme elasticities. The major advantage of the topological approach is that it provides a visual framework for (1) calculating the control coefficients of the enzymes, (2) analyzing the cause-effect relationships of the individual enzymes, (3) assessing the relative importance of the enzymes in metabolic regulation, and (4) simplifying the structure of a given pathway, from a regulatory viewpoint. Results are obtained for (a) an unbranched pathway in the absence of feedback the feedforward regulation and (b) an unbranched pathway with feedback inhibition. Our formulation is based on the metabolic control theory of Kacser and Burns (1973) and Heinrich and Rapoport (1974).

A comparison of video modeling, text-based instruction, and no instruction for creating multiple baseline graphs in Microsoft Excel.

PubMed

Tyner, Bryan C; Fienup, Daniel M

2015-09-01

Graphing is socially significant for behavior analysts; however, graphing can be difficult to learn. Video modeling (VM) may be a useful instructional method but lacks evidence for effective teaching of computer skills. A between-groups design compared the effects of VM, text-based instruction, and no instruction on graphing performance. Participants who used VM constructed graphs significantly faster and with fewer errors than those who used text-based instruction or no instruction. Implications for instruction are discussed. © Society for the Experimental Analysis of Behavior.

Application of advanced machine learning methods on resting-state fMRI network for identification of mild cognitive impairment and Alzheimer's disease.

PubMed

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

2016-09-01

The study of brain networks by resting-state functional magnetic resonance imaging (rs-fMRI) is a promising method for identifying patients with dementia from healthy controls (HC). Using graph theory, different aspects of the brain network can be efficiently characterized by calculating measures of integration and segregation. In this study, we combined a graph theoretical approach with advanced machine learning methods to study the brain network in 89 patients with mild cognitive impairment (MCI), 34 patients with Alzheimer's disease (AD), and 45 age-matched HC. The rs-fMRI connectivity matrix was constructed using a brain parcellation based on a 264 putative functional areas. Using the optimal features extracted from the graph measures, we were able to accurately classify three groups (i.e., HC, MCI, and AD) with accuracy of 88.4 %. We also investigated performance of our proposed method for a binary classification of a group (e.g., MCI) from two other groups (e.g., HC and AD). The classification accuracies for identifying HC from AD and MCI, AD from HC and MCI, and MCI from HC and AD, were 87.3, 97.5, and 72.0 %, respectively. In addition, results based on the parcellation of 264 regions were compared to that of the automated anatomical labeling atlas (AAL), consisted of 90 regions. The accuracy of classification of three groups using AAL was degraded to 83.2 %. Our results show that combining the graph measures with the machine learning approach, on the basis of the rs-fMRI connectivity analysis, may assist in diagnosis of AD and MCI.

Graph reconstruction using covariance-based methods.

PubMed

Sulaimanov, Nurgazy; Koeppl, Heinz

2016-12-01

Methods based on correlation and partial correlation are today employed in the reconstruction of a statistical interaction graph from high-throughput omics data. These dedicated methods work well even for the case when the number of variables exceeds the number of samples. In this study, we investigate how the graphs extracted from covariance and concentration matrix estimates are related by using Neumann series and transitive closure and through discussing concrete small examples. Considering the ideal case where the true graph is available, we also compare correlation and partial correlation methods for large realistic graphs. In particular, we perform the comparisons with optimally selected parameters based on the true underlying graph and with data-driven approaches where the parameters are directly estimated from the data.

Flocking of multiple mobile robots based on backstepping.

PubMed

Dong, Wenjie

2011-04-01

This paper considers the flocking of multiple nonholonomic wheeled mobile robots. Distributed controllers are proposed with the aid of backstepping techniques, results from graph theory, and singular perturbation theory. The proposed controllers can make the states of a group of robots converge to a desired geometric pattern whose centroid moves along a desired trajectory under the condition that the desired trajectory is available to a portion of the group of robots. Since communication delay is inevitable in distributed control, its effect on the performance of the closed-loop systems is analyzed. It is shown that the proposed controllers work well if communication delays are constant. To show effectiveness of the proposed controllers, simulation results are included.

Gravity on-shell diagrams

DOE PAGES

Herrmann, Enrico; Trnka, Jaroslav

2016-11-22

Here, we study on-shell diagrams for gravity theories with any number of super-symmetries and find a compact Grassmannian formula in terms of edge variables of the graphs. Unlike in gauge theory where the analogous form involves only d log-factors, in gravity there is a non-trivial numerator as well as higher degree poles in the edge variables. Based on the structure of the Grassmannian formula for N = 8 supergravity we conjecture that gravity loop amplitudes also possess similar properties. In particular, we find that there are only logarithmic singularities on cuts with finite loop momentum and that poles at infinitymore » are present, in complete agreement with the conjecture presented in.« less

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

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.

Constructing compact and effective graphs for recommender systems via node and edge aggregations

DOE PAGES

Lee, Sangkeun; Kahng, Minsuk; Lee, Sang-goo

2014-12-10

Exploiting graphs for recommender systems has great potential to flexibly incorporate heterogeneous information for producing better recommendation results. As our baseline approach, we first introduce a naive graph-based recommendation method, which operates with a heterogeneous log-metadata graph constructed from user log and content metadata databases. Although the na ve graph-based recommendation method is simple, it allows us to take advantages of heterogeneous information and shows promising flexibility and recommendation accuracy. However, it often leads to extensive processing time due to the sheer size of the graphs constructed from entire user log and content metadata databases. In this paper, we proposemore » node and edge aggregation approaches to constructing compact and e ective graphs called Factor-Item bipartite graphs by aggregating nodes and edges of a log-metadata graph. Furthermore, experimental results using real world datasets indicate that our approach can significantly reduce the size of graphs exploited for recommender systems without sacrificing the recommendation quality.« less

graphkernels: R and Python packages for graph comparison

PubMed Central

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

2018-01-01

Abstract Summary Measuring the similarity of graphs is a fundamental step in the analysis of graph-structured data, which is omnipresent in computational biology. Graph kernels have been proposed as a powerful and efficient approach to this problem of graph comparison. Here we provide graphkernels, the first R and Python graph kernel libraries including baseline kernels such as label histogram based kernels, classic graph kernels such as random walk based kernels, and the state-of-the-art Weisfeiler-Lehman graph kernel. The core of all graph kernels is implemented in C ++ for efficiency. Using the kernel matrices computed by the package, we can easily perform tasks such as classification, regression and clustering on graph-structured samples. Availability and implementation The R and Python packages including source code are available at https://CRAN.R-project.org/package=graphkernels and https://pypi.python.org/pypi/graphkernels. Contact mahito@nii.ac.jp or elisabetta.ghisu@bsse.ethz.ch Supplementary information Supplementary data are available online at Bioinformatics. PMID:29028902

graphkernels: R and Python packages for graph comparison.

PubMed

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

2018-02-01

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

An MBO Scheme for Minimizing the Graph Ohta-Kawasaki Functional

NASA Astrophysics Data System (ADS)

van Gennip, Yves

2018-06-01

We study a graph-based version of the Ohta-Kawasaki functional, which was originally introduced in a continuum setting to model pattern formation in diblock copolymer melts and has been studied extensively as a paradigmatic example of a variational model for pattern formation. Graph-based problems inspired by partial differential equations (PDEs) and variational methods have been the subject of many recent papers in the mathematical literature, because of their applications in areas such as image processing and data classification. This paper extends the area of PDE inspired graph-based problems to pattern-forming models, while continuing in the tradition of recent papers in the field. We introduce a mass conserving Merriman-Bence-Osher (MBO) scheme for minimizing the graph Ohta-Kawasaki functional with a mass constraint. We present three main results: (1) the Lyapunov functionals associated with this MBO scheme Γ -converge to the Ohta-Kawasaki functional (which includes the standard graph-based MBO scheme and total variation as a special case); (2) there is a class of graphs on which the Ohta-Kawasaki MBO scheme corresponds to a standard MBO scheme on a transformed graph and for which generalized comparison principles hold; (3) this MBO scheme allows for the numerical computation of (approximate) minimizers of the graph Ohta-Kawasaki functional with a mass constraint.

Annotation Graphs: A Graph-Based Visualization for Meta-Analysis of Data Based on User-Authored Annotations.

PubMed

Zhao, Jian; Glueck, Michael; Breslav, Simon; Chevalier, Fanny; Khan, Azam

2017-01-01

User-authored annotations of data can support analysts in the activity of hypothesis generation and sensemaking, where it is not only critical to document key observations, but also to communicate insights between analysts. We present annotation graphs, a dynamic graph visualization that enables meta-analysis of data based on user-authored annotations. The annotation graph topology encodes annotation semantics, which describe the content of and relations between data selections, comments, and tags. We present a mixed-initiative approach to graph layout that integrates an analyst's manual manipulations with an automatic method based on similarity inferred from the annotation semantics. Various visual graph layout styles reveal different perspectives on the annotation semantics. Annotation graphs are implemented within C8, a system that supports authoring annotations during exploratory analysis of a dataset. We apply principles of Exploratory Sequential Data Analysis (ESDA) in designing C8, and further link these to an existing task typology in the visualization literature. We develop and evaluate the system through an iterative user-centered design process with three experts, situated in the domain of analyzing HCI experiment data. The results suggest that annotation graphs are effective as a method of visually extending user-authored annotations to data meta-analysis for discovery and organization of ideas.

Massively parallel sparse matrix function calculations with NTPoly

NASA Astrophysics Data System (ADS)

Dawson, William; Nakajima, Takahito

2018-04-01

We present NTPoly, a massively parallel library for computing the functions of sparse, symmetric matrices. The theory of matrix functions is a well developed framework with a wide range of applications including differential equations, graph theory, and electronic structure calculations. One particularly important application area is diagonalization free methods in quantum chemistry. When the input and output of the matrix function are sparse, methods based on polynomial expansions can be used to compute matrix functions in linear time. We present a library based on these methods that can compute a variety of matrix functions. Distributed memory parallelization is based on a communication avoiding sparse matrix multiplication algorithm. OpenMP task parallellization is utilized to implement hybrid parallelization. We describe NTPoly's interface and show how it can be integrated with programs written in many different programming languages. We demonstrate the merits of NTPoly by performing large scale calculations on the K computer.

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.

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.

An internet graph model based on trade-off optimization

NASA Astrophysics Data System (ADS)

Alvarez-Hamelin, J. I.; Schabanel, N.

2004-03-01

This paper presents a new model for the Internet graph (AS graph) based on the concept of heuristic trade-off optimization, introduced by Fabrikant, Koutsoupias and Papadimitriou in[CITE] to grow a random tree with a heavily tailed degree distribution. We propose here a generalization of this approach to generate a general graph, as a candidate for modeling the Internet. We present the results of our simulations and an analysis of the standard parameters measured in our model, compared with measurements from the physical Internet graph.

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).

PRIMAL: Page Rank-Based Indoor Mapping and Localization Using Gene-Sequenced Unlabeled WLAN Received Signal Strength

PubMed Central

Zhou, Mu; Zhang, Qiao; Xu, Kunjie; Tian, Zengshan; Wang, Yanmeng; He, Wei

2015-01-01

Due to the wide deployment of wireless local area networks (WLAN), received signal strength (RSS)-based indoor WLAN localization has attracted considerable attention in both academia and industry. In this paper, we propose a novel page rank-based indoor mapping and localization (PRIMAL) by using the gene-sequenced unlabeled WLAN RSS for simultaneous localization and mapping (SLAM). Specifically, first of all, based on the observation of the motion patterns of the people in the target environment, we use the Allen logic to construct the mobility graph to characterize the connectivity among different areas of interest. Second, the concept of gene sequencing is utilized to assemble the sporadically-collected RSS sequences into a signal graph based on the transition relations among different RSS sequences. Third, we apply the graph drawing approach to exhibit both the mobility graph and signal graph in a more readable manner. Finally, the page rank (PR) algorithm is proposed to construct the mapping from the signal graph into the mobility graph. The experimental results show that the proposed approach achieves satisfactory localization accuracy and meanwhile avoids the intensive time and labor cost involved in the conventional location fingerprinting-based indoor WLAN localization. PMID:26404274

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.

An efficient graph theory based method to identify every minimal reaction set in a metabolic network

PubMed Central

2014-01-01

Background Development of cells with minimal metabolic functionality is gaining importance due to their efficiency in producing chemicals and fuels. Existing computational methods to identify minimal reaction sets in metabolic networks are computationally expensive. Further, they identify only one of the several possible minimal reaction sets. Results In this paper, we propose an efficient graph theory based recursive optimization approach to identify all minimal reaction sets. Graph theoretical insights offer systematic methods to not only reduce the number of variables in math programming and increase its computational efficiency, but also provide efficient ways to find multiple optimal solutions. The efficacy of the proposed approach is demonstrated using case studies from Escherichia coli and Saccharomyces cerevisiae. In case study 1, the proposed method identified three minimal reaction sets each containing 38 reactions in Escherichia coli central metabolic network with 77 reactions. Analysis of these three minimal reaction sets revealed that one of them is more suitable for developing minimal metabolism cell compared to other two due to practically achievable internal flux distribution. In case study 2, the proposed method identified 256 minimal reaction sets from the Saccharomyces cerevisiae genome scale metabolic network with 620 reactions. The proposed method required only 4.5 hours to identify all the 256 minimal reaction sets and has shown a significant reduction (approximately 80%) in the solution time when compared to the existing methods for finding minimal reaction set. Conclusions Identification of all minimal reactions sets in metabolic networks is essential since different minimal reaction sets have different properties that effect the bioprocess development. The proposed method correctly identified all minimal reaction sets in a both the case studies. The proposed method is computationally efficient compared to other methods for finding minimal reaction sets and useful to employ with genome-scale metabolic networks. PMID:24594118

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.

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.

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

ERIC Educational Resources Information Center

Tyner, Bryan C.; Fienup, Daniel M.

2015-01-01

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

Real World Cognitive Multi-Tasking and Problem Solving: A Large Scale Cognitive Architecture Simulation Through High Performance Computing-Project Casie

DTIC Science & Technology

2008-03-01

computational version of the CASIE architecture serves to demonstrate the functionality of our primary theories. However, implementation of several other...following facts. First, based on Theorem 3 and Theorem 5, the objective function is non -increasing under updating rule (6); second, by the criteria for...reassignment in updating rule (7), it is trivial to show that the objective function is non -increasing under updating rule (7). A Unified View to Graph

LDRD final report :

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

Brost, Randolph C.; McLendon, William Clarence,

2013-01-01

Modeling geospatial information with semantic graphs enables search for sites of interest based on relationships between features, without requiring strong a priori models of feature shape or other intrinsic properties. Geospatial semantic graphs can be constructed from raw sensor data with suitable preprocessing to obtain a discretized representation. This report describes initial work toward extending geospatial semantic graphs to include temporal information, and initial results applying semantic graph techniques to SAR image data. We describe an efficient graph structure that includes geospatial and temporal information, which is designed to support simultaneous spatial and temporal search queries. We also report amore » preliminary implementation of feature recognition, semantic graph modeling, and graph search based on input SAR data. The report concludes with lessons learned and suggestions for future improvements.« less

Data-based Decision-making: Teachers' Comprehension of Curriculum-based Measurement Progress-monitoring Graphs

ERIC Educational Resources Information Center

van den Bosch, Roxette M.; Espin, Christine A.; Chung, Siuman; Saab, Nadira

2017-01-01

Teachers have difficulty using data from Curriculum-based Measurement (CBM) progress graphs of students with learning difficulties for instructional decision-making. As a first step in unraveling those difficulties, we studied teachers' comprehension of CBM graphs. Using think-aloud methodology, we examined 23 teachers' ability to…

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.

Key-Node-Separated Graph Clustering and Layouts for Human Relationship Graph Visualization.

PubMed

Itoh, Takayuki; Klein, Karsten

2015-01-01

Many graph-drawing methods apply node-clustering techniques based on the density of edges to find tightly connected subgraphs and then hierarchically visualize the clustered graphs. However, users may want to focus on important nodes and their connections to groups of other nodes for some applications. For this purpose, it is effective to separately visualize the key nodes detected based on adjacency and attributes of the nodes. This article presents a graph visualization technique for attribute-embedded graphs that applies a graph-clustering algorithm that accounts for the combination of connections and attributes. The graph clustering step divides the nodes according to the commonality of connected nodes and similarity of feature value vectors. It then calculates the distances between arbitrary pairs of clusters according to the number of connecting edges and the similarity of feature value vectors and finally places the clusters based on the distances. Consequently, the technique separates important nodes that have connections to multiple large clusters and improves the visibility of such nodes' connections. To test this technique, this article presents examples with human relationship graph datasets, including a coauthorship and Twitter communication network dataset.

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.

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.

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.

Scenario driven data modelling: a method for integrating diverse sources of data and data streams

DOEpatents

Brettin, Thomas S.; Cottingham, Robert W.; Griffith, Shelton D.; Quest, Daniel J.

2015-09-08

A system and method of integrating diverse sources of data and data streams is presented. The method can include selecting a scenario based on a topic, creating a multi-relational directed graph based on the scenario, identifying and converting resources in accordance with the scenario and updating the multi-directed graph based on the resources, identifying data feeds in accordance with the scenario and updating the multi-directed graph based on the data feeds, identifying analytical routines in accordance with the scenario and updating the multi-directed graph using the analytical routines and identifying data outputs in accordance with the scenario and defining queries to produce the data outputs from the multi-directed graph.

Using circuit theory to model connectivity in ecology, evolution, and conservation.

PubMed

McRae, Brad H; Dickson, Brett G; Keitt, Timothy H; Shah, Viral B

2008-10-01

Connectivity among populations and habitats is important for a wide range of ecological processes. Understanding, preserving, and restoring connectivity in complex landscapes requires connectivity models and metrics that are reliable, efficient, and process based. We introduce a new class of ecological connectivity models based in electrical circuit theory. Although they have been applied in other disciplines, circuit-theoretic connectivity models are new to ecology. They offer distinct advantages over common analytic connectivity models, including a theoretical basis in random walk theory and an ability to evaluate contributions of multiple dispersal pathways. Resistance, current, and voltage calculated across graphs or raster grids can be related to ecological processes (such as individual movement and gene flow) that occur across large population networks or landscapes. Efficient algorithms can quickly solve networks with millions of nodes, or landscapes with millions of raster cells. Here we review basic circuit theory, discuss relationships between circuit and random walk theories, and describe applications in ecology, evolution, and conservation. We provide examples of how circuit models can be used to predict movement patterns and fates of random walkers in complex landscapes and to identify important habitat patches and movement corridors for conservation planning.

Multi-label literature classification based on the Gene Ontology graph.

PubMed

Jin, Bo; Muller, Brian; Zhai, Chengxiang; Lu, Xinghua

2008-12-08

The Gene Ontology is a controlled vocabulary for representing knowledge related to genes and proteins in a computable form. The current effort of manually annotating proteins with the Gene Ontology is outpaced by the rate of accumulation of biomedical knowledge in literature, which urges the development of text mining approaches to facilitate the process by automatically extracting the Gene Ontology annotation from literature. The task is usually cast as a text classification problem, and contemporary methods are confronted with unbalanced training data and the difficulties associated with multi-label classification. In this research, we investigated the methods of enhancing automatic multi-label classification of biomedical literature by utilizing the structure of the Gene Ontology graph. We have studied three graph-based multi-label classification algorithms, including a novel stochastic algorithm and two top-down hierarchical classification methods for multi-label literature classification. We systematically evaluated and compared these graph-based classification algorithms to a conventional flat multi-label algorithm. The results indicate that, through utilizing the information from the structure of the Gene Ontology graph, the graph-based multi-label classification methods can significantly improve predictions of the Gene Ontology terms implied by the analyzed text. Furthermore, the graph-based multi-label classifiers are capable of suggesting Gene Ontology annotations (to curators) that are closely related to the true annotations even if they fail to predict the true ones directly. A software package implementing the studied algorithms is available for the research community. Through utilizing the information from the structure of the Gene Ontology graph, the graph-based multi-label classification methods have better potential than the conventional flat multi-label classification approach to facilitate protein annotation based on the literature.

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…

[Procedural analysis of acid-base balance disorder: case serials in 4 patents].

PubMed

Ma, Chunyuan; Wang, Guijie

2017-05-01

To establish the standardization process of acid-base balance analysis, analyze cases of acid-base balance disorder with the aid of acid-base balance coordinate graph. The acid-base balance theory were reviewed systematically on recent research progress, and the important concepts, definitions, formulas, parameters, regularity and inference in the analysis of acid-base balance were studied. The analysis of acid-base balance disordered processes and steps were figured. The application of acid-base balance coordinate graph in the cases was introduced. The method of "four parameters-four steps" analysis was put forward to analyze the acid-base balance disorders completely. "Four parameters" included pH, arterial partial pressure of carbon dioxide (PaCO 2 ), HCO 3 - and anion gap (AG). "Four steps" were outlined by following aspects: (1) according to the pH, PaCO 2 and HCO 3 - , the primary or main types of acid-base balance disorder was determined; (2) primary or main types of acid-base disorder were used to choose the appropriate compensation formula and to determine the presence of double mixed acid-base balance disorder; (3) the primary acid-base balance disorders were divided into two parts: respiratory acidosis or respiratory alkalosis, at the same time, the potential HCO 3 - should be calculated, the measured HCO 3 - should be replaced with potential HCO 3 - , to determine whether there were three mixed acid-base disorders; (4) based on the above analysis the data judged as the simple AG increased-metabolic acidosis was needed to be further analyzed. The ratio of ΔAG↑/ΔHCO 3 - ↓ was also needed to be calculated, to determine whether there was normal AG metabolic acidosis or metabolic alkalosis. In the clinical practice, PaCO 2 (as the abscissa) and HCO 3 - (as the ordinate) were used to establish a rectangular coordinate system, through origin (0, 0) and coordinate point (40, 24) could be a straight line, and all points on the straight line pH were equal to 7.40. The acid-base balance coordinate graph could be divided into seven areas by three straight lines [namely pH = 7.40 isoline, PaCO 2 = 40 mmHg (1 mmHg = 0.133 kPa) line and HCO 3 - = 24 mmol/L line]: main respiratory alkalosis area, main metabolic alkalosis area, respiratory + metabolic alkalosis area, main respiratory acidosis area, main metabolic acidosis area, respiratory + metabolic acidosis area and normal area. It was easier to determine the type of acid-base balance disorders by identifying the location of the (PaCO 2 , HCO 3 - ) or (PaCO 2 , potential HCO 3 - ) point on the acid-base balance coordinate graph. "Four parameters-four steps" method is systematic and comprehensive. At the same time, by using the acid-base balance coordinate graph, it is simpler to estimate the types of acid-base balance disorders. It is worthy of popularizing and generalizing.