4-{[4-(Hy­droxy­meth­yl)piperidin-1-yl]meth­yl}phenol

PubMed Central

Simões, M. C. R.; Landre, I. M. R.; Moreira, M. S.; Viegas Jr, C.; Doriguetto, A. C.

2012-01-01

In the title compound, C13H19NO2, the piperidine ring has a chair conformation with the exocyclic N—C bond in an equatorial position. In the crystal, mol­ecules are linked head-to-tail by phenol O—H⋯O hydrogen bonds to hy­droxy­methyl­ene O-atom acceptors, forming chains which extend along [100]. These chains form two-dimensional networks lying parallel to (101) through cyclic hydrogen-bonding associations [graph set R 4 4(30)], involving hy­droxy O—H donors and piperidine N-atom acceptors. PMID:22798921

Tracing the Fingerprint of Chemical Bonds within the Electron Densities of Hydrocarbons: A Comparative Analysis of the Optimized and the Promolecule Densities.

PubMed

Keyvani, Zahra Alimohammadi; Shahbazian, Shant; Zahedi, Mansour

2016-10-18

The equivalence of the molecular graphs emerging from the comparative analysis of the optimized and the promolecule electron densities in two hundred and twenty five unsubstituted hydrocarbons was recently demonstrated [Keyvani et al. Chem. Eur. J. 2016, 22, 5003]. Thus, the molecular graph of an optimized molecular electron density is not shaped by the formation of the C-H and C-C bonds. In the present study, to trace the fingerprint of the C-H and C-C bonds in the electron densities of the same set of hydrocarbons, the amount of electron density and its Laplacian at the (3, -1) critical points associated with these bonds are derived from both optimized and promolecule densities, and compared in a newly proposed comparative analysis. The analysis not only conforms to the qualitative picture of the electron density build up between two atoms upon formation of a bond in between, but also quantifies the resulting accumulation of the electron density at the (3, -1) critical points. The comparative analysis also reveals a unified mode of density accumulation in the case of 2318 studied C-H bonds, but various modes of density accumulation are observed in the case of 1509 studied C-C bonds and they are classified into four groups. The four emerging groups do not always conform to the traditional classification based on the bond orders. Furthermore, four C-C bonds described as exotic bonds in previous studies, for example the inverted C-C bond in 1,1,1-propellane, are naturally distinguished from the analysis. © 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

N,N-Dimethyl-N′-[3-(trifluoro­methyl)­phenyl]­urea

PubMed Central

Yu, Da-sheng; Li, Fang-shi; Yao, Wei; Liu, Yin-hong; Lu, Chui

2008-01-01

The title compound, C10H11F3N2O, is an important urea-based herbicide. In the crystal structure, the mol­ecular packing is stabilized by two intra­molecular C—H⋯O hydrogen bonds and one inter­molecular N—H⋯O hydrogen bond, generating a C(4) graph-set motif running parallel to the [001] direction. The F atoms are disordered over two sites, with occupancies of 0.176 (9) and 0.824 (9). PMID:21202857

Crystal structures and hydrogen bonding in the anhydrous tryptaminium salts of the isomeric (2,4-di­chloro­phen­oxy)acetic and (3,5-di­chloro­phen­oxy)acetic acids

PubMed Central

Smith, Graham; Lynch, Daniel E.

2015-01-01

The anhydrous salts of 2-(1H-indol-3-yl)ethanamine (tryptamine) with isomeric (2,4-di­chloro­phen­oxy)acetic acid (2,4-D) and (3,5-di­chloro­phen­oxy)acetic (3,5-D), both C10H13N2 +·C8H5Cl2O3 − [(I) and (II), respectively], have been determined and their one-dimensional hydrogen-bonded polymeric structures are described. In the crystal of (I), the aminium H atoms are involved in three separate inter-species N—H⋯O hydrogen-bonding inter­actions, two with carboxyl­ate O-atom acceptors and the third in an asymmetric three-centre bidentate carboxyl­ate O,O′ chelate [graph set R 1 2(4)]. The indole H atom forms an N—H⋯Ocarboxyl­ate hydrogen bond, extending the chain structure along the b-axis direction. In (II), two of the three aminium H atoms are also involved in N—H⋯Ocarboxyl­ate hydrogen bonds similar to (I) but with the third, a three-centre asymmetric inter­action with carboxyl­ate and phen­oxy O atoms is found [graph set R 1 2(5)]. The chain polymeric extension is also along b. There are no π–π ring inter­actions in either of the structures. The aminium side-chain conformations differ significantly between the two structures, reflecting the conformational ambivalence of the tryptaminium cation, as found also in the benzoate salts. PMID:26090147

Hydrogen bonding in phytohormone-auxin (IAA) and its derivatives

NASA Astrophysics Data System (ADS)

Kojić-Prodić, Biserka; Kroon, Jan; Puntarec, Vitomir

1994-06-01

The significant importance of hydrogen bonds in biological structures and enzymatic reactions has been demonstrated in many examples. As a part of the molecular recognition study of auxins (plant growth hormones) the influence of hydrogen bonding on molecular conformation, particularly of the carboxyl group, which is one of the biologically active ligand sites, has been studied by X-ray diffraction and computational chemistry methods. The survey includes about 40 crystal structures of free auxins such as indol-3-ylacetic acid and its n-alkylated and halogenated derivatives but also bound auxins such as N-(indol-3-ylacetyl)- L-amino acids, and carbohydrate conjugates. The study includes hydrogen bonds of the NH⋯O and OH⋯O types. The classification of hydrogen bond patterns based on the discrimination between the centrosymmetric and non-centrosymmetric space groups and several examples of hydrogen bond systematics on graph set analysis are also shown.

Eccentric connectivity index of chemical trees

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

Haoer, R. S., E-mail: raadsehen@gmail.com; Department of Mathematics, Faculty of Computer Sciences and Mathematics, University Of Kufa, Najaf; Atan, K. A., E-mail: kamel@upm.edu.my

Let G = (V, E) be a simple connected molecular graph. In such a simple molecular graph, vertices and edges are depicted atoms and chemical bonds respectively, we refer to the sets of vertices by V (G) and edges by E (G). If d(u, v) be distance between two vertices u, v ∈ V(G) and can be defined as the length of a shortest path joining them. Then, the eccentricity connectivity index (ECI) of a molecular graph G is ξ(G) = ∑{sub v∈V(G)} d(v) ec(v), where d(v) is degree of a vertex v ∈ V(G). ec(v) is the length ofmore » a greatest path linking to another vertex of v. In this study, we focus the general formula for the eccentricity connectivity index (ECI) of some chemical trees as alkenes.« less

An Interactive Teaching System for Bond Graph Modeling and Simulation in Bioengineering

ERIC Educational Resources Information Center

Roman, Monica; Popescu, Dorin; Selisteanu, Dan

2013-01-01

The objective of the present work was to implement a teaching system useful in modeling and simulation of biotechnological processes. The interactive system is based on applications developed using 20-sim modeling and simulation software environment. A procedure for the simulation of bioprocesses modeled by bond graphs is proposed and simulators…

Site- and bond-percolation thresholds in K_{n,n}-based lattices: Vulnerability of quantum annealers to random qubit and coupler failures on chimera topologies.

PubMed

Melchert, O; Katzgraber, Helmut G; Novotny, M A

2016-04-01

We estimate the critical thresholds of bond and site percolation on nonplanar, effectively two-dimensional graphs with chimeralike topology. The building blocks of these graphs are complete and symmetric bipartite subgraphs of size 2n, referred to as K_{n,n} graphs. For the numerical simulations we use an efficient union-find-based algorithm and employ a finite-size scaling analysis to obtain the critical properties for both bond and site percolation. We report the respective percolation thresholds for different sizes of the bipartite subgraph and verify that the associated universality class is that of standard two-dimensional percolation. For the canonical chimera graph used in the D-Wave Systems Inc. quantum annealer (n=4), we discuss device failure in terms of network vulnerability, i.e., we determine the critical fraction of qubits and couplers that can be absent due to random failures prior to losing large-scale connectivity throughout the device.

Automatic Molecular Design using Evolutionary Techniques

NASA Technical Reports Server (NTRS)

Globus, Al; Lawton, John; Wipke, Todd; Saini, Subhash (Technical Monitor)

1998-01-01

Molecular nanotechnology is the precise, three-dimensional control of materials and devices at the atomic scale. An important part of nanotechnology is the design of molecules for specific purposes. This paper describes early results using genetic software techniques to automatically design molecules under the control of a fitness function. The fitness function must be capable of determining which of two arbitrary molecules is better for a specific task. The software begins by generating a population of random molecules. The population is then evolved towards greater fitness by randomly combining parts of the better individuals to create new molecules. These new molecules then replace some of the worst molecules in the population. The unique aspect of our approach is that we apply genetic crossover to molecules represented by graphs, i.e., sets of atoms and the bonds that connect them. We present evidence suggesting that crossover alone, operating on graphs, can evolve any possible molecule given an appropriate fitness function and a population containing both rings and chains. Prior work evolved strings or trees that were subsequently processed to generate molecular graphs. In principle, genetic graph software should be able to evolve other graph representable systems such as circuits, transportation networks, metabolic pathways, computer networks, etc.

Truncated Long-Range Percolation on Oriented Graphs

NASA Astrophysics Data System (ADS)

van Enter, A. C. D.; de Lima, B. N. B.; Valesin, D.

2016-07-01

We consider different problems within the general theme of long-range percolation on oriented graphs. Our aim is to settle the so-called truncation question, described as follows. We are given probabilities that certain long-range oriented bonds are open; assuming that the sum of these probabilities is infinite, we ask if the probability of percolation is positive when we truncate the graph, disallowing bonds of range above a possibly large but finite threshold. We give some conditions in which the answer is affirmative. We also translate some of our results on oriented percolation to the context of a long-range contact process.

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.

Mining chemical reactions using neighborhood behavior and condensed graphs of reactions approaches.

PubMed

de Luca, Aurélie; Horvath, Dragos; Marcou, Gilles; Solov'ev, Vitaly; Varnek, Alexandre

2012-09-24

This work addresses the problem of similarity search and classification of chemical reactions using Neighborhood Behavior (NB) and Condensed Graphs of Reaction (CGR) approaches. The CGR formalism represents chemical reactions as a classical molecular graph with dynamic bonds, enabling descriptor calculations on this graph. Different types of the ISIDA fragment descriptors generated for CGRs in combination with two metrics--Tanimoto and Euclidean--were considered as chemical spaces, to serve for reaction dissimilarity scoring. The NB method has been used to select an optimal combination of descriptors which distinguish different types of chemical reactions in a database containing 8544 reactions of 9 classes. Relevance of NB analysis has been validated in generic (multiclass) similarity search and in clustering with Self-Organizing Maps (SOM). NB-compliant sets of descriptors were shown to display enhanced mapping propensities, allowing the construction of better Self-Organizing Maps and similarity searches (NB and classical similarity search criteria--AUC ROC--correlate at a level of 0.7). The analysis of the SOM clusters proved chemically meaningful CGR substructures representing specific reaction signatures.

N-Benzyl­pyridin-2-amine

PubMed Central

Wang, Jun; Dai, Chuntao; Nie, Jianhua

2010-01-01

In the crystal of the title compound, C12H12N2, inter­molecular N—H⋯N hydrogen bonds form rings of graph-set motif R 2 2(8) and C—H⋯π inter­actions further consolidate the dimers. Neighbouring dimers are further connected into a three-dimensional network by C—H⋯π inter­actions. The benzyl and pyridyl rings form a dihedral angle of 67.2 (1)° PMID:21589385

Property Graph vs RDF Triple Store: A Comparison on Glycan Substructure Search

PubMed Central

Alocci, Davide; Mariethoz, Julien; Horlacher, Oliver; Bolleman, Jerven T.; Campbell, Matthew P.; Lisacek, Frederique

2015-01-01

Resource description framework (RDF) and Property Graph databases are emerging technologies that are used for storing graph-structured data. We compare these technologies through a molecular biology use case: glycan substructure search. Glycans are branched tree-like molecules composed of building blocks linked together by chemical bonds. The molecular structure of a glycan can be encoded into a direct acyclic graph where each node represents a building block and each edge serves as a chemical linkage between two building blocks. In this context, Graph databases are possible software solutions for storing glycan structures and Graph query languages, such as SPARQL and Cypher, can be used to perform a substructure search. Glycan substructure searching is an important feature for querying structure and experimental glycan databases and retrieving biologically meaningful data. This applies for example to identifying a region of the glycan recognised by a glycan binding protein (GBP). In this study, 19,404 glycan structures were selected from GlycomeDB (www.glycome-db.org) and modelled for being stored into a RDF triple store and a Property Graph. We then performed two different sets of searches and compared the query response times and the results from both technologies to assess performance and accuracy. The two implementations produced the same results, but interestingly we noted a difference in the query response times. Qualitative measures such as portability were also used to define further criteria for choosing the technology adapted to solving glycan substructure search and other comparable issues. PMID:26656740

Hierarchical graphs for rule-based modeling of biochemical systems

PubMed Central

2011-01-01

Background In rule-based modeling, graphs are used to represent molecules: a colored vertex represents a component of a molecule, a vertex attribute represents the internal state of a component, and an edge represents a bond between components. Components of a molecule share the same color. Furthermore, graph-rewriting rules are used to represent molecular interactions. A rule that specifies addition (removal) of an edge represents a class of association (dissociation) reactions, and a rule that specifies a change of a vertex attribute represents a class of reactions that affect the internal state of a molecular component. A set of rules comprises an executable model that can be used to determine, through various means, the system-level dynamics of molecular interactions in a biochemical system. Results For purposes of model annotation, we propose the use of hierarchical graphs to represent structural relationships among components and subcomponents of molecules. We illustrate how hierarchical graphs can be used to naturally document the structural organization of the functional components and subcomponents of two proteins: the protein tyrosine kinase Lck and the T cell receptor (TCR) complex. We also show that computational methods developed for regular graphs can be applied to hierarchical graphs. In particular, we describe a generalization of Nauty, a graph isomorphism and canonical labeling algorithm. The generalized version of the Nauty procedure, which we call HNauty, can be used to assign canonical labels to hierarchical graphs or more generally to graphs with multiple edge types. The difference between the Nauty and HNauty procedures is minor, but for completeness, we provide an explanation of the entire HNauty algorithm. Conclusions Hierarchical graphs provide more intuitive formal representations of proteins and other structured molecules with multiple functional components than do the regular graphs of current languages for specifying rule-based models, such as the BioNetGen language (BNGL). Thus, the proposed use of hierarchical graphs should promote clarity and better understanding of rule-based models. PMID:21288338

Linear finite-difference bond graph model of an ionic polymer actuator

NASA Astrophysics Data System (ADS)

Bentefrit, M.; Grondel, S.; Soyer, C.; Fannir, A.; Cattan, E.; Madden, J. D.; Nguyen, T. M. G.; Plesse, C.; Vidal, F.

2017-09-01

With the recent growing interest for soft actuation, many new types of ionic polymers working in air have been developed. Due to the interrelated mechanical, electrical, and chemical properties which greatly influence the characteristics of such actuators, their behavior is complex and difficult to understand, predict and optimize. In light of this challenge, an original linear multiphysics finite difference bond graph model was derived to characterize this ionic actuation. This finite difference scheme was divided into two coupled subparts, each related to a specific physical, electrochemical or mechanical domain, and then converted into a bond graph model as this language is particularly suited for systems from multiple energy domains. Simulations were then conducted and a good agreement with the experimental results was obtained. Furthermore, an analysis of the power efficiency of such actuators as a function of space and time was proposed and allowed to evaluate their performance.

Hierarchical graphs for better annotations of rule-based models of biochemical systems

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

Hu, Bin; Hlavacek, William

2009-01-01

In the graph-based formalism of the BioNetGen language (BNGL), graphs are used to represent molecules, with a colored vertex representing a component of a molecule, a vertex label representing the internal state of a component, and an edge representing a bond between components. Components of a molecule share the same color. Furthermore, graph-rewriting rules are used to represent molecular interactions, with a rule that specifies addition (removal) of an edge representing a class of association (dissociation) reactions and with a rule that specifies a change of vertex label representing a class of reactions that affect the internal state of amore » molecular component. A set of rules comprises a mathematical/computational model that can be used to determine, through various means, the system-level dynamics of molecular interactions in a biochemical system. Here, for purposes of model annotation, we propose an extension of BNGL that involves the use of hierarchical graphs to represent (1) relationships among components and subcomponents of molecules and (2) relationships among classes of reactions defined by rules. We illustrate how hierarchical graphs can be used to naturally document the structural organization of the functional components and subcomponents of two proteins: the protein tyrosine kinase Lck and the T cell receptor (TCR)/CD3 complex. Likewise, we illustrate how hierarchical graphs can be used to document the similarity of two related rules for kinase-catalyzed phosphorylation of a protein substrate. We also demonstrate how a hierarchical graph representing a protein can be encoded in an XML-based format.« less

Ethyl 2-[(carbamoyl-amino)-imino]-propano-ate hemihydrate.

PubMed

Corrêa, Charlane C; Graúdo, José Eugênio J C; de Oliveira, Luiz Fernando C; de Almeida, Mauro V; Diniz, Renata

2011-08-01

The title compound, C(6)H(11)N(3)O(3)·0.5H(2)O, has two independent mol-ecules and one mol-ecule of water in the asymmetric unit. The crystal packing is stabilized by inter-molecular N-H⋯N, O-H⋯O, N-H⋯O and C-H⋯O hydrogen bonds. These inter-actions form a two-dimensional array in the ab plane with a zigzag motif which has an angle close to 35° between the zigzag planes. The hydrogen bonding can be best described using the graph-set notation as N(1) = C(10)R(2) (2)(10)R(2) (2)(8) and N(2) = R(6) (4)(20)R(2) (2)(8).

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.

Engineering solid-state materials. Strategies for modeling and packing control of molecular assemblies into 3-D networks

NASA Astrophysics Data System (ADS)

Videnova-Adrabinska, V.; Etter, M. C.; Ward, M. D.

1993-04-01

The crystal structure and properties of a number of urea cocrystals are studied with regard to symmetry of the hydrogen-bonded molecular assemblies. The logical consequences of hydrogen bonding interactions are followed step-by-step. The problems of aggregate formation, nucleation, and crystal growth are also elucidated. Endeavor is made to envisage the 2-D and 3-D hydrogen bond network in a manageable way by exploiting graph set short hand. Strategies of how to control the symmetry of molecular packing are still to be elaborated. In our strategy, the programmed self-assembly has been based on the principle of molecular recognition of self- and hetero-complementary functional groups. However, the main focus for pre-organizational control has been put on the two-fold axis estimator of the urea molecule.

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.

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.

Investigation of supramolecular synthons and structural characterisation of aminopyridine-carboxylic acid derivatives

PubMed Central

2014-01-01

Background Co-crystal is a structurally homogeneous crystalline material that contains two or more neutral building blocks that are present in definite stoichiometric amounts. The main advantage of co-crystals is their ability to generate a variety of solid forms of a drug that have distinct physicochemical properties from the solid co-crystal components. In the present investigation, five co-crystals containing 2-amino-6-chloropyridine (AMPY) moiety were synthesized and characterized. Results The crystal structure of 2-amino-6-chloropyridine (AMPY) (I), and the robustness of pyridine-acid supramolecular synthon were discussed in four stoichiometry co-crystals of AMPY…BA (II), AMPY…2ABA (III), AMPY…3CLBA (IV) and AMPY…4NBA (V). The abbreviated designations used are benzoic acid (BA), 2-aminobenzoic acid (2ABA), 3-chlorobenzoic acid (3CLBA) and 4-nitrobenzoic acid (4NBA). All the crystalline materials have been characterized by 1HNMR, 13CNMR, IR, photoluminescence, TEM analysis and X-ray diffraction. The supramolecular assembly of each co-crystal is analyzed and discussed. Conclusions Extensive N---H · · · N/N---H · · · O/O---H · · · N hydrogen bonds are found in (I-V), featuring different supramolecular synthons. In the crystal structure, for compound (I), the 2-amino-6-chloropyridine molecules are linked together into centrosymmetric dimers by hydrogen bonds to form homosynthon, whereas for compounds (II-V), the carboxylic group of the respective acids (benzoic acid, 2-aminobenzoic acid, 3-chlorobenzoic acid and 4-nitrobenzoic acid) interacts with pyridine molecule in a linear fashion through a pair of N---H · · · O and O---H · · · N hydrogen bonds, generating cyclic hydrogen-bonded motifs with the graph-set notation R 2 2 8 , to form heterosynthon. In compound (II), another intermolecular N---H · · · O hydrogen bonds further link these heterosynthons into zig-zag chains. Whereas in compounds (IV) and (V), these heterosynthons are centrosymmetrically paired via N---H · · · O hydrogen bonds and each forms a complementary DADA [D = donor and A = acceptor] array of quadruple hydrogen bonds, with graph-set notation R238, R228 and R238. PMID:24887234

Investigation of supramolecular synthons and structural characterisation of aminopyridine-carboxylic acid derivatives.

PubMed

Hemamalini, Madhukar; Loh, Wan-Sin; Quah, Ching Kheng; Fun, Hoong-Kun

2014-01-01

Co-crystal is a structurally homogeneous crystalline material that contains two or more neutral building blocks that are present in definite stoichiometric amounts. The main advantage of co-crystals is their ability to generate a variety of solid forms of a drug that have distinct physicochemical properties from the solid co-crystal components. In the present investigation, five co-crystals containing 2-amino-6-chloropyridine (AMPY) moiety were synthesized and characterized. The crystal structure of 2-amino-6-chloropyridine (AMPY) (I), and the robustness of pyridine-acid supramolecular synthon were discussed in four stoichiometry co-crystals of AMPY…BA (II), AMPY…2ABA (III), AMPY…3CLBA (IV) and AMPY…4NBA (V). The abbreviated designations used are benzoic acid (BA), 2-aminobenzoic acid (2ABA), 3-chlorobenzoic acid (3CLBA) and 4-nitrobenzoic acid (4NBA). All the crystalline materials have been characterized by (1)HNMR, (13)CNMR, IR, photoluminescence, TEM analysis and X-ray diffraction. The supramolecular assembly of each co-crystal is analyzed and discussed. Extensive N---H · · · N/N---H · · · O/O---H · · · N hydrogen bonds are found in (I-V), featuring different supramolecular synthons. In the crystal structure, for compound (I), the 2-amino-6-chloropyridine molecules are linked together into centrosymmetric dimers by hydrogen bonds to form homosynthon, whereas for compounds (II-V), the carboxylic group of the respective acids (benzoic acid, 2-aminobenzoic acid, 3-chlorobenzoic acid and 4-nitrobenzoic acid) interacts with pyridine molecule in a linear fashion through a pair of N---H · · · O and O---H · · · N hydrogen bonds, generating cyclic hydrogen-bonded motifs with the graph-set notation [Formula: see text] , to form heterosynthon. In compound (II), another intermolecular N---H · · · O hydrogen bonds further link these heterosynthons into zig-zag chains. Whereas in compounds (IV) and (V), these heterosynthons are centrosymmetrically paired via N---H · · · O hydrogen bonds and each forms a complementary DADA [D = donor and A = acceptor] array of quadruple hydrogen bonds, with graph-set notation [Formula: see text], [Formula: see text] and [Formula: see text].

TSAR, a new graph-theoretical approach to computational modeling of protein side-chain flexibility: modeling of ionization properties of proteins.

PubMed

Stroganov, Oleg V; Novikov, Fedor N; Zeifman, Alexey A; Stroylov, Viktor S; Chilov, Ghermes G

2011-09-01

A new graph-theoretical approach called thermodynamic sampling of amino acid residues (TSAR) has been elaborated to explicitly account for the protein side chain flexibility in modeling conformation-dependent protein properties. In TSAR, a protein is viewed as a graph whose nodes correspond to structurally independent groups and whose edges connect the interacting groups. Each node has its set of states describing conformation and ionization of the group, and each edge is assigned an array of pairwise interaction potentials between the adjacent groups. By treating the obtained graph as a belief-network-a well-established mathematical abstraction-the partition function of each node is found. In the current work we used TSAR to calculate partition functions of the ionized forms of protein residues. A simplified version of a semi-empirical molecular mechanical scoring function, borrowed from our Lead Finder docking software, was used for energy calculations. The accuracy of the resulting model was validated on a set of 486 experimentally determined pK(a) values of protein residues. The average correlation coefficient (R) between calculated and experimental pK(a) values was 0.80, ranging from 0.95 (for Tyr) to 0.61 (for Lys). It appeared that the hydrogen bond interactions and the exhaustiveness of side chain sampling made the most significant contribution to the accuracy of pK(a) calculations. Copyright © 2011 Wiley-Liss, Inc.

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.

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.

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

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.

Transport in simple networks described by an integrable discrete nonlinear Schrödinger equation.

PubMed

Nakamura, K; Sobirov, Z A; Matrasulov, D U; Sawada, S

2011-08-01

We elucidate the case in which the Ablowitz-Ladik (AL)-type discrete nonlinear Schrödinger equation (NLSE) on simple networks (e.g., star graphs and tree graphs) becomes completely integrable just as in the case of a simple one-dimensional (1D) discrete chain. The strength of cubic nonlinearity is different from bond to bond, and networks are assumed to have at least two semi-infinite bonds with one of them working as an incoming bond. The present work is a nontrivial extension of our preceding one [Sobirov et al., Phys. Rev. E 81, 066602 (2010)] on the continuum NLSE to the discrete case. We find (1) the solution on each bond is a part of the universal (bond-independent) AL soliton solution on the 1D discrete chain, but it is multiplied by the inverse of the square root of bond-dependent nonlinearity; (2) nonlinearities at individual bonds around each vertex must satisfy a sum rule; and (3) under findings 1 and 2, there exist an infinite number of constants of motion. As a practical issue, with the use of an AL soliton injected through the incoming bond, we obtain transmission probabilities inversely proportional to the strength of nonlinearity on the outgoing bonds.

Importance of Kier-Hall topological indices in the QSAR of anticancer drug design.

PubMed

Nandi, Sisir; Bagchi, Manish C

2012-06-01

An important area of theoretical drug design research is quantitative structure activity relationship (QSAR) using structural invariants. The impetus for this research trend comes from various directions. Researchers in chemical documentation have searched for a set of invariants which will be more convenient than the adjacency matrix (or connection table) for the storage and comparison of chemical structures. Molecular structure can be looked upon as the representation of the relationship among its various constituents. The term molecular structure represents a set of nonequivalent and probably disjoint concepts. There is no reason to believe that when we discuss diverse topics (e.g. chemical synthesis, reaction rates, spectroscopic transitions, reaction mechanisms, and ab initio calculations) using the notion of molecular structure, the different meanings we attach to the single term molecular structure originate from the same fundamental concept. On the contrary, there is a theoretical and philosophical basis for the non-homogeneity of concepts covered by the term molecular structure. In the context of molecular science, the various concepts of molecular structure (e.g. classical valence bond representations, various chemical graph-theoretic representations, ball and spoke model of a molecule, representation of a molecule by minimum energy conformation, semi symbolic contour map of a molecule, or symbolic representation of chemical species by Hamiltonian operators) are model objects derived through different abstractions of the same chemical reality. In each instance, the equivalence class (concept or model of molecular structure) is generated by selecting certain aspects while ignoring some unique properties of those actual events. This explains the plurality of the concept of molecular structure and their autonomous nature, the word autonomous being used in the same sense that one concept is not logically derived from the other. At the most fundamental level, the structural model of an assembled entity (e.g. a molecule consisting of atoms) may be defined as the pattern of relationship among its parts as distinct from the values associated with them. Constitutional formulae of molecules are graphs where vertices represent the set of atoms and edges represent chemical bonds. The pattern of connectedness of atoms in a molecule is preserved by constitutional graphs. A graph (more correctly a non-directed graph) G = [V, E] consists of a finite non-empty set V of points together with a prescribed set E of unordered pairs of distinct points of V. Thus the mathematical characterization of structures represents structural invariants having successful applications in chemical documentation, characterization of molecular branching, enumeration of molecular constitutional associated with a particular empirical formula, calculation of quantum chemical parameters for the generation of quantitative structure-property-activity correlations. Kier developed a number of structural invariants which are now-a-days called as topological indices with wide range of practical applications for QSAR and drug design. The present paper is restricted to the review of Kier-Hall topological indices for QSAR and anticancer drug design for 2,5-bis(1-aziridinyl) 1,4-benzoquinone (BABQ), pyridopyrimidine, 4-anilinoquinazoline and 2-Phenylindoles compounds utilizing various statistical multivariate regression analyses.

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.

Consequences of theory level choice evaluated with new tools from QTAIM and the stress tensor for a dipeptide conformer

NASA Astrophysics Data System (ADS)

Li, Jiahui; Xu, Tianlv; Ping, Yang; van Mourik, Tanja; Früchtl, Herbert; Kirk, Steven R.; Jenkins, Samantha

2018-03-01

QTAIM and the stress tensor were used to provide a detailed analysis of the topology of the molecular graph, BCP and bond-path properties, including the new introduced helicity length H, of a Tyr-Gly dipeptide conformer subjected to a torsion with four levels of theory; MP2, M06-2X, B3LYP-D3 and B3LYP and a modest-sized basis set, 6-31+G(d). Structural effects and bonding properties are quantified and reflect differences in the BSSE and lack of inclusion of dispersion effects in the B3LYP calculations. The helicity length H demonstrated that MP2 produced a unique response to the torsion suggesting future use as a diagnostic tool.

Ethyl 2-[(carbamoyl­amino)­imino]­propano­ate hemihydrate

PubMed Central

Corrêa, Charlane C.; Graúdo, José Eugênio J. C.; de Oliveira, Luiz Fernando C.; de Almeida, Mauro V.; Diniz, Renata

2011-01-01

The title compound, C6H11N3O3·0.5H2O, has two independent mol­ecules and one mol­ecule of water in the asymmetric unit. The crystal packing is stabilized by inter­molecular N—H⋯N, O—H⋯O, N—H⋯O and C—H⋯O hydrogen bonds. These inter­actions form a two-dimensional array in the ab plane with a zigzag motif which has an angle close to 35° between the zigzag planes. The hydrogen bonding can be best described using the graph-set notation as N 1 = C(10)R 2 2(10)R 2 2(8) and N 2 = R 6 4(20)R 2 2(8). PMID:22090934

Continuous system modeling

NASA Technical Reports Server (NTRS)

Cellier, Francois E.

1991-01-01

A comprehensive and systematic introduction is presented for the concepts associated with 'modeling', involving the transition from a physical system down to an abstract description of that system in the form of a set of differential and/or difference equations, and basing its treatment of modeling on the mathematics of dynamical systems. Attention is given to the principles of passive electrical circuit modeling, planar mechanical systems modeling, hierarchical modular modeling of continuous systems, and bond-graph modeling. Also discussed are modeling in equilibrium thermodynamics, population dynamics, and system dynamics, inductive reasoning, artificial neural networks, and automated model synthesis.

How Does Your College Rate? A Credit Rating Tool for Colleges Seeking Bond Financing.

ERIC Educational Resources Information Center

Cassin, Jan; White, Lee

1995-01-01

A credit-rating tool for colleges seeking bond financing is described, using The Colorado College experience as a case study. The process discussed gives college chief financial officers a better understanding of how the bond rating agencies evaluate institutions' credit-worthiness. Substantial data charts and graphs are use for illustration. (MSE)

Complexity and approximability for a problem of intersecting of proximity graphs with minimum number of equal disks

NASA Astrophysics Data System (ADS)

Kobylkin, Konstantin

2016-10-01

Computational complexity and approximability are studied for the problem of intersecting of a set of straight line segments with the smallest cardinality set of disks of fixed radii r > 0 where the set of segments forms straight line embedding of possibly non-planar geometric graph. This problem arises in physical network security analysis for telecommunication, wireless and road networks represented by specific geometric graphs defined by Euclidean distances between their vertices (proximity graphs). It can be formulated in a form of known Hitting Set problem over a set of Euclidean r-neighbourhoods of segments. Being of interest computational complexity and approximability of Hitting Set over so structured sets of geometric objects did not get much focus in the literature. Strong NP-hardness of the problem is reported over special classes of proximity graphs namely of Delaunay triangulations, some of their connected subgraphs, half-θ6 graphs and non-planar unit disk graphs as well as APX-hardness is given for non-planar geometric graphs at different scales of r with respect to the longest graph edge length. Simple constant factor approximation algorithm is presented for the case where r is at the same scale as the longest edge length.

Venlafaxine besylate monohydrate

PubMed Central

Corvalan, Carolina H.; Vega, Daniel R.

2013-01-01

The title compound {systematic name: [2-(1-hydroxycyclohexyl)-2-(4-methoxyphenyl)ethyl]dimethylazanium benzene­sulfonate monohydrate}, C17H28NO2 +·C6H5O3S−·H2O, is a besylate salt hydrate of the anti­depressant drug venlafaxine. In the crystal, besylate anions and water mol­ecules self-assemble, forming hydrogen-bonded dimers linked around inversion centers, with graph set R 4 4(6). The crystal packing features a chain of alternate dimers and venlafaxine cations in the b-axis direction with the components linked by O—H⋯O hydrogen bonds and C—H⋯O and C—H⋯π inter­actions. This is the first example of a venlafaxine cation with a closed conformation, as it features an intra­molecular N—H⋯O inter­action involving the protonated N atom. PMID:24454196

Mathematics of Web science: structure, dynamics and incentives.

PubMed

Chayes, Jennifer

2013-03-28

Dr Chayes' talk described how, to a discrete mathematician, 'all the world's a graph, and all the people and domains merely vertices'. A graph is represented as a set of vertices V and a set of edges E, so that, for instance, in the World Wide Web, V is the set of pages and E the directed hyperlinks; in a social network, V is the people and E the set of relationships; and in the autonomous system Internet, V is the set of autonomous systems (such as AOL, Yahoo! and MSN) and E the set of connections. This means that mathematics can be used to study the Web (and other large graphs in the online world) in the following way: first, we can model online networks as large finite graphs; second, we can sample pieces of these graphs; third, we can understand and then control processes on these graphs; and fourth, we can develop algorithms for these graphs and apply them to improve the online experience.

Dynamic graph of an oxy-fuel combustion system using autocatalytic set model

NASA Astrophysics Data System (ADS)

Harish, Noor Ainy; Bakar, Sumarni Abu

2017-08-01

Evaporation process is one of the main processes besides combustion process in an oxy-combustion boiler system. An Autocatalytic Set (ASC) Model has successfully applied in developing graphical representation of the chemical reactions that occurs in the evaporation process in the system. Seventeen variables identified in the process are represented as nodes and the catalytic relationships are represented as edges in the graph. In addition, in this paper graph dynamics of ACS is further investigated. By using Dynamic Autocatalytic Set Graph Algorithm (DAGA), the adjacency matrix for each of the graphs and its relations to Perron-Frobenius Theorem is investigated. The dynamic graph obtained is further investigated where the connection of the graph to fuzzy graph Type 1 is established.

Distance Domination Number of Graphs Resulting from Edge Comb Product

NASA Astrophysics Data System (ADS)

Slamin; Dafik; Angger Waspodo, Gembong

2018-05-01

Let G be a simple, finite and connected graph with a vertex-set V (G) and an edge-set E(G). For an integer 1 ≤ k ≤ diam (G), a distance k-dominating set of a connected graph G is a set S of vertices of G such that every vertex of V (G)\\S is at distance at most k from some vertex of S. The k-domination number of G, denoted by γk (G), is the minimum cardinality of a k-dominating set of G. In this paper, we determine the exact value of k-domination number of graphs resulting from an edge comb product of two graphs G 1 and G 2, where G 1 is a wheel, a friendship graph, or a triangular book and G 2 is a cycle.

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.

Identifying the minor set cover of dense connected bipartite graphs via random matching edge sets

NASA Astrophysics Data System (ADS)

Hamilton, Kathleen E.; Humble, Travis S.

2017-04-01

Using quantum annealing to solve an optimization problem requires minor embedding a logic graph into a known hardware graph. In an effort to reduce the complexity of the minor embedding problem, we introduce the minor set cover (MSC) of a known graph G: a subset of graph minors which contain any remaining minor of the graph as a subgraph. Any graph that can be embedded into G will be embeddable into a member of the MSC. Focusing on embedding into the hardware graph of commercially available quantum annealers, we establish the MSC for a particular known virtual hardware, which is a complete bipartite graph. We show that the complete bipartite graph K_{N,N} has a MSC of N minors, from which K_{N+1} is identified as the largest clique minor of K_{N,N}. The case of determining the largest clique minor of hardware with faults is briefly discussed but remains an open question.

Identifying the minor set cover of dense connected bipartite graphs via random matching edge sets

DOE PAGES

Hamilton, Kathleen E.; Humble, Travis S.

2017-02-23

Using quantum annealing to solve an optimization problem requires minor embedding a logic graph into a known hardware graph. We introduce the minor set cover (MSC) of a known graph GG : a subset of graph minors which contain any remaining minor of the graph as a subgraph, in an effort to reduce the complexity of the minor embedding problem. Any graph that can be embedded into GG will be embeddable into a member of the MSC. Focusing on embedding into the hardware graph of commercially available quantum annealers, we establish the MSC for a particular known virtual hardware, whichmore » is a complete bipartite graph. Furthermore, we show that the complete bipartite graph K N,N has a MSC of N minors, from which K N+1 is identified as the largest clique minor of K N,N. In the case of determining the largest clique minor of hardware with faults we briefly discussed this open question.« less

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.

Noncontiguous atom matching structural similarity function.

PubMed

Teixeira, Ana L; Falcao, Andre O

2013-10-28

Measuring similarity between molecules is a fundamental problem in cheminformatics. Given that similar molecules tend to have similar physical, chemical, and biological properties, the notion of molecular similarity plays an important role in the exploration of molecular data sets, query-retrieval in molecular databases, and in structure-property/activity modeling. Various methods to define structural similarity between molecules are available in the literature, but so far none has been used with consistent and reliable results for all situations. We propose a new similarity method based on atom alignment for the analysis of structural similarity between molecules. This method is based on the comparison of the bonding profiles of atoms on comparable molecules, including features that are seldom found in other structural or graph matching approaches like chirality or double bond stereoisomerism. The similarity measure is then defined on the annotated molecular graph, based on an iterative directed graph similarity procedure and optimal atom alignment between atoms using a pairwise matching algorithm. With the proposed approach the similarities detected are more intuitively understood because similar atoms in the molecules are explicitly shown. This noncontiguous atom matching structural similarity method (NAMS) was tested and compared with one of the most widely used similarity methods (fingerprint-based similarity) using three difficult data sets with different characteristics. Despite having a higher computational cost, the method performed well being able to distinguish either different or very similar hydrocarbons that were indistinguishable using a fingerprint-based approach. NAMS also verified the similarity principle using a data set of structurally similar steroids with differences in the binding affinity to the corticosteroid binding globulin receptor by showing that pairs of steroids with a high degree of similarity (>80%) tend to have smaller differences in the absolute value of binding activity. Using a highly diverse set of compounds with information about the monoamine oxidase inhibition level, the method was also able to recover a significantly higher average fraction of active compounds when the seed is active for different cutoff threshold values of similarity. Particularly, for the cutoff threshold values of 86%, 93%, and 96.5%, NAMS was able to recover a fraction of actives of 0.57, 0.63, and 0.83, respectively, while the fingerprint-based approach was able to recover a fraction of actives of 0.41, 0.40, and 0.39, respectively. NAMS is made available freely for the whole community in a simple Web based tool as well as the Python source code at http://nams.lasige.di.fc.ul.pt/.

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.

Non-isolated Resolving Sets of certain Graphs Cartesian Product with a Path

NASA Astrophysics Data System (ADS)

Hasibuan, I. M.; Salman, A. N. M.; Saputro, S. W.

2018-04-01

Let G be a connected, simple, and finite graph. For an ordered subset W = {w 1 , w 2 , · · ·, wk } of vertices in a graph G and a vertex v of G, the metric representation of v with respect to W is the k-vector r(v|W ) = (d(v, w 1), d(v, w 2), · · ·, d(v, wk )). The set W is called a resolving set for G if every vertex of G has a distinct representation. The minimum cardinality of W is called the metric dimension of G, denoted by dim(G). If the induced subgraph < W> has no isolated vertices, then W is called a non-isolated resolving set. The minimum cardinality of non-isolated resolving set of G is called the non-isolated resolving number of G, denoted by nr(G). In this paper, we consider H\\square {P}n that is a graph obtained from Cartesian product between a connected graph H and a path Pn . We determine nr(H\\square {P}n), for some classes of H, including cycles, complete graphs, complete bipartite graphs, and friendship graphs.

Critical percolation clusters in seven dimensions and on a complete graph

NASA Astrophysics Data System (ADS)

Huang, Wei; Hou, Pengcheng; Wang, Junfeng; Ziff, Robert M.; Deng, Youjin

2018-02-01

We study critical bond percolation on a seven-dimensional hypercubic lattice with periodic boundary conditions (7D) and on the complete graph (CG) of finite volume (number of vertices) V . We numerically confirm that for both cases, the critical number density n (s ,V ) of clusters of size s obeys a scaling form n (s ,V ) ˜s-τn ˜(s /Vdf*) with identical volume fractal dimension df*=2 /3 and exponent τ =1 +1 /df*=5 /2 . We then classify occupied bonds into bridge bonds, which includes branch and junction bonds, and nonbridge bonds; a bridge bond is a branch bond if and only if its deletion produces at least one tree. Deleting branch bonds from percolation configurations produces leaf-free configurations, whereas deleting all bridge bonds leads to bridge-free configurations composed of blobs. It is shown that the fraction of nonbridge (biconnected) bonds vanishes, ρn ,CG→0 , for large CGs, but converges to a finite value, ρn ,7 D=0.006 193 1 (7 ) , for the 7D hypercube. Further, we observe that while the bridge-free dimension dbf*=1 /3 holds for both the CG and 7D cases, the volume fractal dimensions of the leaf-free clusters are different: dlf,7 D *=0.669 (9 ) ≈2 /3 and dlf,CG *=0.3337 (17 ) ≈1 /3 . On the CG and in 7D, the whole, leaf-free, and bridge-free clusters all have the shortest-path volume fractal dimension dmin*≈1 /3 , characterizing their graph diameters. We also study the behavior of the number and the size distribution of leaf-free and bridge-free clusters. For the number of clusters, we numerically find the number of leaf-free and bridge-free clusters on the CG scale as ˜lnV , while for 7D they scale as ˜V . For the size distribution, we find the behavior on the CG is governed by a modified Fisher exponent τ'=1 , while for leaf-free clusters in 7D, it is governed by Fisher exponent τ =5 /2 . The size distribution of bridge-free clusters in 7D displays two-scaling behavior with exponents τ =4 and τ'=1 . The probability distribution P (C1,V ) d C1 of the largest cluster of size C1 for whole percolation configurations is observed to follow a single-variable function P ¯(x ) d x , with x ≡C1/Vdf* for both CG and 7D. Up to a rescaling factor for the variable x , the probability functions for CG and 7D collapse on top of each other within the entire range of x . The analytical expressions in the x →0 and x →∞ limits are further confirmed. Our work demonstrates that the geometric structure of high-dimensional percolation clusters cannot be fully accounted for by their complete-graph counterparts.

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

NASA Astrophysics Data System (ADS)

Yunia Mayasari, Ratih; Atmojo Kusmayadi, Tri

2018-04-01

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

A generalized graph-theoretical matrix of heterosystems and its application to the VMV procedure.

PubMed

Mozrzymas, Anna

2011-12-14

The extensions of generalized (molecular) graph-theoretical matrix and vector-matrix-vector procedure are considered. The elements of the generalized matrix are redefined in order to describe molecules containing heteroatoms and multiple bonds. The adjacency, distance, detour and reciprocal distance matrices of heterosystems, and corresponding vectors are derived from newly defined generalized graph matrix. The topological indices, which are most widely used in predicting physicochemical and biological properties/activities of various compounds, can be calculated from the new generalized vector-matrix-vector invariant. Copyright © 2011 Elsevier Ltd. All rights reserved.

An efficient randomized algorithm for contact-based NMR backbone resonance assignment.

PubMed

Kamisetty, Hetunandan; Bailey-Kellogg, Chris; Pandurangan, Gopal

2006-01-15

Backbone resonance assignment is a critical bottleneck in studies of protein structure, dynamics and interactions by nuclear magnetic resonance (NMR) spectroscopy. A minimalist approach to assignment, which we call 'contact-based', seeks to dramatically reduce experimental time and expense by replacing the standard suite of through-bond experiments with the through-space (nuclear Overhauser enhancement spectroscopy, NOESY) experiment. In the contact-based approach, spectral data are represented in a graph with vertices for putative residues (of unknown relation to the primary sequence) and edges for hypothesized NOESY interactions, such that observed spectral peaks could be explained if the residues were 'close enough'. Due to experimental ambiguity, several incorrect edges can be hypothesized for each spectral peak. An assignment is derived by identifying consistent patterns of edges (e.g. for alpha-helices and beta-sheets) within a graph and by mapping the vertices to the primary sequence. The key algorithmic challenge is to be able to uncover these patterns even when they are obscured by significant noise. This paper develops, analyzes and applies a novel algorithm for the identification of polytopes representing consistent patterns of edges in a corrupted NOESY graph. Our randomized algorithm aggregates simplices into polytopes and fixes inconsistencies with simple local modifications, called rotations, that maintain most of the structure already uncovered. In characterizing the effects of experimental noise, we employ an NMR-specific random graph model in proving that our algorithm gives optimal performance in expected polynomial time, even when the input graph is significantly corrupted. We confirm this analysis in simulation studies with graphs corrupted by up to 500% noise. Finally, we demonstrate the practical application of the algorithm on several experimental beta-sheet datasets. Our approach is able to eliminate a large majority of noise edges and to uncover large consistent sets of interactions. Our algorithm has been implemented in the platform-independent Python code. The software can be freely obtained for academic use by request from the authors.

The topology of fullerenes

PubMed Central

Schwerdtfeger, Peter; Wirz, Lukas N; Avery, James

2015-01-01

Fullerenes are carbon molecules that form polyhedral cages. Their bond structures are exactly the planar cubic graphs that have only pentagon and hexagon faces. Strikingly, a number of chemical properties of a fullerene can be derived from its graph structure. A rich mathematics of cubic planar graphs and fullerene graphs has grown since they were studied by Goldberg, Coxeter, and others in the early 20th century, and many mathematical properties of fullerenes have found simple and beautiful solutions. Yet many interesting chemical and mathematical problems in the field remain open. In this paper, we present a general overview of recent topological and graph theoretical developments in fullerene research over the past two decades, describing both solved and open problems. WIREs Comput Mol Sci 2015, 5:96–145. doi: 10.1002/wcms.1207 Conflict of interest: The authors have declared no conflicts of interest for this article. For further resources related to this article, please visit the WIREs website. PMID:25678935

Efficient dynamic graph construction for inductive semi-supervised learning.

PubMed

Dornaika, F; Dahbi, R; Bosaghzadeh, A; Ruichek, Y

2017-10-01

Most of graph construction techniques assume a transductive setting in which the whole data collection is available at construction time. Addressing graph construction for inductive setting, in which data are coming sequentially, has received much less attention. For inductive settings, constructing the graph from scratch can be very time consuming. This paper introduces a generic framework that is able to make any graph construction method incremental. This framework yields an efficient and dynamic graph construction method that adds new samples (labeled or unlabeled) to a previously constructed graph. As a case study, we use the recently proposed Two Phase Weighted Regularized Least Square (TPWRLS) graph construction method. The paper has two main contributions. First, we use the TPWRLS coding scheme to represent new sample(s) with respect to an existing database. The representative coefficients are then used to update the graph affinity matrix. The proposed method not only appends the new samples to the graph but also updates the whole graph structure by discovering which nodes are affected by the introduction of new samples and by updating their edge weights. The second contribution of the article is the application of the proposed framework to the problem of graph-based label propagation using multiple observations for vision-based recognition tasks. Experiments on several image databases show that, without any significant loss in the accuracy of the final classification, the proposed dynamic graph construction is more efficient than the batch graph construction. Copyright © 2017 Elsevier Ltd. All rights reserved.

Locating domination number of m-shadowing of graphs

NASA Astrophysics Data System (ADS)

Dafik; Hesti Agustin, Ika; Rizki Albirri, Ermita; Alfarisi, Ridho; Prihandini, R. M.

2018-04-01

Let G = (V, E) be a connected, undirected and simple graph. We define a set D as a dominating set if for every vertex u\\in V-D is adjacent to some vertex v\\in D. The domination number γ (G) is the minimum cardinality of dominating set. A vertex set D in graph G = (V, E) is called locating dominating set if for every pair of different vertex u and v in V(G) ‑ D which occupies \\rlap{/}{0}\

Probing Factors Influencing Students' Graph Comprehension Regarding Four Operations in Kinematics Graphs

ERIC Educational Resources Information Center

Phage, Itumeleng B.; Lemmer, Miriam; Hitge, Mariette

2017-01-01

Students' graph comprehension may be affected by the background of the students who are the readers or interpreters of the graph, their knowledge of the context in which the graph is set, and the inferential processes required by the graph operation. This research study investigated these aspects of graph comprehension for 152 first year…

Quantum walk on a chimera graph

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Modeling the free-radical polymerization of hexanediol diacrylate (HDDA): a molecular dynamics and graph theory approach.

PubMed

Torres-Knoop, Ariana; Kryven, Ivan; Schamboeck, Verena; Iedema, Piet D

2018-05-02

In the printing, coating and ink industries, photocurable systems are becoming increasingly popular and multi-functional acrylates are one of the most commonly used monomers due to their high reactivity (fast curing). In this paper, we use molecular dynamics and graph theory tools to investigate the thermo-mechanical properties and topology of hexanediol diacrylate (HDDA) polymer networks. The gel point was determined as the point where a giant component was formed. For the conditions of our simulations, we found the gel point to be around 0.18 bond conversion. A detailed analysis of the network topology showed, unexpectedly, that the flexibility of the HDDA molecules plays an important role in increasing the conversion of double bonds, while delaying the gel point. This is due to a back-biting type of reaction mechanism that promotes the formation of small cycles. The glass transition temperature for several degrees of curing was obtained from the change in the thermal expansion coefficient. For a bond conversion close to experimental values we obtained a glass transition temperature around 400 K. For the same bond conversion we estimate a Young's modulus of 3 GPa. Both of these values are in good agreement with experiments.

Output-Sensitive Construction of Reeb Graphs.

PubMed

Doraiswamy, H; Natarajan, V

2012-01-01

The Reeb graph of a scalar function represents the evolution of the topology of its level sets. This paper describes a near-optimal output-sensitive algorithm for computing the Reeb graph of scalar functions defined over manifolds or non-manifolds in any dimension. Key to the simplicity and efficiency of the algorithm is an alternate definition of the Reeb graph that considers equivalence classes of level sets instead of individual level sets. The algorithm works in two steps. The first step locates all critical points of the function in the domain. Critical points correspond to nodes in the Reeb graph. Arcs connecting the nodes are computed in the second step by a simple search procedure that works on a small subset of the domain that corresponds to a pair of critical points. The paper also describes a scheme for controlled simplification of the Reeb graph and two different graph layout schemes that help in the effective presentation of Reeb graphs for visual analysis of scalar fields. Finally, the Reeb graph is employed in four different applications-surface segmentation, spatially-aware transfer function design, visualization of interval volumes, and interactive exploration of time-varying data.

A path following algorithm for the graph matching problem.

PubMed

Zaslavskiy, Mikhail; Bach, Francis; Vert, Jean-Philippe

2009-12-01

We propose a convex-concave programming approach for the labeled weighted graph matching problem. The convex-concave programming formulation is obtained by rewriting the weighted graph matching problem as a least-square problem on the set of permutation matrices and relaxing it to two different optimization problems: a quadratic convex and a quadratic concave optimization problem on the set of doubly stochastic matrices. The concave relaxation has the same global minimum as the initial graph matching problem, but the search for its global minimum is also a hard combinatorial problem. We, therefore, construct an approximation of the concave problem solution by following a solution path of a convex-concave problem obtained by linear interpolation of the convex and concave formulations, starting from the convex relaxation. This method allows to easily integrate the information on graph label similarities into the optimization problem, and therefore, perform labeled weighted graph matching. The algorithm is compared with some of the best performing graph matching methods on four data sets: simulated graphs, QAPLib, retina vessel images, and handwritten Chinese characters. In all cases, the results are competitive with the state of the art.

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.

Classification of ligand molecules in PDB with graph match-based structural superposition.

PubMed

Shionyu-Mitsuyama, Clara; Hijikata, Atsushi; Tsuji, Toshiyuki; Shirai, Tsuyoshi

2016-12-01

The fast heuristic graph match algorithm for small molecules, COMPLIG, was improved by adding a structural superposition process to verify the atom-atom matching. The modified method was used to classify the small molecule ligands in the Protein Data Bank (PDB) by their three-dimensional structures, and 16,660 types of ligands in the PDB were classified into 7561 clusters. In contrast, a classification by a previous method (without structure superposition) generated 3371 clusters from the same ligand set. The characteristic feature in the current classification system is the increased number of singleton clusters, which contained only one ligand molecule in a cluster. Inspections of the singletons in the current classification system but not in the previous one implied that the major factors for the isolation were differences in chirality, cyclic conformations, separation of substructures, and bond length. Comparisons between current and previous classification systems revealed that the superposition-based classification was effective in clustering functionally related ligands, such as drugs targeted to specific biological processes, owing to the strictness of the atom-atom matching.

Comparison of University Students' Understanding of Graphs in Different Contexts

ERIC Educational Resources Information Center

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

2013-01-01

This study investigates university students' understanding of graphs in three different domains: mathematics, physics (kinematics), and contexts other than physics. Eight sets of parallel mathematics, physics, and other context questions about graphs were developed. A test consisting of these eight sets of questions (24 questions in all) was…

Real World Graph Connectivity

ERIC Educational Resources Information Center

Lind, Joy; Narayan, Darren

2009-01-01

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

Graph Coloring Used to Model Traffic Lights.

ERIC Educational Resources Information Center

Williams, John

1992-01-01

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

Supermanifolds from Feynman graphs

NASA Astrophysics Data System (ADS)

Marcolli, Matilde; Rej, Abhijnan

2008-08-01

We generalize the computation of Feynman integrals of log divergent graphs in terms of the Kirchhoff polynomial to the case of graphs with both fermionic and bosonic edges, to which we assign a set of ordinary and Grassmann variables. This procedure gives a computation of the Feynman integrals in terms of a period on a supermanifold, for graphs admitting a basis of the first homology satisfying a condition generalizing the log divergence in this context. The analog in this setting of the graph hypersurfaces is a graph supermanifold given by the divisor of zeros and poles of the Berezinian of a matrix associated with the graph, inside a superprojective space. We introduce a Grothendieck group for supermanifolds and identify the subgroup generated by the graph supermanifolds. This can be seen as a general procedure for constructing interesting classes of supermanifolds with associated periods.

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.

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.

Distributed Computation of the knn Graph for Large High-Dimensional Point Sets

PubMed Central

Plaku, Erion; Kavraki, Lydia E.

2009-01-01

High-dimensional problems arising from robot motion planning, biology, data mining, and geographic information systems often require the computation of k nearest neighbor (knn) graphs. The knn graph of a data set is obtained by connecting each point to its k closest points. As the research in the above-mentioned fields progressively addresses problems of unprecedented complexity, the demand for computing knn graphs based on arbitrary distance metrics and large high-dimensional data sets increases, exceeding resources available to a single machine. In this work we efficiently distribute the computation of knn graphs for clusters of processors with message passing. Extensions to our distributed framework include the computation of graphs based on other proximity queries, such as approximate knn or range queries. Our experiments show nearly linear speedup with over one hundred processors and indicate that similar speedup can be obtained with several hundred processors. PMID:19847318

Crystal structure of 5''-benzyl-idene-1'-methyl-4'-phenyl-tri-spiro-[ace-naphthyl-ene-1,2'-pyrrolidine-3',1''-cyclo-hexane-3'',2'''-[1,3]dioxane]-2,6''-dione.

PubMed

Chandralekha, Kuppan; Gavaskar, Deivasigamani; Sureshbabu, Adukamparai Rajukrishnan; Lakshmi, Srinivasakannan

2016-03-01

In the title compound, C36H31NO4, two spiro links connect the methyl-substituted pyrrolidine ring to the ace-naphthyl-ene and cyclo-hexa-none rings. The cyclo-hexa-none ring is further connected to the dioxalane ring by a third spiro junction. The five-membered ring of the ace-naphthylen-1-one ring system adopts a flattened envelope conformation with the ketonic C atom as flap, whereas the dioxalane and pyrrolidine rings each have a twist conformation. The cyclo-hexa-none ring assumes a boat conformation. Three intra-molecular C-H⋯O hydrogen bonds involving both ketonic O atoms as acceptors are present. In the crystal, C-H⋯O hydrogen bonds connect centrosymmetrically related mol-ecule into chains parallel to the b axis, forming rings of R 2 (2)(10)and R 2 (2)(8) graph-set motifs.

Complexity of chemical graphs in terms of size, branching, and cyclicity.

PubMed

Balaban, A T; Mills, D; Kodali, V; Basak, S C

2006-08-01

Chemical graph complexity depends on many factors, but the main ones are size, branching, and cyclicity. Some molecular descriptors embrace together all these three parameters, which cannot then be disentangled. The topological index J (and its refinements that include accounting for bond multiplicity and the presence of heteroatoms) was designed to compensate in a significant measure for graph size and cyclicity, and therefore it contains information mainly on branching. In order to separate these factors, two new indices (F and G) related with J are proposed, which allow to group together graphs with the same size into families of constitutional formulas differing in their branching and cyclicity. A comparison with other topological indices revealed that a few other topological indices vary similarly with index G, notably DN2S4 among the triplet indices, and TOTOP among the indices contained in the Molconn-Z program. This comparison involved all possible chemical graphs (i.e. connected planar graphs with vertex degrees not higher than four) with four through six vertices, and all possible alkanes with four through nine carbon atoms.

Spectral and cyclic voltammetric studies on some intramolecularly hydrogen bonded arylhydrazones: Crystal and molecular structure of 2-(2-(3-nitrophenyl)hydrazono)-5,5-dimethylcyclohexane-1,3-dione

NASA Astrophysics Data System (ADS)

Sethukumar, A.; Arul Prakasam, B.

2010-01-01

A series of arylhydrazone derivatives ( 1- 7) were prepared by the coupling of acetylacetone/dimedone with respective aromatic diazonium salts and characterized by IR, 1H and 13C NMR spectra. The IR and NMR spectral data clearly manifests the effective intramolecular hydrogen bonding in all the cases. Cyclic voltammetric studies certainly indicate that in all the cases the reduced center is C dbnd N bond of hydrazonic moiety. The single crystal X-ray structural analysis of 2-(2-(3-nitrophenyl)hydrazono)-5,5-dimethylcyclohexane-1,3-dione ( 6) is also reported. Single crystal X-ray analysis of 6 evidences the intramolecular hydrogen bonding with the N(2)⋯O(4) distance of 2.642(15) Å, which can be designated as S(6) according to Etter's graph nomenclature. The cyclohexane ring conformation in the molecule ( 6) can be described as an envelope. RAHB studies suggest that the resonance assistance for hydrogen bonding is significantly reduced for the compound ( 6) due to the non-planarity of the six atoms which are involved in resonant cycle S(6) of Etter's graph. The planarity of the resonant cycle S(6) is very much disturbed by the conformational requirement of the cyclohexane ring and hence RAHB concept is less operative in this case.

Weights and topology: a study of the effects of graph construction on 3D image segmentation.

PubMed

Grady, Leo; Jolly, Marie-Pierre

2008-01-01

Graph-based algorithms have become increasingly popular for medical image segmentation. The fundamental process for each of these algorithms is to use the image content to generate a set of weights for the graph and then set conditions for an optimal partition of the graph with respect to these weights. To date, the heuristics used for generating the weighted graphs from image intensities have largely been ignored, while the primary focus of attention has been on the details of providing the partitioning conditions. In this paper we empirically study the effects of graph connectivity and weighting function on the quality of the segmentation results. To control for algorithm-specific effects, we employ both the Graph Cuts and Random Walker algorithms in our experiments.

Mechanical device for determining the stiffness and the viscous friction coefficient of shock absorber elements modelled by bond graph

NASA Astrophysics Data System (ADS)

Ibănescu, R.; Ibănescu, M.

2016-11-01

The present paper presents a mechanical device for the assessment of the fundamental parameters of a shock absorber: the spring stiffness and the viscous friction coefficient, without disassembling the absorber. The device produces an oscillatory motion of the shock absorber and can measure its amplitude and angular velocities. The dynamic model of the system, consisting of the mechanical device and the shock absorber, is performed by using the bond- graph method. Based on this model, the motion equations are obtained, which by integration lead to the motion law. The two previously mentioned parameters are determined by using this law and the measured values of two amplitudes and of their corresponding angular velocities. They result as solutions of a system of two non-linear algebraic equations.

Bond graph modeling and experimental verification of a novel scheme for fault diagnosis of rolling element bearings in special operating conditions

NASA Astrophysics Data System (ADS)

Mishra, C.; Samantaray, A. K.; Chakraborty, G.

2016-09-01

Vibration analysis for diagnosis of faults in rolling element bearings is complicated when the rotor speed is variable or slow. In the former case, the time interval between the fault-induced impact responses in the vibration signal are non-uniform and the signal strength is variable. In the latter case, the fault-induced impact response strength is weak and generally gets buried in the noise, i.e. noise dominates the signal. This article proposes a diagnosis scheme based on a combination of a few signal processing techniques. The proposed scheme initially represents the vibration signal in terms of uniformly resampled angular position of the rotor shaft by using the interpolated instantaneous angular position measurements. Thereafter, intrinsic mode functions (IMFs) are generated through empirical mode decomposition (EMD) of resampled vibration signal which is followed by thresholding of IMFs and signal reconstruction to de-noise the signal and envelope order tracking to diagnose the faults. Data for validating the proposed diagnosis scheme are initially generated from a multi-body simulation model of rolling element bearing which is developed using bond graph approach. This bond graph model includes the ball and cage dynamics, localized fault geometry, contact mechanics, rotor unbalance, and friction and slip effects. The diagnosis scheme is finally validated with experiments performed with the help of a machine fault simulator (MFS) system. Some fault scenarios which could not be experimentally recreated are then generated through simulations and analyzed through the developed diagnosis scheme.

Resolving Transition Metal Chemical Space: Feature Selection for Machine Learning and Structure-Property Relationships.

PubMed

Janet, Jon Paul; Kulik, Heather J

2017-11-22

Machine learning (ML) of quantum mechanical properties shows promise for accelerating chemical discovery. For transition metal chemistry where accurate calculations are computationally costly and available training data sets are small, the molecular representation becomes a critical ingredient in ML model predictive accuracy. We introduce a series of revised autocorrelation functions (RACs) that encode relationships of the heuristic atomic properties (e.g., size, connectivity, and electronegativity) on a molecular graph. We alter the starting point, scope, and nature of the quantities evaluated in standard ACs to make these RACs amenable to inorganic chemistry. On an organic molecule set, we first demonstrate superior standard AC performance to other presently available topological descriptors for ML model training, with mean unsigned errors (MUEs) for atomization energies on set-aside test molecules as low as 6 kcal/mol. For inorganic chemistry, our RACs yield 1 kcal/mol ML MUEs on set-aside test molecules in spin-state splitting in comparison to 15-20× higher errors for feature sets that encode whole-molecule structural information. Systematic feature selection methods including univariate filtering, recursive feature elimination, and direct optimization (e.g., random forest and LASSO) are compared. Random-forest- or LASSO-selected subsets 4-5× smaller than the full RAC set produce sub- to 1 kcal/mol spin-splitting MUEs, with good transferability to metal-ligand bond length prediction (0.004-5 Å MUE) and redox potential on a smaller data set (0.2-0.3 eV MUE). Evaluation of feature selection results across property sets reveals the relative importance of local, electronic descriptors (e.g., electronegativity, atomic number) in spin-splitting and distal, steric effects in redox potential and bond lengths.

A graph theoretic approach to scene matching

NASA Technical Reports Server (NTRS)

Ranganath, Heggere S.; Chipman, Laure J.

1991-01-01

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

Metric learning with spectral graph convolutions on brain connectivity networks.

PubMed

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

2018-04-01

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

EarthVision 2000: Examining Students' Representations of Complex Data Sets.

ERIC Educational Resources Information Center

Vellom, R. Paul; Pape, Stephen J.

2000-01-01

Examines pencil-and-paper graphs produced by students at the beginning of a 1-week summer teacher/student institute as well as computer-based graphs produced by those same students at the end of the institute. Initial problems with managing data sets and producing meaningful graphs disappeared quickly as students used the process of "building…

CUDA Enabled Graph Subset Examiner

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

Johnston, Jeremy T.

2016-12-22

Finding Godsil-McKay switching sets in graphs is one way to demonstrate that a specific graph is not determined by its spectrum--the eigenvalues of its adjacency matrix. An important area of active research in pure mathematics is determining which graphs are determined by their spectra, i.e. when the spectrum of the adjacency matrix uniquely determines the underlying graph. We are interested in exploring the spectra of graphs in the Johnson scheme and specifically seek to determine which of these graphs are determined by their spectra. Given a graph G, a Godsil-McKay switching set is an induced subgraph H on 2k verticesmore » with the following properties: I) H is regular, ii) every vertex in G/H is adjacent to either 0, k, or 2k vertices of H, and iii) at least one vertex in G/H is adjacent to k vertices in H. The software package examines each subset of a user specified size to determine whether or not it satisfies those 3 conditions. The software makes use of the massive parallel processing power of CUDA enabled GPUs. It also exploits the vertex transitivity of graphs in the Johnson scheme by reasoning that if G has a Godsil-McKay switching set, then it has a switching set which includes vertex 1. While the code (in its current state) is tuned to this specific problem, the method of examining each induced subgraph of G can be easily re-written to check for any user specified conditions on the subgraphs and can therefore be used much more broadly.« less

Finite-size scaling of clique percolation on two-dimensional Moore lattices

NASA Astrophysics Data System (ADS)

Dong, Jia-Qi; Shen, Zhou; Zhang, Yongwen; Huang, Zi-Gang; Huang, Liang; Chen, Xiaosong

2018-05-01

Clique percolation has attracted much attention due to its significance in understanding topological overlap among communities and dynamical instability of structured systems. Rich critical behavior has been observed in clique percolation on Erdős-Rényi (ER) random graphs, but few works have discussed clique percolation on finite dimensional systems. In this paper, we have defined a series of characteristic events, i.e., the historically largest size jumps of the clusters, in the percolating process of adding bonds and developed a new finite-size scaling scheme based on the interval of the characteristic events. Through the finite-size scaling analysis, we have found, interestingly, that, in contrast to the clique percolation on an ER graph where the critical exponents are parameter dependent, the two-dimensional (2D) clique percolation simply shares the same critical exponents with traditional site or bond percolation, independent of the clique percolation parameters. This has been corroborated by bridging two special types of clique percolation to site percolation on 2D lattices. Mechanisms for the difference of the critical behaviors between clique percolation on ER graphs and on 2D lattices are also discussed.

Percolation critical polynomial as a graph invariant

DOE PAGES

Scullard, Christian R.

2012-10-18

Every lattice for which the bond percolation critical probability can be found exactly possesses a critical polynomial, with the root in [0; 1] providing the threshold. Recent work has demonstrated that this polynomial may be generalized through a definition that can be applied on any periodic lattice. The polynomial depends on the lattice and on its decomposition into identical finite subgraphs, but once these are specified, the polynomial is essentially unique. On lattices for which the exact percolation threshold is unknown, the polynomials provide approximations for the critical probability with the estimates appearing to converge to the exact answer withmore » increasing subgraph size. In this paper, I show how the critical polynomial can be viewed as a graph invariant like the Tutte polynomial. In particular, the critical polynomial is computed on a finite graph and may be found using the deletion-contraction algorithm. This allows calculation on a computer, and I present such results for the kagome lattice using subgraphs of up to 36 bonds. For one of these, I find the prediction p c = 0:52440572:::, which differs from the numerical value, p c = 0:52440503(5), by only 6:9 X 10 -7.« less

Passivity-based control of linear time-invariant systems modelled by bond graph

NASA Astrophysics Data System (ADS)

Galindo, R.; Ngwompo, R. F.

2018-02-01

Closed-loop control systems are designed for linear time-invariant (LTI) controllable and observable systems modelled by bond graph (BG). Cascade and feedback interconnections of BG models are realised through active bonds with no loading effect. The use of active bonds may lead to non-conservation of energy and the overall system is modelled by proposed pseudo-junction structures. These structures are build by adding parasitic elements to the BG models and the overall system may become singularly perturbed. The structures for these interconnections can be seen as consisting of inner structures that satisfy energy conservation properties and outer structures including multiport-coupled dissipative fields. These fields highlight energy properties like passivity that are useful for control design. In both interconnections, junction structures and dissipative fields for the controllers are proposed, and passivity is guaranteed for the closed-loop systems assuring robust stability. The cascade interconnection is applied to the structural representation of closed-loop transfer functions, when a stabilising controller is applied to a given nominal plant. Applications are given when the plant and the controller are described by state-space realisations. The feedback interconnection is used getting necessary and sufficient stability conditions based on the closed-loop characteristic polynomial, solving a pole-placement problem and achieving zero-stationary state error.

Genus Ranges of 4-Regular Rigid Vertex Graphs

PubMed Central

Buck, Dorothy; Dolzhenko, Egor; Jonoska, Nataša; Saito, Masahico; Valencia, Karin

2016-01-01

A rigid vertex of a graph is one that has a prescribed cyclic order of its incident edges. We study orientable genus ranges of 4-regular rigid vertex graphs. The (orientable) genus range is a set of genera values over all orientable surfaces into which a graph is embedded cellularly, and the embeddings of rigid vertex graphs are required to preserve the prescribed cyclic order of incident edges at every vertex. The genus ranges of 4-regular rigid vertex graphs are sets of consecutive integers, and we address two questions: which intervals of integers appear as genus ranges of such graphs, and what types of graphs realize a given genus range. For graphs with 2n vertices (n > 1), we prove that all intervals [a, b] for all a < b ≤ n, and singletons [h, h] for some h ≤ n, are realized as genus ranges. For graphs with 2n − 1 vertices (n ≥ 1), we prove that all intervals [a, b] for all a < b ≤ n except [0, n], and [h, h] for some h ≤ n, are realized as genus ranges. We also provide constructions of graphs that realize these ranges. PMID:27807395

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

PubMed

Warnke-Sommer, Julia; Ali, Hesham

2016-05-06

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

Directed Laplacians For Fuzzy Autocatalytic Set Of Fuzzy Graph Type-3 Of An Incineration Process

NASA Astrophysics Data System (ADS)

Ahmad, Tahir; Baharun, Sabariah; Bakar, Sumarni Abu

2010-11-01

Fuzzy Autocatalytic Set (FACS) of Fuzzy Graph Type-3 was used in the modeling of a clinical waste incineration process in Malacca. FACS provided more accurate explanations of the incineration process than using crisp graph. In this paper we explore further FACS. Directed and combinatorial Laplacian of FACS are developed and their basic properties are presented.

Nested Tracking Graphs

DOE PAGES

Lukasczyk, Jonas; Weber, Gunther; Maciejewski, Ross; ...

2017-06-01

Tracking graphs are a well established tool in topological analysis to visualize the evolution of components and their properties over time, i.e., when components appear, disappear, merge, and split. However, tracking graphs are limited to a single level threshold and the graphs may vary substantially even under small changes to the threshold. To examine the evolution of features for varying levels, users have to compare multiple tracking graphs without a direct visual link between them. We propose a novel, interactive, nested graph visualization based on the fact that the tracked superlevel set components for different levels are related to eachmore » other through their nesting hierarchy. This approach allows us to set multiple tracking graphs in context to each other and enables users to effectively follow the evolution of components for different levels simultaneously. We show the effectiveness of our approach on datasets from finite pointset methods, computational fluid dynamics, and cosmology simulations.« less

On cordial labeling of double duplication for some families of graph

NASA Astrophysics Data System (ADS)

Shobana, L.; Remigius Perpetua Mary, F.

2018-04-01

Let G (V, E) be a simple undirected graph where V,E are its vertex set and edge set respectively. Consider a labeling where f bea function from the vertices of G to {0, 1} and for each edge xy assign the label|f(x)-f(y)|. Then f is called cordial of G if the number of vertices labeled 0 and the number of vertices labeled 1 differs by at most 1 and the number of edges labeled 0 and the number of edges labeled 1 differs by at most 1. In this paper we proved the existence of cordial labeling for double duplication of path graph Pn: n≥2, cycle graph Cn: n≥3 except for n≡2 (mod 4), wheel graph Wn:n≥5 except for n≥3 (mod 4), flower graph Fn: n≥5 and bistar graph Bm,n: m,n≥2.

Efficient enumeration of monocyclic chemical graphs with given path frequencies

PubMed Central

2014-01-01

Background The enumeration of chemical graphs (molecular graphs) satisfying given constraints is one of the fundamental problems in chemoinformatics and bioinformatics because it leads to a variety of useful applications including structure determination and development of novel chemical compounds. Results We consider the problem of enumerating chemical graphs with monocyclic structure (a graph structure that contains exactly one cycle) from a given set of feature vectors, where a feature vector represents the frequency of the prescribed paths in a chemical compound to be constructed and the set is specified by a pair of upper and lower feature vectors. To enumerate all tree-like (acyclic) chemical graphs from a given set of feature vectors, Shimizu et al. and Suzuki et al. proposed efficient branch-and-bound algorithms based on a fast tree enumeration algorithm. In this study, we devise a novel method for extending these algorithms to enumeration of chemical graphs with monocyclic structure by designing a fast algorithm for testing uniqueness. The results of computational experiments reveal that the computational efficiency of the new algorithm is as good as those for enumeration of tree-like chemical compounds. Conclusions We succeed in expanding the class of chemical graphs that are able to be enumerated efficiently. PMID:24955135

A note on Kirchhoff index

NASA Astrophysics Data System (ADS)

Zhou, Bo; Trinajstić, Nenad

2008-03-01

We report lower bounds for the Kirchhoff index of a connected (molecular) graph in terms of its structural parameters such as the number of vertices (atoms), the number of edges (bonds), maximum vertex degree (valency), connectivity and chromatic number.

Mechatronic modeling of a 750kW fixed-speed wind energy conversion system using the Bond Graph Approach.

PubMed

Khaouch, Zakaria; Zekraoui, Mustapha; Bengourram, Jamaa; Kouider, Nourreeddine; Mabrouki, Mustapha

2016-11-01

In this paper, we would like to focus on modeling main parts of the wind turbines (blades, gearbox, tower, generator and pitching system) from a mechatronics viewpoint using the Bond-Graph Approach (BGA). Then, these parts are combined together in order to simulate the complete system. Moreover, the real dynamic behavior of the wind turbine is taken into account and with the new model; final load simulation is more realistic offering benefits and reliable system performance. This model can be used to develop control algorithms to reduce fatigue loads and enhance power production. Different simulations are carried-out in order to validate the proposed wind turbine model, using real data provided in the open literature (blade profile and gearbox parameters for a 750 kW wind turbine). Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

On the locating domination number of corona product

NASA Astrophysics Data System (ADS)

Nur Santi, Risan; Hesti Agustin, Ika; Dafik; Alfarisi, Ridho

2018-04-01

Let G = (V(G), E(G) be a connected graph and vɛV(G). A dominating set for a graph G = (V, E) is a subset D of V such that every vertex not in D is adjacent to at least one member of D. The domination number γ(G) is the number of vertices in a smallest dominating set for G. Vertex set S in graph G = (V, E) is a locating dominating set if for each pair of distinct vertices u and v in V(G) ‑ S we have N(u)\\cap S\

Retina verification system based on biometric graph matching.

PubMed

Lajevardi, Seyed Mehdi; Arakala, Arathi; Davis, Stephen A; Horadam, Kathy J

2013-09-01

This paper presents an automatic retina verification framework based on the biometric graph matching (BGM) algorithm. The retinal vasculature is extracted using a family of matched filters in the frequency domain and morphological operators. Then, retinal templates are defined as formal spatial graphs derived from the retinal vasculature. The BGM algorithm, a noisy graph matching algorithm, robust to translation, non-linear distortion, and small rotations, is used to compare retinal templates. The BGM algorithm uses graph topology to define three distance measures between a pair of graphs, two of which are new. A support vector machine (SVM) classifier is used to distinguish between genuine and imposter comparisons. Using single as well as multiple graph measures, the classifier achieves complete separation on a training set of images from the VARIA database (60% of the data), equaling the state-of-the-art for retina verification. Because the available data set is small, kernel density estimation (KDE) of the genuine and imposter score distributions of the training set are used to measure performance of the BGM algorithm. In the one dimensional case, the KDE model is validated with the testing set. A 0 EER on testing shows that the KDE model is a good fit for the empirical distribution. For the multiple graph measures, a novel combination of the SVM boundary and the KDE model is used to obtain a fair comparison with the KDE model for the single measure. A clear benefit in using multiple graph measures over a single measure to distinguish genuine and imposter comparisons is demonstrated by a drop in theoretical error of between 60% and more than two orders of magnitude.

Graph determined symbolic dynamics and hybrid systems

NASA Astrophysics Data System (ADS)

Ayers, Kimberly Danielle

In this paper we explore the concept of symbolic dynamical systems whose structure is determined by a directed graph, and then discrete-continuous hybrid systems that arise from such dynamical systems. Typically, symbolic dynamics involve the study of a left shift of a bi-infinite sequence. We examine the case when the bi-infinite system is dictated by a graph; that is, the sequence is a bi-infinite path of a directed graph. We then use the concept to study a system of dynamical systems all on the same compact space M, where "switching" between the systems occurs as given by the bi-infinite sequence in question. The concepts of limit sets, chain recurrent sets, chaos, and Morse sets for these systems are explored.

Graph Mining Meets the Semantic Web

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

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

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

catena-Poly[[[di-aqua-bis-[1,2-bis-(pyridin-4-yl)diazene]copper(II)]-μ-1,2-bis-(pyridin-4-yl)diazene] bis-(perchlorate)].

PubMed

Ballestero-Martínez, Ernesto; Campos-Fernández, Cristian Saul; Soto-Tellini, Victor Hugo; Gonzalez-Montiel, Simplicio; Martínez-Otero, Diego

2013-06-01

In the title compound, {[Cu(C10H8N4)3(H2O)2](ClO4)2} n , the coordination environment of the cationic Cu(II) atom is distorted octa-hedral, formed by pairs of symmetry-equivalent 1,2-bis-(pyridin-4-yl)diazene ligands, bridging 1,2-bis-(pyridin-4-yl)diazene ligands and two non-equivalent water mol-ecules. The 1,2-bis-(pyridin-4-yl)diazene mol-ecules form polymeric chains parallel to [-101] via azo bonds which are situated about inversion centres. Since the Cu(II) atom is situated on a twofold rotation axis, the monomeric unit has point symmetry 2. The perchlorate anions are disordered in a 0.536 (9):0.464 (9) ratio and are acceptors of water H atoms in medium-strong O-H⋯O hydrogen bonds with graph set R 4 (4)(12). The water mol-ecules, which are coordinated to the Cu(II) atom and are hydrogen-bonded to the perchlorate anions, form columns parallel to [010]. A π-π inter-action [centroid-centroid distance = 3.913 (2) Å] occurs between pyridine rings, and weak C-H⋯O inter-actions also occur.

Total edge irregularity strength of (n,t)-kite graph

NASA Astrophysics Data System (ADS)

Winarsih, Tri; Indriati, Diari

2018-04-01

Let G(V, E) be a simple, connected, and undirected graph with vertex set V and edge set E. A total k-labeling is a map that carries vertices and edges of a graph G into a set of positive integer labels {1, 2, …, k}. An edge irregular total k-labeling λ :V(G)\\cup E(G)\\to \\{1,2,\\ldots,k\\} of a graph G is a labeling of vertices and edges of G in such a way that for any different edges e and f, weights wt(e) and wt(f) are distinct. The weight wt(e) of an edge e = xy is the sum of the labels of vertices x and y and the label of the edge e. The total edge irregularity strength of G, tes(G), is defined as the minimum k for which a graph G has an edge irregular total k-labeling. An (n, t)-kite graph consist of a cycle of length n with a t-edge path (the tail) attached to one vertex of a cycle. In this paper, we investigate the total edge irregularity strength of the (n, t)-kite graph, with n > 3 and t > 1. We obtain the total edge irregularity strength of the (n, t)-kite graph is tes((n, t)-kite) = \\lceil \\frac{n+t+2}{3}\\rceil .

Scaling Up Graph-Based Semisupervised Learning via Prototype Vector Machines

PubMed Central

Zhang, Kai; Lan, Liang; Kwok, James T.; Vucetic, Slobodan; Parvin, Bahram

2014-01-01

When the amount of labeled data are limited, semi-supervised learning can improve the learner's performance by also using the often easily available unlabeled data. In particular, a popular approach requires the learned function to be smooth on the underlying data manifold. By approximating this manifold as a weighted graph, such graph-based techniques can often achieve state-of-the-art performance. However, their high time and space complexities make them less attractive on large data sets. In this paper, we propose to scale up graph-based semisupervised learning using a set of sparse prototypes derived from the data. These prototypes serve as a small set of data representatives, which can be used to approximate the graph-based regularizer and to control model complexity. Consequently, both training and testing become much more efficient. Moreover, when the Gaussian kernel is used to define the graph affinity, a simple and principled method to select the prototypes can be obtained. Experiments on a number of real-world data sets demonstrate encouraging performance and scaling properties of the proposed approach. It also compares favorably with models learned via ℓ1-regularization at the same level of model sparsity. These results demonstrate the efficacy of the proposed approach in producing highly parsimonious and accurate models for semisupervised learning. PMID:25720002

Spreadsheet Works: Graphing Functions on a Spreadsheet.

ERIC Educational Resources Information Center

Ramamurthi, V. S.

1989-01-01

Explains graphing functions when using LOTUS 1-2-3. Provides examples and explains keystroke entries needed to make the graphs. Notes up to six functions can be displayed on the same set of axes. (MVL)

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.

Graph-state formalism for mutually unbiased bases

NASA Astrophysics Data System (ADS)

Spengler, Christoph; Kraus, Barbara

2013-11-01

A pair of orthonormal bases is called mutually unbiased if all mutual overlaps between any element of one basis and an arbitrary element of the other basis coincide. In case the dimension, d, of the considered Hilbert space is a power of a prime number, complete sets of d+1 mutually unbiased bases (MUBs) exist. Here we present a method based on the graph-state formalism to construct such sets of MUBs. We show that for n p-level systems, with p being prime, one particular graph suffices to easily construct a set of pn+1 MUBs. In fact, we show that a single n-dimensional vector, which is associated with this graph, can be used to generate a complete set of MUBs and demonstrate that this vector can be easily determined. Finally, we discuss some advantages of our formalism regarding the analysis of entanglement structures in MUBs, as well as experimental realizations.

A Critical Review of Line Graphs in Behavior Analytic Journals

ERIC Educational Resources Information Center

Kubina, Richard M., Jr.; Kostewicz, Douglas E.; Brennan, Kaitlyn M.; King, Seth A.

2017-01-01

Visual displays such as graphs have played an instrumental role in psychology. One discipline relies almost exclusively on graphs in both applied and basic settings, behavior analysis. The most common graphic used in behavior analysis falls under the category of time series. The line graph represents the most frequently used display for visual…

A complementary graphical method for reducing and analyzing large data sets. Case studies demonstrating thresholds setting and selection.

PubMed

Jing, X; Cimino, J J

2014-01-01

Graphical displays can make data more understandable; however, large graphs can challenge human comprehension. We have previously described a filtering method to provide high-level summary views of large data sets. In this paper we demonstrate our method for setting and selecting thresholds to limit graph size while retaining important information by applying it to large single and paired data sets, taken from patient and bibliographic databases. Four case studies are used to illustrate our method. The data are either patient discharge diagnoses (coded using the International Classification of Diseases, Clinical Modifications [ICD9-CM]) or Medline citations (coded using the Medical Subject Headings [MeSH]). We use combinations of different thresholds to obtain filtered graphs for detailed analysis. The thresholds setting and selection, such as thresholds for node counts, class counts, ratio values, p values (for diff data sets), and percentiles of selected class count thresholds, are demonstrated with details in case studies. The main steps include: data preparation, data manipulation, computation, and threshold selection and visualization. We also describe the data models for different types of thresholds and the considerations for thresholds selection. The filtered graphs are 1%-3% of the size of the original graphs. For our case studies, the graphs provide 1) the most heavily used ICD9-CM codes, 2) the codes with most patients in a research hospital in 2011, 3) a profile of publications on "heavily represented topics" in MEDLINE in 2011, and 4) validated knowledge about adverse effects of the medication of rosiglitazone and new interesting areas in the ICD9-CM hierarchy associated with patients taking the medication of pioglitazone. Our filtering method reduces large graphs to a manageable size by removing relatively unimportant nodes. The graphical method provides summary views based on computation of usage frequency and semantic context of hierarchical terminology. The method is applicable to large data sets (such as a hundred thousand records or more) and can be used to generate new hypotheses from data sets coded with hierarchical terminologies.

Bayesian segmentation of atrium wall using globally-optimal graph cuts on 3D meshes.

PubMed

Veni, Gopalkrishna; Fu, Zhisong; Awate, Suyash P; Whitaker, Ross T

2013-01-01

Efficient segmentation of the left atrium (LA) wall from delayed enhancement MRI is challenging due to inconsistent contrast, combined with noise, and high variation in atrial shape and size. We present a surface-detection method that is capable of extracting the atrial wall by computing an optimal a-posteriori estimate. This estimation is done on a set of nested meshes, constructed from an ensemble of segmented training images, and graph cuts on an associated multi-column, proper-ordered graph. The graph/mesh is a part of a template/model that has an associated set of learned intensity features. When this mesh is overlaid onto a test image, it produces a set of costs which lead to an optimal segmentation. The 3D mesh has an associated weighted, directed multi-column graph with edges that encode smoothness and inter-surface penalties. Unlike previous graph-cut methods that impose hard constraints on the surface properties, the proposed method follows from a Bayesian formulation resulting in soft penalties on spatial variation of the cuts through the mesh. The novelty of this method also lies in the construction of proper-ordered graphs on complex shapes for choosing among distinct classes of base shapes for automatic LA segmentation. We evaluate the proposed segmentation framework on simulated and clinical cardiac MRI.

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

EAGLE: 'EAGLE'Is an' Algorithmic Graph Library for Exploration

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

2015-01-16

The Resource Description Framework (RDF) and SPARQL Protocol and RDF Query Language (SPARQL) were introduced about a decade ago to enable flexible schema-free data interchange on the Semantic Web. Today data scientists use the framework as a scalable graph representation for integrating, querying, exploring and analyzing data sets hosted at different sources. With increasing adoption, the need for graph mining capabilities for the Semantic Web has emerged. Today there is no tools to conduct "graph mining" on RDF standard data sets. We address that need through implementation of popular iterative Graph Mining algorithms (Triangle count, Connected component analysis, degree distribution,more » diversity degree, PageRank, etc.). We implement these algorithms as SPARQL queries, wrapped within Python scripts and call our software tool as EAGLE. In RDF style, EAGLE stands for "EAGLE 'Is an' algorithmic graph library for exploration. EAGLE is like 'MATLAB' for 'Linked Data.'« less

An experimental study of graph connectivity for unsupervised word sense disambiguation.

PubMed

Navigli, Roberto; Lapata, Mirella

2010-04-01

Word sense disambiguation (WSD), the task of identifying the intended meanings (senses) of words in context, has been a long-standing research objective for natural language processing. In this paper, we are concerned with graph-based algorithms for large-scale WSD. Under this framework, finding the right sense for a given word amounts to identifying the most "important" node among the set of graph nodes representing its senses. We introduce a graph-based WSD algorithm which has few parameters and does not require sense-annotated data for training. Using this algorithm, we investigate several measures of graph connectivity with the aim of identifying those best suited for WSD. We also examine how the chosen lexicon and its connectivity influences WSD performance. We report results on standard data sets and show that our graph-based approach performs comparably to the state of the art.

A local search for a graph clustering problem

NASA Astrophysics Data System (ADS)

Navrotskaya, Anna; Il'ev, Victor

2016-10-01

In the clustering problems one has to partition a given set of objects (a data set) into some subsets (called clusters) taking into consideration only similarity of the objects. One of most visual formalizations of clustering is graph clustering, that is grouping the vertices of a graph into clusters taking into consideration the edge structure of the graph whose vertices are objects and edges represent similarities between the objects. In the graph k-clustering problem the number of clusters does not exceed k and the goal is to minimize the number of edges between clusters and the number of missing edges within clusters. This problem is NP-hard for any k ≥ 2. We propose a polynomial time (2k-1)-approximation algorithm for graph k-clustering. Then we apply a local search procedure to the feasible solution found by this algorithm and hold experimental research of obtained heuristics.

On the Parameterized Complexity of Some Optimization Problems Related to Multiple-Interval Graphs

NASA Astrophysics Data System (ADS)

Jiang, Minghui

We show that for any constant t ≥ 2, K -Independent Set and K-Dominating Set in t-track interval graphs are W[1]-hard. This settles an open question recently raised by Fellows, Hermelin, Rosamond, and Vialette. We also give an FPT algorithm for K-Clique in t-interval graphs, parameterized by both k and t, with running time max { t O(k), 2 O(klogk) } ·poly(n), where n is the number of vertices in the graph. This slightly improves the previous FPT algorithm by Fellows, Hermelin, Rosamond, and Vialette. Finally, we use the W[1]-hardness of K-Independent Set in t-track interval graphs to obtain the first parameterized intractability result for a recent bioinformatics problem called Maximal Strip Recovery (MSR). We show that MSR-d is W[1]-hard for any constant d ≥ 4 when the parameter is either the total length of the strips, or the total number of adjacencies in the strips, or the number of strips in the optimal solution.

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

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

Lee, Sangkeun; Sukumar, Sreenivas R; Hong, Seokyong

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

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

DOE PAGES

Lee, Sangkeun; Sukumar, Sreenivas R; Hong, Seokyong; ...

2016-01-01

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

Development of acceptance criteria for batches of silane primer for external tank thermal protection system bonding applications

NASA Technical Reports Server (NTRS)

Mikes, F.; Mowrey, C.; Reis, E.

1985-01-01

Results of lap shear tests of various silane primers are presented in graphs and tables. The OH-absorption of these primers (FTIR area values) are correlated with the lap shear tests of coated panels.

Local metric dimension of circulant graph c i r c (n :1 ,2 ,…,n/+1 2 )

NASA Astrophysics Data System (ADS)

Rimadhany, Ruzika; Darmaji

2017-08-01

Let G be a connected graph with two vertices u and v. The distance between u and v, denoted by d(u, v), is defined as length of the shortest path from u to v in G. For an ordered set W = {w1, w2, w3, … , wk} of k distinct vertices in a nontrivial connected graph G, the representation of a vertex v of V(G) respect to W is r(v|W) = (d(v, w1), d(v, w2), … , d(v, wk)). The set W is a resolving set of G if r(v|W) for each vertex v ∈ V(G) is distinct. A resolving set of minimum cardinality is a metric dimension and denoted by dim(G). The set W is a local resolving set of G if r(v|W) for every two adjacent vertices of V(G) is distinct. The minimum cardinality of local resolving set of G is a local metric dimension and denoted by ldim(G). In this research, we determine local metric dimension of circulant graph c i r c (n :1 ,2 ,3 ,…,n/+1 2 ) .

Elastic constants for superplastically formed/diffusion-bonded corrugated sandwich core

NASA Technical Reports Server (NTRS)

Ko, W. L.

1980-01-01

Formulas and associated graphs for evaluating the effective elastic constants for a superplastically formed/diffusion bonded (SPF/DB) corrugated sandwich core, are presented. A comparison of structural stiffnesses of the sandwich core and a honeycomb core under conditions of equal sandwich core density was made. The stiffness in the thickness direction of the optimum SPF/DB corrugated core (that is, triangular truss core) is lower than that of the honeycomb core, and that the former has higher transverse shear stiffness than the latter.

Strong parameterization and coordination encirclements of graph of Penrose tiling vertices

NASA Astrophysics Data System (ADS)

Shutov, A. V.; Maleev, A. V.

2017-07-01

The coordination encirclements in a graph of Penrose tiling vertices have been investigated based on the analysis of vertice parameters. A strong parameterization of these vertices is developed in the form of a tiling of a parameter set in the region corresponding to different first coordination encirclements of vertices. An algorithm for constructing tilings of a set of parameters determining different coordination encirclements in a graph of Penrose tiling vertices of order n is proposed.

Survey of Approaches to Generate Realistic Synthetic Graphs

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

Lim, Seung-Hwan; Lee, Sangkeun; Powers, Sarah S

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

Simple scale interpolator facilitates reading of graphs

NASA Technical Reports Server (NTRS)

Fazio, A.; Henry, B.; Hood, D.

1966-01-01

Set of cards with scale divisions and a scale finder permits accurate reading of the coordinates of points on linear or logarithmic graphs plotted on rectangular grids. The set contains 34 different scales for linear plotting and 28 single cycle scales for log plots.

Crystal structure of a photolysis product of vitamin B6: A pyridodihydrofuran-condensed skeleton compound of pyridoxal 5‧-phosphate

NASA Astrophysics Data System (ADS)

Aoki, Katsuyuki; Nakamura, Hideyuki; Hattori, Toshiaki; Hu, Ning-Hai; Onishi, Masayoshi

2017-11-01

An aqueous solution dissolving pyridoxal 5‧-phosphate (PLP) was exposed to sun-light at room temperature to yield a photolysis product, 4b,9b-dihydro-4b,9b-dihydroxy-1,6-dimethyl-4,9-bis(phosphonooxymethyl){pyrido[3‧,4‧:2,3]furo[4,5-b]}pyrido[4,3-d]furan (1), whose structure was crystallographically determined. The product 1 was found to be a novel C(sp3)-C(sp3) side-sharing pyridodihydrofuran-condensed skeleton compound with the two pyridodihydrofuran planes taking a 'V-shape'-like molecular configuration. Hydrogen bonding patterns of molecules of 1 in the crystal lattice are analyzed by the graph set approach. The most probable mechanism for the formation of 1 is described.

Using Graphs. Supervising: Technical Aspects of Supervision. The Choice Series #32. A Self Learning Opportunity.

ERIC Educational Resources Information Center

Carr, Linda

This learning unit on using graphs is one in the Choice Series, a self-learning development program for supervisors. Purpose stated for the approximately eight-hour-long unit is to enable the supervisor to look at the usefulness of graphs in displaying figures, use graphs to compare sets of figures, identify trends and seasonal variations in…

Extracting Knowledge from Graph Data in Adversarial Settings

NASA Astrophysics Data System (ADS)

Skillicorn, David

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

Existence of the Harmonic Measure for Random Walks on Graphs and in Random Environments

NASA Astrophysics Data System (ADS)

Boivin, Daniel; Rau, Clément

2013-01-01

We give a sufficient condition for the existence of the harmonic measure from infinity of transient random walks on weighted graphs. In particular, this condition is verified by the random conductance model on ℤ d , d≥3, when the conductances are i.i.d. and the bonds with positive conductance percolate. The harmonic measure from infinity also exists for random walks on supercritical clusters of ℤ2. This is proved using results of Barlow (Ann. Probab. 32:3024-3084, 2004) and Barlow and Hambly (Electron. J. Probab. 14(1):1-27, 2009).

Simulation of an Asynchronous Machine by using a Pseudo Bond Graph

NASA Astrophysics Data System (ADS)

Romero, Gregorio; Felez, Jesus; Maroto, Joaquin; Martinez, M. Luisa

2008-11-01

For engineers, computer simulation, is a basic tool since it enables them to understand how systems work without actually needing to see them. They can learn how they work in different circumstances and optimize their design with considerably less cost in terms of time and money than if they had to carry out tests on a physical system. However, if computer simulation is to be reliable it is essential for the simulation model to be validated. There is a wide range of commercial brands on the market offering products for electrical domain simulation (SPICE, LabVIEW PSCAD,Dymola, Simulink, Simplorer,...). These are powerful tools, but require the engineer to have a perfect knowledge of the electrical field. This paper shows an alternative methodology to can simulate an asynchronous machine using the multidomain Bond Graph technique and apply it in any program that permit the simulation of models based in this technique; no extraordinary knowledge of this technique and electric field are required to understand the process .

G-Hash: Towards Fast Kernel-based Similarity Search in Large Graph Databases.

PubMed

Wang, Xiaohong; Smalter, Aaron; Huan, Jun; Lushington, Gerald H

2009-01-01

Structured data including sets, sequences, trees and graphs, pose significant challenges to fundamental aspects of data management such as efficient storage, indexing, and similarity search. With the fast accumulation of graph databases, similarity search in graph databases has emerged as an important research topic. Graph similarity search has applications in a wide range of domains including cheminformatics, bioinformatics, sensor network management, social network management, and XML documents, among others.Most of the current graph indexing methods focus on subgraph query processing, i.e. determining the set of database graphs that contains the query graph and hence do not directly support similarity search. In data mining and machine learning, various graph kernel functions have been designed to capture the intrinsic similarity of graphs. Though successful in constructing accurate predictive and classification models for supervised learning, graph kernel functions have (i) high computational complexity and (ii) non-trivial difficulty to be indexed in a graph database.Our objective is to bridge graph kernel function and similarity search in graph databases by proposing (i) a novel kernel-based similarity measurement and (ii) an efficient indexing structure for graph data management. Our method of similarity measurement builds upon local features extracted from each node and their neighboring nodes in graphs. A hash table is utilized to support efficient storage and fast search of the extracted local features. Using the hash table, a graph kernel function is defined to capture the intrinsic similarity of graphs and for fast similarity query processing. We have implemented our method, which we have named G-hash, and have demonstrated its utility on large chemical graph databases. Our results show that the G-hash method achieves state-of-the-art performance for k-nearest neighbor (k-NN) classification. Most importantly, the new similarity measurement and the index structure is scalable to large database with smaller indexing size, faster indexing construction time, and faster query processing time as compared to state-of-the-art indexing methods such as C-tree, gIndex, and GraphGrep.

Architecture Aware Partitioning Algorithms

DTIC Science & Technology

2006-01-19

follows: Given a graph G = (V, E ), where V is the set of vertices, n = |V | is the number of vertices, and E is the set of edges in the graph, partition the...communication link l(pi, pj) is associated with a graph edge weight e ∗(pi, pj) that represents the communication cost per unit of communication between...one that is local for each one. For our model we assume that communication in either direction across a given link is the same, therefore e ∗(pi, pj

Measuring graph similarity through continuous-time quantum walks and the quantum Jensen-Shannon divergence.

PubMed

Rossi, Luca; Torsello, Andrea; Hancock, Edwin R

2015-02-01

In this paper we propose a quantum algorithm to measure the similarity between a pair of unattributed graphs. We design an experiment where the two graphs are merged by establishing a complete set of connections between their nodes and the resulting structure is probed through the evolution of continuous-time quantum walks. In order to analyze the behavior of the walks without causing wave function collapse, we base our analysis on the recently introduced quantum Jensen-Shannon divergence. In particular, we show that the divergence between the evolution of two suitably initialized quantum walks over this structure is maximum when the original pair of graphs is isomorphic. We also prove that under special conditions the divergence is minimum when the sets of eigenvalues of the Hamiltonians associated with the two original graphs have an empty intersection.

Student Reasoning about Graphs in Different Contexts

ERIC Educational Resources Information Center

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

2016-01-01

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

The X-Ray Optics for the High Angular Resolution Imager (HARI)

NASA Technical Reports Server (NTRS)

Weisskopf, M. C.

2010-01-01

This slide presentation shows the basic parameters of the x-ray optics, the housing,a graph of the effective area vs energy, another graph showing the angular off-set vs HEW, and a series of graphs showing the detector offsets and tilts,

Upper bound for the span of pencil graph

NASA Astrophysics Data System (ADS)

Parvathi, N.; Vimala Rani, A.

2018-04-01

An L(2,1)-Coloring or Radio Coloring or λ coloring of a graph is a function f from the vertex set V(G) to the set of all nonnegative integers such that |f(x) ‑ f(y)| ≥ 2 if d(x,y) = 1 and |f(x) ‑ f(y)| ≥ 1 if d(x,y)=2, where d(x,y) denotes the distance between x and y in G. The L(2,1)-coloring number or span number λ(G) of G is the smallest number k such that G has an L(2,1)-coloring with max{f(v) : v ∈ V(G)} = k. [2]The minimum number of colors used in L(2,1)-coloring is called the radio number rn(G) of G (Positive integer). Griggs and yeh conjectured that λ(G) ≤ Δ2 for any simple graph with maximum degree Δ>2. In this article, we consider some special graphs like, n-sunlet graph, pencil graph families and derive its upper bound of (G) and rn(G).

Exploring and Making Sense of Large Graphs

DTIC Science & Technology

2015-08-01

and bold) are n × n ; vectors (lower-case bold) are n × 1 column vectors, and scalars (in lower-case plain font) typically correspond to strength of...graph is often denoted as |V| or n . Edges or Links: A finite set E of lines between objects in a graph. The edges represent relationships between the...Adjacency matrix of a simple, unweighted and undirected graph. Adjacency matrix: The adjacency matrix of a graph G is an n × n matrix A, whose element aij

Graphs and Tracks Revisited

NASA Astrophysics Data System (ADS)

Christian, Wolfgang; Belloni, Mario

2013-04-01

We have recently developed a Graphs and Tracks model based on an earlier program by David Trowbridge, as shown in Fig. 1. Our model can show position, velocity, acceleration, and energy graphs and can be used for motion-to-graphs exercises. Users set the heights of the track segments, and the model displays the motion of the ball on the track together with position, velocity, and acceleration graphs. This ready-to-run model is available in the ComPADRE OSP Collection at www.compadre.org/osp/items/detail.cfm?ID=12023.

Multiclass Data Segmentation using Diffuse Interface Methods on Graphs

DTIC Science & Technology

2014-01-01

37] that performs interac- tive image segmentation using the solution to a combinatorial Dirichlet problem. Elmoataz et al . have developed general...izations of the graph Laplacian [25] for image denoising and manifold smoothing. Couprie et al . in [18] define a conve- niently parameterized graph...continuous setting carry over to the discrete graph representation. For general data segmentation, Bresson et al . in [8], present rigorous convergence

One-dimensional long-range percolation: A numerical study

NASA Astrophysics Data System (ADS)

Gori, G.; Michelangeli, M.; Defenu, N.; Trombettoni, A.

2017-07-01

In this paper we study bond percolation on a one-dimensional chain with power-law bond probability C /rd +σ , where r is the distance length between distinct sites and d =1 . We introduce and test an order-N Monte Carlo algorithm and we determine as a function of σ the critical value Cc at which percolation occurs. The critical exponents in the range 0 <σ <1 are reported. Our analysis is in agreement, up to a numerical precision ≈10-3 , with the mean-field result for the anomalous dimension η =2 -σ , showing that there is no correction to η due to correlation effects. The obtained values for Cc are compared with a known exact bound, while the critical exponent ν is compared with results from mean-field theory, from an expansion around the point σ =1 and from the ɛ -expansion used with the introduction of a suitably defined effective dimension deff relating the long-range model with a short-range one in dimension deff. We finally present a formulation of our algorithm for bond percolation on general graphs, with order N efficiency on a large class of graphs including short-range percolation and translationally invariant long-range models in any spatial dimension d with σ >0 .

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.

Analyzing and synthesizing phylogenies using tree alignment graphs.

PubMed

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

2013-01-01

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

Analyzing and Synthesizing Phylogenies Using Tree Alignment Graphs

PubMed Central

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

2013-01-01

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

On the Total Edge Irregularity Strength of Generalized Butterfly Graph

NASA Astrophysics Data System (ADS)

Dwi Wahyuna, Hafidhyah; Indriati, Diari

2018-04-01

Let G(V, E) be a connected, simple, and undirected graph with vertex set V and edge set E. A total k-labeling is a map that carries vertices and edges of a graph G into a set of positive integer labels {1, 2, …, k}. An edge irregular total k-labeling λ: V(G) ∪ E(G) → {1, 2, …, k} of a graph G is a total k-labeling such that the weights calculated for all edges are distinct. The weight of an edge uv in G, denoted by wt(uv), is defined as the sum of the label of u, the label of v, and the label of uv. The total edge irregularity strength of G, denoted by tes(G), is the minimum value of the largest label k over all such edge irregular total k-labelings. A generalized butterfly graph, BFn , obtained by inserting vertices to every wing with assumption that sum of inserting vertices to every wing are same then it has 2n + 1 vertices and 4n ‑ 2 edges. In this paper, we investigate the total edge irregularity strength of generalized butterfly graph, BFn , for n > 2. The result is tes(B{F}n)=\\lceil \\frac{4n}{3}\\rceil .

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.

Graphical Language for Data Processing

NASA Technical Reports Server (NTRS)

Alphonso, Keith

2011-01-01

A graphical language for processing data allows processing elements to be connected with virtual wires that represent data flows between processing modules. The processing of complex data, such as lidar data, requires many different algorithms to be applied. The purpose of this innovation is to automate the processing of complex data, such as LIDAR, without the need for complex scripting and programming languages. The system consists of a set of user-interface components that allow the user to drag and drop various algorithmic and processing components onto a process graph. By working graphically, the user can completely visualize the process flow and create complex diagrams. This innovation supports the nesting of graphs, such that a graph can be included in another graph as a single step for processing. In addition to the user interface components, the system includes a set of .NET classes that represent the graph internally. These classes provide the internal system representation of the graphical user interface. The system includes a graph execution component that reads the internal representation of the graph (as described above) and executes that graph. The execution of the graph follows the interpreted model of execution in that each node is traversed and executed from the original internal representation. In addition, there are components that allow external code elements, such as algorithms, to be easily integrated into the system, thus making the system infinitely expandable.

catena-Poly[[[di­aqua­bis­[1,2-bis­(pyridin-4-yl)diazene]copper(II)]-μ-1,2-bis­(pyridin-4-yl)diazene] bis­(perchlorate)

PubMed Central

Ballestero-Martínez, Ernesto; Campos-Fernández, Cristian Saul; Soto-Tellini, Victor Hugo; Gonzalez-Montiel, Simplicio; Martínez-Otero, Diego

2013-01-01

In the title compound, {[Cu(C10H8N4)3(H2O)2](ClO4)2}n, the coordination environment of the cationic CuII atom is distorted octa­hedral, formed by pairs of symmetry-equivalent 1,2-bis­(pyridin-4-yl)diazene ligands, bridging 1,2-bis­(pyridin-4-yl)diazene ligands and two non-equivalent water mol­ecules. The 1,2-bis­(pyridin-4-yl)diazene mol­ecules form polymeric chains parallel to [-101] via azo bonds which are situated about inversion centres. Since the CuII atom is situated on a twofold rotation axis, the monomeric unit has point symmetry 2. The perchlorate anions are disordered in a 0.536 (9):0.464 (9) ratio and are acceptors of water H atoms in medium–strong O—H⋯O hydrogen bonds with graph set R 4 4(12). The water mol­ecules, which are coordinated to the CuII atom and are hydrogen-bonded to the perchlorate anions, form columns parallel to [010]. A π–π inter­action [centroid–centroid distance = 3.913 (2) Å] occurs between pyridine rings, and weak C—H⋯O inter­actions also occur. PMID:23794983

Of cuts and cracks: data analytics on constrained graphs for early prediction of failure in cementitious materials

NASA Astrophysics Data System (ADS)

Kahagalage, Sanath; Tordesillas, Antoinette; Nitka, Michał; Tejchman, Jacek

2017-06-01

Using data from discrete element simulations, we develop a data analytics approach using network flow theory to study force transmission and failure in a `dog-bone' concrete specimen submitted to uniaxial tension. With this approach, we establish the extent to which the bottlenecks, i.e., a subset of contacts that impedes flow and are prone to becoming overloaded, can predict the location of the ultimate macro-crack. At the heart of this analysis is a capacity function that quantifies, in relative terms, the maximum force that can be transmitted through the different contacts or edges in the network. Here we set this function to be solely governed by the size of the contact area between the deformable spherical grains. During all the initial stages of the loading history, when no bonds are broken, we find the bottlenecks coincide consistently with, and therefore predict, the location of the crack that later forms in the failure regime after peak force. When bonds do start to break, they are spread throughout the specimen: in, near, and far from, the bottlenecks. In one stage leading up to peak force, bonds collectively break in the lower portion of the specimen, momentarily shifting the bottlenecks to this location. Just before and around peak force, however, the bottlenecks return to their original location and remain there until the macro-crack emerges right along the bottlenecks.

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.

Edge Antimagic Total Labeling on Two Copies of Path

NASA Astrophysics Data System (ADS)

Nurdin; Abrar, A. M.; Bhayangkara, A. R. M.; Muliani; Samsir, A. U.; Nahdi, M. R. An

2018-03-01

A graph G = (V(G), E(G)) denotes the vertex set and the edge set, respectively. A (p,q)-graph G is a graph such that |V(G) | = p and |E(G) | = q. Graph of order p and size q is called (a,d)-edge-anti magic total if there exists a bijection f : V(G) U E(G)→ {1,2,..., p + q} such that the edge weights w(u,v) = f(u) + f(uv) + f(v) form an arithmetic sequence {a, a + d, a + 2d,...,a + (q - 1)d} with the first term a and common difference d. Two copies of path is disjoint union of two path graph with same order (Pn ∪Pn ) denoted by 2Pn . In this paper we construct the (a,d)-edge-anti magic total labeling in two copies of path for some differences d.

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

Multi-INT Complex Event Processing using Approximate, Incremental Graph Pattern Search

DTIC Science & Technology

2012-06-01

graph pattern search and SPARQL queries . Total execution time for 10 executions each of 5 random pattern searches in synthetic data sets...01/11 1000 10000 100000 RDF triples Time (secs) 10 20 Graph pattern algorithm SPARQL queries Initial Performance Comparisons 09/18/11 2011 Thrust Area

A technology mapping based on graph of excitations and outputs for finite state machines

NASA Astrophysics Data System (ADS)

Kania, Dariusz; Kulisz, Józef

2017-11-01

A new, efficient technology mapping method of FSMs, dedicated for PAL-based PLDs is proposed. The essence of the method consists in searching for the minimal set of PAL-based logic blocks that cover a set of multiple-output implicants describing the transition and output functions of an FSM. The method is based on a new concept of graph: the Graph of Excitations and Outputs. The proposed algorithm was tested using the FSM benchmarks. The obtained results were compared with the classical technology mapping of FSM.

On Atom-Bond Connectivity Index

NASA Astrophysics Data System (ADS)

Zhou, Bo; Xing, Rundan

2011-02-01

The atom-bond connectivity (ABC) index, introduced by Estrada et al. in 1998, displays an excellent correlation with the formation heat of alkanes. We give upper bounds for this graph invariant using the number of vertices, the number of edges, the Randíc connectivity indices, and the first Zagreb index. We determine the unique tree with the maximum ABC index among trees with given numbers of vertices and pendant vertices, and the n-vertex trees with the maximum, and the second, the third, and the fourth maximum ABC indices for n ≥ 6.

On Certain Topological Indices of Boron Triangular Nanotubes

NASA Astrophysics Data System (ADS)

Aslam, Adnan; Ahmad, Safyan; Gao, Wei

2017-08-01

The topological index gives information about the whole structure of a chemical graph, especially degree-based topological indices that are very useful. Boron triangular nanotubes are now replacing usual carbon nanotubes due to their excellent properties. We have computed general Randić (Rα), first Zagreb (M1) and second Zagreb (M2), atom-bond connectivity (ABC), and geometric-arithmetic (GA) indices of boron triangular nanotubes. Also, we have computed the fourth version of atom-bond connectivity (ABC4) and the fifth version of geometric-arithmetic (GA5) indices of boron triangular nanotubes.

mpiGraph

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

Moody, Adam

2007-05-22

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

On Topological Indices of Certain Families of Nanostar Dendrimers.

PubMed

Husin, Mohamad Nazri; Hasni, Roslan; Arif, Nabeel Ezzulddin; Imran, Muhammad

2016-06-24

A topological index of graph G is a numerical parameter related to G which characterizes its molecular topology and is usually graph invariant. In the field of quantitative structure-activity (QSAR)/quantitative structure-activity structure-property (QSPR) research, theoretical properties of the chemical compounds and their molecular topological indices such as the Randić connectivity index, atom-bond connectivity (ABC) index and geometric-arithmetic (GA) index are used to predict the bioactivity of different chemical compounds. A dendrimer is an artificially manufactured or synthesized molecule built up from the branched units called monomers. In this paper, the fourth version of ABC index and the fifth version of GA index of certain families of nanostar dendrimers are investigated. We derive the analytical closed formulas for these families of nanostar dendrimers. The obtained results can be of use in molecular data mining, particularly in researching the uniqueness of tested (hyper-branched) molecular graphs.

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.

Graphical Methods for Reducing, Visualizing and Analyzing Large Data Sets Using Hierarchical Terminologies

PubMed Central

Jing, Xia; Cimino, James J.

2011-01-01

Objective: To explore new graphical methods for reducing and analyzing large data sets in which the data are coded with a hierarchical terminology. Methods: We use a hierarchical terminology to organize a data set and display it in a graph. We reduce the size and complexity of the data set by considering the terminological structure and the data set itself (using a variety of thresholds) as well as contributions of child level nodes to parent level nodes. Results: We found that our methods can reduce large data sets to manageable size and highlight the differences among graphs. The thresholds used as filters to reduce the data set can be used alone or in combination. We applied our methods to two data sets containing information about how nurses and physicians query online knowledge resources. The reduced graphs make the differences between the two groups readily apparent. Conclusions: This is a new approach to reduce size and complexity of large data sets and to simplify visualization. This approach can be applied to any data sets that are coded with hierarchical terminologies. PMID:22195119

Querying graphs in protein-protein interactions networks using feedback vertex set.

PubMed

Blin, Guillaume; Sikora, Florian; Vialette, Stéphane

2010-01-01

Recent techniques increase rapidly the amount of our knowledge on interactions between proteins. The interpretation of these new information depends on our ability to retrieve known substructures in the data, the Protein-Protein Interactions (PPIs) networks. In an algorithmic point of view, it is an hard task since it often leads to NP-hard problems. To overcome this difficulty, many authors have provided tools for querying patterns with a restricted topology, i.e., paths or trees in PPI networks. Such restriction leads to the development of fixed parameter tractable (FPT) algorithms, which can be practicable for restricted sizes of queries. Unfortunately, Graph Homomorphism is a W[1]-hard problem, and hence, no FPT algorithm can be found when patterns are in the shape of general graphs. However, Dost et al. gave an algorithm (which is not implemented) to query graphs with a bounded treewidth in PPI networks (the treewidth of the query being involved in the time complexity). In this paper, we propose another algorithm for querying pattern in the shape of graphs, also based on dynamic programming and the color-coding technique. To transform graphs queries into trees without loss of informations, we use feedback vertex set coupled to a node duplication mechanism. Hence, our algorithm is FPT for querying graphs with a bounded size of their feedback vertex set. It gives an alternative to the treewidth parameter, which can be better or worst for a given query. We provide a python implementation which allows us to validate our implementation on real data. Especially, we retrieve some human queries in the shape of graphs into the fly PPI network.

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…

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.…

Graph Structure in Three National Academic Webs: Power Laws with Anomalies.

ERIC Educational Resources Information Center

Thelwall, Mike; Wilkinson, David

2003-01-01

Explains how the Web can be modeled as a mathematical graph and analyzes the graph structures of three national university publicly indexable Web sites from Australia, New Zealand, and the United Kingdom. Topics include commercial search engines and academic Web link research; method-analysis environment and data sets; and power laws. (LRW)

Copying Helps Novice Learners Build Orthographic Knowledge: Methods for Teaching Devanagari Akshara

ERIC Educational Resources Information Center

Bhide, Adeetee

2018-01-01

Hindi graphs, called akshara, are difficult to learn because of their visual complexity and large set of graphs. Akshara containing multiple consonants (complex akshara) are particularly difficult. In Hindi, complex akshara are formed by fusing individual consonantal graphs. Some complex akshara look similar to their component parts (transparent),…

Graph traversals, genes, and matroids: An efficient case of the travelling salesman problem

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

Gusfield, D.; Stelling, P.; Wang, Lusheng

1996-12-31

In this paper the authors consider graph traversal problems that arise from a particular technology for DNA sequencing - sequencing by hybridization (SBH). They first explain the connection of the graph problems to SBH and then focus on the traversal problems. They describe a practical polynomial time solution to the Travelling Salesman Problem in a rich class of directed graphs (including edge weighted binary de Bruijn graphs), and provide a bounded-error approximation algorithm for the maximum weight TSP in a superset of those directed graphs. The authors also establish the existence of a matroid structure defined on the set ofmore » Euler and Hamilton paths in the restricted class of graphs. 8 refs., 5 figs.« less

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

Hamilton, Kathleen E.; Humble, Travis S.

Using quantum annealing to solve an optimization problem requires minor embedding a logic graph into a known hardware graph. We introduce the minor set cover (MSC) of a known graph GG : a subset of graph minors which contain any remaining minor of the graph as a subgraph, in an effort to reduce the complexity of the minor embedding problem. Any graph that can be embedded into GG will be embeddable into a member of the MSC. Focusing on embedding into the hardware graph of commercially available quantum annealers, we establish the MSC for a particular known virtual hardware, whichmore » is a complete bipartite graph. Furthermore, we show that the complete bipartite graph K N,N has a MSC of N minors, from which K N+1 is identified as the largest clique minor of K N,N. In the case of determining the largest clique minor of hardware with faults we briefly discussed this open question.« less

Fisher metric, geometric entanglement, and spin networks

NASA Astrophysics Data System (ADS)

Chirco, Goffredo; Mele, Fabio M.; Oriti, Daniele; Vitale, Patrizia

2018-02-01

Starting from recent results on the geometric formulation of quantum mechanics, we propose a new information geometric characterization of entanglement for spin network states in the context of quantum gravity. For the simple case of a single-link fixed graph (Wilson line), we detail the construction of a Riemannian Fisher metric tensor and a symplectic structure on the graph Hilbert space, showing how these encode the whole information about separability and entanglement. In particular, the Fisher metric defines an entanglement monotone which provides a notion of distance among states in the Hilbert space. In the maximally entangled gauge-invariant case, the entanglement monotone is proportional to a power of the area of the surface dual to the link thus supporting a connection between entanglement and the (simplicial) geometric properties of spin network states. We further extend such analysis to the study of nonlocal correlations between two nonadjacent regions of a generic spin network graph characterized by the bipartite unfolding of an intertwiner state. Our analysis confirms the interpretation of spin network bonds as a result of entanglement and to regard the same spin network graph as an information graph, whose connectivity encodes, both at the local and nonlocal level, the quantum correlations among its parts. This gives a further connection between entanglement and geometry.

Phase transitions in Ising models on directed networks

NASA Astrophysics Data System (ADS)

Lipowski, Adam; Ferreira, António Luis; Lipowska, Dorota; Gontarek, Krzysztof

2015-11-01

We examine Ising models with heat-bath dynamics on directed networks. Our simulations show that Ising models on directed triangular and simple cubic lattices undergo a phase transition that most likely belongs to the Ising universality class. On the directed square lattice the model remains paramagnetic at any positive temperature as already reported in some previous studies. We also examine random directed graphs and show that contrary to undirected ones, percolation of directed bonds does not guarantee ferromagnetic ordering. Only above a certain threshold can a random directed graph support finite-temperature ferromagnetic ordering. Such behavior is found also for out-homogeneous random graphs, but in this case the analysis of magnetic and percolative properties can be done exactly. Directed random graphs also differ from undirected ones with respect to zero-temperature freezing. Only at low connectivity do they remain trapped in a disordered configuration. Above a certain threshold, however, the zero-temperature dynamics quickly drives the model toward a broken symmetry (magnetized) state. Only above this threshold, which is almost twice as large as the percolation threshold, do we expect the Ising model to have a positive critical temperature. With a very good accuracy, the behavior on directed random graphs is reproduced within a certain approximate scheme.

A strand graph semantics for DNA-based computation

PubMed Central

Petersen, Rasmus L.; Lakin, Matthew R.; Phillips, Andrew

2015-01-01

DNA nanotechnology is a promising approach for engineering computation at the nanoscale, with potential applications in biofabrication and intelligent nanomedicine. DNA strand displacement is a general strategy for implementing a broad range of nanoscale computations, including any computation that can be expressed as a chemical reaction network. Modelling and analysis of DNA strand displacement systems is an important part of the design process, prior to experimental realisation. As experimental techniques improve, it is important for modelling languages to keep pace with the complexity of structures that can be realised experimentally. In this paper we present a process calculus for modelling DNA strand displacement computations involving rich secondary structures, including DNA branches and loops. We prove that our calculus is also sufficiently expressive to model previous work on non-branching structures, and propose a mapping from our calculus to a canonical strand graph representation, in which vertices represent DNA strands, ordered sites represent domains, and edges between sites represent bonds between domains. We define interactions between strands by means of strand graph rewriting, and prove the correspondence between the process calculus and strand graph behaviours. Finally, we propose a mapping from strand graphs to an efficient implementation, which we use to perform modelling and simulation of DNA strand displacement systems with rich secondary structure. PMID:27293306

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.

Men's interpretations of graphical information in a videotape decision aid 1

PubMed Central

Pylar, Jan; Wills, Celia E.; Lillie, Janet; Rovner, David R.; Kelly‐Blake, Karen; Holmes‐Rovner, Margaret

2007-01-01

Abstract Objective  To examine men's interpretations of graphical information types viewed in a high‐quality, previously tested videotape decision aid (DA). Setting, participants, design  A community‐dwelling sample of men >50 years of age (N = 188) balanced by education (college/non‐college) and race (Black/White) were interviewed just following their viewing of a videotape DA. A descriptive study design was used to examine men's interpretations of a representative sample of the types of graphs that were shown in the benign prostatic hyperplasia videotape DA. Main variables studied  Men provided their interpretation of graphs information presented in three formats that varied in complexity: pictograph, line and horizontal bar graph. Audiotape transcripts of men's responses were coded for meaning and content‐related interpretation statements. Results  Men provided both meaning and content‐focused interpretations of the graphs. Accuracy of interpretation was lower than hypothesized on the basis of literature review (85.4% for pictograph, 65.7% for line graph, 47.8% for horizontal bar graph). Accuracy for pictograph and line graphs was associated with education level,  = 3.94, P = 0.047, and  = 7.55, P = 0.006, respectively. Accuracy was uncorrelated with men's reported liking of the graphs,  = 2.00, P = 0.441. Conclusion  While men generally liked the DA, accuracy of graphs interpretation was associated with format complexity and education level. Graphs are often recommended to improve comprehension of information in DAs. However, additional evaluation is needed in experimental and naturalistic observational settings to develop best practice standards for data representation. PMID:17524011

Graph-Based Semi-Supervised Hyperspectral Image Classification Using Spatial Information

NASA Astrophysics Data System (ADS)

Jamshidpour, N.; Homayouni, S.; Safari, A.

2017-09-01

Hyperspectral image classification has been one of the most popular research areas in the remote sensing community in the past decades. However, there are still some problems that need specific attentions. For example, the lack of enough labeled samples and the high dimensionality problem are two most important issues which degrade the performance of supervised classification dramatically. The main idea of semi-supervised learning is to overcome these issues by the contribution of unlabeled samples, which are available in an enormous amount. In this paper, we propose a graph-based semi-supervised classification method, which uses both spectral and spatial information for hyperspectral image classification. More specifically, two graphs were designed and constructed in order to exploit the relationship among pixels in spectral and spatial spaces respectively. Then, the Laplacians of both graphs were merged to form a weighted joint graph. The experiments were carried out on two different benchmark hyperspectral data sets. The proposed method performed significantly better than the well-known supervised classification methods, such as SVM. The assessments consisted of both accuracy and homogeneity analyses of the produced classification maps. The proposed spectral-spatial SSL method considerably increased the classification accuracy when the labeled training data set is too scarce.When there were only five labeled samples for each class, the performance improved 5.92% and 10.76% compared to spatial graph-based SSL, for AVIRIS Indian Pine and Pavia University data sets respectively.

Graph processing platforms at scale: practices and experiences

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

Lim, Seung-Hwan; Lee, Sangkeun; Brown, Tyler C

2015-01-01

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

Function plot response: A scalable system for teaching kinematics graphs

NASA Astrophysics Data System (ADS)

Laverty, James; Kortemeyer, Gerd

2012-08-01

Understanding and interpreting graphs are essential skills in all sciences. While students are mostly proficient in plotting given functions and reading values off graphs, they frequently lack the ability to construct and interpret graphs in a meaningful way. Students can use graphs as representations of value pairs, but often fail to interpret them as the representation of functions, and mostly fail to use them as representations of physical reality. Working with graphs in classroom settings has been shown to improve student abilities with graphs, particularly when the students can interact with them. We introduce a novel problem type in an online homework system, which requires students to construct the graphs themselves in free form, and requires no hand-grading by instructors. Initial experiences using the new problem type in an introductory physics course are reported.

Solid-state supramolecular architectures formed by co-crystallization of melamine and 2-, 3- and 4-fluorophenylacetic acids

NASA Astrophysics Data System (ADS)

Perpétuo, Genivaldo Julio; Janczak, Jan

2018-01-01

A family of supramolecular complexes of melamine with fluorophenylacetic acid isomers using solvent-assisted and evaporation-based techniques has been prepared. Crystallization of melamine with 2-fluorophenylacetic acid yield hydrated ionic supramolecular complex (1), whereas crystallization of melamine with 3- and 4-fluorophenylacetic acids leads to formation of neutral supramolecular complexes (2, 3), all with base to acid ratio of 1:2. The supramolecular assembly is driven by the noncovalent interactions, most commonly by the hydrogen bonds. The components of the crystal 1 interact via Nsbnd H⋯O and Osbnd H⋯N hydrogen bonds with R22(8) and R32(10) graphs forming ionic supramolecular complex, whereas the components in the crystals 2 and 3 interact with a graph of R22(8) forming neutral supramolecular complexes. The singly protonated melamin-1-ium residues in 1 interact each other via a pair of Nsbnd H⋯N hydrogen bonds forming one dimensional chains along [-110] that interact via Nsbnd H⋯O with deprotonated and neutral 2-fluorophenylacetic acid units and water molecules forming ribbon. In 2 and 3 co-crystals the melamine interacts with 3- and 4-fluorophenylacetic acids via a pair of Nsbnd H⋯O hydrogen bonds forming pseudo one-dimensional supramolecular chains along [010] direction. Hirshfeld surface and analysis of 2D fingerprint plots have been analysed both quantitatively and qualitatively interactions that governing the supramolecular organisation. The IR and Raman vibrational characterization of the supramolecular complexes 1-3 was supported by the spectra of their deuterated analogues.

Individualized Math Problems in Graphs and Tables. Oregon Vo-Tech Mathematics Problem Sets.

ERIC Educational Resources Information Center

Cosler, Norma, Ed.

This is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic and contains problems related to diverse vocations. Solutions are provided for all problems. Problems involving the construction and interpretation of graphs and…

On the locating domination number of P n [trianglerightequal] H graph

NASA Astrophysics Data System (ADS)

Agustin Retno Wardani, Dwi; Hesti Agustin, Ika; Dafik; Alfarisi, Ridho

2018-04-01

A subset D of V(G) is called a vertex dominating set of G if every vertex not in D is adjacent to some vertices in D. A graph G = (V, E) is called a locating dominating set if for every two vertices u,v\\in V(G)-D, N(v)\\cap D\

Invasion Percolation and Global Optimization

NASA Astrophysics Data System (ADS)

Barabási, Albert-László

1996-05-01

Invasion bond percolation (IBP) is mapped exactly into Prim's algorithm for finding the shortest spanning tree of a weighted random graph. Exploring this mapping, which is valid for arbitrary dimensions and lattices, we introduce a new IBP model that belongs to the same universality class as IBP and generates the minimal energy tree spanning the IBP cluster.

The Impact of a Common MDM2 SNP on the Sensitivity of Breast Cancer to Treatment

DTIC Science & Technology

2011-06-01

Kirchhoff T, Alexe G, Bond EE, Robins H, Bartel F, Taubert H, Wuerl P, Hait W, Toppmeyer D, Offit K, and Levine A. MDM2 SNP309 accelerates tumor...the Western blot analysis corresponding to the quantification in the upper graphs . 29 Figure 5. Effect of

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.

MoleculaRnetworks: an integrated graph theoretic and data mining tool to explore solvent organization in molecular simulation.

PubMed

Mooney, Barbara Logan; Corrales, L René; Clark, Aurora E

2012-03-30

This work discusses scripts for processing molecular simulations data written using the software package R: A Language and Environment for Statistical Computing. These scripts, named moleculaRnetworks, are intended for the geometric and solvent network analysis of aqueous solutes and can be extended to other H-bonded solvents. New algorithms, several of which are based on graph theory, that interrogate the solvent environment about a solute are presented and described. This includes a novel method for identifying the geometric shape adopted by the solvent in the immediate vicinity of the solute and an exploratory approach for describing H-bonding, both based on the PageRank algorithm of Google search fame. The moleculaRnetworks codes include a preprocessor, which distills simulation trajectories into physicochemical data arrays, and an interactive analysis script that enables statistical, trend, and correlation analysis, and other data mining. The goal of these scripts is to increase access to the wealth of structural and dynamical information that can be obtained from molecular simulations. Copyright © 2012 Wiley Periodicals, Inc.

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)

Hamiltonian Cycle Enumeration via Fermion-Zeon Convolution

NASA Astrophysics Data System (ADS)

Staples, G. Stacey

2017-12-01

Beginning with a simple graph having finite vertex set V, operators are induced on fermion and zeon algebras by the action of the graph's adjacency matrix and combinatorial Laplacian on the vector space spanned by the graph's vertices. When the graph is simple (undirected with no loops or multiple edges), the matrices are symmetric and the induced operators are self-adjoint. The goal of the current paper is to recover a number of known graph-theoretic results from quantum observables constructed as linear operators on fermion and zeon Fock spaces. By considering an "indeterminate" fermion/zeon Fock space, a fermion-zeon convolution operator is defined whose trace recovers the number of Hamiltonian cycles in the graph. This convolution operator is a quantum observable whose expectation reveals the number of Hamiltonian cycles in the graph.

A clustering-based graph Laplacian framework for value function approximation in reinforcement learning.

PubMed

Xu, Xin; Huang, Zhenhua; Graves, Daniel; Pedrycz, Witold

2014-12-01

In order to deal with the sequential decision problems with large or continuous state spaces, feature representation and function approximation have been a major research topic in reinforcement learning (RL). In this paper, a clustering-based graph Laplacian framework is presented for feature representation and value function approximation (VFA) in RL. By making use of clustering-based techniques, that is, K-means clustering or fuzzy C-means clustering, a graph Laplacian is constructed by subsampling in Markov decision processes (MDPs) with continuous state spaces. The basis functions for VFA can be automatically generated from spectral analysis of the graph Laplacian. The clustering-based graph Laplacian is integrated with a class of approximation policy iteration algorithms called representation policy iteration (RPI) for RL in MDPs with continuous state spaces. Simulation and experimental results show that, compared with previous RPI methods, the proposed approach needs fewer sample points to compute an efficient set of basis functions and the learning control performance can be improved for a variety of parameter settings.

Multiple Illuminant Colour Estimation via Statistical Inference on Factor Graphs.

PubMed

Mutimbu, Lawrence; Robles-Kelly, Antonio

2016-08-31

This paper presents a method to recover a spatially varying illuminant colour estimate from scenes lit by multiple light sources. Starting with the image formation process, we formulate the illuminant recovery problem in a statistically datadriven setting. To do this, we use a factor graph defined across the scale space of the input image. In the graph, we utilise a set of illuminant prototypes computed using a data driven approach. As a result, our method delivers a pixelwise illuminant colour estimate being devoid of libraries or user input. The use of a factor graph also allows for the illuminant estimates to be recovered making use of a maximum a posteriori (MAP) inference process. Moreover, we compute the probability marginals by performing a Delaunay triangulation on our factor graph. We illustrate the utility of our method for pixelwise illuminant colour recovery on widely available datasets and compare against a number of alternatives. We also show sample colour correction results on real-world images.

A characterization of horizontal visibility graphs and combinatorics on words

NASA Astrophysics Data System (ADS)

Gutin, Gregory; Mansour, Toufik; Severini, Simone

2011-06-01

A Horizontal Visibility Graph (HVG) is defined in association with an ordered set of non-negative reals. HVGs realize a methodology in the analysis of time series, their degree distribution being a good discriminator between randomness and chaos Luque et al. [B. Luque, L. Lacasa, F. Ballesteros, J. Luque, Horizontal visibility graphs: exact results for random time series, Phys. Rev. E 80 (2009), 046103]. We prove that a graph is an HVG if and only if it is outerplanar and has a Hamilton path. Therefore, an HVG is a noncrossing graph, as defined in algebraic combinatorics Flajolet and Noy [P. Flajolet, M. Noy, Analytic combinatorics of noncrossing configurations, Discrete Math., 204 (1999) 203-229]. Our characterization of HVGs implies a linear time recognition algorithm. Treating ordered sets as words, we characterize subfamilies of HVGs highlighting various connections with combinatorial statistics and introducing the notion of a visible pair. With this technique, we determine asymptotically the average number of edges of HVGs.

An Xdata Architecture for Federated Graph Models and Multi-tier Asymmetric Computing

DTIC Science & Technology

2014-01-01

Wikipedia, a scale-free random graph (kron), Akamai trace route data, Bitcoin transaction data, and a Twitter follower network. We present results for...3x (SSSP on a random graph) and nearly 300x (Akamai and Bitcoin ) over the CPU performance of a well-known and widely deployed CPU-based graph...provided better throughput for smaller frontiers such as roadmaps or the Bitcoin data set. In our work, we have focused on two-phase kernels, but it

Graph wavelet alignment kernels for drug virtual screening.

PubMed

Smalter, Aaron; Huan, Jun; Lushington, Gerald

2009-06-01

In this paper, we introduce a novel statistical modeling technique for target property prediction, with applications to virtual screening and drug design. In our method, we use graphs to model chemical structures and apply a wavelet analysis of graphs to summarize features capturing graph local topology. We design a novel graph kernel function to utilize the topology features to build predictive models for chemicals via Support Vector Machine classifier. We call the new graph kernel a graph wavelet-alignment kernel. We have evaluated the efficacy of the wavelet-alignment kernel using a set of chemical structure-activity prediction benchmarks. Our results indicate that the use of the kernel function yields performance profiles comparable to, and sometimes exceeding that of the existing state-of-the-art chemical classification approaches. In addition, our results also show that the use of wavelet functions significantly decreases the computational costs for graph kernel computation with more than ten fold speedup.

Integrated Network Decompositions and Dynamic Programming for Graph Optimization (INDDGO)

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

The INDDGO software package offers a set of tools for finding exact solutions to graph optimization problems via tree decompositions and dynamic programming algorithms. Currently the framework offers serial and parallel (distributed memory) algorithms for finding tree decompositions and solving the maximum weighted independent set problem. The parallel dynamic programming algorithm is implemented on top of the MADNESS task-based runtime.

On the Certain Topological Indices of Titania Nanotube TiO2[m, n

NASA Astrophysics Data System (ADS)

Javaid, M.; Liu, Jia-Bao; Rehman, M. A.; Wang, Shaohui

2017-07-01

A numeric quantity that characterises the whole structure of a molecular graph is called the topological index that predicts the physical features, chemical reactivities, and boiling activities of the involved chemical compound in the molecular graph. In this article, we give new mathematical expressions for the multiple Zagreb indices, the generalised Zagreb index, the fourth version of atom-bond connectivity (ABC4) index, and the fifth version of geometric-arithmetic (GA5) index of TiO2[m, n]. In addition, we compute the latest developed topological index called by Sanskruti index. At the end, a comparison is also included to estimate the efficiency of the computed indices. Our results extended some known conclusions.

Disease Spreading Model with Partial Isolation

NASA Astrophysics Data System (ADS)

Chakraborty, Abhijit; Manna, S. S.

2013-08-01

The effect of partial isolation has been studied in disease spreading processes using the framework of susceptible-infected-susceptible (SIS) and susceptible-infected-recovered (SIR) models. The partial isolation is introduced by imposing a restriction: each infected individual can probabilistically infect up to a maximum number n of his susceptible neighbors, but not all. It has been observed that the critical values of the spreading rates for endemic states are non-zero in both models and decrease as 1/n with n, on all graphs including scale-free graphs. In particular, the SIR model with n = 2 turned out to be a special case, characterized by a new bond percolation threshold on square lattice.

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.

Classification of user interfaces for graph-based online analytical processing

NASA Astrophysics Data System (ADS)

Michaelis, James R.

2016-05-01

In the domain of business intelligence, user-oriented software for conducting multidimensional analysis via Online- Analytical Processing (OLAP) is now commonplace. In this setting, datasets commonly have well-defined sets of dimensions and measures around which analysis tasks can be conducted. However, many forms of data used in intelligence operations - deriving from social networks, online communications, and text corpora - will consist of graphs with varying forms of potential dimensional structure. Hence, enabling OLAP over such data collections requires explicit definition and extraction of supporting dimensions and measures. Further, as Graph OLAP remains an emerging technique, limited research has been done on its user interface requirements. Namely, on effective pairing of interface designs to different types of graph-derived dimensions and measures. This paper presents a novel technique for pairing of user interface designs to Graph OLAP datasets, rooted in Analytic Hierarchy Process (AHP) driven comparisons. Attributes of the classification strategy are encoded through an AHP ontology, developed in our alternate work and extended to support pairwise comparison of interfaces. Specifically, according to their ability, as perceived by Subject Matter Experts, to support dimensions and measures corresponding to Graph OLAP dataset attributes. To frame this discussion, a survey is provided both on existing variations of Graph OLAP, as well as existing interface designs previously applied in multidimensional analysis settings. Following this, a review of our AHP ontology is provided, along with a listing of corresponding dataset and interface attributes applicable toward SME recommendation structuring. A walkthrough of AHP-based recommendation encoding via the ontology-based approach is then provided. The paper concludes with a short summary of proposed future directions seen as essential for this research area.

NeAT: a toolbox for the analysis of biological networks, clusters, classes and pathways.

PubMed

Brohée, Sylvain; Faust, Karoline; Lima-Mendez, Gipsi; Sand, Olivier; Janky, Rekin's; Vanderstocken, Gilles; Deville, Yves; van Helden, Jacques

2008-07-01

The network analysis tools (NeAT) (http://rsat.ulb.ac.be/neat/) provide a user-friendly web access to a collection of modular tools for the analysis of networks (graphs) and clusters (e.g. microarray clusters, functional classes, etc.). A first set of tools supports basic operations on graphs (comparison between two graphs, neighborhood of a set of input nodes, path finding and graph randomization). Another set of programs makes the connection between networks and clusters (graph-based clustering, cliques discovery and mapping of clusters onto a network). The toolbox also includes programs for detecting significant intersections between clusters/classes (e.g. clusters of co-expression versus functional classes of genes). NeAT are designed to cope with large datasets and provide a flexible toolbox for analyzing biological networks stored in various databases (protein interactions, regulation and metabolism) or obtained from high-throughput experiments (two-hybrid, mass-spectrometry and microarrays). The web interface interconnects the programs in predefined analysis flows, enabling to address a series of questions about networks of interest. Each tool can also be used separately by entering custom data for a specific analysis. NeAT can also be used as web services (SOAP/WSDL interface), in order to design programmatic workflows and integrate them with other available resources.

F-RAG: Generating Atomic Coordinates from RNA Graphs by Fragment Assembly.

PubMed

Jain, Swati; Schlick, Tamar

2017-11-24

Coarse-grained models represent attractive approaches to analyze and simulate ribonucleic acid (RNA) molecules, for example, for structure prediction and design, as they simplify the RNA structure to reduce the conformational search space. Our structure prediction protocol RAGTOP (RNA-As-Graphs Topology Prediction) represents RNA structures as tree graphs and samples graph topologies to produce candidate graphs. However, for a more detailed study and analysis, construction of atomic from coarse-grained models is required. Here we present our graph-based fragment assembly algorithm (F-RAG) to convert candidate three-dimensional (3D) tree graph models, produced by RAGTOP into atomic structures. We use our related RAG-3D utilities to partition graphs into subgraphs and search for structurally similar atomic fragments in a data set of RNA 3D structures. The fragments are edited and superimposed using common residues, full atomic models are scored using RAGTOP's knowledge-based potential, and geometries of top scoring models is optimized. To evaluate our models, we assess all-atom RMSDs and Interaction Network Fidelity (a measure of residue interactions) with respect to experimentally solved structures and compare our results to other fragment assembly programs. For a set of 50 RNA structures, we obtain atomic models with reasonable geometries and interactions, particularly good for RNAs containing junctions. Additional improvements to our protocol and databases are outlined. These results provide a good foundation for further work on RNA structure prediction and design applications. Copyright © 2017 Elsevier Ltd. All rights reserved.

Decision net, directed graph, and neural net processing of imaging spectrometer data

NASA Technical Reports Server (NTRS)

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

1989-01-01

A decision-net solution involving a novel hierarchical classifier and a set of multiple directed graphs, as well as a neural-net solution, are respectively presented for large-class problem and mixture problem treatments of imaging spectrometer data. The clustering method for hierarchical classifier design, when used with multiple directed graphs, yields an efficient decision net. New directed-graph rules for reducing local maxima as well as the number of perturbations required, and the new starting-node rules for extending the reachability and reducing the search time of the graphs, are noted to yield superior results, as indicated by an illustrative 500-class imaging spectrometer problem.

Characterizing the performance of XOR games and the Shannon capacity of graphs.

PubMed

Ramanathan, Ravishankar; Kay, Alastair; Murta, Gláucia; Horodecki, Paweł

2014-12-12

In this Letter we give a set of necessary and sufficient conditions such that quantum players of a two-party XOR game cannot perform any better than classical players. With any such game, we associate a graph and examine its zero-error communication capacity. This allows us to specify a broad new class of graphs for which the Shannon capacity can be calculated. The conditions also enable the parametrization of new families of games that have no quantum advantage for arbitrary input probability distributions, up to certain symmetries. In the future, these might be used in information-theoretic studies on reproducing the set of quantum nonlocal correlations.

A Benes-like theorem for the shuffle-exchange graph

NASA Technical Reports Server (NTRS)

Schwabe, Eric J.

1992-01-01

One of the first theorems on permutation routing, proved by V. E. Beness (1965), shows that given a set of source-destination pairs in an N-node butterfly network with at most a constant number of sources or destinations in each column of the butterfly, there exists a set of paths of lengths O(log N) connecting each pair such that the total congestion is constant. An analogous theorem yielding constant-congestion paths for off-line routing in the shuffle-exchange graph is proved here. The necklaces of the shuffle-exchange graph play the same structural role as the columns of the butterfly in Beness' theorem.

Integrating Graphing Assignments into a Money and Banking Course Using FRED

ERIC Educational Resources Information Center

Staveley-O'Carroll, James

2018-01-01

Over the course of one semester, six empirical assignments that utilize FRED are used to introduce students of money and banking courses to the economic analysis required for the conduct of monetary policy. The first five assignments cover the following topics: inflation, bonds and stocks, monetary aggregates, the Taylor rule, and employment.…

SING: Subgraph search In Non-homogeneous Graphs

PubMed Central

2010-01-01

Background Finding the subgraphs of a graph database that are isomorphic to a given query graph has practical applications in several fields, from cheminformatics to image understanding. Since subgraph isomorphism is a computationally hard problem, indexing techniques have been intensively exploited to speed up the process. Such systems filter out those graphs which cannot contain the query, and apply a subgraph isomorphism algorithm to each residual candidate graph. The applicability of such systems is limited to databases of small graphs, because their filtering power degrades on large graphs. Results In this paper, SING (Subgraph search In Non-homogeneous Graphs), a novel indexing system able to cope with large graphs, is presented. The method uses the notion of feature, which can be a small subgraph, subtree or path. Each graph in the database is annotated with the set of all its features. The key point is to make use of feature locality information. This idea is used to both improve the filtering performance and speed up the subgraph isomorphism task. Conclusions Extensive tests on chemical compounds, biological networks and synthetic graphs show that the proposed system outperforms the most popular systems in query time over databases of medium and large graphs. Other specific tests show that the proposed system is effective for single large graphs. PMID:20170516

Crystal structure of N'-[(E)-(4-chloro-phen-yl)(phen-yl)methyl-idene]-4-methyl-benzene-sulfono-hydrazide.

PubMed

Balaji, J; Prabu, S; Xavier, J J F; Srinivasan, P

2015-01-01

The title compound, C20H17ClN2O2S, was obtained by a condensation reaction between 4-chloro-benzo-phenone and tosyl hydrazide. The plane of the methyl-substituted benzene ring forms dihedral angles of 20.12 (12) and 78.43 (13)° with those of the chlorine-substituted benzene ring and the benzene ring, respectively, with the last two rings forming a dihedral angle of 67.81 (13)°. The chlorine substituent was also found to be 0.868 (2):0.132 (2) disordered over these two rings. In the crystal, mol-ecules are linked through pairs of N-H⋯O hydrogen bonds, giving centrosymmetric cyclic dimers [graph set R 2 (2)(8)], which are linked by weak C-H⋯O and C-H⋯Cl inter-actions into a chain structure which extends along the a-axis direction.

The minimal-ABC trees with B1-branches.

PubMed

Dimitrov, Darko; Du, Zhibin; Fonseca, Carlos M da

2018-01-01

The atom-bond connectivity index (or, for short, ABC index) is a molecular structure descriptor bridging chemistry to graph theory. It is probably the most studied topological index among all numerical parameters of a graph that characterize its topology. For a given graph G = (V, E), the ABC index of G is defined as [Formula: see text], where di denotes the degree of the vertex i, and ij is the edge incident to the vertices i and j. A combination of physicochemical and the ABC index properties are commonly used to foresee the bioactivity of different chemical composites. Additionally, the applicability of the ABC index in chemical thermodynamics and other areas of chemistry, such as in dendrimer nanostars, benzenoid systems, fluoranthene congeners, and phenylenes is well studied in the literature. While finding of the graphs with the greatest ABC-value is a straightforward assignment, the characterization of the tree(s) with minimal ABC index is a problem largely open and has recently given rise to numerous studies and conjectures. A B1-branch of a graph is a pendent path of order 2. In this paper, we provide an important step forward to the full characterization of these minimal trees. Namely, we show that a minimal-ABC tree contains neither 4 nor 3 B1-branches. The case when the number of B1-branches is 2 is also considered.

Super local edge antimagic total coloring of {P}_{n}\\vartriangleright H

NASA Astrophysics Data System (ADS)

Yuli Kurniawati, Elsa; Hesti Agustin, Ika; Dafik; Alfarisi, Ridho

2018-04-01

In this paper, we consider that all graphs are finite, simple and connected. Let G(V, E) be a graph of vertex set V and edge set E. A bijection f:V(G)\\to \\{1,2,3,\\ldots,|V(G)|\\} is called a local edge antimagic labeling if for any two adjacent edges e 1 and e 2, w({e}1)\

Student reasoning about graphs in different contexts

NASA Astrophysics Data System (ADS)

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

2016-06-01

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

Cycle/Cocycle Oblique Projections on Oriented Graphs

NASA Astrophysics Data System (ADS)

Polettini, Matteo

2015-01-01

It is well known that the edge vector space of an oriented graph can be decomposed in terms of cycles and cocycles (alias cuts, or bonds), and that a basis for the cycle and the cocycle spaces can be generated by adding and removing edges to an arbitrarily chosen spanning tree. In this paper, we show that the edge vector space can also be decomposed in terms of cycles and the generating edges of cocycles (called cochords), or of cocycles and the generating edges of cycles (called chords). From this observation follows a construction in terms of oblique complementary projection operators. We employ this algebraic construction to prove several properties of unweighted Kirchhoff-Symanzik matrices, encoding the mutual superposition between cycles and cocycles. In particular, we prove that dual matrices of planar graphs have the same spectrum (up to multiplicities). We briefly comment on how this construction provides a refined formalization of Kirchhoff's mesh analysis of electrical circuits, which has lately been applied to generic thermodynamic networks.

3D segmentation of lung CT data with graph-cuts: analysis of parameter sensitivities

NASA Astrophysics Data System (ADS)

Cha, Jung won; Dunlap, Neal; Wang, Brian; Amini, Amir

2016-03-01

Lung boundary image segmentation is important for many tasks including for example in development of radiation treatment plans for subjects with thoracic malignancies. In this paper, we describe a method and parameter settings for accurate 3D lung boundary segmentation based on graph-cuts from X-ray CT data1. Even though previously several researchers have used graph-cuts for image segmentation, to date, no systematic studies have been performed regarding the range of parameter that give accurate results. The energy function in the graph-cuts algorithm requires 3 suitable parameter settings: K, a large constant for assigning seed points, c, the similarity coefficient for n-links, and λ, the terminal coefficient for t-links. We analyzed the parameter sensitivity with four lung data sets from subjects with lung cancer using error metrics. Large values of K created artifacts on segmented images, and relatively much larger value of c than the value of λ influenced the balance between the boundary term and the data term in the energy function, leading to unacceptable segmentation results. For a range of parameter settings, we performed 3D image segmentation, and in each case compared the results with the expert-delineated lung boundaries. We used simple 6-neighborhood systems for n-link in 3D. The 3D image segmentation took 10 minutes for a 512x512x118 ~ 512x512x190 lung CT image volume. Our results indicate that the graph-cuts algorithm was more sensitive to the K and λ parameter settings than to the C parameter and furthermore that amongst the range of parameters tested, K=5 and λ=0.5 yielded good results.

Graph Structured Program Evolution: Evolution of Loop Structures

NASA Astrophysics Data System (ADS)

Shirakawa, Shinichi; Nagao, Tomoharu

Recently, numerous automatic programming techniques have been developed and applied in various fields. A typical example is genetic programming (GP), and various extensions and representations of GP have been proposed thus far. Complex programs and hand-written programs, however, may contain several loops and handle multiple data types. In this chapter, we propose a new method called Graph Structured Program Evolution (GRAPE). The representation of GRAPE is a graph structure; therefore, it can represent branches and loops using this structure. Each programis constructed as an arbitrary directed graph of nodes and a data set. The GRAPE program handles multiple data types using the data set for each type, and the genotype of GRAPE takes the form of a linear string of integers. We apply GRAPE to three test problems, factorial, exponentiation, and list sorting, and demonstrate that the optimum solution in each problem is obtained by the GRAPE system.

Comparison of university students' understanding of graphs in different contexts

NASA Astrophysics Data System (ADS)

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

2013-12-01

This study investigates university students’ understanding of graphs in three different domains: mathematics, physics (kinematics), and contexts other than physics. Eight sets of parallel mathematics, physics, and other context questions about graphs were developed. A test consisting of these eight sets of questions (24 questions in all) was administered to 385 first year students at University of Zagreb who were either prospective physics or mathematics teachers or prospective physicists or mathematicians. Rasch analysis of data was conducted and linear measures for item difficulties were obtained. Average difficulties of items in three domains (mathematics, physics, and other contexts) and over two concepts (graph slope, area under the graph) were computed and compared. Analysis suggests that the variation of average difficulty among the three domains is much smaller for the concept of graph slope than for the concept of area under the graph. Most of the slope items are very close in difficulty, suggesting that students who have developed sufficient understanding of graph slope in mathematics are generally able to transfer it almost equally successfully to other contexts. A large difference was found between the difficulty of the concept of area under the graph in physics and other contexts on one side and mathematics on the other side. Comparison of average difficulty of the three domains suggests that mathematics without context is the easiest domain for students. Adding either physics or other context to mathematical items generally seems to increase item difficulty. No significant difference was found between the average item difficulty in physics and contexts other than physics, suggesting that physics (kinematics) remains a difficult context for most students despite the received instruction on kinematics in high school.

The Time Window Vehicle Routing Problem Considering Closed Route

NASA Astrophysics Data System (ADS)

Irsa Syahputri, Nenna; Mawengkang, Herman

2017-12-01

The Vehicle Routing Problem (VRP) determines the optimal set of routes used by a fleet of vehicles to serve a given set of customers on a predefined graph; the objective is to minimize the total travel cost (related to the travel times or distances) and operational cost (related to the number of vehicles used). In this paper we study a variant of the predefined graph: given a weighted graph G and vertices a and b, and given a set X of closed paths in G, find the minimum total travel cost of a-b path P such that no path in X is a subpath of P. Path P is allowed to repeat vertices and edges. We use integer programming model to describe the problem. A feasible neighbourhood approach is proposed to solve the model

Knowledge Representation Issues in Semantic Graphs for Relationship Detection

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

Barthelemy, M; Chow, E; Eliassi-Rad, T

2005-02-02

An important task for Homeland Security is the prediction of threat vulnerabilities, such as through the detection of relationships between seemingly disjoint entities. A structure used for this task is a ''semantic graph'', also known as a ''relational data graph'' or an ''attributed relational graph''. These graphs encode relationships as typed links between a pair of typed nodes. Indeed, semantic graphs are very similar to semantic networks used in AI. The node and link types are related through an ontology graph (also known as a schema). Furthermore, each node has a set of attributes associated with it (e.g., ''age'' maymore » be an attribute of a node of type ''person''). Unfortunately, the selection of types and attributes for both nodes and links depends on human expertise and is somewhat subjective and even arbitrary. This subjectiveness introduces biases into any algorithm that operates on semantic graphs. Here, we raise some knowledge representation issues for semantic graphs and provide some possible solutions using recently developed ideas in the field of complex networks. In particular, we use the concept of transitivity to evaluate the relevance of individual links in the semantic graph for detecting relationships. We also propose new statistical measures for semantic graphs and illustrate these semantic measures on graphs constructed from movies and terrorism data.« less

Validation of five minimally obstructive methods to estimate physical activity energy expenditure in young adults in semi-standardized settings.

PubMed

Schneller, Mikkel B; Pedersen, Mogens T; Gupta, Nidhi; Aadahl, Mette; Holtermann, Andreas

2015-03-13

We compared the accuracy of five objective methods, including two newly developed methods combining accelerometry and activity type recognition (Acti4), against indirect calorimetry, to estimate total energy expenditure (EE) of different activities in semi-standardized settings. Fourteen participants performed a standardized and semi-standardized protocol including seven daily life activity types, while having their EE measured by indirect calorimetry. Simultaneously, physical activity was quantified by an ActivPAL3, two ActiGraph GT3X+'s and an Actiheart. EE was estimated by the standard ActivPAL3 software (ActivPAL), ActiGraph GT3X+ (ActiGraph) and Actiheart (Actiheart), and by a combination of activity type recognition via Acti4 software and activity counts per minute (CPM) of either a hip- or thigh-worn ActiGraph GT3X+ (AGhip + Acti4 and AGthigh + Acti4). At group level, estimated physical activities EE by Actiheart (MSE = 2.05) and AGthigh + Acti4 (MSE = 0.25) were not significantly different from measured EE by indirect calorimetry, while significantly underestimated by ActiGraph, ActivPAL and AGhip + Acti4. AGthigh + Acti4 and Actiheart explained 77% and 45%, of the individual variations in measured physical activity EE by indirect calorimetry, respectively. This study concludes that combining accelerometer data from a thigh-worn ActiGraph GT3X+ with activity type recognition improved the accuracy of activity specific EE estimation against indirect calorimetry in semi-standardized settings compared to previously validated methods using CPM only.

Towards accurate modeling of noncovalent interactions for protein rigidity analysis.

PubMed

Fox, Naomi; Streinu, Ileana

2013-01-01

Protein rigidity analysis is an efficient computational method for extracting flexibility information from static, X-ray crystallography protein data. Atoms and bonds are modeled as a mechanical structure and analyzed with a fast graph-based algorithm, producing a decomposition of the flexible molecule into interconnected rigid clusters. The result depends critically on noncovalent atomic interactions, primarily on how hydrogen bonds and hydrophobic interactions are computed and modeled. Ongoing research points to the stringent need for benchmarking rigidity analysis software systems, towards the goal of increasing their accuracy and validating their results, either against each other and against biologically relevant (functional) parameters. We propose two new methods for modeling hydrogen bonds and hydrophobic interactions that more accurately reflect a mechanical model, without being computationally more intensive. We evaluate them using a novel scoring method, based on the B-cubed score from the information retrieval literature, which measures how well two cluster decompositions match. To evaluate the modeling accuracy of KINARI, our pebble-game rigidity analysis system, we use a benchmark data set of 20 proteins, each with multiple distinct conformations deposited in the Protein Data Bank. Cluster decompositions for them were previously determined with the RigidFinder method from Gerstein's lab and validated against experimental data. When KINARI's default tuning parameters are used, an improvement of the B-cubed score over a crude baseline is observed in 30% of this data. With our new modeling options, improvements were observed in over 70% of the proteins in this data set. We investigate the sensitivity of the cluster decomposition score with case studies on pyruvate phosphate dikinase and calmodulin. To substantially improve the accuracy of protein rigidity analysis systems, thorough benchmarking must be performed on all current systems and future extensions. We have measured the gain in performance by comparing different modeling methods for noncovalent interactions. We showed that new criteria for modeling hydrogen bonds and hydrophobic interactions can significantly improve the results. The two new methods proposed here have been implemented and made publicly available in the current version of KINARI (v1.3), together with the benchmarking tools, which can be downloaded from our software's website, http://kinari.cs.umass.edu.

Towards accurate modeling of noncovalent interactions for protein rigidity analysis

PubMed Central

2013-01-01

Background Protein rigidity analysis is an efficient computational method for extracting flexibility information from static, X-ray crystallography protein data. Atoms and bonds are modeled as a mechanical structure and analyzed with a fast graph-based algorithm, producing a decomposition of the flexible molecule into interconnected rigid clusters. The result depends critically on noncovalent atomic interactions, primarily on how hydrogen bonds and hydrophobic interactions are computed and modeled. Ongoing research points to the stringent need for benchmarking rigidity analysis software systems, towards the goal of increasing their accuracy and validating their results, either against each other and against biologically relevant (functional) parameters. We propose two new methods for modeling hydrogen bonds and hydrophobic interactions that more accurately reflect a mechanical model, without being computationally more intensive. We evaluate them using a novel scoring method, based on the B-cubed score from the information retrieval literature, which measures how well two cluster decompositions match. Results To evaluate the modeling accuracy of KINARI, our pebble-game rigidity analysis system, we use a benchmark data set of 20 proteins, each with multiple distinct conformations deposited in the Protein Data Bank. Cluster decompositions for them were previously determined with the RigidFinder method from Gerstein's lab and validated against experimental data. When KINARI's default tuning parameters are used, an improvement of the B-cubed score over a crude baseline is observed in 30% of this data. With our new modeling options, improvements were observed in over 70% of the proteins in this data set. We investigate the sensitivity of the cluster decomposition score with case studies on pyruvate phosphate dikinase and calmodulin. Conclusion To substantially improve the accuracy of protein rigidity analysis systems, thorough benchmarking must be performed on all current systems and future extensions. We have measured the gain in performance by comparing different modeling methods for noncovalent interactions. We showed that new criteria for modeling hydrogen bonds and hydrophobic interactions can significantly improve the results. The two new methods proposed here have been implemented and made publicly available in the current version of KINARI (v1.3), together with the benchmarking tools, which can be downloaded from our software's website, http://kinari.cs.umass.edu. PMID:24564209

DELTACON: A Principled Massive-Graph Similarity Function with Attribution

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

Koutra, Danai; Shah, Neil; Vogelstein, Joshua T.

How much did a network change since yesterday? How different is the wiring between Bob's brain (a left-handed male) and Alice's brain (a right-handed female)? Graph similarity with known node correspondence, i.e. the detection of changes in the connectivity of graphs, arises in numerous settings. In this work, we formally state the axioms and desired properties of the graph similarity functions, and evaluate when state-of-the-art methods fail to detect crucial connectivity changes in graphs. We propose DeltaCon, a principled, intuitive, and scalable algorithm that assesses the similarity between two graphs on the same nodes (e.g. employees of a company, customersmore » of a mobile carrier). In our experiments on various synthetic and real graphs we showcase the advantages of our method over existing similarity measures. We also employ DeltaCon to real applications: (a) we classify people to groups of high and low creativity based on their brain connectivity graphs, and (b) do temporal anomaly detection in the who-emails-whom Enron graph.« less

DELTACON: A Principled Massive-Graph Similarity Function with Attribution

DOE PAGES

Koutra, Danai; Shah, Neil; Vogelstein, Joshua T.; ...

2014-05-22

How much did a network change since yesterday? How different is the wiring between Bob's brain (a left-handed male) and Alice's brain (a right-handed female)? Graph similarity with known node correspondence, i.e. the detection of changes in the connectivity of graphs, arises in numerous settings. In this work, we formally state the axioms and desired properties of the graph similarity functions, and evaluate when state-of-the-art methods fail to detect crucial connectivity changes in graphs. We propose DeltaCon, a principled, intuitive, and scalable algorithm that assesses the similarity between two graphs on the same nodes (e.g. employees of a company, customersmore » of a mobile carrier). In our experiments on various synthetic and real graphs we showcase the advantages of our method over existing similarity measures. We also employ DeltaCon to real applications: (a) we classify people to groups of high and low creativity based on their brain connectivity graphs, and (b) do temporal anomaly detection in the who-emails-whom Enron graph.« less

On the local vertex antimagic total coloring of some families tree

NASA Astrophysics Data System (ADS)

Febriani Putri, Desi; Dafik; Hesti Agustin, Ika; Alfarisi, Ridho

2018-04-01

Let G(V, E) be a graph of vertex set V and edge set E. Local vertex antimagic total coloring developed from local edge and local vertex antimagic coloring of graph. Local vertex antimagic total coloring is defined f:V(G)\\cup E(G)\\to \\{1,2,3,\\ldots,|V(G)|+|E(G)|\\} if for any two adjacent vertices v 1 and v 2, w({v}1)\

Acceleration of Binding Site Comparisons by Graph Partitioning.

PubMed

Krotzky, Timo; Klebe, Gerhard

2015-08-01

The comparison of protein binding sites is a prominent task in computational chemistry and has been studied in many different ways. For the automatic detection and comparison of putative binding cavities the Cavbase system has been developed which uses a coarse-grained set of pseudocenters to represent the physicochemical properties of a binding site and employs a graph-based procedure to calculate similarities between two binding sites. However, the comparison of two graphs is computationally quite demanding which makes large-scale studies such as the rapid screening of entire databases hardly feasible. In a recent work, we proposed the method Local Cliques (LC) for the efficient comparison of Cavbase binding sites. It employs a clique heuristic to detect the maximum common subgraph of two binding sites and an extended graph model to additionally compare the shape of individual surface patches. In this study, we present an alternative to further accelerate the LC method by partitioning the binding-site graphs into disjoint components prior to their comparisons. The pseudocenter sets are split with regard to their assigned phyiscochemical type, which leads to seven much smaller graphs than the original one. Applying this approach on the same test scenarios as in the former comprehensive way results in a significant speed-up without sacrificing accuracy. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Edge compression techniques for visualization of dense directed graphs.

PubMed

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

2013-12-01

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

Automatic classification of protein structures relying on similarities between alignments

PubMed Central

2012-01-01

Background Identification of protein structural cores requires isolation of sets of proteins all sharing a same subset of structural motifs. In the context of an ever growing number of available 3D protein structures, standard and automatic clustering algorithms require adaptations so as to allow for efficient identification of such sets of proteins. Results When considering a pair of 3D structures, they are stated as similar or not according to the local similarities of their matching substructures in a structural alignment. This binary relation can be represented in a graph of similarities where a node represents a 3D protein structure and an edge states that two 3D protein structures are similar. Therefore, classifying proteins into structural families can be viewed as a graph clustering task. Unfortunately, because such a graph encodes only pairwise similarity information, clustering algorithms may include in the same cluster a subset of 3D structures that do not share a common substructure. In order to overcome this drawback we first define a ternary similarity on a triple of 3D structures as a constraint to be satisfied by the graph of similarities. Such a ternary constraint takes into account similarities between pairwise alignments, so as to ensure that the three involved protein structures do have some common substructure. We propose hereunder a modification algorithm that eliminates edges from the original graph of similarities and gives a reduced graph in which no ternary constraints are violated. Our approach is then first to build a graph of similarities, then to reduce the graph according to the modification algorithm, and finally to apply to the reduced graph a standard graph clustering algorithm. Such method was used for classifying ASTRAL-40 non-redundant protein domains, identifying significant pairwise similarities with Yakusa, a program devised for rapid 3D structure alignments. Conclusions We show that filtering similarities prior to standard graph based clustering process by applying ternary similarity constraints i) improves the separation of proteins of different classes and consequently ii) improves the classification quality of standard graph based clustering algorithms according to the reference classification SCOP. PMID:22974051

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

Modeling surgical tool selection patterns as a "traveling salesman problem" for optimizing a modular surgical tool system.

PubMed

Nelson, Carl A; Miller, David J; Oleynikov, Dmitry

2008-01-01

As modular systems come into the forefront of robotic telesurgery, streamlining the process of selecting surgical tools becomes an important consideration. This paper presents a method for optimal queuing of tools in modular surgical tool systems, based on patterns in tool-use sequences, in order to minimize time spent changing tools. The solution approach is to model the set of tools as a graph, with tool-change frequency expressed as edge weights in the graph, and to solve the Traveling Salesman Problem for the graph. In a set of simulations, this method has shown superior performance at optimizing tool arrangements for streamlining surgical procedures.

The partition dimension of cycle books graph

NASA Astrophysics Data System (ADS)

Santoso, Jaya; Darmaji

2018-03-01

Let G be a nontrivial and connected graph with vertex set V(G), edge set E(G) and S ⊆ V(G) with v ∈ V(G), the distance between v and S is d(v,S) = min{d(v,x)|x ∈ S}. For an ordered partition ∏ = {S 1, S 2, S 3,…, Sk } of V(G), the representation of v with respect to ∏ is defined by r(v|∏) = (d(v, S 1), d(v, S 2),…, d(v, Sk )). The partition ∏ is called a resolving partition of G if all representations of vertices are distinct. The partition dimension pd(G) is the smallest integer k such that G has a resolving partition set with k members. In this research, we will determine the partition dimension of Cycle Books {B}{Cr,m}. Cycle books graph {B}{Cr,m} is a graph consisting of m copies cycle Cr with the common path P 2. It is shown that the partition dimension of cycle books graph, pd({B}{C3,m}) is 3 for m = 2, 3, and m for m ≥ 4. pd({B}{C4,m}) is 3 + 2k for m = 3k + 2, 4 + 2(k ‑ 1) for m = 3k + 1, and 3 + 2(k ‑ 1) for m = 3k. pd({B}{C5,m}) is m + 1.

Structure cristalline et analyses thermique et de surface Hirshfeld du diperchlorate de 4-aza­niumyl-2,2,6,6-tétraméthylpipéridin-1-ium

PubMed Central

Boumakhla, Abdessalem; Zid, Mohamed Faouzi; Guesmi, Abderrahmen

2017-01-01

The synthesis of 4-aza­niumyl-2,2,6,6-tetra­methyl­piperidin-1-ium diperchlorate, C9H22N2 2+·2ClO4 −, was carried out from an aqueous reaction of perchloric acid with 4-amino-2,2,6,6-tetra­methyl­piperidine. This compound was characterized by TGA–DSC analysis and single-crystal X-ray diffraction. The piperidine ring of the dication adopts a chair conformation and the orientation of the C—NH3 bond is equatorial. One of the two crystallographically independent perchlorate anions exhibits disorder [occupancies 0.625 (7) and 0.375 (7)]. The crystal packing is constituted by a succession of mixed layers parallel to the (-102) plane, made up of C9H22N2 2+ dications and ClO4 − anions. These ions are linked by normal and bifurcated N—H⋯O hydrogen bonds with R 4 4(12) graph-set motifs, generating a two-dimensional network. The inter­molecular inter­actions in the crystal structure were qu­anti­fied and analysed using Hirshfeld surface analysis. PMID:29250357

A model of language inflection graphs

NASA Astrophysics Data System (ADS)

Fukś, Henryk; Farzad, Babak; Cao, Yi

2014-01-01

Inflection graphs are highly complex networks representing relationships between inflectional forms of words in human languages. For so-called synthetic languages, such as Latin or Polish, they have particularly interesting structure due to the abundance of inflectional forms. We construct the simplest form of inflection graphs, namely a bipartite graph in which one group of vertices corresponds to dictionary headwords and the other group to inflected forms encountered in a given text. We, then, study projection of this graph on the set of headwords. The projection decomposes into a large number of connected components, to be called word groups. Distribution of sizes of word group exhibits some remarkable properties, resembling cluster distribution in a lattice percolation near the critical point. We propose a simple model which produces graphs of this type, reproducing the desired component distribution and other topological features.

Compound analysis via graph kernels incorporating chirality.

PubMed

Brown, J B; Urata, Takashi; Tamura, Takeyuki; Arai, Midori A; Kawabata, Takeo; Akutsu, Tatsuya

2010-12-01

High accuracy is paramount when predicting biochemical characteristics using Quantitative Structural-Property Relationships (QSPRs). Although existing graph-theoretic kernel methods combined with machine learning techniques are efficient for QSPR model construction, they cannot distinguish topologically identical chiral compounds which often exhibit different biological characteristics. In this paper, we propose a new method that extends the recently developed tree pattern graph kernel to accommodate stereoisomers. We show that Support Vector Regression (SVR) with a chiral graph kernel is useful for target property prediction by demonstrating its application to a set of human vitamin D receptor ligands currently under consideration for their potential anti-cancer effects.

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

Top-k similar graph matching using TraM in biological networks.

PubMed

Amin, Mohammad Shafkat; Finley, Russell L; Jamil, Hasan M

2012-01-01

Many emerging database applications entail sophisticated graph-based query manipulation, predominantly evident in large-scale scientific applications. To access the information embedded in graphs, efficient graph matching tools and algorithms have become of prime importance. Although the prohibitively expensive time complexity associated with exact subgraph isomorphism techniques has limited its efficacy in the application domain, approximate yet efficient graph matching techniques have received much attention due to their pragmatic applicability. Since public domain databases are noisy and incomplete in nature, inexact graph matching techniques have proven to be more promising in terms of inferring knowledge from numerous structural data repositories. In this paper, we propose a novel technique called TraM for approximate graph matching that off-loads a significant amount of its processing on to the database making the approach viable for large graphs. Moreover, the vector space embedding of the graphs and efficient filtration of the search space enables computation of approximate graph similarity at a throw-away cost. We annotate nodes of the query graphs by means of their global topological properties and compare them with neighborhood biased segments of the datagraph for proper matches. We have conducted experiments on several real data sets, and have demonstrated the effectiveness and efficiency of the proposed method

A Scalable Distributed Syntactic, Semantic, and Lexical Language Model

DTIC Science & Technology

2012-09-01

Here pa(τ) denotes the set of parent states of τ. If the recursive factorization refers to a graph , then we have a Bayesian network (Lauritzen 1996...Broadly speaking, however, the recursive factorization can refer to a representation more complicated than a graph with a fixed set of nodes and edges...factored language (FL) model (Bilmes and Kirchhoff 2003) is close to the smoothing technique we propose here, the major difference is that FL

Three faces of node importance in network epidemiology: Exact results for small graphs

NASA Astrophysics Data System (ADS)

Holme, Petter

2017-12-01

We investigate three aspects of the importance of nodes with respect to susceptible-infectious-removed (SIR) disease dynamics: influence maximization (the expected outbreak size given a set of seed nodes), the effect of vaccination (how much deleting nodes would reduce the expected outbreak size), and sentinel surveillance (how early an outbreak could be detected with sensors at a set of nodes). We calculate the exact expressions of these quantities, as functions of the SIR parameters, for all connected graphs of three to seven nodes. We obtain the smallest graphs where the optimal node sets are not overlapping. We find that (i) node separation is more important than centrality for more than one active node, (ii) vaccination and influence maximization are the most different aspects of importance, and (iii) the three aspects are more similar when the infection rate is low.

Statistics of Gaussian packets on metric and decorated graphs.

PubMed

Chernyshev, V L; Shafarevich, A I

2014-01-28

We study a semiclassical asymptotics of the Cauchy problem for a time-dependent Schrödinger equation on metric and decorated graphs with a localized initial function. A decorated graph is a topological space obtained from a graph via replacing vertices with smooth Riemannian manifolds. The main term of an asymptotic solution at an arbitrary finite time is a sum of Gaussian packets and generalized Gaussian packets (localized near a certain set of codimension one). We study the number of packets as time tends to infinity. We prove that under certain assumptions this number grows in time as a polynomial and packets fill the graph uniformly. We discuss a simple example of the opposite situation: in this case, a numerical experiment shows a subexponential growth.

Plane representations of graphs and visibility between parallel segments

NASA Astrophysics Data System (ADS)

Tamassia, R.; Tollis, I. G.

1985-04-01

Several layout compaction strategies for VLSI are based on the concept of visibility between parallel segments, where we say that two parallel segments of a given set are visible if they can be joined by a segment orthogonal to them, which does not intersect any other segment. This paper studies visibility representations of graphs, which are constructed by mapping vertices to horizontal segments, and edges to vertical segments drawn between visible vertex-segments. Clearly, every graph that admits such a representation must be a planar. The authors consider three types of visibility representations, and give complete characterizations of the classes of graphs that admit them. Furthermore, they present linear time algorithms for testing the existence of and constructing visibility representations of planar graphs.

Polynomial sequences for bond percolation critical thresholds

DOE PAGES

Scullard, Christian R.

2011-09-22

In this paper, I compute the inhomogeneous (multi-probability) bond critical surfaces for the (4, 6, 12) and (3 4, 6) using the linearity approximation described in (Scullard and Ziff, J. Stat. Mech. 03021), implemented as a branching process of lattices. I find the estimates for the bond percolation thresholds, pc(4, 6, 12) = 0.69377849... and p c(3 4, 6) = 0.43437077..., compared with Parviainen’s numerical results of p c = 0.69373383... and p c = 0.43430621... . These deviations are of the order 10 -5, as is standard for this method. Deriving thresholds in this way for a given latticemore » leads to a polynomial with integer coefficients, the root in [0, 1] of which gives the estimate for the bond threshold and I show how the method can be refined, leading to a series of higher order polynomials making predictions that likely converge to the exact answer. Finally, I discuss how this fact hints that for certain graphs, such as the kagome lattice, the exact bond threshold may not be the root of any polynomial with integer coefficients.« less

Affinity learning with diffusion on tensor product graph.

PubMed

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

2013-01-01

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

Metal-metal bonding and aromaticity in [M2(NHCHNH)3]2 (μ-E)2 (E = O, S; M = Nb, Mo, Tc, Ru, Rh).

PubMed

Yan, Xiuli; Meng, Lingpeng; Sun, Zheng; Li, Xiaoyan

2016-02-01

The nature of M-M bonding and aromaticity of [M2(NHCHNH)3]2(μ-E)2 (E = O, S; M = Nb, Mo, Tc, Ru, Rh) was investigated using atoms in molecules (AIM) theory, electron localization function (ELF), natural bond orbital (NBO) and molecular orbital analysis. These analyses led to the following main conclusions: in [M2(NHCHNH)3]2(μ-E)2 (E = O, S; M = Nb, Mo, Tc, Ru, Rh), the Nb-Nb, Ru-Ru, and Rh-Rh bonds belong to "metallic" bonds, whereas Mo-Mo and Tc-Tc drifted toward the "dative" side; all these bonds are partially covalent in character. The Nb-Nb, Mo-Mo, and Tc-Tc bonds are stronger than Ru-Ru and Rh-Rh bonds. The M-M bonds in [M2(NHCHNH)3]2(μ-S)2 are stronger than those in [M2(NHCHNH)3]2(μ-O)2 for M = Nb, Mo, Tc, and Ru. The NICS(1)ZZ values show that all of the studied molecules, except [Ru2(NHCHNH)3]2(μ-O)2, are aromaticity molecules. O-bridged compounds have more aromaticity than S-bridged compounds. Graphical Abstract Left Molecular graph, and right electron localization function (ELF) isosurface of [M2(NHCHNH)3]2(μ-E)2(E = O, S; M = Nb, Mo, Tc, Ru, Rh).

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.

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.

Graph-Based Object Class Discovery

NASA Astrophysics Data System (ADS)

Xia, Shengping; Hancock, Edwin R.

We are interested in the problem of discovering the set of object classes present in a database of images using a weakly supervised graph-based framework. Rather than making use of the ”Bag-of-Features (BoF)” approach widely used in current work on object recognition, we represent each image by a graph using a group of selected local invariant features. Using local feature matching and iterative Procrustes alignment, we perform graph matching and compute a similarity measure. Borrowing the idea of query expansion , we develop a similarity propagation based graph clustering (SPGC) method. Using this method class specific clusters of the graphs can be obtained. Such a cluster can be generally represented by using a higher level graph model whose vertices are the clustered graphs, and the edge weights are determined by the pairwise similarity measure. Experiments are performed on a dataset, in which the number of images increases from 1 to 50K and the number of objects increases from 1 to over 500. Some objects have been discovered with total recall and a precision 1 in a single cluster.

Solving graph data issues using a layered architecture approach with applications to web spam detection.

PubMed

Scarselli, Franco; Tsoi, Ah Chung; Hagenbuchner, Markus; Noi, Lucia Di

2013-12-01

This paper proposes the combination of two state-of-the-art algorithms for processing graph input data, viz., the probabilistic mapping graph self organizing map, an unsupervised learning approach, and the graph neural network, a supervised learning approach. We organize these two algorithms in a cascade architecture containing a probabilistic mapping graph self organizing map, and a graph neural network. We show that this combined approach helps us to limit the long-term dependency problem that exists when training the graph neural network resulting in an overall improvement in performance. This is demonstrated in an application to a benchmark problem requiring the detection of spam in a relatively large set of web sites. It is found that the proposed method produces results which reach the state of the art when compared with some of the best results obtained by others using quite different approaches. A particular strength of our method is its applicability towards any input domain which can be represented as a graph. Copyright © 2013 Elsevier Ltd. All rights reserved.

Label Information Guided Graph Construction for Semi-Supervised Learning.

PubMed

Zhuang, Liansheng; Zhou, Zihan; Gao, Shenghua; Yin, Jingwen; Lin, Zhouchen; Ma, Yi

2017-09-01

In the literature, most existing graph-based semi-supervised learning methods only use the label information of observed samples in the label propagation stage, while ignoring such valuable information when learning the graph. In this paper, we argue that it is beneficial to consider the label information in the graph learning stage. Specifically, by enforcing the weight of edges between labeled samples of different classes to be zero, we explicitly incorporate the label information into the state-of-the-art graph learning methods, such as the low-rank representation (LRR), and propose a novel semi-supervised graph learning method called semi-supervised low-rank representation. This results in a convex optimization problem with linear constraints, which can be solved by the linearized alternating direction method. Though we take LRR as an example, our proposed method is in fact very general and can be applied to any self-representation graph learning methods. Experiment results on both synthetic and real data sets demonstrate that the proposed graph learning method can better capture the global geometric structure of the data, and therefore is more effective for semi-supervised learning tasks.

Evaluating structural pattern recognition for handwritten math via primitive label graphs

NASA Astrophysics Data System (ADS)

Zanibbi, Richard; Mouchère, Harold; Viard-Gaudin, Christian

2013-01-01

Currently, structural pattern recognizer evaluations compare graphs of detected structure to target structures (i.e. ground truth) using recognition rates, recall and precision for object segmentation, classification and relationships. In document recognition, these target objects (e.g. symbols) are frequently comprised of multiple primitives (e.g. connected components, or strokes for online handwritten data), but current metrics do not characterize errors at the primitive level, from which object-level structure is obtained. Primitive label graphs are directed graphs defined over primitives and primitive pairs. We define new metrics obtained by Hamming distances over label graphs, which allow classification, segmentation and parsing errors to be characterized separately, or using a single measure. Recall and precision for detected objects may also be computed directly from label graphs. We illustrate the new metrics by comparing a new primitive-level evaluation to the symbol-level evaluation performed for the CROHME 2012 handwritten math recognition competition. A Python-based set of utilities for evaluating, visualizing and translating label graphs is publicly available.

MISAGA: An Algorithm for Mining Interesting Subgraphs in Attributed Graphs.

PubMed

He, Tiantian; Chan, Keith C C

2018-05-01

An attributed graph contains vertices that are associated with a set of attribute values. Mining clusters or communities, which are interesting subgraphs in the attributed graph is one of the most important tasks of graph analytics. Many problems can be defined as the mining of interesting subgraphs in attributed graphs. Algorithms that discover subgraphs based on predefined topologies cannot be used to tackle these problems. To discover interesting subgraphs in the attributed graph, we propose an algorithm called mining interesting subgraphs in attributed graph algorithm (MISAGA). MISAGA performs its tasks by first using a probabilistic measure to determine whether the strength of association between a pair of attribute values is strong enough to be interesting. Given the interesting pairs of attribute values, then the degree of association is computed for each pair of vertices using an information theoretic measure. Based on the edge structure and degree of association between each pair of vertices, MISAGA identifies interesting subgraphs by formulating it as a constrained optimization problem and solves it by identifying the optimal affiliation of subgraphs for the vertices in the attributed graph. MISAGA has been tested with several large-sized real graphs and is found to be potentially very useful for various applications.

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.

Handling Big Data in Medical Imaging: Iterative Reconstruction with Large-Scale Automated Parallel Computation

PubMed Central

Lee, Jae H.; Yao, Yushu; Shrestha, Uttam; Gullberg, Grant T.; Seo, Youngho

2014-01-01

The primary goal of this project is to implement the iterative statistical image reconstruction algorithm, in this case maximum likelihood expectation maximum (MLEM) used for dynamic cardiac single photon emission computed tomography, on Spark/GraphX. This involves porting the algorithm to run on large-scale parallel computing systems. Spark is an easy-to- program software platform that can handle large amounts of data in parallel. GraphX is a graph analytic system running on top of Spark to handle graph and sparse linear algebra operations in parallel. The main advantage of implementing MLEM algorithm in Spark/GraphX is that it allows users to parallelize such computation without any expertise in parallel computing or prior knowledge in computer science. In this paper we demonstrate a successful implementation of MLEM in Spark/GraphX and present the performance gains with the goal to eventually make it useable in clinical setting. PMID:27081299

Handling Big Data in Medical Imaging: Iterative Reconstruction with Large-Scale Automated Parallel Computation.

PubMed

Lee, Jae H; Yao, Yushu; Shrestha, Uttam; Gullberg, Grant T; Seo, Youngho

2014-11-01

The primary goal of this project is to implement the iterative statistical image reconstruction algorithm, in this case maximum likelihood expectation maximum (MLEM) used for dynamic cardiac single photon emission computed tomography, on Spark/GraphX. This involves porting the algorithm to run on large-scale parallel computing systems. Spark is an easy-to- program software platform that can handle large amounts of data in parallel. GraphX is a graph analytic system running on top of Spark to handle graph and sparse linear algebra operations in parallel. The main advantage of implementing MLEM algorithm in Spark/GraphX is that it allows users to parallelize such computation without any expertise in parallel computing or prior knowledge in computer science. In this paper we demonstrate a successful implementation of MLEM in Spark/GraphX and present the performance gains with the goal to eventually make it useable in clinical setting.

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.

Visualizing multiattribute Web transactions using a freeze technique

NASA Astrophysics Data System (ADS)

Hao, Ming C.; Cotting, Daniel; Dayal, Umeshwar; Machiraju, Vijay; Garg, Pankaj

2003-05-01

Web transactions are multidimensional and have a number of attributes: client, URL, response times, and numbers of messages. One of the key questions is how to simultaneously lay out in a graph the multiple relationships, such as the relationships between the web client response times and URLs in a web access application. In this paper, we describe a freeze technique to enhance a physics-based visualization system for web transactions. The idea is to freeze one set of objects before laying out the next set of objects during the construction of the graph. As a result, we substantially reduce the force computation time. This technique consists of three steps: automated classification, a freeze operation, and a graph layout. These three steps are iterated until the final graph is generated. This iterated-freeze technique has been prototyped in several e-service applications at Hewlett Packard Laboratories. It has been used to visually analyze large volumes of service and sales transactions at online web sites.

Lessons Learned With a Global Graph and Ozone Widget Framework (OWF) Testbed

DTIC Science & Technology

2013-05-01

of operating system and database environments. The following is one example. Requirements are: Java 1.6 + and a Relational Database Management...We originally tried to use MySQL as our database, because we were more familiar with it, but since the database dumps as well as most of the...Global Graph Rest Services In order to set up the Global Graph Rest Services, you will need to have the following dependencies installed: Java 1.6

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.

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.

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.

Integer sequence discovery from small graphs

PubMed Central

Hoppe, Travis; Petrone, Anna

2015-01-01

We have exhaustively enumerated all simple, connected graphs of a finite order and have computed a selection of invariants over this set. Integer sequences were constructed from these invariants and checked against the Online Encyclopedia of Integer Sequences (OEIS). 141 new sequences were added and six sequences were extended. From the graph database, we were able to programmatically suggest relationships among the invariants. It will be shown that we can readily visualize any sequence of graphs with a given criteria. The code has been released as an open-source framework for further analysis and the database was constructed to be extensible to invariants not considered in this work. PMID:27034526

Efficient parallel and out of core algorithms for constructing large bi-directed de Bruijn graphs.

PubMed

Kundeti, Vamsi K; Rajasekaran, Sanguthevar; Dinh, Hieu; Vaughn, Matthew; Thapar, Vishal

2010-11-15

Assembling genomic sequences from a set of overlapping reads is one of the most fundamental problems in computational biology. Algorithms addressing the assembly problem fall into two broad categories - based on the data structures which they employ. The first class uses an overlap/string graph and the second type uses a de Bruijn graph. However with the recent advances in short read sequencing technology, de Bruijn graph based algorithms seem to play a vital role in practice. Efficient algorithms for building these massive de Bruijn graphs are very essential in large sequencing projects based on short reads. In an earlier work, an O(n/p) time parallel algorithm has been given for this problem. Here n is the size of the input and p is the number of processors. This algorithm enumerates all possible bi-directed edges which can overlap with a node and ends up generating Θ(nΣ) messages (Σ being the size of the alphabet). In this paper we present a Θ(n/p) time parallel algorithm with a communication complexity that is equal to that of parallel sorting and is not sensitive to Σ. The generality of our algorithm makes it very easy to extend it even to the out-of-core model and in this case it has an optimal I/O complexity of Θ(nlog(n/B)Blog(M/B)) (M being the main memory size and B being the size of the disk block). We demonstrate the scalability of our parallel algorithm on a SGI/Altix computer. A comparison of our algorithm with the previous approaches reveals that our algorithm is faster--both asymptotically and practically. We demonstrate the scalability of our sequential out-of-core algorithm by comparing it with the algorithm used by VELVET to build the bi-directed de Bruijn graph. Our experiments reveal that our algorithm can build the graph with a constant amount of memory, which clearly outperforms VELVET. We also provide efficient algorithms for the bi-directed chain compaction problem. The bi-directed de Bruijn graph is a fundamental data structure for any sequence assembly program based on Eulerian approach. Our algorithms for constructing Bi-directed de Bruijn graphs are efficient in parallel and out of core settings. These algorithms can be used in building large scale bi-directed de Bruijn graphs. Furthermore, our algorithms do not employ any all-to-all communications in a parallel setting and perform better than the prior algorithms. Finally our out-of-core algorithm is extremely memory efficient and can replace the existing graph construction algorithm in VELVET.

Fast Inbound Top-K Query for Random Walk with Restart.

PubMed

Zhang, Chao; Jiang, Shan; Chen, Yucheng; Sun, Yidan; Han, Jiawei

2015-09-01

Random walk with restart (RWR) is widely recognized as one of the most important node proximity measures for graphs, as it captures the holistic graph structure and is robust to noise in the graph. In this paper, we study a novel query based on the RWR measure, called the inbound top-k (Ink) query. Given a query node q and a number k , the Ink query aims at retrieving k nodes in the graph that have the largest weighted RWR scores to q . Ink queries can be highly useful for various applications such as traffic scheduling, disease treatment, and targeted advertising. Nevertheless, none of the existing RWR computation techniques can accurately and efficiently process the Ink query in large graphs. We propose two algorithms, namely Squeeze and Ripple, both of which can accurately answer the Ink query in a fast and incremental manner. To identify the top- k nodes, Squeeze iteratively performs matrix-vector multiplication and estimates the lower and upper bounds for all the nodes in the graph. Ripple employs a more aggressive strategy by only estimating the RWR scores for the nodes falling in the vicinity of q , the nodes outside the vicinity do not need to be evaluated because their RWR scores are propagated from the boundary of the vicinity and thus upper bounded. Ripple incrementally expands the vicinity until the top- k result set can be obtained. Our extensive experiments on real-life graph data sets show that Ink queries can retrieve interesting results, and the proposed algorithms are orders of magnitude faster than state-of-the-art method.

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

PubMed

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

2006-01-17

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

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

PubMed Central

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

2006-01-01

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

Enhancing Community Detection By Affinity-based Edge Weighting Scheme

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

Yoo, Andy; Sanders, Geoffrey; Henson, Van

Community detection refers to an important graph analytics problem of finding a set of densely-connected subgraphs in a graph and has gained a great deal of interest recently. The performance of current community detection algorithms is limited by an inherent constraint of unweighted graphs that offer very little information on their internal community structures. In this paper, we propose a new scheme to address this issue that weights the edges in a given graph based on recently proposed vertex affinity. The vertex affinity quantifies the proximity between two vertices in terms of their clustering strength, and therefore, it is idealmore » for graph analytics applications such as community detection. We also demonstrate that the affinity-based edge weighting scheme can improve the performance of community detection algorithms significantly.« less

A Negative Partition Relation

PubMed Central

Hajnal, A.

1971-01-01

If the continuum hypothesis is assumed, there is a graph G whose vertices form an ordered set of type ω12; G does not contain triangles or complete even graphs of form [[unk]0,[unk]0], and there is no independent subset of vertices of type ω12. PMID:16591893

An industrial robot singular trajectories planning based on graphs and neural networks

NASA Astrophysics Data System (ADS)

Łęgowski, Adrian; Niezabitowski, Michał

2016-06-01

Singular trajectories are rarely used because of issues during realization. A method of planning trajectories for given set of points in task space with use of graphs and neural networks is presented. In every desired point the inverse kinematics problem is solved in order to derive all possible solutions. A graph of solutions is made. The shortest path is determined to define required nodes in joint space. Neural networks are used to define the path between these nodes.

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

Mining Tasks from the Web Anchor Text Graph: MSR Notebook Paper for the TREC 2015 Tasks Track

DTIC Science & Technology

2015-11-20

Mining Tasks from the Web Anchor Text Graph: MSR Notebook Paper for the TREC 2015 Tasks Track Paul N. Bennett Microsoft Research Redmond, USA pauben...anchor text graph has proven useful in the general realm of query reformulation [2], we sought to quantify the value of extracting key phrases from...anchor text in the broader setting of the task understanding track. Given a query, our approach considers a simple method for identifying a relevant

Complexity and non-commutativity of learning operations on graphs.

PubMed

Atmanspacher, Harald; Filk, Thomas

2006-07-01

We present results from numerical studies of supervised learning operations in small recurrent networks considered as graphs, leading from a given set of input conditions to predetermined outputs. Graphs that have optimized their output for particular inputs with respect to predetermined outputs are asymptotically stable and can be characterized by attractors, which form a representation space for an associative multiplicative structure of input operations. As the mapping from a series of inputs onto a series of such attractors generally depends on the sequence of inputs, this structure is generally non-commutative. Moreover, the size of the set of attractors, indicating the complexity of learning, is found to behave non-monotonically as learning proceeds. A tentative relation between this complexity and the notion of pragmatic information is indicated.

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.

Fully automatic lesion segmentation in breast MRI using mean-shift and graph-cuts on a region adjacency graph.

PubMed

McClymont, Darryl; Mehnert, Andrew; Trakic, Adnan; Kennedy, Dominic; Crozier, Stuart

2014-04-01

To present and evaluate a fully automatic method for segmentation (i.e., detection and delineation) of suspicious tissue in breast MRI. The method, based on mean-shift clustering and graph-cuts on a region adjacency graph, was developed and its parameters tuned using multimodal (T1, T2, DCE-MRI) clinical breast MRI data from 35 subjects (training data). It was then tested using two data sets. Test set 1 comprises data for 85 subjects (93 lesions) acquired using the same protocol and scanner system used to acquire the training data. Test set 2 comprises data for eight subjects (nine lesions) acquired using a similar protocol but a different vendor's scanner system. Each lesion was manually delineated in three-dimensions by an experienced breast radiographer to establish segmentation ground truth. The regions of interest identified by the method were compared with the ground truth and the detection and delineation accuracies quantitatively evaluated. One hundred percent of the lesions were detected with a mean of 4.5 ± 1.2 false positives per subject. This false-positive rate is nearly 50% better than previously reported for a fully automatic breast lesion detection system. The median Dice coefficient for Test set 1 was 0.76 (interquartile range, 0.17), and 0.75 (interquartile range, 0.16) for Test set 2. The results demonstrate the efficacy and accuracy of the proposed method as well as its potential for direct application across different MRI systems. It is (to the authors' knowledge) the first fully automatic method for breast lesion detection and delineation in breast MRI.

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.

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

NASA Astrophysics Data System (ADS)

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

2012-06-01

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

Discriminative graph embedding for label propagation.

PubMed

Nguyen, Canh Hao; Mamitsuka, Hiroshi

2011-09-01

In many applications, the available information is encoded in graph structures. This is a common problem in biological networks, social networks, web communities and document citations. We investigate the problem of classifying nodes' labels on a similarity graph given only a graph structure on the nodes. Conventional machine learning methods usually require data to reside in some Euclidean spaces or to have a kernel representation. Applying these methods to nodes on graphs would require embedding the graphs into these spaces. By embedding and then learning the nodes on graphs, most methods are either flexible with different learning objectives or efficient enough for large scale applications. We propose a method to embed a graph into a feature space for a discriminative purpose. Our idea is to include label information into the embedding process, making the space representation tailored to the task. We design embedding objective functions that the following learning formulations become spectral transforms. We then reformulate these spectral transforms into multiple kernel learning problems. Our method, while being tailored to the discriminative tasks, is efficient and can scale to massive data sets. We show the need of discriminative embedding on some simulations. Applying to biological network problems, our method is shown to outperform baselines.

Relevance of graph literacy in the development of patient-centered communication tools.

PubMed

Nayak, Jasmir G; Hartzler, Andrea L; Macleod, Liam C; Izard, Jason P; Dalkin, Bruce M; Gore, John L

2016-03-01

To determine the literacy skill sets of patients in the context of graphical interpretation of interactive dashboards. We assessed literacy characteristics of prostate cancer patients and assessed comprehension of quality of life dashboards. Health literacy, numeracy and graph literacy were assessed with validated tools. We divided patients into low vs. high numeracy and graph literacy. We report descriptive statistics on literacy, dashboard comprehension, and relationships between groups. We used correlation and multiple linear regressions to examine factors associated with dashboard comprehension. Despite high health literacy in educated patients (78% college educated), there was variation in numeracy and graph literacy. Numeracy and graph literacy scores were correlated (r=0.37). In those with low literacy, graph literacy scores most strongly correlated with dashboard comprehension (r=0.59-0.90). On multivariate analysis, graph literacy was independently associated with dashboard comprehension, adjusting for age, education, and numeracy level. Even among higher educated patients; variation in the ability to comprehend graphs exists. Clinicians must be aware of these differential proficiencies when counseling patients. Tools for patient-centered communication that employ visual displays need to account for literacy capabilities to ensure that patients can effectively engage these resources. Copyright © 2015 Elsevier Ireland Ltd. All rights reserved.

Collaborative mining and transfer learning for relational data

NASA Astrophysics Data System (ADS)

Levchuk, Georgiy; Eslami, Mohammed

2015-06-01

Many of the real-world problems, - including human knowledge, communication, biological, and cyber network analysis, - deal with data entities for which the essential information is contained in the relations among those entities. Such data must be modeled and analyzed as graphs, with attributes on both objects and relations encode and differentiate their semantics. Traditional data mining algorithms were originally designed for analyzing discrete objects for which a set of features can be defined, and thus cannot be easily adapted to deal with graph data. This gave rise to the relational data mining field of research, of which graph pattern learning is a key sub-domain [11]. In this paper, we describe a model for learning graph patterns in collaborative distributed manner. Distributed pattern learning is challenging due to dependencies between the nodes and relations in the graph, and variability across graph instances. We present three algorithms that trade-off benefits of parallelization and data aggregation, compare their performance to centralized graph learning, and discuss individual benefits and weaknesses of each model. Presented algorithms are designed for linear speedup in distributed computing environments, and learn graph patterns that are both closer to ground truth and provide higher detection rates than centralized mining algorithm.

Evolutionary Games of Multiplayer Cooperation on Graphs

PubMed Central

Arranz, Jordi; Traulsen, Arne

2016-01-01

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

Hydride, hydrogen, proton, and electron affinities of imines and their reaction intermediates in acetonitrile and construction of thermodynamic characteristic graphs (TCGs) of imines as a "molecule ID card".

PubMed

Zhu, Xiao-Qing; Liu, Qiao-Yun; Chen, Qiang; Mei, Lian-Rui

2010-02-05

A series of 61 imines with various typical structures were synthesized, and the thermodynamic affinities (defined as enthalpy changes or redox potentials in this work) of the imines to abstract hydride anions, hydrogen atoms, and electrons, the thermodynamic affinities of the radical anions of the imines to abstract hydrogen atoms and protons, and the thermodynamic affinities of the hydrogen adducts of the imines to abstract electrons in acetonitrile were determined by using titration calorimetry and electrochemical methods. The pure heterolytic and homolytic dissociation energies of the C=N pi-bond in the imines were estimated. The polarity of the C=N double bond in the imines was examined using a linear free-energy relationship. The idea of a thermodynamic characteristic graph (TCG) of imines as an efficient "Molecule ID Card" was introduced. The TCG can be used to quantitatively diagnose and predict the characteristic chemical properties of imines and their various reaction intermediates as well as the reduction mechanism of the imines. The information disclosed in this work could not only supply a gap of thermodynamics for the chemistry of imines but also strongly promote the fast development of the applications of imines.

Movement Forms: A Graph-Dynamic Perspective

PubMed Central

Saltzman, Elliot; Holt, Ken

2014-01-01

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

Movement Forms: A Graph-Dynamic Perspective.

PubMed

Saltzman, Elliot; Holt, Ken

2014-01-01

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

Multiscale weighted colored graphs for protein flexibility and rigidity analysis

NASA Astrophysics Data System (ADS)

Bramer, David; Wei, Guo-Wei

2018-02-01

Protein structural fluctuation, measured by Debye-Waller factors or B-factors, is known to correlate to protein flexibility and function. A variety of methods has been developed for protein Debye-Waller factor prediction and related applications to domain separation, docking pose ranking, entropy calculation, hinge detection, stability analysis, etc. Nevertheless, none of the current methodologies are able to deliver an accuracy of 0.7 in terms of the Pearson correlation coefficients averaged over a large set of proteins. In this work, we introduce a paradigm-shifting geometric graph model, multiscale weighted colored graph (MWCG), to provide a new generation of computational algorithms to significantly change the current status of protein structural fluctuation analysis. Our MWCG model divides a protein graph into multiple subgraphs based on interaction types between graph nodes and represents the protein rigidity by generalized centralities of subgraphs. MWCGs not only predict the B-factors of protein residues but also accurately analyze the flexibility of all atoms in a protein. The MWCG model is validated over a number of protein test sets and compared with many standard methods. An extensive numerical study indicates that the proposed MWCG offers an accuracy of over 0.8 and thus provides perhaps the first reliable method for estimating protein flexibility and B-factors. It also simultaneously predicts all-atom flexibility in a molecule.

Dynamic Uncertain Causality Graph for Knowledge Representation and Probabilistic Reasoning: Directed Cyclic Graph and Joint Probability Distribution.

PubMed

Zhang, Qin

2015-07-01

Probabilistic graphical models (PGMs) such as Bayesian network (BN) have been widely applied in uncertain causality representation and probabilistic reasoning. Dynamic uncertain causality graph (DUCG) is a newly presented model of PGMs, which can be applied to fault diagnosis of large and complex industrial systems, disease diagnosis, and so on. The basic methodology of DUCG has been previously presented, in which only the directed acyclic graph (DAG) was addressed. However, the mathematical meaning of DUCG was not discussed. In this paper, the DUCG with directed cyclic graphs (DCGs) is addressed. In contrast, BN does not allow DCGs, as otherwise the conditional independence will not be satisfied. The inference algorithm for the DUCG with DCGs is presented, which not only extends the capabilities of DUCG from DAGs to DCGs but also enables users to decompose a large and complex DUCG into a set of small, simple sub-DUCGs, so that a large and complex knowledge base can be easily constructed, understood, and maintained. The basic mathematical definition of a complete DUCG with or without DCGs is proved to be a joint probability distribution (JPD) over a set of random variables. The incomplete DUCG as a part of a complete DUCG may represent a part of JPD. Examples are provided to illustrate the methodology.

Isoniazid cocrystals with anti-oxidant hydroxy benzoic acids

NASA Astrophysics Data System (ADS)

Mashhadi, Syed Muddassir Ali; Yunus, Uzma; Bhatti, Moazzam Hussain; Tahir, Muhammad Nawaz

2014-11-01

Isoniazid is the primary constituent of “triple therapy” used to effectively treat tuberculosis. In tuberculosis and other diseases, tissue inflammation and free radical burst from macrophages results in oxidative stress. These free radicals cause pulmonary inflammation if not countered by anti-oxidants. Therefore, in the present study cocrystals of isoniazid with four anti-oxidant hydroxy benzoic acids have been reported. Gallic acid, 2,3-dihydroxybenzoic acid, 3,5-dihydroxybenzoic acid, and 3-hydroxybenzoic acid resulted in the formation of cocrystals when reacted with isoniazid. Cocrystal structure analysis confirmed the existence of pyridine-carboxylic acid synthon in the cocrystals of isoniazid with Gallic acid, 2,3-dihydroxybenzoic acid and 3-hydroxybenzoic acid. While cocrystal of 3,5-dihydroxybenzoic acid formed the pyridine-hydroxy group synthon. Other synthons of different graph sets are formed between hydrazide group of isoniazid and coformers involving Nsbnd H⋯O and Osbnd H⋯N bonds. All the cocrystals were in 1:1 stoichiometric ratio.

Multi-thresholds for fault isolation in the presence of uncertainties.

PubMed

Touati, Youcef; Mellal, Mohamed Arezki; Benazzouz, Djamel

2016-05-01

Monitoring of the faults is an important task in mechatronics. It involves the detection and isolation of faults which are performed by using the residuals. These residuals represent numerical values that define certain intervals called thresholds. In fact, the fault is detected if the residuals exceed the thresholds. In addition, each considered fault must activate a unique set of residuals to be isolated. However, in the presence of uncertainties, false decisions can occur due to the low sensitivity of certain residuals towards faults. In this paper, an efficient approach to make decision on fault isolation in the presence of uncertainties is proposed. Based on the bond graph tool, the approach is developed in order to generate systematically the relations between residuals and faults. The generated relations allow the estimation of the minimum detectable and isolable fault values. The latter is used to calculate the thresholds of isolation for each residual. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Temporal heating profile influence on the immediate bond strength following laser tissue soldering.

PubMed

Rabi, Yaron; Katzir, Abraham

2010-07-01

Bonding of tissues by laser heating is considered as a future alternative to sutures and staples. Increasing the post-operative bond strength remains a challenging issue for laser tissue bonding, especially in organs that have to sustain considerable tension or pressure. In this study, we investigated the influence of different temporal heating profiles on the strength of soldered incisions. The thermal damage following each heating procedure was quantified, in order to assess the effect of each heating profile on the thermal damage. Incisions in porcine bowel tissue strips (1 cmx4 cm) were soldered, using a 44% liquid albumin mixed with indocyanine green and a temperature controlled laser (830 nm) tissue bonding system. Heating was done either with a linear or a step temporal heating profile. The incisions were bonded by soldering at three points, separated by 2 mm. Set-point temperatures of T(set) = 60, 70, 80, 90, 100, 110, 150 degrees C and dwell times of t(d) = 10, 20, 30, 40 seconds were investigated. The bond strength was measured immediately following each soldering by applying a gradually increased tension on the tissue edges until the bond break. Bonds formed by linear heating were stronger than the ones formed by step heating: at T(set) = 80 degrees C the bonds were 40% stronger and at T(set) = 90 degrees C the bonds strength was nearly doubled. The bond strength difference between the heating methods was larger as T(set) increased. Linear heating produced stronger bonds than step heating. The difference in the bond strength was more pronounced at high set-point temperatures and short dwell times. The bond strength could be increased with either higher set-point temperature or a longer dwell time.

Building dynamic population graph for accurate correspondence detection.

PubMed

Du, Shaoyi; Guo, Yanrong; Sanroma, Gerard; Ni, Dong; Wu, Guorong; Shen, Dinggang

2015-12-01

In medical imaging studies, there is an increasing trend for discovering the intrinsic anatomical difference across individual subjects in a dataset, such as hand images for skeletal bone age estimation. Pair-wise matching is often used to detect correspondences between each individual subject and a pre-selected model image with manually-placed landmarks. However, the large anatomical variability across individual subjects can easily compromise such pair-wise matching step. In this paper, we present a new framework to simultaneously detect correspondences among a population of individual subjects, by propagating all manually-placed landmarks from a small set of model images through a dynamically constructed image graph. Specifically, we first establish graph links between models and individual subjects according to pair-wise shape similarity (called as forward step). Next, we detect correspondences for the individual subjects with direct links to any of model images, which is achieved by a new multi-model correspondence detection approach based on our recently-published sparse point matching method. To correct those inaccurate correspondences, we further apply an error detection mechanism to automatically detect wrong correspondences and then update the image graph accordingly (called as backward step). After that, all subject images with detected correspondences are included into the set of model images, and the above two steps of graph expansion and error correction are repeated until accurate correspondences for all subject images are established. Evaluations on real hand X-ray images demonstrate that our proposed method using a dynamic graph construction approach can achieve much higher accuracy and robustness, when compared with the state-of-the-art pair-wise correspondence detection methods as well as a similar method but using static population graph. Copyright © 2015 Elsevier B.V. All rights reserved.

Information-optimal genome assembly via sparse read-overlap graphs.

PubMed

Shomorony, Ilan; Kim, Samuel H; Courtade, Thomas A; Tse, David N C

2016-09-01

In the context of third-generation long-read sequencing technologies, read-overlap-based approaches are expected to play a central role in the assembly step. A fundamental challenge in assembling from a read-overlap graph is that the true sequence corresponds to a Hamiltonian path on the graph, and, under most formulations, the assembly problem becomes NP-hard, restricting practical approaches to heuristics. In this work, we avoid this seemingly fundamental barrier by first setting the computational complexity issue aside, and seeking an algorithm that targets information limits In particular, we consider a basic feasibility question: when does the set of reads contain enough information to allow unambiguous reconstruction of the true sequence? Based on insights from this information feasibility question, we present an algorithm-the Not-So-Greedy algorithm-to construct a sparse read-overlap graph. Unlike most other assembly algorithms, Not-So-Greedy comes with a performance guarantee: whenever information feasibility conditions are satisfied, the algorithm reduces the assembly problem to an Eulerian path problem on the resulting graph, and can thus be solved in linear time. In practice, this theoretical guarantee translates into assemblies of higher quality. Evaluations on both simulated reads from real genomes and a PacBio Escherichia coli K12 dataset demonstrate that Not-So-Greedy compares favorably with standard string graph approaches in terms of accuracy of the resulting read-overlap graph and contig N50. Available at github.com/samhykim/nsg courtade@eecs.berkeley.edu or dntse@stanford.edu Supplementary data are available at Bioinformatics online. © The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

A Graph Summarization Algorithm Based on RFID Logistics

NASA Astrophysics Data System (ADS)

Sun, Yan; Hu, Kongfa; Lu, Zhipeng; Zhao, Li; Chen, Ling

Radio Frequency Identification (RFID) applications are set to play an essential role in object tracking and supply chain management systems. The volume of data generated by a typical RFID application will be enormous as each item will generate a complete history of all the individual locations that it occupied at every point in time. The movement trails of such RFID data form gigantic commodity flowgraph representing the locations and durations of the path stages traversed by each item. In this paper, we use graph to construct a warehouse of RFID commodity flows, and introduce a database-style operation to summarize graphs, which produces a summary graph by grouping nodes based on user-selected node attributes, further allows users to control the hierarchy of summaries. It can cut down the size of graphs, and provide convenience for users to study just on the shrunk graph which they interested. Through extensive experiments, we demonstrate the effectiveness and efficiency of the proposed method.

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.

Theoretical and vibrational spectroscopic approach to keto-enol tautomerism in methyl-2-(4-methoxybenzoyl)-3-(4-methoxyphenyl)-3-oxopropanoylcarbamate

NASA Astrophysics Data System (ADS)

Arı, Hatice; Özpozan, Talat; Büyükmumcu, Zeki; Kabacalı, Yiğit; Saçmaci, Mustafa

2016-10-01

A carbamate compound having tricarbonyl groups, methyl-2-(4-methoxybenzoyl)-3-(4-methoxyphenyl)-3-oxopropanoylcarbamate (BPOC) was investigated from theoretical and vibrational spectroscopic point of view employing quantum chemical methods. Hybrid Density Functionals (B3LYP, X3LYP and B3PW91) with 6-311 G(d,p) basis set were used for the calculations. Rotational barrier and conformational analyses were performed to find the most stable conformers of keto and enol forms of the molecule. Three transition states for keto-enol tautomerism in gas phase were determined. The results of the calculations show that enol-1 form of BPOC is more stable than keto and enol-2 forms. Hydrogen bonding investigation including Natural bond orbital analysis (NBO) for all the tautomeric structures was employed to compare intra-molecular interactions. The energies of HOMO and LUMO molecular orbitals for all tautomeric forms of BPOC were predicted. Normal Coordinate Analysis (NCA) was carried out for the enol-1 to assign vibrational bands of IR and Raman spectra. The scaling factors were calculated as 0.9721, 0.9697 and 0.9685 for B3LYP, X3LYP and B3PW91 methods, respectively. The correlation graphs of experimental versus calculated vibrational wavenumbers were plotted and X3LYP method gave better frequency agreement than the others.

Evidence for side-chain π-delocalization in a planar substituted benzene: an experimental and theoretical charge density study on 2,5-dimethoxybenzaldehyde thiosemicarbazone.

PubMed

Farrugia, Louis J; Khalaji, Aliakbar Dehno

2011-11-17

The charge density in 2,5-dimethoxybenzaldehyde thiosemicarbazone (1) has been studied experimentally using Mo-K(α) X-ray diffraction at 100 K, and by theory using DFT calculations at the B3LYP/6-311++G(2d,2p) level. The quantum theory of atoms in molecules (QTAIM) was used to investigate the extent of π-delocalization in the thioamide side-chain, which is virtually coplanar with the benzene ring. The experimental and theoretical ellipticity profiles along the bond paths were in excellent agreement, and showed that some of the formal single bonds in the side-chain have significant π-bond character. This view was supported by the magnitudes of the topological bond orders and by the delocalization indices δ(Ω(A), Ω(B)). An orbital decomposition of δ(Ω(A), Ω(B)) demonstrated that there was significant π-character in all the interchain non-H chemical bonds. On the other hand, the source function referenced at the interchain bond critical points could not provide any evidence for π-delocalization, showing instead only limited σ-delocalization between nearest neighbors. Overall, the topological evidence and the atomic graphs of the oxygen atoms did not provide convincing evidence for π-delocalization involving the methoxy substituents.

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…

Target, Act, Graph (TAG): Teachers Empowering Classroom Resource Personnel in Monitoring Student Progress

ERIC Educational Resources Information Center

Rizzi, Gleides A. L.

2016-01-01

This article provides teachers in rural settings with suggestions on how to engage classroom resource personnel (i.e., volunteers, instructional assistants) in monitoring students' achievement. The target, act, and graph (TAG) strategy offers rural special educators ways to empower classroom resource persons through training and use of the TAG…

Using Self-Recording, Evaluation, and Graphing to Increase Completion of Homework Assignments.

ERIC Educational Resources Information Center

Trammel, Diana Lynn; And Others

1994-01-01

Self-monitoring procedures were effective in increasing the number of daily homework assignments completed by eight secondary level students with learning disabilities. A daily listing of all assignments given by regular classroom teachers was used. Goal setting and self-graphing of data appeared to increase self-monitoring effectiveness. (DB)

A Novel Coarsening Method for Scalable and Efficient Mesh Generation

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

Yoo, A; Hysom, D; Gunney, B

2010-12-02

In this paper, we propose a novel mesh coarsening method called brick coarsening method. The proposed method can be used in conjunction with any graph partitioners and scales to very large meshes. This method reduces problem space by decomposing the original mesh into fixed-size blocks of nodes called bricks, layered in a similar way to conventional brick laying, and then assigning each node of the original mesh to appropriate brick. Our experiments indicate that the proposed method scales to very large meshes while allowing simple RCB partitioner to produce higher-quality partitions with significantly less edge cuts. Our results further indicatemore » that the proposed brick-coarsening method allows more complicated partitioners like PT-Scotch to scale to very large problem size while still maintaining good partitioning performance with relatively good edge-cut metric. Graph partitioning is an important problem that has many scientific and engineering applications in such areas as VLSI design, scientific computing, and resource management. Given a graph G = (V,E), where V is the set of vertices and E is the set of edges, (k-way) graph partitioning problem is to partition the vertices of the graph (V) into k disjoint groups such that each group contains roughly equal number of vertices and the number of edges connecting vertices in different groups is minimized. Graph partitioning plays a key role in large scientific computing, especially in mesh-based computations, as it is used as a tool to minimize the volume of communication and to ensure well-balanced load across computing nodes. The impact of graph partitioning on the reduction of communication can be easily seen, for example, in different iterative methods to solve a sparse system of linear equation. Here, a graph partitioning technique is applied to the matrix, which is basically a graph in which each edge is a non-zero entry in the matrix, to allocate groups of vertices to processors in such a way that many of matrix-vector multiplication can be performed locally on each processor and hence to minimize communication. Furthermore, a good graph partitioning scheme ensures the equal amount of computation performed on each processor. Graph partitioning is a well known NP-complete problem, and thus the most commonly used graph partitioning algorithms employ some forms of heuristics. These algorithms vary in terms of their complexity, partition generation time, and the quality of partitions, and they tend to trade off these factors. A significant challenge we are currently facing at the Lawrence Livermore National Laboratory is how to partition very large meshes on massive-size distributed memory machines like IBM BlueGene/P, where scalability becomes a big issue. For example, we have found that the ParMetis, a very popular graph partitioning tool, can only scale to 16K processors. An ideal graph partitioning method on such an environment should be fast and scale to very large meshes, while producing high quality partitions. This is an extremely challenging task, as to scale to that level, the partitioning algorithm should be simple and be able to produce partitions that minimize inter-processor communications and balance the load imposed on the processors. Our goals in this work are two-fold: (1) To develop a new scalable graph partitioning method with good load balancing and communication reduction capability. (2) To study the performance of the proposed partitioning method on very large parallel machines using actual data sets and compare the performance to that of existing methods. The proposed method achieves the desired scalability by reducing the mesh size. For this, it coarsens an input mesh into a smaller size mesh by coalescing the vertices and edges of the original mesh into a set of mega-vertices and mega-edges. A new coarsening method called brick algorithm is developed in this research. In the brick algorithm, the zones in a given mesh are first grouped into fixed size blocks called bricks. These brick are then laid in a way similar to conventional brick laying technique, which reduces the number of neighboring blocks each block needs to communicate. Contributions of this research are as follows: (1) We have developed a novel method that scales to a really large problem size while producing high quality mesh partitions; (2) We measured the performance and scalability of the proposed method on a machine of massive size using a set of actual large complex data sets, where we have scaled to a mesh with 110 million zones using our method. To the best of our knowledge, this is the largest complex mesh that a partitioning method is successfully applied to; and (3) We have shown that proposed method can reduce the number of edge cuts by as much as 65%.« less

Effects of self-graphing and goal setting on the math fact fluency of students with disabilities.

PubMed

Figarola, Patricia M; Gunter, Philip L; Reffel, Julia M; Worth, Susan R; Hummel, John; Gerber, Brian L

2008-01-01

We evaluated the impact of goal setting and students' participation in graphing their own performance data on the rate of math fact calculations. Participants were 3 students with mild disabilities in the first and second grades; 2 of the 3 students were also identified with Attention-Deficit/Hyperactivity Disorder (ADHD). They were taught to use Microsoft Excel® software to graph their rate of correct calculations when completing timed, independent practice sheets consisting of single-digit mathematics problems. Two students' rates of correct calculations nearly always met or exceeded the aim line established for their correct calculations. Additional interventions were required for the third student. Results are discussed in terms of implications and future directions for increasing the use of evaluation components in classrooms for students at risk for behavior disorders and academic failure.

Assembly planning based on subassembly extraction

NASA Technical Reports Server (NTRS)

Lee, Sukhan; Shin, Yeong Gil

1990-01-01

A method is presented for the automatic determination of assembly partial orders from a liaison graph representation of an assembly through the extraction of preferred subassemblies. In particular, the authors show how to select a set of tentative subassemblies by decomposing a liaison graph into a set of subgraphs based on feasibility and difficulty of disassembly, how to evaluate each of the tentative subassemblies in terms of assembly cost using the subassembly selection indices, and how to construct a hierarchical partial order graph (HPOG) as an assembly plan. The method provides an approach to assembly planning by identifying spatial parallelism in assembly as a means of constructing temporal relationships among assembly operations and solves the problem of finding a cost-effective assembly plan in a flexible environment. A case study of the assembly planning of a mechanical assembly is presented.

Solving Set Cover with Pairs Problem using Quantum Annealing

NASA Astrophysics Data System (ADS)

Cao, Yudong; Jiang, Shuxian; Perouli, Debbie; Kais, Sabre

2016-09-01

Here we consider using quantum annealing to solve Set Cover with Pairs (SCP), an NP-hard combinatorial optimization problem that plays an important role in networking, computational biology, and biochemistry. We show an explicit construction of Ising Hamiltonians whose ground states encode the solution of SCP instances. We numerically simulate the time-dependent Schrödinger equation in order to test the performance of quantum annealing for random instances and compare with that of simulated annealing. We also discuss explicit embedding strategies for realizing our Hamiltonian construction on the D-wave type restricted Ising Hamiltonian based on Chimera graphs. Our embedding on the Chimera graph preserves the structure of the original SCP instance and in particular, the embedding for general complete bipartite graphs and logical disjunctions may be of broader use than that the specific problem we deal with.

A tool for filtering information in complex systems

NASA Astrophysics Data System (ADS)

Tumminello, M.; Aste, T.; Di Matteo, T.; Mantegna, R. N.

2005-07-01

We introduce a technique to filter out complex data sets by extracting a subgraph of representative links. Such a filtering can be tuned up to any desired level by controlling the genus of the resulting graph. We show that this technique is especially suitable for correlation-based graphs, giving filtered graphs that preserve the hierarchical organization of the minimum spanning tree but containing a larger amount of information in their internal structure. In particular in the case of planar filtered graphs (genus equal to 0), triangular loops and four-element cliques are formed. The application of this filtering procedure to 100 stocks in the U.S. equity markets shows that such loops and cliques have important and significant relationships with the market structure and properties. This paper was submitted directly (Track II) to the PNAS office.Abbreviations: MST, minimum spanning tree; PMFG, Planar Maximally Filtered Graph; r-clique, clique of r elements.

The braingraph.org database of high resolution structural connectomes and the brain graph tools.

PubMed

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

2017-10-01

Based on the data of the NIH-funded Human Connectome Project, we have computed structural connectomes of 426 human subjects in five different resolutions of 83, 129, 234, 463 and 1015 nodes and several edge weights. The graphs are given in anatomically annotated GraphML format that facilitates better further processing and visualization. For 96 subjects, the anatomically classified sub-graphs can also be accessed, formed from the vertices corresponding to distinct lobes or even smaller regions of interests of the brain. For example, one can easily download and study the connectomes, restricted to the frontal lobes or just to the left precuneus of 96 subjects using the data. Partially directed connectomes of 423 subjects are also available for download. We also present a GitHub-deposited set of tools, called the Brain Graph Tools, for several processing tasks of the connectomes on the site http://braingraph.org.

On Super Edge-magic Total Labeling of Modified Watermill Graph

NASA Astrophysics Data System (ADS)

Nurdin; Ungko, T. S.; Gormantara, J.; Abdullah, A.; Aulyah, S.; Nikita

2018-03-01

An edge-magic total labeling on a graph G is one-to-one map from V(G) ∪ E(G) onto the set of integers 1,2, ...,ν + e, where ν = |V(G)| and e = |E(G)|, with the property that, given any edge uv, f(u) + f(u, ν}) + f(ν) = k for every u,v ∈ V(G), and k is called magic valuation. An edge-magic total labeling f is called super edge-magic total if f(v(G)) = {1,2 ...,|V(G)|} and f(E(G)) = {|V(G)| + 1, |V(G)| + 2,... |V(G) + E(G)|}. In this paper we investigate edge-magic total labeling of a new graph called modified Watermill graph. Furthermore, the magic valuation of the modified Watermill graph WM(n) is k=\\frac{1}{2}(21n+3), for n odd, n ≥ 3.

The correlation of metrics in complex networks with applications in functional brain networks

NASA Astrophysics Data System (ADS)

Li, C.; Wang, H.; de Haan, W.; Stam, C. J.; Van Mieghem, P.

2011-11-01

An increasing number of network metrics have been applied in network analysis. If metric relations were known better, we could more effectively characterize networks by a small set of metrics to discover the association between network properties/metrics and network functioning. In this paper, we investigate the linear correlation coefficients between widely studied network metrics in three network models (Bárabasi-Albert graphs, Erdös-Rényi random graphs and Watts-Strogatz small-world graphs) as well as in functional brain networks of healthy subjects. The metric correlations, which we have observed and theoretically explained, motivate us to propose a small representative set of metrics by including only one metric from each subset of mutually strongly dependent metrics. The following contributions are considered important. (a) A network with a given degree distribution can indeed be characterized by a small representative set of metrics. (b) Unweighted networks, which are obtained from weighted functional brain networks with a fixed threshold, and Erdös-Rényi random graphs follow a similar degree distribution. Moreover, their metric correlations and the resultant representative metrics are similar as well. This verifies the influence of degree distribution on metric correlations. (c) Most metric correlations can be explained analytically. (d) Interestingly, the most studied metrics so far, the average shortest path length and the clustering coefficient, are strongly correlated and, thus, redundant. Whereas spectral metrics, though only studied recently in the context of complex networks, seem to be essential in network characterizations. This representative set of metrics tends to both sufficiently and effectively characterize networks with a given degree distribution. In the study of a specific network, however, we have to at least consider the representative set so that important network properties will not be neglected.

Graph Laplacian Regularization for Image Denoising: Analysis in the Continuous Domain.

PubMed

Pang, Jiahao; Cheung, Gene

2017-04-01

Inverse imaging problems are inherently underdetermined, and hence, it is important to employ appropriate image priors for regularization. One recent popular prior-the graph Laplacian regularizer-assumes that the target pixel patch is smooth with respect to an appropriately chosen graph. However, the mechanisms and implications of imposing the graph Laplacian regularizer on the original inverse problem are not well understood. To address this problem, in this paper, we interpret neighborhood graphs of pixel patches as discrete counterparts of Riemannian manifolds and perform analysis in the continuous domain, providing insights into several fundamental aspects of graph Laplacian regularization for image denoising. Specifically, we first show the convergence of the graph Laplacian regularizer to a continuous-domain functional, integrating a norm measured in a locally adaptive metric space. Focusing on image denoising, we derive an optimal metric space assuming non-local self-similarity of pixel patches, leading to an optimal graph Laplacian regularizer for denoising in the discrete domain. We then interpret graph Laplacian regularization as an anisotropic diffusion scheme to explain its behavior during iterations, e.g., its tendency to promote piecewise smooth signals under certain settings. To verify our analysis, an iterative image denoising algorithm is developed. Experimental results show that our algorithm performs competitively with state-of-the-art denoising methods, such as BM3D for natural images, and outperforms them significantly for piecewise smooth images.

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.

Multi-Level Anomaly Detection on Time-Varying Graph Data

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

Bridges, Robert A; Collins, John P; Ferragut, Erik M

This work presents a novel modeling and analysis framework for graph sequences which addresses the challenge of detecting and contextualizing anomalies in labelled, streaming graph data. We introduce a generalization of the BTER model of Seshadhri et al. by adding flexibility to community structure, and use this model to perform multi-scale graph anomaly detection. Specifically, probability models describing coarse subgraphs are built by aggregating probabilities at finer levels, and these closely related hierarchical models simultaneously detect deviations from expectation. This technique provides insight into a graph's structure and internal context that may shed light on a detected event. Additionally, thismore » multi-scale analysis facilitates intuitive visualizations by allowing users to narrow focus from an anomalous graph to particular subgraphs or nodes causing the anomaly. For evaluation, two hierarchical anomaly detectors are tested against a baseline Gaussian method on a series of sampled graphs. We demonstrate that our graph statistics-based approach outperforms both a distribution-based detector and the baseline in a labeled setting with community structure, and it accurately detects anomalies in synthetic and real-world datasets at the node, subgraph, and graph levels. To illustrate the accessibility of information made possible via this technique, the anomaly detector and an associated interactive visualization tool are tested on NCAA football data, where teams and conferences that moved within the league are identified with perfect recall, and precision greater than 0.786.« less

Zwitterionic and free forms of arylmethyl Meldrum's acids.

PubMed

Mierina, Inese; Mishnev, Anatoly; Jure, Mara

2015-09-01

C-Alkyl (including C-arylmethyl) derivatives of Meldrum's acids are attractive building blocks in organic synthesis, mainly due to the unusually high acidity of the resulting compounds. Three examples, namely 5-[4-(diethylamino)benzyl]-2,2-dimethyl-1,3-dioxane-4,6-dione, C17H23NO4, (I), 2,2-dimethyl-5-(2,4,6-trimethoxybenzyl)-1,3-dioxane-4,6-dione, C16H20O7, (II), and 5-(4-hydroxy-3,5-dimethoxybenzyl)-2,2-dimethyl-1,3-dioxane-4,6-dione, C15H18O7, (III), have been synthesized, characterized by NMR and IR spectroscopy, and studied by single-crystal X-ray structure analysis. The nature of the different substituents resulted in remarkable differences in both the molecular conformations and the crystal packing arrangements. The presence of a substituent with a basic centre in compound (I) leads to the formation of an inner salt accompanied by drastic changes in the conformation of the 1,3-dioxane-4,6-dione fragment. By virtue of strong N-H···O hydrogen bonds, the residues are assembled into infinite chains with the graph-set descriptor C(10). Compound (II) contains methoxy groups in both the ortho- and para-positions of the arylmethyl fragment. Because of the absence of classical hydrogen-bond donors in this structure, the crystal packing is controlled by van der Waals forces and weak C-H···O interactions. Compound (III) contains methoxy groups in both meta-positions and a hydroxy group in the para-position. Supramolecular tetrameric synthons which comprise hydrogen-bonded dimers associated into tetramers through π-π interactions of overlapping benzene rings were observed.

Inferring ontology graph structures using OWL reasoning.

PubMed

Rodríguez-García, Miguel Ángel; Hoehndorf, Robert

2018-01-05

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

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

Pal, Suresh, E-mail: ajay-phy@rediffmail.com; Tiwari, R. K.; Gupta, D. C.

In this paper, we present the expressions relating the inter atomic force constants like as bond-stretching force constant (α in N/m) and bond-bending force constant (β in N/m) for the binary (zinc blende structure) and ternary (chalcopyrite structure) semiconductors with the product of ionic charges (PIC) and crystal ionicity (f{sub i}). Interatomic force constants of these compounds exhibit a linear relationship; when plot a graph between Interatomic force constants and the nearest neighbor distance d (Å) with crystal ionicity (f{sub i}), but fall on different straight lines according to the product of ionic charges of these compounds. A fairly goodmore » agreement has been found between the observed and calculated values of the α and β for binary and ternary tetrahedral semiconductors.« less

Temperature and porosity effects on wave propagation in nanobeams using bi-Helmholtz nonlocal strain-gradient elasticity

NASA Astrophysics Data System (ADS)

Reza Barati, Mohammad

2018-05-01

In this paper, applying a general nonlocal strain-gradient elasticity model with two nonlocal and one strain-gradient parameters, wave dispersion behavior of thermally affected and elastically bonded nanobeams is investigated. The two nanobeams are considered to have material imperfections or porosities evenly dispersed across the thickness. Each nanobeam has uniform thickness and is modeled by refined shear deformation beam theory with sinusoidal transverse shear strains. The governing equations of the system are derived by Hamilton's rule and are analytically solved to obtain wave frequencies and the velocity of wave propagation. In the presented graphs, one can see that porosities, temperature, nonlocal, strain gradient and bonding springs have great influences on the wave characteristics of the system.

A tool for filtering information in complex systems

PubMed Central

Tumminello, M.; Aste, T.; Di Matteo, T.; Mantegna, R. N.

2005-01-01

We introduce a technique to filter out complex data sets by extracting a subgraph of representative links. Such a filtering can be tuned up to any desired level by controlling the genus of the resulting graph. We show that this technique is especially suitable for correlation-based graphs, giving filtered graphs that preserve the hierarchical organization of the minimum spanning tree but containing a larger amount of information in their internal structure. In particular in the case of planar filtered graphs (genus equal to 0), triangular loops and four-element cliques are formed. The application of this filtering procedure to 100 stocks in the U.S. equity markets shows that such loops and cliques have important and significant relationships with the market structure and properties. PMID:16027373

A tool for filtering information in complex systems.

PubMed

Tumminello, M; Aste, T; Di Matteo, T; Mantegna, R N

2005-07-26

We introduce a technique to filter out complex data sets by extracting a subgraph of representative links. Such a filtering can be tuned up to any desired level by controlling the genus of the resulting graph. We show that this technique is especially suitable for correlation-based graphs, giving filtered graphs that preserve the hierarchical organization of the minimum spanning tree but containing a larger amount of information in their internal structure. In particular in the case of planar filtered graphs (genus equal to 0), triangular loops and four-element cliques are formed. The application of this filtering procedure to 100 stocks in the U.S. equity markets shows that such loops and cliques have important and significant relationships with the market structure and properties.

A dynamic model of Flo-Tron flowmeters

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

Cichy, M.; Bossio, R.B.

1984-08-01

The optimization of diagnostic equipment for reciprocating both internal and external combustion engines are deeply affected by suitability of simulation models. One of the most attractive and difficult diagnostic aspect deals with the fuel instantaneous mass flow rate measurement. A new model of the dynamic simulation of the Flo-Tron flowmeter, whose working principle is based on the hydraulic Wheatstone's bridge is then presented, dealing with the state space equations and bond-graph method.

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.

Proton-transfer compounds with 4-amino-N-(4,6-dimethylpyrimidin-2-yl)benzenesulfonamide (sulfamethazine): the structures and hydrogen bonding in the salts with 5-nitrosalicylic acid and picric acid.

PubMed

Smith, Graham; Wermuth, Urs D

2013-05-01

The structures of the anhydrous proton-transfer compounds of the sulfa drug sulfamethazine with 5-nitrosalicylic acid and picric acid, namely 2-(4-aminobenzenesulfonamido)-4,6-dimethylpyrimidinium 2-hydroxy-5-nitrobenzoate, C12H15N4O2S(+)·C7H4NO4(-), (I), and 2-(4-aminobenzenesulfonamido)-4,6-dimethylpyrimidinium 2,4,6-trinitrophenolate, C12H15N4O2S(+)·C6H2N3O7(-), (II), respectively, have been determined. In the asymmetric unit of (I), there are two independent but conformationally similar cation-anion heterodimer pairs which are formed through duplex intermolecular N(+)-H···O(carboxylate) and N-H···O(carboxylate) hydrogen-bond pairs, giving a cyclic motif [graph set R2(2)(8)]. These heterodimers form separate and different non-associated substructures through aniline N-H···O hydrogen bonds, one one-dimensional, involving carboxylate O-atom acceptors, the other two-dimensional, involving both carboxylate and hydroxy O-atom acceptors. The overall two-dimensional structure is stabilized by π-π interactions between the pyrimidinium ring and the 5-nitrosalicylate ring in both heterodimers [minimum ring-centroid separation = 3.4580 (8) Å]. For picrate (II), the cation-anion interaction involves a slightly asymmetric chelating N-H···O R2(1)(6) hydrogen-bonding association with the phenolate O atom, together with peripheral conjoint R1(2)(6) interactions between the same N-H groups and O atoms of the ortho-related nitro groups. An inter-unit amine N-H···O(sulfone) hydrogen bond gives one-dimensional chains which extend along a and inter-associate through π-π interactions between the pyrimidinium rings [centroid-centroid separation = 3.4752 (9) Å]. The two structures reported here now bring to a total of four the crystallographically characterized examples of proton-transfer salts of sulfamethazine with strong organic acids.

Enabling Graph Appliance for Genome Assembly

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

Singh, Rina; Graves, Jeffrey A; Lee, Sangkeun

2015-01-01

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

Representation mutations from standard genetic codes

NASA Astrophysics Data System (ADS)

Aisah, I.; Suyudi, M.; Carnia, E.; Suhendi; Supriatna, A. K.

2018-03-01

Graph is widely used in everyday life especially to describe model problem and describe it concretely and clearly. In addition graph is also used to facilitate solve various kinds of problems that are difficult to be solved by calculation. In Biology, graph can be used to describe the process of protein synthesis in DNA. Protein has an important role for DNA (deoxyribonucleic acid) or RNA (ribonucleic acid). Proteins are composed of amino acids. In this study, amino acids are related to genetics, especially the genetic code. The genetic code is also known as the triplet or codon code which is a three-letter arrangement of DNA nitrogen base. The bases are adenine (A), thymine (T), guanine (G) and cytosine (C). While on RNA thymine (T) is replaced with Urasil (U). The set of all Nitrogen bases in RNA is denoted by N = {C U, A, G}. This codon works at the time of protein synthesis inside the cell. This codon also encodes the stop signal as a sign of the stop of protein synthesis process. This paper will examine the process of protein synthesis through mathematical studies and present it in three-dimensional space or graph. The study begins by analysing the set of all codons denoted by NNN such that to obtain geometric representations. At this stage there is a matching between the sets of all nitrogen bases N with Z 2 × Z 2; C=(\\overline{0},\\overline{0}),{{U}}=(\\overline{0},\\overline{1}),{{A}}=(\\overline{1},\\overline{0}),{{G}}=(\\overline{1},\\overline{1}). By matching the algebraic structure will be obtained such as group, group Klein-4,Quotien group etc. With the help of Geogebra software, the set of all codons denoted by NNN can be presented in a three-dimensional space as a multicube NNN and also can be represented as a graph, so that can easily see relationship between the codon.

Admissible Strategies in Infinite Games over Graphs

NASA Astrophysics Data System (ADS)

Faella, Marco

We consider games played on finite graphs, whose objective is to obtain a trace belonging to a given set of accepting traces. We focus on the states from which Player 1 cannot force a win. We compare several criteria for establishing what is the preferable behavior of Player 1 from those states, eventually settling on the notion of admissible strategy.

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

ERIC Educational Resources Information Center

Botzer, Galit; Yerushalmy, Michal

2008-01-01

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

Fusion And Inference From Multiple And Massive Disparate Distributed Dynamic Data Sets

DTIC Science & Technology

2017-07-01

principled methodology for two-sample graph testing; designed a provably almost-surely perfect vertex clustering algorithm for block model graphs; proved...3.7 Semi-Supervised Clustering Methodology ...................................................................... 9 3.8 Robust Hypothesis Testing...dimensional Euclidean space – allows the full arsenal of statistical and machine learning methodology for multivariate Euclidean data to be deployed for

On total irregularity strength of caterpillar graphs with two leaves on each internal vertex

NASA Astrophysics Data System (ADS)

Rosyida, I.; Widodo; Indriati, D.

2018-04-01

Let G(V, E) be a graph. A function f from V(G)\\cup E(G) to the set {1, 2, …, k} is said to be a totally irregular total k-labeling of G if the weights of any two different vertices x and y in V (G) satisfy {w}f(x)\

On Vieta's Formulas and the Determination of a Set of Positive Integers by Their Sum and Product

ERIC Educational Resources Information Center

Valahas, Theodoros; Boukas, Andreas

2011-01-01

In Years 9 and 10 of secondary schooling students are typically introduced to quadratic expressions and functions and related modelling, algebra, and graphing. This includes work on the expansion and factorisation of quadratic expressions (typically with integer values of coefficients), graphing quadratic functions, finding the roots of quadratic…

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.

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

High-order graph matching based feature selection for Alzheimer's disease identification.

PubMed

Liu, Feng; Suk, Heung-Il; Wee, Chong-Yaw; Chen, Huafu; Shen, Dinggang

2013-01-01

One of the main limitations of l1-norm feature selection is that it focuses on estimating the target vector for each sample individually without considering relations with other samples. However, it's believed that the geometrical relation among target vectors in the training set may provide useful information, and it would be natural to expect that the predicted vectors have similar geometric relations as the target vectors. To overcome these limitations, we formulate this as a graph-matching feature selection problem between a predicted graph and a target graph. In the predicted graph a node is represented by predicted vector that may describe regional gray matter volume or cortical thickness features, and in the target graph a node is represented by target vector that include class label and clinical scores. In particular, we devise new regularization terms in sparse representation to impose high-order graph matching between the target vectors and the predicted ones. Finally, the selected regional gray matter volume and cortical thickness features are fused in kernel space for classification. Using the ADNI dataset, we evaluate the effectiveness of the proposed method and obtain the accuracies of 92.17% and 81.57% in AD and MCI classification, respectively.

A simple method for finding the scattering coefficients of quantum graphs

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

Cottrell, Seth S.

2015-09-15

Quantum walks are roughly analogous to classical random walks, and similar to classical walks they have been used to find new (quantum) algorithms. When studying the behavior of large graphs or combinations of graphs, it is useful to find the response of a subgraph to signals of different frequencies. In doing so, we can replace an entire subgraph with a single vertex with variable scattering coefficients. In this paper, a simple technique for quickly finding the scattering coefficients of any discrete-time quantum graph will be presented. These scattering coefficients can be expressed entirely in terms of the characteristic polynomial ofmore » the graph’s time step operator. This is a marked improvement over previous techniques which have traditionally required finding eigenstates for a given eigenvalue, which is far more computationally costly. With the scattering coefficients we can easily derive the “impulse response” which is the key to predicting the response of a graph to any signal. This gives us a powerful set of tools for rapidly understanding the behavior of graphs or for reducing a large graph into its constituent subgraphs regardless of how they are connected.« less

Systematic Dimensionality Reduction for Quantum Walks: Optimal Spatial Search and Transport on Non-Regular Graphs

PubMed Central

Novo, Leonardo; Chakraborty, Shantanav; Mohseni, Masoud; Neven, Hartmut; Omar, Yasser

2015-01-01

Continuous time quantum walks provide an important framework for designing new algorithms and modelling quantum transport and state transfer problems. Often, the graph representing the structure of a problem contains certain symmetries that confine the dynamics to a smaller subspace of the full Hilbert space. In this work, we use invariant subspace methods, that can be computed systematically using the Lanczos algorithm, to obtain the reduced set of states that encompass the dynamics of the problem at hand without the specific knowledge of underlying symmetries. First, we apply this method to obtain new instances of graphs where the spatial quantum search algorithm is optimal: complete graphs with broken links and complete bipartite graphs, in particular, the star graph. These examples show that regularity and high-connectivity are not needed to achieve optimal spatial search. We also show that this method considerably simplifies the calculation of quantum transport efficiencies. Furthermore, we observe improved efficiencies by removing a few links from highly symmetric graphs. Finally, we show that this reduction method also allows us to obtain an upper bound for the fidelity of a single qubit transfer on an XY spin network. PMID:26330082

Primitive graphs with small exponent and small scrambling index

NASA Astrophysics Data System (ADS)

Surbakti, Ita Y.; Suwilo, Saib; Butar-butar, Ericha A.; Oktaviani, Helda

2018-01-01

A connected graph G is primitive provide there is a positive integer k such that for each pair of vertices u and v there is a uv-walk of length k. The smallest of such positive integer k is the exponent of G and is denoted by exp(G). The scrambling index of a primitive graph G, denoted by k(G), is the smallest positive integer k such that for each pair of vertices u and v there is a vertex w such that there is a uw-walk and a vw-walk of length k. By an n-chainring CR(n) we mean a graph obtained from an n-cycle by replacing each edge of the n-cycle by a triangle. By a (q,p)-dory, D(q,p), we mean a graph with vertex set V(D(q,p)) = V(P q × P p ) ∪ {w 1, w 2} and edge set E(D(q,p)) = E(P q × Pp ) ∪ {w 1 - (u i ,v 1) : i = 1, 2,…, q}∪{w 2 -(u i ,vp ) : i = 1, 2,…, q}, where Pn is a path on n vertices. We discus the exponent and scrambling index of an n- chainring and (q, p)-dory. We present formulae for exponent and scrambling index in terms of their diameter.

Using Peano Curves to Construct Laplacians on Fractals

NASA Astrophysics Data System (ADS)

Molitor, Denali; Ott, Nadia; Strichartz, Robert

2015-12-01

We describe a new method to construct Laplacians on fractals using a Peano curve from the circle onto the fractal, extending an idea that has been used in the case of certain Julia sets. The Peano curve allows us to visualize eigenfunctions of the Laplacian by graphing the pullback to the circle. We study in detail three fractals: the pentagasket, the octagasket and the magic carpet. We also use the method for two nonfractal self-similar sets, the torus and the equilateral triangle, obtaining appealing new visualizations of eigenfunctions on the triangle. In contrast to the many familiar pictures of approximations to standard Peano curves, that do no show self-intersections, our descriptions of approximations to the Peano curves have self-intersections that play a vital role in constructing graph approximations to the fractal with explicit graph Laplacians that give the fractal Laplacian in the limit.

L(2,1)-Labeling of the Strong Product of Paths and Cycles

PubMed Central

2014-01-01

An L(2,1)-labeling of a graph G = (V, E) is a function f from the vertex set V(G) to the set of nonnegative integers such that the labels on adjacent vertices differ by at least two and the labels on vertices at distance two differ by at least one. The span of f is the difference between the largest and the smallest numbers in f(V). The λ-number of G, denoted by λ(G), is the minimum span over all L(2,1)-labelings of G. We consider the λ-number of P n⊠C m and for n ≤ 11 the λ-number of C n⊠C m. We determine λ-numbers of graphs of interest with the exception of a finite number of graphs and we improve the bounds on the λ-number of C n⊠C m, m ≥ 24 and n ≥ 26. PMID:24711734

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.

FPFH-based graph matching for 3D point cloud registration

NASA Astrophysics Data System (ADS)

Zhao, Jiapeng; Li, Chen; Tian, Lihua; Zhu, Jihua

2018-04-01

Correspondence detection is a vital step in point cloud registration and it can help getting a reliable initial alignment. In this paper, we put forward an advanced point feature-based graph matching algorithm to solve the initial alignment problem of rigid 3D point cloud registration with partial overlap. Specifically, Fast Point Feature Histograms are used to determine the initial possible correspondences firstly. Next, a new objective function is provided to make the graph matching more suitable for partially overlapping point cloud. The objective function is optimized by the simulated annealing algorithm for final group of correct correspondences. Finally, we present a novel set partitioning method which can transform the NP-hard optimization problem into a O(n3)-solvable one. Experiments on the Stanford and UWA public data sets indicates that our method can obtain better result in terms of both accuracy and time cost compared with other point cloud registration methods.

Effects of Self-Graphing and Goal Setting on the Math Fact Fluency of Students with Disabilities

PubMed Central

Figarola, Patricia M; Gunter, Philip L; Reffel, Julia M; Worth, Susan R; Hummel, John; Gerber, Brian L

2008-01-01

We evaluated the impact of goal setting and students' participation in graphing their own performance data on the rate of math fact calculations. Participants were 3 students with mild disabilities in the first and second grades; 2 of the 3 students were also identified with Attention-Deficit/Hyperactivity Disorder (ADHD). They were taught to use Microsoft Excel® software to graph their rate of correct calculations when completing timed, independent practice sheets consisting of single-digit mathematics problems. Two students' rates of correct calculations nearly always met or exceeded the aim line established for their correct calculations. Additional interventions were required for the third student. Results are discussed in terms of implications and future directions for increasing the use of evaluation components in classrooms for students at risk for behavior disorders and academic failure. PMID:22477686

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.

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

NASA Astrophysics Data System (ADS)

Laverty, James T.

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

Evidence flow graph methods for validation and verification of expert systems

NASA Technical Reports Server (NTRS)

Becker, Lee A.; Green, Peter G.; Bhatnagar, Jayant

1989-01-01

The results of an investigation into the use of evidence flow graph techniques for performing validation and verification of expert systems are given. A translator to convert horn-clause rule bases into evidence flow graphs, a simulation program, and methods of analysis were developed. These tools were then applied to a simple rule base which contained errors. It was found that the method was capable of identifying a variety of problems, for example that the order of presentation of input data or small changes in critical parameters could affect the output from a set of rules.

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.

One-dimensional swarm algorithm packaging

NASA Astrophysics Data System (ADS)

Lebedev, Boris K.; Lebedev, Oleg B.; Lebedeva, Ekaterina O.

2018-05-01

The paper considers an algorithm for solving the problem of onedimensional packaging based on the adaptive behavior model of an ant colony. The key role in the development of the ant algorithm is the choice of representation (interpretation) of the solution. The structure of the solution search graph, the procedure for finding solutions on the graph, the methods of deposition and evaporation of pheromone are described. Unlike the canonical paradigm of an ant algorithm, an ant on the solution search graph generates sets of elements distributed across blocks. Experimental studies were conducted on IBM PC. Compared with the existing algorithms, the results are improved.

Graph drawing using tabu search coupled with path relinking.

PubMed

Dib, Fadi K; Rodgers, Peter

2018-01-01

Graph drawing, or the automatic layout of graphs, is a challenging problem. There are several search based methods for graph drawing which are based on optimizing an objective function which is formed from a weighted sum of multiple criteria. In this paper, we propose a new neighbourhood search method which uses a tabu search coupled with path relinking to optimize such objective functions for general graph layouts with undirected straight lines. To our knowledge, before our work, neither of these methods have been previously used in general multi-criteria graph drawing. Tabu search uses a memory list to speed up searching by avoiding previously tested solutions, while the path relinking method generates new solutions by exploring paths that connect high quality solutions. We use path relinking periodically within the tabu search procedure to speed up the identification of good solutions. We have evaluated our new method against the commonly used neighbourhood search optimization techniques: hill climbing and simulated annealing. Our evaluation examines the quality of the graph layout (objective function's value) and the speed of layout in terms of the number of evaluated solutions required to draw a graph. We also examine the relative scalability of each method. Our experimental results were applied to both random graphs and a real-world dataset. We show that our method outperforms both hill climbing and simulated annealing by producing a better layout in a lower number of evaluated solutions. In addition, we demonstrate that our method has greater scalability as it can layout larger graphs than the state-of-the-art neighbourhood search methods. Finally, we show that similar results can be produced in a real world setting by testing our method against a standard public graph dataset.

Graph drawing using tabu search coupled with path relinking

PubMed Central

Rodgers, Peter

2018-01-01

Graph drawing, or the automatic layout of graphs, is a challenging problem. There are several search based methods for graph drawing which are based on optimizing an objective function which is formed from a weighted sum of multiple criteria. In this paper, we propose a new neighbourhood search method which uses a tabu search coupled with path relinking to optimize such objective functions for general graph layouts with undirected straight lines. To our knowledge, before our work, neither of these methods have been previously used in general multi-criteria graph drawing. Tabu search uses a memory list to speed up searching by avoiding previously tested solutions, while the path relinking method generates new solutions by exploring paths that connect high quality solutions. We use path relinking periodically within the tabu search procedure to speed up the identification of good solutions. We have evaluated our new method against the commonly used neighbourhood search optimization techniques: hill climbing and simulated annealing. Our evaluation examines the quality of the graph layout (objective function’s value) and the speed of layout in terms of the number of evaluated solutions required to draw a graph. We also examine the relative scalability of each method. Our experimental results were applied to both random graphs and a real-world dataset. We show that our method outperforms both hill climbing and simulated annealing by producing a better layout in a lower number of evaluated solutions. In addition, we demonstrate that our method has greater scalability as it can layout larger graphs than the state-of-the-art neighbourhood search methods. Finally, we show that similar results can be produced in a real world setting by testing our method against a standard public graph dataset. PMID:29746576

From Many Records to One Graph: Heterogeneity Conflicts in the Linked Data Restructuring Cycle

ERIC Educational Resources Information Center

Tallerås, Kim

2013-01-01

Introduction: During the last couple of years the library community has developed a number of comprehensive metadata standardization projects inspired by the idea of linked data, such as the BIBFRAME model. Linked data is a set of best practice principles of publishing and exposing data on the Web utilizing a graph based data model powered with…

Simulator for heterogeneous dataflow architectures

NASA Technical Reports Server (NTRS)

Malekpour, Mahyar R.

1993-01-01

A new simulator is developed to simulate the execution of an algorithm graph in accordance with the Algorithm to Architecture Mapping Model (ATAMM) rules. ATAMM is a Petri Net model which describes the periodic execution of large-grained, data-independent dataflow graphs and which provides predictable steady state time-optimized performance. This simulator extends the ATAMM simulation capability from a heterogenous set of resources, or functional units, to a more general heterogenous architecture. Simulation test cases show that the simulator accurately executes the ATAMM rules for both a heterogenous architecture and a homogenous architecture, which is the special case for only one processor type. The simulator forms one tool in an ATAMM Integrated Environment which contains other tools for graph entry, graph modification for performance optimization, and playback of simulations for analysis.

A multi-level anomaly detection algorithm for time-varying graph data with interactive visualization

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

Bridges, Robert A.; Collins, John P.; Ferragut, Erik M.

This work presents a novel modeling and analysis framework for graph sequences which addresses the challenge of detecting and contextualizing anomalies in labelled, streaming graph data. We introduce a generalization of the BTER model of Seshadhri et al. by adding flexibility to community structure, and use this model to perform multi-scale graph anomaly detection. Specifically, probability models describing coarse subgraphs are built by aggregating node probabilities, and these related hierarchical models simultaneously detect deviations from expectation. This technique provides insight into a graph's structure and internal context that may shed light on a detected event. Additionally, this multi-scale analysis facilitatesmore » intuitive visualizations by allowing users to narrow focus from an anomalous graph to particular subgraphs or nodes causing the anomaly. For evaluation, two hierarchical anomaly detectors are tested against a baseline Gaussian method on a series of sampled graphs. We demonstrate that our graph statistics-based approach outperforms both a distribution-based detector and the baseline in a labeled setting with community structure, and it accurately detects anomalies in synthetic and real-world datasets at the node, subgraph, and graph levels. Furthermore, to illustrate the accessibility of information made possible via this technique, the anomaly detector and an associated interactive visualization tool are tested on NCAA football data, where teams and conferences that moved within the league are identified with perfect recall, and precision greater than 0.786.« less

A multi-level anomaly detection algorithm for time-varying graph data with interactive visualization

DOE PAGES

Bridges, Robert A.; Collins, John P.; Ferragut, Erik M.; ...

2016-01-01

This work presents a novel modeling and analysis framework for graph sequences which addresses the challenge of detecting and contextualizing anomalies in labelled, streaming graph data. We introduce a generalization of the BTER model of Seshadhri et al. by adding flexibility to community structure, and use this model to perform multi-scale graph anomaly detection. Specifically, probability models describing coarse subgraphs are built by aggregating node probabilities, and these related hierarchical models simultaneously detect deviations from expectation. This technique provides insight into a graph's structure and internal context that may shed light on a detected event. Additionally, this multi-scale analysis facilitatesmore » intuitive visualizations by allowing users to narrow focus from an anomalous graph to particular subgraphs or nodes causing the anomaly. For evaluation, two hierarchical anomaly detectors are tested against a baseline Gaussian method on a series of sampled graphs. We demonstrate that our graph statistics-based approach outperforms both a distribution-based detector and the baseline in a labeled setting with community structure, and it accurately detects anomalies in synthetic and real-world datasets at the node, subgraph, and graph levels. Furthermore, to illustrate the accessibility of information made possible via this technique, the anomaly detector and an associated interactive visualization tool are tested on NCAA football data, where teams and conferences that moved within the league are identified with perfect recall, and precision greater than 0.786.« less

HodDB: Design and Analysis of a Query Processor for Brick.

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

Fierro, Gabriel; Culler, David

Brick is a recently proposed metadata schema and ontology for describing building components and the relationships between them. It represents buildings as directed labeled graphs using the RDF data model. Using the SPARQL query language, building-agnostic applications query a Brick graph to discover the set of resources and relationships they require to operate. Latency-sensitive applications, such as user interfaces, demand response and modelpredictive control, require fast queries — conventionally less than 100ms. We benchmark a set of popular open-source and commercial SPARQL databases against three real Brick models using seven application queries and find that none of them meet thismore » performance target. This lack of performance can be attributed to design decisions that optimize for queries over large graphs consisting of billions of triples, but give poor spatial locality and join performance on the small dense graphs typical of Brick. We present the design and evaluation of HodDB, a RDF/SPARQL database for Brick built over a node-based index structure. HodDB performs Brick queries 3-700x faster than leading SPARQL databases and consistently meets the 100ms threshold, enabling the portability of important latency-sensitive building applications.« less

Gaussian covariance graph models accounting for correlated marker effects in genome-wide prediction.

PubMed

Martínez, C A; Khare, K; Rahman, S; Elzo, M A

2017-10-01

Several statistical models used in genome-wide prediction assume uncorrelated marker allele substitution effects, but it is known that these effects may be correlated. In statistics, graphical models have been identified as a useful tool for covariance estimation in high-dimensional problems and it is an area that has recently experienced a great expansion. In Gaussian covariance graph models (GCovGM), the joint distribution of a set of random variables is assumed to be Gaussian and the pattern of zeros of the covariance matrix is encoded in terms of an undirected graph G. In this study, methods adapting the theory of GCovGM to genome-wide prediction were developed (Bayes GCov, Bayes GCov-KR and Bayes GCov-H). In simulated data sets, improvements in correlation between phenotypes and predicted breeding values and accuracies of predicted breeding values were found. Our models account for correlation of marker effects and permit to accommodate general structures as opposed to models proposed in previous studies, which consider spatial correlation only. In addition, they allow incorporation of biological information in the prediction process through its use when constructing graph G, and their extension to the multi-allelic loci case is straightforward. © 2017 Blackwell Verlag GmbH.

Princeton VLSI Project.

DTIC Science & Technology

1982-01-01

a rectilinear graph. iefnition 2.1: A rectiliwr graph G is a triple (V. E. X). where V is the vertex set, E is the edge set, and X:Vx V-E U le , where...G,(V, ,) as follows: . =e(z) I =z(a),a E Viand E., = (z, ) I Z1 >Z2E:I, V and E-V are similarly defined. It can be easily shown that C is consistent...width of the layout after the introduction the le .’gths of the drivers introduced on wn to u _-, If we of drivers, which is given by so,+m. is 0(m2

The triangular kagomé lattices revisited

NASA Astrophysics Data System (ADS)

Liu, Xiaoyun; Yan, Weigen

2013-11-01

The dimer problem, Ising spins and bond percolation on the triangular kagomé lattice have been studied extensively by physicists. In this paper, based on the fact the triangular kagomé lattice with toroidal boundary condition can be regarded as the line graph of 3.12.12 lattice with toroidal boundary condition, we derive the formulae of the number of spanning trees, the energy, and the Kirchhoff index of the triangular kagomé lattice with toroidal boundary condition.

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

Application of graph theory to the statistical thermodynamics of lattice polymers. I. Elements of theory and test for dimers

NASA Astrophysics Data System (ADS)

Brazhnik, Olga D.; Freed, Karl F.

1996-07-01

The lattice cluster theory (LCT) is extended to enable inclusion of longer range correlation contributions to the partition function of lattice model polymers in the athermal limit. A diagrammatic technique represents the expansion of the partition function in powers of the inverse lattice coordination number. Graph theory is applied to sort, classify, and evaluate the numerous diagrams appearing in higher orders. New general theorems are proven that provide a significant reduction in the computational labor required to evaluate the contributions from higher order correlations. The new algorithm efficiently generates the correction to the Flory mean field approximation from as many as eight sterically interacting bonds. While the new results contain the essential ingredients for treating a system of flexible chains with arbitrary lengths and concentrations, the complexity of our new algorithm motivates us to test the theory here for the simplest case of a system of lattice dimers by comparison to the dimer packing entropies from the work of Gaunt. This comparison demonstrates that the eight bond LCT is exact through order φ5 for dimers in one through three dimensions, where φ is the volume fraction of dimers. A subsequent work will use the contracted diagrams, derived and tested here, to treat the packing entropy for a system of flexible N-mers at a volume fraction of φ on hypercubic lattices.

Ion aggregation in high salt solutions. VII. The effect of cations on the structures of ion aggregates and water hydrogen-bonding network

NASA Astrophysics Data System (ADS)

Choi, Jun-Ho; Choi, Hyung Ran; Jeon, Jonggu; Cho, Minhaeng

2017-10-01

Ions in high salt solutions have a strong propensity to form polydisperse ion aggregates with broad size and shape distributions. In a series of previous comparative investigations using femtosecond IR pump-probe spectroscopy, molecular dynamics simulation, and graph theoretical analysis, we have shown that there exists a morphological difference in the structures of ion aggregates formed in various salt solutions. As salt concentration increases, the ions in high salt solutions form either cluster-like structures excluding water molecules or network-like structures entwined with water hydrogen-bonding networks. Interestingly, such morphological characteristics of the ion aggregates have been found to be in correlation with the solubility limits of salts. An important question that still remains unexplored is why certain salts with different cations have notably different solubility limits in water. Here, carrying out a series of molecular dynamics simulations of aqueous salt solutions and analyzing the distributions and connectivity patterns of ion aggregates with a spectral graph analysis method, we establish the relationship between the salt solubility and the ion aggregate morphology with a special emphasis on the cationic effects on water structures and ion aggregation. We anticipate that the understanding of large scale ion aggregate structures revealed in this study will be critical for elucidating the specific ion effects on the solubility and conformational stability of co-solute molecules such as proteins in water.

Math Description Engine Software Development Kit

NASA Technical Reports Server (NTRS)

Shelton, Robert O.; Smith, Stephanie L.; Dexter, Dan E.; Hodgson, Terry R.

2010-01-01

The Math Description Engine Software Development Kit (MDE SDK) can be used by software developers to make computer-rendered graphs more accessible to blind and visually-impaired users. The MDE SDK generates alternative graph descriptions in two forms: textual descriptions and non-verbal sound renderings, or sonification. It also enables display of an animated trace of a graph sonification on a visual graph component, with color and line-thickness options for users having low vision or color-related impairments. A set of accessible graphical user interface widgets is provided for operation by end users and for control of accessible graph displays. Version 1.0 of the MDE SDK generates text descriptions for 2D graphs commonly seen in math and science curriculum (and practice). The mathematically rich text descriptions can also serve as a virtual math and science assistant for blind and sighted users, making graphs more accessible for everyone. The MDE SDK has a simple application programming interface (API) that makes it easy for programmers and Web-site developers to make graphs accessible with just a few lines of code. The source code is written in Java for cross-platform compatibility and to take advantage of Java s built-in support for building accessible software application interfaces. Compiled-library and NASA Open Source versions are available with API documentation and Programmer s Guide at http:/ / prim e.jsc.n asa. gov.

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

An automatic graph-based approach for artery/vein classification in retinal images.

PubMed

Dashtbozorg, Behdad; Mendonça, Ana Maria; Campilho, Aurélio

2014-03-01

The classification of retinal vessels into artery/vein (A/V) is an important phase for automating the detection of vascular changes, and for the calculation of characteristic signs associated with several systemic diseases such as diabetes, hypertension, and other cardiovascular conditions. This paper presents an automatic approach for A/V classification based on the analysis of a graph extracted from the retinal vasculature. The proposed method classifies the entire vascular tree deciding on the type of each intersection point (graph nodes) and assigning one of two labels to each vessel segment (graph links). Final classification of a vessel segment as A/V is performed through the combination of the graph-based labeling results with a set of intensity features. The results of this proposed method are compared with manual labeling for three public databases. Accuracy values of 88.3%, 87.4%, and 89.8% are obtained for the images of the INSPIRE-AVR, DRIVE, and VICAVR databases, respectively. These results demonstrate that our method outperforms recent approaches for A/V classification.

Learning locality preserving graph from data.

PubMed

Zhang, Yan-Ming; Huang, Kaizhu; Hou, Xinwen; Liu, Cheng-Lin

2014-11-01

Machine learning based on graph representation, or manifold learning, has attracted great interest in recent years. As the discrete approximation of data manifold, the graph plays a crucial role in these kinds of learning approaches. In this paper, we propose a novel learning method for graph construction, which is distinct from previous methods in that it solves an optimization problem with the aim of directly preserving the local information of the original data set. We show that the proposed objective has close connections with the popular Laplacian Eigenmap problem, and is hence well justified. The optimization turns out to be a quadratic programming problem with n(n-1)/2 variables (n is the number of data points). Exploiting the sparsity of the graph, we further propose a more efficient cutting plane algorithm to solve the problem, making the method better scalable in practice. In the context of clustering and semi-supervised learning, we demonstrated the advantages of our proposed method by experiments.

A Set of Handwriting Features for Use in Automated Writer Identification.

PubMed

Miller, John J; Patterson, Robert Bradley; Gantz, Donald T; Saunders, Christopher P; Walch, Mark A; Buscaglia, JoAnn

2017-05-01

A writer's biometric identity can be characterized through the distribution of physical feature measurements ("writer's profile"); a graph-based system that facilitates the quantification of these features is described. To accomplish this quantification, handwriting is segmented into basic graphical forms ("graphemes"), which are "skeletonized" to yield the graphical topology of the handwritten segment. The graph-based matching algorithm compares the graphemes first by their graphical topology and then by their geometric features. Graphs derived from known writers can be compared against graphs extracted from unknown writings. The process is computationally intensive and relies heavily upon statistical pattern recognition algorithms. This article focuses on the quantification of these physical features and the construction of the associated pattern recognition methods for using the features to discriminate among writers. The graph-based system described in this article has been implemented in a highly accurate and approximately language-independent biometric recognition system of writers of cursive documents. © 2017 American Academy of Forensic Sciences.

A graph lattice approach to maintaining and learning dense collections of subgraphs as image features.

PubMed

Saund, Eric

2013-10-01

Effective object and scene classification and indexing depend on extraction of informative image features. This paper shows how large families of complex image features in the form of subgraphs can be built out of simpler ones through construction of a graph lattice—a hierarchy of related subgraphs linked in a lattice. Robustness is achieved by matching many overlapping and redundant subgraphs, which allows the use of inexpensive exact graph matching, instead of relying on expensive error-tolerant graph matching to a minimal set of ideal model graphs. Efficiency in exact matching is gained by exploitation of the graph lattice data structure. Additionally, the graph lattice enables methods for adaptively growing a feature space of subgraphs tailored to observed data. We develop the approach in the domain of rectilinear line art, specifically for the practical problem of document forms recognition. We are especially interested in methods that require only one or very few labeled training examples per category. We demonstrate two approaches to using the subgraph features for this purpose. Using a bag-of-words feature vector we achieve essentially single-instance learning on a benchmark forms database, following an unsupervised clustering stage. Further performance gains are achieved on a more difficult dataset using a feature voting method and feature selection procedure.

Graph Databases for Large-Scale Healthcare Systems: A Framework for Efficient Data Management and Data Services

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

Park, Yubin; Shankar, Mallikarjun; Park, Byung H.

Designing a database system for both efficient data management and data services has been one of the enduring challenges in the healthcare domain. In many healthcare systems, data services and data management are often viewed as two orthogonal tasks; data services refer to retrieval and analytic queries such as search, joins, statistical data extraction, and simple data mining algorithms, while data management refers to building error-tolerant and non-redundant database systems. The gap between service and management has resulted in rigid database systems and schemas that do not support effective analytics. We compose a rich graph structure from an abstracted healthcaremore » RDBMS to illustrate how we can fill this gap in practice. We show how a healthcare graph can be automatically constructed from a normalized relational database using the proposed 3NF Equivalent Graph (3EG) transformation.We discuss a set of real world graph queries such as finding self-referrals, shared providers, and collaborative filtering, and evaluate their performance over a relational database and its 3EG-transformed graph. Experimental results show that the graph representation serves as multiple de-normalized tables, thus reducing complexity in a database and enhancing data accessibility of users. Based on this finding, we propose an ensemble framework of databases for healthcare applications.« less

GreedyMAX-type Algorithms for the Maximum Independent Set Problem

NASA Astrophysics Data System (ADS)

Borowiecki, Piotr; Göring, Frank

A maximum independent set problem for a simple graph G = (V,E) is to find the largest subset of pairwise nonadjacent vertices. The problem is known to be NP-hard and it is also hard to approximate. Within this article we introduce a non-negative integer valued function p defined on the vertex set V(G) and called a potential function of a graph G, while P(G) = max v ∈ V(G) p(v) is called a potential of G. For any graph P(G) ≤ Δ(G), where Δ(G) is the maximum degree of G. Moreover, Δ(G) - P(G) may be arbitrarily large. A potential of a vertex lets us get a closer insight into the properties of its neighborhood which leads to the definition of the family of GreedyMAX-type algorithms having the classical GreedyMAX algorithm as their origin. We establish a lower bound 1/(P + 1) for the performance ratio of GreedyMAX-type algorithms which favorably compares with the bound 1/(Δ + 1) known to hold for GreedyMAX. The cardinality of an independent set generated by any GreedyMAX-type algorithm is at least sum_{vin V(G)} (p(v)+1)^{-1}, which strengthens the bounds of Turán and Caro-Wei stated in terms of vertex degrees.

Graph-matching based CTA.

PubMed

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

2009-12-01

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

A revised set of values of single-bond radii derived from the observed interatomic distances in metals by correction for bond number and resonance energy

PubMed Central

Pauling, Linus; Kamb, Barclay

1986-01-01

An earlier discussion [Pauling, L. (1947) J. Am. Chem. Soc. 69, 542] of observed bond lengths in elemental metals with correction for bond number and resonance energy led to a set of single-bond metallic radii with values usually somewhat less than the corresponding values obtained from molecules and complex ions. A theory of resonating covalent bonds has now been developed that permits calculation of the number of resonance structures per atom and of the effective resonance energy per bond. With this refined method of correcting the observed bond lengths for the effect of resonance energy, a new set of single-bond covalent radii, in better agreement with values from molecules and complex ions, has been constructed. PMID:16593698

EEG analysis of seizure patterns using visibility graphs for detection of generalized seizures.

PubMed

Wang, Lei; Long, Xi; Arends, Johan B A M; Aarts, Ronald M

2017-10-01

The traditional EEG features in the time and frequency domain show limited seizure detection performance in the epileptic population with intellectual disability (ID). In addition, the influence of EEG seizure patterns on detection performance was less studied. A single-channel EEG signal can be mapped into visibility graphs (VGS), including basic visibility graph (VG), horizontal VG (HVG), and difference VG (DVG). These graphs were used to characterize different EEG seizure patterns. To demonstrate its effectiveness in identifying EEG seizure patterns and detecting generalized seizures, EEG recordings of 615h on one EEG channel from 29 epileptic patients with ID were analyzed. A novel feature set with discriminative power for seizure detection was obtained by using the VGS method. The degree distributions (DDs) of DVG can clearly distinguish EEG of each seizure pattern. The degree entropy and power-law degree power in DVG were proposed here for the first time, and they show significant difference between seizure and non-seizure EEG. The connecting structure measured by HVG can better distinguish seizure EEG from background than those by VG and DVG. A traditional EEG feature set based on frequency analysis was used here as a benchmark feature set. With a support vector machine (SVM) classifier, the seizure detection performance of the benchmark feature set (sensitivity of 24%, FD t /h of 1.8s) can be improved by combining our proposed VGS features extracted from one EEG channel (sensitivity of 38%, FD t /h of 1.4s). The proposed VGS-based features can help improve seizure detection for ID patients. Copyright © 2017 Elsevier B.V. All rights reserved.

Separation of ion types in tandem mass spectrometry data interpretation -- a graph-theoretic approach.

PubMed

Yan, Bo; Pan, Chongle; Olman, Victor N; Hettich, Robert L; Xu, Ying

2004-01-01

Mass spectrometry is one of the most popular analytical techniques for identification of individual proteins in a protein mixture, one of the basic problems in proteomics. It identifies a protein through identifying its unique mass spectral pattern. While the problem is theoretically solvable, it remains a challenging problem computationally. One of the key challenges comes from the difficulty in distinguishing the N- and C-terminus ions, mostly b- and y-ions respectively. In this paper, we present a graph algorithm for solving the problem of separating bfrom y-ions in a set of mass spectra. We represent each spectral peak as a node and consider two types of edges: a type-1 edge connects two peaks possibly of the same ion types and a type-2 edge connects two peaks possibly of different ion types, predicted based on local information. The ion-separation problem is then formulated and solved as a graph partition problem, which is to partition the graph into three subgraphs, namely b-, y-ions and others respectively, so to maximize the total weight of type-1 edges while minimizing the total weight of type-2 edges within each subgraph. We have developed a dynamic programming algorithm for rigorously solving this graph partition problem and implemented it as a computer program PRIME. We have tested PRIME on 18 data sets of high accurate FT-ICR tandem mass spectra and found that it achieved ~90% accuracy for separation of b- and y- ions.

Study on some useful Operators for Graph-theoretic Image Processing

NASA Astrophysics Data System (ADS)

Moghani, Ali; Nasiri, Parviz

2010-11-01

In this paper we describe a human perception based approach to pixel color segmentation which applied in color reconstruction by numerical method associated with graph-theoretic image processing algorithm typically in grayscale. Fuzzy sets defined on the Hue, Saturation and Value components of the HSV color space, provide a fuzzy logic model that aims to follow the human intuition of color classification.

Validation of the Actigraph GT3X and ActivPAL Accelerometers for the Assessment of Sedentary Behavior

ERIC Educational Resources Information Center

Kim, Youngdeok; Barry, Vaughn W.; Kang, Minsoo

2015-01-01

This study examined (a) the validity of two accelerometers (ActiGraph GT3X [ActiGraph LLC, Pensacola, FL, USA] and activPAL [PAL Technologies Ltd., Glasgow, Scotland]) for the assessment of sedentary behavior; and (b) the variations in assessment accuracy by setting minimum sedentary bout durations against a proxy for direct observation using an…

Sampling Large Graphs for Anticipatory Analytics

DTIC Science & Technology

2015-05-15

low. C. Random Area Sampling Random area sampling [8] is a “ snowball ” sampling method in which a set of random seed vertices are selected and areas... Sampling Large Graphs for Anticipatory Analytics Lauren Edwards, Luke Johnson, Maja Milosavljevic, Vijay Gadepally, Benjamin A. Miller Lincoln...systems, greater human-in-the-loop involvement, or through complex algorithms. We are investigating the use of sampling to mitigate these challenges

Graphs as a Visual Aid in English for Special Purposes. Lenguas para objetivos especificos (Languages for Special Purposes), No. 5.

ERIC Educational Resources Information Center

Stark, Merritt W.; Stark, Kathleen LaPiana

Visual aids have been developed to strengthen non-English speaking students' ability to speak and write English effectively in their subject areas. Among these aids, graphs have been valuable for economics students because they readily illustrate the nature of the relationship between two sets of numbers. Frequently, the ability to analyze graphs…

A global/local affinity graph for image segmentation.

PubMed

Xiaofang Wang; Yuxing Tang; Masnou, Simon; Liming Chen

2015-04-01

Construction of a reliable graph capturing perceptual grouping cues of an image is fundamental for graph-cut based image segmentation methods. In this paper, we propose a novel sparse global/local affinity graph over superpixels of an input image to capture both short- and long-range grouping cues, and thereby enabling perceptual grouping laws, including proximity, similarity, continuity, and to enter in action through a suitable graph-cut algorithm. Moreover, we also evaluate three major visual features, namely, color, texture, and shape, for their effectiveness in perceptual segmentation and propose a simple graph fusion scheme to implement some recent findings from psychophysics, which suggest combining these visual features with different emphases for perceptual grouping. In particular, an input image is first oversegmented into superpixels at different scales. We postulate a gravitation law based on empirical observations and divide superpixels adaptively into small-, medium-, and large-sized sets. Global grouping is achieved using medium-sized superpixels through a sparse representation of superpixels' features by solving a ℓ0-minimization problem, and thereby enabling continuity or propagation of local smoothness over long-range connections. Small- and large-sized superpixels are then used to achieve local smoothness through an adjacent graph in a given feature space, and thus implementing perceptual laws, for example, similarity and proximity. Finally, a bipartite graph is also introduced to enable propagation of grouping cues between superpixels of different scales. Extensive experiments are carried out on the Berkeley segmentation database in comparison with several state-of-the-art graph constructions. The results show the effectiveness of the proposed approach, which outperforms state-of-the-art graphs using four different objective criteria, namely, the probabilistic rand index, the variation of information, the global consistency error, and the boundary displacement error.

Local dependence in random graph models: characterization, properties and statistical inference

PubMed Central

Schweinberger, Michael; Handcock, Mark S.

2015-01-01

Summary Dependent phenomena, such as relational, spatial and temporal phenomena, tend to be characterized by local dependence in the sense that units which are close in a well-defined sense are dependent. In contrast with spatial and temporal phenomena, though, relational phenomena tend to lack a natural neighbourhood structure in the sense that it is unknown which units are close and thus dependent. Owing to the challenge of characterizing local dependence and constructing random graph models with local dependence, many conventional exponential family random graph models induce strong dependence and are not amenable to statistical inference. We take first steps to characterize local dependence in random graph models, inspired by the notion of finite neighbourhoods in spatial statistics and M-dependence in time series, and we show that local dependence endows random graph models with desirable properties which make them amenable to statistical inference. We show that random graph models with local dependence satisfy a natural domain consistency condition which every model should satisfy, but conventional exponential family random graph models do not satisfy. In addition, we establish a central limit theorem for random graph models with local dependence, which suggests that random graph models with local dependence are amenable to statistical inference. We discuss how random graph models with local dependence can be constructed by exploiting either observed or unobserved neighbourhood structure. In the absence of observed neighbourhood structure, we take a Bayesian view and express the uncertainty about the neighbourhood structure by specifying a prior on a set of suitable neighbourhood structures. We present simulation results and applications to two real world networks with ‘ground truth’. PMID:26560142

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.

Communicating projected survival with treatments for chronic kidney disease: patient comprehension and perspectives on visual aids.

PubMed

Dowen, Frances; Sidhu, Karishma; Broadbent, Elizabeth; Pilmore, Helen

2017-09-21

Mortality in end stage renal disease (ESRD) is higher than many malignancies. There is no data about the optimal way to present information about projected survival to patients with ESRD. In other areas, graphs have been shown to be more easily understood than narrative. We examined patient comprehension and perspectives on graphs in communicating projected survival in chronic kidney disease (CKD). One hundred seventy-seven patients with CKD were shown 4 different graphs presenting post transplantation survival data. Patients were asked to interpret a Kaplan Meier curve, pie chart, histogram and pictograph and answer a multi-choice question to determine understanding. We measured interpretation, usefulness and preference for the graphs. Most patients correctly interpreted the graphs. There was asignificant difference in the percentage of correct answers when comparing different graph types (p = 0.0439). The pictograph was correctly interpreted by 81% of participants, the histogram by 79%, pie chart by 77% and Kaplan Meier by 69%. Correct interpretation of the histogram was associated with educational level (p = 0.008) and inversely associated with age > 65 (p = 0.008). Of those who interpreted all four graphs correctly, there was an association with employment (p = 0.001) and New Zealand European ethnicity (p = 0.002). 87% of patients found the graphs useful. The pie chart was the most preferred graph (p 0.002). The readability of the graphs may have been improved with an alternative colour choice, especially in the setting of visual impairment. Visual aids, can be beneficial adjuncts to discussing survival in CKD.

Integer Flows and Circuit Covers of Graphs and Signed Graphs

NASA Astrophysics Data System (ADS)

Cheng, Jian

The work in Chapter 2 is motivated by Tutte and Jaeger's pioneering work on converting modulo flows into integer-valued flows for ordinary graphs. For a signed graphs (G, sigma), we first prove that for each k ∈ {2, 3}, if (G, sigma) is (k - 1)-edge-connected and contains an even number of negative edges when k = 2, then every modulo k-flow of (G, sigma) can be converted into an integer-valued ( k + 1)-ow with a larger or the same support. We also prove that if (G, sigma) is odd-(2p+1)-edge-connected, then (G, sigma) admits a modulo circular (2 + 1/ p)-flows if and only if it admits an integer-valued circular (2 + 1/p)-flows, which improves all previous result by Xu and Zhang (DM2005), Schubert and Steffen (EJC2015), and Zhu (JCTB2015). Shortest circuit cover conjecture is one of the major open problems in graph theory. It states that every bridgeless graph G contains a set of circuits F such that each edge is contained in at least one member of F and the length of F is at most 7/5∥E(G)∥. This concept was recently generalized to signed graphs by Macajova et al. (JGT2015). In Chapter 3, we improve their upper bound from 11∥E( G)∥ to 14/3 ∥E(G)∥, and if G is 2-edgeconnected and has even negativeness, then it can be further reduced to 11/3 ∥E(G)∥. Tutte's 3-flow conjecture has been studied by many graph theorists in the last several decades. As a new approach to this conjecture, DeVos and Thomassen considered the vectors as ow values and found that there is a close relation between vector S1-flows and integer 3-NZFs. Motivated by their observation, in Chapter 4, we prove that if a graph G admits a vector S1-flow with rank at most two, then G admits an integer 3-NZF. The concept of even factors is highly related to the famous Four Color Theorem. We conclude this dissertation in Chapter 5 with an improvement of a recent result by Chen and Fan (JCTB2016) on the upperbound of even factors. We show that if a graph G contains an even factor, then it contains an even factor H with. ∥E(H)∥ ≥ 4/7 (∥ E(G)∥+1)+ 1/7 ∥V2 (G)∥, where V2( G) is the set of vertices of degree two.

Evidence flow graph methods for validation and verification of expert systems

NASA Technical Reports Server (NTRS)

Becker, Lee A.; Green, Peter G.; Bhatnagar, Jayant

1988-01-01

This final report describes the results of an investigation into the use of evidence flow graph techniques for performing validation and verification of expert systems. This was approached by developing a translator to convert horn-clause rule bases into evidence flow graphs, a simulation program, and methods of analysis. These tools were then applied to a simple rule base which contained errors. It was found that the method was capable of identifying a variety of problems, for example that the order of presentation of input data or small changes in critical parameters could effect the output from a set of rules.

Design tool for multiprocessor scheduling and evaluation of iterative dataflow algorithms

NASA Technical Reports Server (NTRS)

Jones, Robert L., III

1995-01-01

A graph-theoretic design process and software tool is defined for selecting a multiprocessing scheduling solution for a class of computational problems. The problems of interest are those that can be described with a dataflow graph and are intended to be executed repetitively on a set of identical processors. Typical applications include signal processing and control law problems. Graph-search algorithms and analysis techniques are introduced and shown to effectively determine performance bounds, scheduling constraints, and resource requirements. The software tool applies the design process to a given problem and includes performance optimization through the inclusion of additional precedence constraints among the schedulable tasks.

On face antimagic labeling of double duplication of graphs

NASA Astrophysics Data System (ADS)

Shobana, L.; Kuppan, R.

2018-04-01

A Labeling of a plane graph G is called d-antimagic if every numbers, the set of s-sided face weights is Ws={as,as+d,as+2d,...,as+(fs-1)d} for some integers as and d (as>0,d≥0),where fs is the number of s-sided faces. We allow differentsets ws of different s.In this paper, we proved the existence of face antimagic labeling of types (1,0,0),(1,0,1),(1,1,0),(0,1,1) and (1,1,1) of double duplication of all vertices by edges of a cycle graph Cn: n≥3 and a tree of order n.

Fast graph-based relaxed clustering for large data sets using minimal enclosing ball.

PubMed

Qian, Pengjiang; Chung, Fu-Lai; Wang, Shitong; Deng, Zhaohong

2012-06-01

Although graph-based relaxed clustering (GRC) is one of the spectral clustering algorithms with straightforwardness and self-adaptability, it is sensitive to the parameters of the adopted similarity measure and also has high time complexity O(N(3)) which severely weakens its usefulness for large data sets. In order to overcome these shortcomings, after introducing certain constraints for GRC, an enhanced version of GRC [constrained GRC (CGRC)] is proposed to increase the robustness of GRC to the parameters of the adopted similarity measure, and accordingly, a novel algorithm called fast GRC (FGRC) based on CGRC is developed in this paper by using the core-set-based minimal enclosing ball approximation. A distinctive advantage of FGRC is that its asymptotic time complexity is linear with the data set size N. At the same time, FGRC also inherits the straightforwardness and self-adaptability from GRC, making the proposed FGRC a fast and effective clustering algorithm for large data sets. The advantages of FGRC are validated by various benchmarking and real data sets.

Development of acceptance criteria for batches of silane primer for external tank thermal protection system bonding applications

NASA Technical Reports Server (NTRS)

Mikes, F.

1984-01-01

Silane primers for use as thermal protection on external tanks were subjected to various analytic techniques to determine the most effective testing method for silane lot evaluation. The analytic methods included high performance liquid chromatography, gas chromatography, thermogravimetry (TGA), and fourier transform infrared spectroscopy (FTIR). It is suggested that FTIR be used as the method for silane lot evaluation. Chromatograms, TGA profiles, bar graphs showing IR absorbances, and FTIR spectra are presented.

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

Representations of mechanical assembly sequences

NASA Technical Reports Server (NTRS)

Homem De Mello, Luiz S.; Sanderson, Arthur C.

1991-01-01

Five types of representations for assembly sequences are reviewed: the directed graph of feasible assembly sequences, the AND/OR graph of feasible assembly sequences, the set of establishment conditions, and two types of sets of precedence relationships. (precedence relationships between the establishment of one connection between parts and the establishment of another connection, and precedence relationships between the establishment of one connection and states of the assembly process). The mappings of one representation into the others are established. The correctness and completeness of these representations are established. The results presented are needed in the proof of correctness and completeness of algorithms for the generation of mechanical assembly sequences.

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

Vyatkina, Kira; Wu, Si; Dekker, Lennard J. M.

De novo sequencing of proteins and peptides is one of the most important problems in mass spectrometry-driven proteomics. A variety of methods have been developed to accomplish this task from a set of bottom-up tandem (MS/MS) mass spectra. However, a more recently emerged top-down technology, now gaining more and more popularity, opens new perspectives for protein analysis and characterization, implying a need in efficient algorithms for processing this kind of MS/MS data. Here we describe a method that allows to retrieve from a set of top-down MS/MS spectra long and accurate sequence fragments of the proteins contained in a sample.more » To this end, we outline a strategy for generating high-quality sequence tags from top-down spectra, and introduce the concept of a T-Bruijn graph by adapting to the case of tags the notion of an A-Bruijn graph widely used in genomics. The output of the proposed approach represents the set of amino acid strings spelled out by optimal paths in the connected components of a T-Bruijn graph. We illustrate its performance on top-down datasets acquired from carbonic anhydrase 2 (CAH2) and the Fab region of alemtuzumab.« less

Object Classification With Joint Projection and Low-Rank Dictionary Learning.

PubMed

Foroughi, Homa; Ray, Nilanjan; Hong Zhang

2018-02-01

For an object classification system, the most critical obstacles toward real-world applications are often caused by large intra-class variability, arising from different lightings, occlusion, and corruption, in limited sample sets. Most methods in the literature would fail when the training samples are heavily occluded, corrupted or have significant illumination or viewpoint variations. Besides, most of the existing methods and especially deep learning-based methods, need large training sets to achieve a satisfactory recognition performance. Although using the pre-trained network on a generic large-scale data set and fine-tune it to the small-sized target data set is a widely used technique, this would not help when the content of base and target data sets are very different. To address these issues simultaneously, we propose a joint projection and low-rank dictionary learning method using dual graph constraints. Specifically, a structured class-specific dictionary is learned in the low-dimensional space, and the discrimination is further improved by imposing a graph constraint on the coding coefficients, that maximizes the intra-class compactness and inter-class separability. We enforce structural incoherence and low-rank constraints on sub-dictionaries to reduce the redundancy among them, and also make them robust to variations and outliers. To preserve the intrinsic structure of data, we introduce a supervised neighborhood graph into the framework to make the proposed method robust to small-sized and high-dimensional data sets. Experimental results on several benchmark data sets verify the superior performance of our method for object classification of small-sized data sets, which include a considerable amount of different kinds of variation, and may have high-dimensional feature vectors.

A novel alignment-free method to classify protein folding types by combining spectral graph clustering with Chou's pseudo amino acid composition.

PubMed

Tripathi, Pooja; Pandey, Paras N

2017-07-07

The present work employs pseudo amino acid composition (PseAAC) for encoding the protein sequences in their numeric form. Later this will be arranged in the similarity matrix, which serves as input for spectral graph clustering method. Spectral methods are used previously also for clustering of protein sequences, but they uses pair wise alignment scores of protein sequences, in similarity matrix. The alignment score depends on the length of sequences, so clustering short and long sequences together may not good idea. Therefore the idea of introducing PseAAC with spectral clustering algorithm came into scene. We extensively tested our method and compared its performance with other existing machine learning methods. It is consistently observed that, the number of clusters that we obtained for a given set of proteins is close to the number of superfamilies in that set and PseAAC combined with spectral graph clustering shows the best classification results. Copyright © 2017 Elsevier Ltd. All rights reserved.

Combination of graph heuristics in producing initial solution of curriculum based course timetabling problem

NASA Astrophysics Data System (ADS)

Wahid, Juliana; Hussin, Naimah Mohd

2016-08-01

The construction of population of initial solution is a crucial task in population-based metaheuristic approach for solving curriculum-based university course timetabling problem because it can affect the convergence speed and also the quality of the final solution. This paper presents an exploration on combination of graph heuristics in construction approach in curriculum based course timetabling problem to produce a population of initial solutions. The graph heuristics were set as single and combination of two heuristics. In addition, several ways of assigning courses into room and timeslot are implemented. All settings of heuristics are then tested on the same curriculum based course timetabling problem instances and are compared with each other in terms of number of population produced. The result shows that combination of saturation degree followed by largest degree heuristic produce the highest number of population of initial solutions. The results from this study can be used in the improvement phase of algorithm that uses population of initial solutions.

Continuum Limit of Total Variation on Point Clouds

NASA Astrophysics Data System (ADS)

García Trillos, Nicolás; Slepčev, Dejan

2016-04-01

We consider point clouds obtained as random samples of a measure on a Euclidean domain. A graph representing the point cloud is obtained by assigning weights to edges based on the distance between the points they connect. Our goal is to develop mathematical tools needed to study the consistency, as the number of available data points increases, of graph-based machine learning algorithms for tasks such as clustering. In particular, we study when the cut capacity, and more generally total variation, on these graphs is a good approximation of the perimeter (total variation) in the continuum setting. We address this question in the setting of Γ-convergence. We obtain almost optimal conditions on the scaling, as the number of points increases, of the size of the neighborhood over which the points are connected by an edge for the Γ-convergence to hold. Taking of the limit is enabled by a transportation based metric which allows us to suitably compare functionals defined on different point clouds.

Assessment of tautomer distribution using the condensed reaction graph approach

NASA Astrophysics Data System (ADS)

Gimadiev, T. R.; Madzhidov, T. I.; Nugmanov, R. I.; Baskin, I. I.; Antipin, I. S.; Varnek, A.

2018-03-01

We report the first direct QSPR modeling of equilibrium constants of tautomeric transformations (logK T ) in different solvents and at different temperatures, which do not require intermediate assessment of acidity (basicity) constants for all tautomeric forms. The key step of the modeling consisted in the merging of two tautomers in one sole molecular graph ("condensed reaction graph") which enables to compute molecular descriptors characterizing entire equilibrium. The support vector regression method was used to build the models. The training set consisted of 785 transformations belonging to 11 types of tautomeric reactions with equilibrium constants measured in different solvents and at different temperatures. The models obtained perform well both in cross-validation (Q2 = 0.81 RMSE = 0.7 logK T units) and on two external test sets. Benchmarking studies demonstrate that our models outperform results obtained with DFT B3LYP/6-311 ++ G(d,p) and ChemAxon Tautomerizer applicable only in water at room temperature.

Discrete Mathematical Approaches to Graph-Based Traffic Analysis

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

Joslyn, Cliff A.; Cowley, Wendy E.; Hogan, Emilie A.

2014-04-01

Modern cyber defense and anlaytics requires general, formal models of cyber systems. Multi-scale network models are prime candidates for such formalisms, using discrete mathematical methods based in hierarchically-structured directed multigraphs which also include rich sets of labels. An exemplar of an application of such an approach is traffic analysis, that is, observing and analyzing connections between clients, servers, hosts, and actors within IP networks, over time, to identify characteristic or suspicious patterns. Towards that end, NetFlow (or more generically, IPFLOW) data are available from routers and servers which summarize coherent groups of IP packets flowing through the network. In thismore » paper, we consider traffic analysis of Netflow using both basic graph statistics and two new mathematical measures involving labeled degree distributions and time interval overlap measures. We do all of this over the VAST test data set of 96M synthetic Netflow graph edges, against which we can identify characteristic patterns of simulated ground-truth network attacks.« less

Synthesis, characterization, solubility and stability studies of hydrate cocrystal of antitubercular Isoniazid with antioxidant and anti-bacterial Protocatechuic acid

NASA Astrophysics Data System (ADS)

Mashhadi, Syed Muddassir Ali; Yunus, Uzma; Bhatti, Moazzam Hussain; Ahmed, Imtiaz; Tahir, Muhammad Nawaz

2016-08-01

Isoniazid is an important component used in "triple therapy" to combat tuberculosis. It has reduced Tabletting formulations stability. Anti-oxidants are obligatory to counter oxidative stress, pulmonary inflammation, and free radical burst from macrophages caused in tuberculosis and other diseases. In the present study a hydrate cocrystal of Isoniazid with anti-oxidant and anti-inflammatory and anti-bacterial Protocatechuic acid (3,4-dihydroxybenzoic acid) in 1:1 is reported. This Cocrystal may have improved tabletting stability and anti-oxidant properties. Cocrystal structure analysis confirmed the existence of pyridine-carboxylic acid synthon in the Cocrystal. Other synthons of different graph sets involving Nsbnd H···O and Osbnd H···N bonds are formed between hydrazide group of isoniazid and coformer. Solubility studies revealed that cocrystal is less soluble as compared to isoniazid in buffer at pH 7.4 at 22 °C while stability studies at 80 °C for 24 h period disclosed the fact that cocrystal has higher stability than that of isoniazid.

Learning and Inductive Inference

DTIC Science & Technology

1982-07-01

a set of graph grammars to describe visual scenes . Other researchers have applied graph grammars to the pattern recognition of handwritten characters...345 1. Issues / 345 2. Mostows’ operationalizer / 350 0. Learning from ezamples / 360 1. Issues / 3t60 2. Learning in control and pattern recognition ...art.icleis on rote learntinig and ailvice- tAik g. K(ennieth Clarkson contributed Ltte article on grmvit atical inference, anid Geoff’ lroiney wrote

Evaluation of the MyWellness Key accelerometer.

PubMed

Herrmann, S D; Hart, T L; Lee, C D; Ainsworth, B E

2011-02-01

to examine the concurrent validity of the Technogym MyWellness Key accelerometer against objective and subjective physical activity (PA) measures. randomised, cross-sectional design with two phases. The laboratory phase compared the MyWellness Key with the ActiGraph GT1M and the Yamax SW200 Digiwalker pedometer during graded treadmill walking, increasing speed each minute. The free-living phase compared the MyWellness Key with the ActiGraph, Digiwalker, Bouchard Activity cord (BAR) and Global Physical Activity Questionnaire (GPAQ) for seven continuous days. Data were analysed using Spearman rank-order correlation coefficients for all comparisons. laboratory and free-living phases. sixteen participants randomly stratified from 41 eligible respondents by sex (n=8 men; n=8 women) and PA levels (n=4 low, n=8 middle and n=4 high active). there was a strong association between the MyWellness Key and the ActiGraph accelerometer during controlled graded treadmill walking (r=0.91, p<0.01) and in free-living settings (r=0.73-0.76 for light to vigorous PA, respectively, p<0.01). No associations were observed between the MyWellness Key and the BAR and GPAQ (p>0.05). the MyWellness Key has a high concurrent validity with the ActiGraph accelerometer to detect PA in both controlled laboratory and free-living settings.

Introducing the slime mold graph repository

NASA Astrophysics Data System (ADS)

Dirnberger, M.; Mehlhorn, K.; Mehlhorn, T.

2017-07-01

We introduce the slime mold graph repository or SMGR, a novel data collection promoting the visibility, accessibility and reuse of experimental data revolving around network-forming slime molds. By making data readily available to researchers across multiple disciplines, the SMGR promotes novel research as well as the reproduction of original results. While SMGR data may take various forms, we stress the importance of graph representations of slime mold networks due to their ease of handling and their large potential for reuse. Data added to the SMGR stands to gain impact beyond initial publications or even beyond its domain of origin. We initiate the SMGR with the comprehensive Kist Europe data set focusing on the slime mold Physarum polycephalum, which we obtained in the course of our original research. It contains sequences of images documenting growth and network formation of the organism under constant conditions. Suitable image sequences depicting the typical P. polycephalum network structures are used to compute sequences of graphs faithfully capturing them. Given such sequences, node identities are computed, tracking the development of nodes over time. Based on this information we demonstrate two out of many possible ways to begin exploring the data. The entire data set is well-documented, self-contained and ready for inspection at http://smgr.mpi-inf.mpg.de.

Maximum-valence radii of transition metals

PubMed Central

Pauling, Linus

1975-01-01

In many of their compounds the transition metals have covalence 9, forming nine bonds with use of nine hybrid spd bond orbitals. A set of maximum-valence single-bond radii is formulated for use in these compounds. These radii are in reasonably good agreement with observed bond lengths. Quadruple bonds between two transition metal atoms are about 50 pm (iron-group atoms) or 55 pm (palladium and platinum-group atoms) shorter than single bonds. This amount of shortening corresponds to four bent single bonds with the best set of bond angles, 79.24° and 128.8°. PMID:16578730

Task scheduling in dataflow computer architectures

NASA Technical Reports Server (NTRS)

Katsinis, Constantine

1994-01-01

Dataflow computers provide a platform for the solution of a large class of computational problems, which includes digital signal processing and image processing. Many typical applications are represented by a set of tasks which can be repetitively executed in parallel as specified by an associated dataflow graph. Research in this area aims to model these architectures, develop scheduling procedures, and predict the transient and steady state performance. Researchers at NASA have created a model and developed associated software tools which are capable of analyzing a dataflow graph and predicting its runtime performance under various resource and timing constraints. These models and tools were extended and used in this work. Experiments using these tools revealed certain properties of such graphs that require further study. Specifically, the transient behavior at the beginning of the execution of a graph can have a significant effect on the steady state performance. Transformation and retiming of the application algorithm and its initial conditions can produce a different transient behavior and consequently different steady state performance. The effect of such transformations on the resource requirements or under resource constraints requires extensive study. Task scheduling to obtain maximum performance (based on user-defined criteria), or to satisfy a set of resource constraints, can also be significantly affected by a transformation of the application algorithm. Since task scheduling is performed by heuristic algorithms, further research is needed to determine if new scheduling heuristics can be developed that can exploit such transformations. This work has provided the initial development for further long-term research efforts. A simulation tool was completed to provide insight into the transient and steady state execution of a dataflow graph. A set of scheduling algorithms was completed which can operate in conjunction with the modeling and performance tools previously developed. Initial studies on the performance of these algorithms were done to examine the effects of application algorithm transformations as measured by such quantities as number of processors, time between outputs, time between input and output, communication time, and memory size.

Anisotropic opinion dynamics

NASA Astrophysics Data System (ADS)

Neirotti, Juan

2016-07-01

We consider the process of opinion formation in a society of interacting agents, where there is a set B of socially accepted rules. In this scenario, we observed that agents, represented by simple feed-forward, adaptive neural networks, may have a conservative attitude (mostly in agreement with B ) or liberal attitude (mostly in agreement with neighboring agents) depending on how much their opinions are influenced by their peers. The topology of the network representing the interaction of the society's members is determined by a graph, where the agents' properties are defined over the vertexes and the interagent interactions are defined over the bonds. The adaptability of the agents allows us to model the formation of opinions as an online learning process, where agents learn continuously as new information becomes available to the whole society (online learning). Through the application of statistical mechanics techniques we deduced a set of differential equations describing the dynamics of the system. We observed that by slowly varying the average peer influence in such a way that the agents attitude changes from conservative to liberal and back, the average social opinion develops a hysteresis cycle. Such hysteretic behavior disappears when the variance of the social influence distribution is large enough. In all the cases studied, the change from conservative to liberal behavior is characterized by the emergence of conservative clusters, i.e., a closed knitted set of society members that follow a leader who agrees with the social status quo when the rule B is challenged.

Browsing schematics: Query-filtered graphs with context nodes

NASA Technical Reports Server (NTRS)

Ciccarelli, Eugene C.; Nardi, Bonnie A.

1988-01-01

The early results of a research project to create tools for building interfaces to intelligent systems on the NASA Space Station are reported. One such tool is the Schematic Browser which helps users engaged in engineering problem solving find and select schematics from among a large set. Users query for schematics with certain components, and the Schematic Browser presents a graph whose nodes represent the schematics with those components. The query greatly reduces the number of choices presented to the user, filtering the graph to a manageable size. Users can reformulate and refine the query serially until they locate the schematics of interest. To help users maintain orientation as they navigate a large body of data, the graph also includes nodes that are not matches but provide global and local context for the matching nodes. Context nodes include landmarks, ancestors, siblings, children and previous matches.

On the mixing time of geographical threshold graphs

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

Bradonjic, Milan

In this paper, we study the mixing time of random graphs generated by the geographical threshold graph (GTG) model, a generalization of random geometric graphs (RGG). In a GTG, nodes are distributed in a Euclidean space, and edges are assigned according to a threshold function involving the distance between nodes as well as randomly chosen node weights. The motivation for analyzing this model is that many real networks (e.g., wireless networks, the Internet, etc.) need to be studied by using a 'richer' stochastic model (which in this case includes both a distance between nodes and weights on the nodes). Wemore » specifically study the mixing times of random walks on 2-dimensional GTGs near the connectivity threshold. We provide a set of criteria on the distribution of vertex weights that guarantees that the mixing time is {Theta}(n log n).« less

Computing the Edge-Neighbour-Scattering Number of Graphs

NASA Astrophysics Data System (ADS)

Wei, Zongtian; Qi, Nannan; Yue, Xiaokui

2013-11-01

A set of edges X is subverted from a graph G by removing the closed neighbourhood N[X] from G. We denote the survival subgraph by G=X. An edge-subversion strategy X is called an edge-cut strategy of G if G=X is disconnected, a single vertex, or empty. The edge-neighbour-scattering number of a graph G is defined as ENS(G) = max{ω(G/X)-|X| : X is an edge-cut strategy of G}, where w(G=X) is the number of components of G=X. This parameter can be used to measure the vulnerability of networks when some edges are failed, especially spy networks and virus-infected networks. In this paper, we prove that the problem of computing the edge-neighbour-scattering number of a graph is NP-complete and give some upper and lower bounds for this parameter.

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.

Lung vessel segmentation in CT images using graph-cuts

NASA Astrophysics Data System (ADS)

Zhai, Zhiwei; Staring, Marius; Stoel, Berend C.

2016-03-01

Accurate lung vessel segmentation is an important operation for lung CT analysis. Filters that are based on analyzing the eigenvalues of the Hessian matrix are popular for pulmonary vessel enhancement. However, due to their low response at vessel bifurcations and vessel boundaries, extracting lung vessels by thresholding the vesselness is not sufficiently accurate. Some methods turn to graph-cuts for more accurate segmentation, as it incorporates neighbourhood information. In this work, we propose a new graph-cuts cost function combining appearance and shape, where CT intensity represents appearance and vesselness from a Hessian-based filter represents shape. Due to the amount of voxels in high resolution CT scans, the memory requirement and time consumption for building a graph structure is very high. In order to make the graph representation computationally tractable, those voxels that are considered clearly background are removed from the graph nodes, using a threshold on the vesselness map. The graph structure is then established based on the remaining voxel nodes, source/sink nodes and the neighbourhood relationship of the remaining voxels. Vessels are segmented by minimizing the energy cost function with the graph-cuts optimization framework. We optimized the parameters used in the graph-cuts cost function and evaluated the proposed method with two manually labeled sub-volumes. For independent evaluation, we used 20 CT scans of the VESSEL12 challenge. The evaluation results of the sub-volume data show that the proposed method produced a more accurate vessel segmentation compared to the previous methods, with F1 score 0.76 and 0.69. In the VESSEL12 data-set, our method obtained a competitive performance with an area under the ROC curve of 0.975, especially among the binary submissions.

On the partition dimension of comb product of path and complete graph

NASA Astrophysics Data System (ADS)

Darmaji, Alfarisi, Ridho

2017-08-01

For a vertex v of a connected graph G(V, E) with vertex set V(G), edge set E(G) and S ⊆ V(G). Given an ordered partition Π = {S1, S2, S3, …, Sk} of the vertex set V of G, the representation of a vertex v ∈ V with respect to Π is the vector r(v|Π) = (d(v, S1), d(v, S2), …, d(v, Sk)), where d(v, Sk) represents the distance between the vertex v and the set Sk and d(v, Sk) = min{d(v, x)|x ∈ Sk}. A partition Π of V(G) is a resolving partition if different vertices of G have distinct representations, i.e., for every pair of vertices u, v ∈ V(G), r(u|Π) ≠ r(v|Π). The minimum k of Π resolving partition is a partition dimension of G, denoted by pd(G). Finding the partition dimension of G is classified to be a NP-Hard problem. In this paper, we will show that the partition dimension of comb product of path and complete graph. The results show that comb product of complete grapph Km and path Pn namely p d (Km⊳Pn)=m where m ≥ 3 and n ≥ 2 and p d (Pn⊳Km)=m where m ≥ 3, n ≥ 2 and m ≥ n.

Functional grouping of similar genes using eigenanalysis on minimum spanning tree based neighborhood graph.

PubMed

Jothi, R; Mohanty, Sraban Kumar; Ojha, Aparajita

2016-04-01

Gene expression data clustering is an important biological process in DNA microarray analysis. Although there have been many clustering algorithms for gene expression analysis, finding a suitable and effective clustering algorithm is always a challenging problem due to the heterogeneous nature of gene profiles. Minimum Spanning Tree (MST) based clustering algorithms have been successfully employed to detect clusters of varying shapes and sizes. This paper proposes a novel clustering algorithm using Eigenanalysis on Minimum Spanning Tree based neighborhood graph (E-MST). As MST of a set of points reflects the similarity of the points with their neighborhood, the proposed algorithm employs a similarity graph obtained from k(') rounds of MST (k(')-MST neighborhood graph). By studying the spectral properties of the similarity matrix obtained from k(')-MST graph, the proposed algorithm achieves improved clustering results. We demonstrate the efficacy of the proposed algorithm on 12 gene expression datasets. Experimental results show that the proposed algorithm performs better than the standard clustering algorithms. Copyright © 2016 Elsevier Ltd. All rights reserved.

Spectral Upscaling for Graph Laplacian Problems with Application to Reservoir Simulation

DOE PAGES

Barker, Andrew T.; Lee, Chak S.; Vassilevski, Panayot S.

2017-10-26

Here, we consider coarsening procedures for graph Laplacian problems written in a mixed saddle-point form. In that form, in addition to the original (vertex) degrees of freedom (dofs), we also have edge degrees of freedom. We extend previously developed aggregation-based coarsening procedures applied to both sets of dofs to now allow more than one coarse vertex dof per aggregate. Those dofs are selected as certain eigenvectors of local graph Laplacians associated with each aggregate. Additionally, we coarsen the edge dofs by using traces of the discrete gradients of the already constructed coarse vertex dofs. These traces are defined on themore » interface edges that connect any two adjacent aggregates. The overall procedure is a modification of the spectral upscaling procedure developed in for the mixed finite element discretization of diffusion type PDEs which has the important property of maintaining inf-sup stability on coarse levels and having provable approximation properties. We consider applications to partitioning a general graph and to a finite volume discretization interpreted as a graph Laplacian, developing consistent and accurate coarse-scale models of a fine-scale problem.« less

Parameterized Complexity Results for General Factors in Bipartite Graphs with an Application to Constraint Programming

NASA Astrophysics Data System (ADS)

Gutin, Gregory; Kim, Eun Jung; Soleimanfallah, Arezou; Szeider, Stefan; Yeo, Anders

The NP-hard general factor problem asks, given a graph and for each vertex a list of integers, whether the graph has a spanning subgraph where each vertex has a degree that belongs to its assigned list. The problem remains NP-hard even if the given graph is bipartite with partition U ⊎ V, and each vertex in U is assigned the list {1}; this subproblem appears in the context of constraint programming as the consistency problem for the extended global cardinality constraint. We show that this subproblem is fixed-parameter tractable when parameterized by the size of the second partite set V. More generally, we show that the general factor problem for bipartite graphs, parameterized by |V |, is fixed-parameter tractable as long as all vertices in U are assigned lists of length 1, but becomes W[1]-hard if vertices in U are assigned lists of length at most 2. We establish fixed-parameter tractability by reducing the problem instance to a bounded number of acyclic instances, each of which can be solved in polynomial time by dynamic programming.

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).

Topological structure and mechanics of glassy polymer networks.

PubMed

Elder, Robert M; Sirk, Timothy W

2017-11-22

The influence of chain-level network architecture (i.e., topology) on mechanics was explored for unentangled polymer networks using a blend of coarse-grained molecular simulations and graph-theoretic concepts. A simple extension of the Watts-Strogatz model is proposed to control the graph properties of the network such that the corresponding physical properties can be studied with simulations. The architecture of polymer networks assembled with a dynamic curing approach were compared with the extended Watts-Strogatz model, and found to agree surprisingly well. The final cured structures of the dynamically-assembled networks were nearly an intermediate between lattice and random connections due to restrictions imposed by the finite length of the chains. Further, the uni-axial stress response, character of the bond breaking, and non-affine displacements of fully-cured glassy networks were analyzed as a function of the degree of disorder in the network architecture. It is shown that the architecture strongly affects the network stability, flow stress, onset of bond breaking, and ultimate stress while leaving the modulus and yield point nearly unchanged. The results show that internal restrictions imposed by the network architecture alter the chain-level response through changes to the crosslink dynamics in the flow regime and through the degree of coordinated chain failure at the ultimate stress. The properties considered here are shown to be sensitive to even incremental changes to the architecture and, therefore, the overall network architecture, beyond simple defects, is predicted to be a meaningful physical parameter in the mechanics of glassy polymer networks.

Particle filter based hybrid prognostics for health monitoring of uncertain systems in bond graph framework

NASA Astrophysics Data System (ADS)

Jha, Mayank Shekhar; Dauphin-Tanguy, G.; Ould-Bouamama, B.

2016-06-01

The paper's main objective is to address the problem of health monitoring of system parameters in Bond Graph (BG) modeling framework, by exploiting its structural and causal properties. The system in feedback control loop is considered uncertain globally. Parametric uncertainty is modeled in interval form. The system parameter is undergoing degradation (prognostic candidate) and its degradation model is assumed to be known a priori. The detection of degradation commencement is done in a passive manner which involves interval valued robust adaptive thresholds over the nominal part of the uncertain BG-derived interval valued analytical redundancy relations (I-ARRs). The latter forms an efficient diagnostic module. The prognostics problem is cast as joint state-parameter estimation problem, a hybrid prognostic approach, wherein the fault model is constructed by considering the statistical degradation model of the system parameter (prognostic candidate). The observation equation is constructed from nominal part of the I-ARR. Using particle filter (PF) algorithms; the estimation of state of health (state of prognostic candidate) and associated hidden time-varying degradation progression parameters is achieved in probabilistic terms. A simplified variance adaptation scheme is proposed. Associated uncertainties which arise out of noisy measurements, parametric degradation process, environmental conditions etc. are effectively managed by PF. This allows the production of effective predictions of the remaining useful life of the prognostic candidate with suitable confidence bounds. The effectiveness of the novel methodology is demonstrated through simulations and experiments on a mechatronic system.

Decentralized Control of Scheduling in Distributed Systems.

DTIC Science & Technology

1983-03-18

the job scheduling algorithm adapts to the changing busyness of the various hosts in the system. The environment in which the job scheduling entities...resources and processes that constitute the node and a set of interfaces for accessing these processes and resources. The structure of a node could change ...parallel. Chang [CHNG82] has also described some algorithms for detecting properties of general graphs by traversing paths in a graph in parallel. One of

Supersonic aerodynamics of delta wings

NASA Technical Reports Server (NTRS)

Wood, Richard M.

1988-01-01

Through the empirical correlation of experimental data and theoretical analysis, a set of graphs has been developed which summarize the inviscid aerodynamics of delta wings at supersonic speeds. The various graphs which detail the aerodynamic performance of delta wings at both zero-lift and lifting conditions were then employed to define a preliminary wing design approach in which both the low-lift and high-lift design criteria were combined to define a feasible design space.

Combinatorial Statistics on Trees and Networks

DTIC Science & Technology

2010-09-29

interaction graph is drawn from the Erdos- Renyi , G(n,p), where each edge is present independently with probability p. For this model we establish a double...special interest is the behavior of Gibbs sampling on the Erdos- Renyi random graph G{n, d/n), where each edge is chosen independently with...which have no counterparts in the coloring setting. Our proof presented here exploits in novel ways the local treelike structure of Erdos- Renyi

miniTri Mantevo miniapp v. 1.0

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

Berry, Johathan; Stark, Dylan; Wolf, Michael

2016-02-02

miniTri is a miniapplication developed as part of the Mantevo project. Given a graph, miniTri enumerates all triangles in this graph and computes a metric for each triangle based on the triangle edge and vertex degree. The output of miniTri is a summary of this metric. miniTri mimics the computational requirements of an important set of data science applications. Several approaches to this problem are included in the miniTri software.

Graphs and matroids weighted in a bounded incline algebra.

PubMed

Lu, Ling-Xia; Zhang, Bei

2014-01-01

Firstly, for a graph weighted in a bounded incline algebra (or called a dioid), a longest path problem (LPP, for short) is presented, which can be considered the uniform approach to the famous shortest path problem, the widest path problem, and the most reliable path problem. The solutions for LPP and related algorithms are given. Secondly, for a matroid weighted in a linear matroid, the maximum independent set problem is studied.

Spacecraft Constrained Maneuver Planning Using Positively Invariant Constraint Admissible Sets (Postprint)

DTIC Science & Technology

2013-08-14

Connectivity Graph; Graph Search; Bounded Disturbances; Linear Time-Varying (LTV); Clohessy - Wiltshire -Hill (CWH) 16. SECURITY CLASSIFICATION OF: 17...the linearization of the relative motion model given by the Hill- Clohessy - Wiltshire (CWH) equations is used [14]. A. Nonlinear equations of motion...equations can be used to describe the motion of the debris. B. Linearized HCW equations in discrete-time For δr << R, the linearized Hill- Clohessy

The Area of a Surface Generated by Revolving a Graph about Any Line

ERIC Educational Resources Information Center

Goins, Edray Herber; Washington, Talitha M.

2013-01-01

We discuss a general formula for the area of the surface that is generated by a graph [t[subscript 0], t[subscript 1] [right arrow] [the set of real numbers][superscript 2] sending t [maps to] (x(t), y(t)) revolved around a general line L : Ax + By = C. As a corollary, we obtain a formula for the area of the surface formed by revolving y = f(x)…

Entity Resolution Workflow Installation Process and User Guide

DTIC Science & Technology

2013-07-01

Program Files\\PostgreSQL\\9.1\\data superuser ( postgres ), service account ( postgres ) password : "password" Port #: 5432 Add an environment variable...in this report. • Run the script found in <GG_HOME>\\ globalgraph-dist-1.4.6-final\\schema- ddl\\postgresSetup.bat. This script will set up Postgres ...Username: postgres DB Admin PWD: password GlobalGraph App User: gguser GlobalGraph App PWD: password • Restart the Postgres service using the Windows

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.

A graph-based system for network-vulnerability analysis

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

Swiler, L.P.; Phillips, C.

1998-06-01

This paper presents a graph-based approach to network vulnerability analysis. The method is flexible, allowing analysis of attacks from both outside and inside the network. It can analyze risks to a specific network asset, or examine the universe of possible consequences following a successful attack. The graph-based tool can identify the set of attack paths that have a high probability of success (or a low effort cost) for the attacker. The system could be used to test the effectiveness of making configuration changes, implementing an intrusion detection system, etc. The analysis system requires as input a database of common attacks,more » broken into atomic steps, specific network configuration and topology information, and an attacker profile. The attack information is matched with the network configuration information and an attacker profile to create a superset attack graph. Nodes identify a stage of attack, for example the class of machines the attacker has accessed and the user privilege level he or she has compromised. The arcs in the attack graph represent attacks or stages of attacks. By assigning probabilities of success on the arcs or costs representing level-of-effort for the attacker, various graph algorithms such as shortest-path algorithms can identify the attack paths with the highest probability of success.« less

Left-ventricle segmentation in real-time 3D echocardiography using a hybrid active shape model and optimal graph search approach

NASA Astrophysics Data System (ADS)

Zhang, Honghai; Abiose, Ademola K.; Campbell, Dwayne N.; Sonka, Milan; Martins, James B.; Wahle, Andreas

2010-03-01

Quantitative analysis of the left ventricular shape and motion patterns associated with left ventricular mechanical dyssynchrony (LVMD) is essential for diagnosis and treatment planning in congestive heart failure. Real-time 3D echocardiography (RT3DE) used for LVMD analysis is frequently limited by heavy speckle noise or partially incomplete data, thus a segmentation method utilizing learned global shape knowledge is beneficial. In this study, the endocardial surface of the left ventricle (LV) is segmented using a hybrid approach combining active shape model (ASM) with optimal graph search. The latter is used to achieve landmark refinement in the ASM framework. Optimal graph search translates the 3D segmentation into the detection of a minimum-cost closed set in a graph and can produce a globally optimal result. Various information-gradient, intensity distributions, and regional-property terms-are used to define the costs for the graph search. The developed method was tested on 44 RT3DE datasets acquired from 26 LVMD patients. The segmentation accuracy was assessed by surface positioning error and volume overlap measured for the whole LV as well as 16 standard LV regions. The segmentation produced very good results that were not achievable using ASM or graph search alone.

Visualization of Morse connection graphs for topologically rich 2D vector fields.

PubMed

Szymczak, Andrzej; Sipeki, Levente

2013-12-01

Recent advances in vector field topologymake it possible to compute its multi-scale graph representations for autonomous 2D vector fields in a robust and efficient manner. One of these representations is a Morse Connection Graph (MCG), a directed graph whose nodes correspond to Morse sets, generalizing stationary points and periodic trajectories, and arcs - to trajectories connecting them. While being useful for simple vector fields, the MCG can be hard to comprehend for topologically rich vector fields, containing a large number of features. This paper describes a visual representation of the MCG, inspired by previous work on graph visualization. Our approach aims to preserve the spatial relationships between the MCG arcs and nodes and highlight the coherent behavior of connecting trajectories. Using simulations of ocean flow, we show that it can provide useful information on the flow structure. This paper focuses specifically on MCGs computed for piecewise constant (PC) vector fields. In particular, we describe extensions of the PC framework that make it more flexible and better suited for analysis of data on complex shaped domains with a boundary. We also describe a topology simplification scheme that makes our MCG visualizations less ambiguous. Despite the focus on the PC framework, our approach could also be applied to graph representations or topological skeletons computed using different methods.

High-Performance Data Analytics Beyond the Relational and Graph Data Models with GEMS

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

Castellana, Vito G.; Minutoli, Marco; Bhatt, Shreyansh

Graphs represent an increasingly popular data model for data-analytics, since they can naturally represent relationships and interactions between entities. Relational databases and their pure table-based data model are not well suitable to store and process sparse data. Consequently, graph databases have gained interest in the last few years and the Resource Description Framework (RDF) became the standard data model for graph data. Nevertheless, while RDF is well suited to analyze the relationships between the entities, it is not efficient in representing their attributes and properties. In this work we propose the adoption of a new hybrid data model, based onmore » attributed graphs, that aims at overcoming the limitations of the pure relational and graph data models. We present how we have re-designed the GEMS data-analytics framework to fully take advantage of the proposed hybrid data model. To improve analysts productivity, in addition to a C++ API for applications development, we adopt GraQL as input query language. We validate our approach implementing a set of queries on net-flow data and we compare our framework performance against Neo4j. Experimental results show significant performance improvement over Neo4j, up to several orders of magnitude when increasing the size of the input data.« less

Orders on Intervals Over Partially Ordered Sets: Extending Allen's Algebra and Interval Graph Results

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

Zapata, Francisco; Kreinovich, Vladik; Joslyn, Cliff A.

2013-08-01

To make a decision, we need to compare the values of quantities. In many practical situations, we know the values with interval uncertainty. In such situations, we need to compare intervals. Allen’s algebra describes all possible relations between intervals on the real line, and ordering relations between such intervals are well studied. In this paper, we extend this description to intervals in an arbitrary partially ordered set (poset). In particular, we explicitly describe ordering relations between intervals that generalize relation between points. As auxiliary results, we provide a logical interpretation of the relation between intervals, and extend the results aboutmore » interval graphs to intervals over posets.« less

Local Table Condensation in Rough Set Approach for Jumping Emerging Pattern Induction

NASA Astrophysics Data System (ADS)

Terlecki, Pawel; Walczak, Krzysztof

This paper extends the rough set approach for JEP induction based on the notion of a condensed decision table. The original transaction database is transformed to a relational form and patterns are induced by means of local reducts. The transformation employs an item aggregation obtained by coloring a graph that re0ects con0icts among items. For e±ciency reasons we propose to perform this preprocessing locally, i.e. at the transaction level, to achieve a higher dimensionality gain. Special maintenance strategy is also used to avoid graph rebuilds. Both global and local approach have been tested and discussed for dense and synthetically generated sparse datasets.

Hierarchical lattice models of hydrogen-bond networks in water

NASA Astrophysics Data System (ADS)

Dandekar, Rahul; Hassanali, Ali A.

2018-06-01

We develop a graph-based model of the hydrogen-bond network in water, with a view toward quantitatively modeling the molecular-level correlational structure of the network. The networks formed are studied by the constructing the model on two infinite-dimensional lattices. Our models are built bottom up, based on microscopic information coming from atomistic simulations, and we show that the predictions of the model are consistent with known results from ab initio simulations of liquid water. We show that simple entropic models can predict the correlations and clustering of local-coordination defects around tetrahedral waters observed in the atomistic simulations. We also find that orientational correlations between bonds are longer ranged than density correlations, determine the directional correlations within closed loops, and show that the patterns of water wires within these structures are also consistent with previous atomistic simulations. Our models show the existence of density and compressibility anomalies, as seen in the real liquid, and the phase diagram of these models is consistent with the singularity-free scenario previously proposed by Sastry and coworkers [Phys. Rev. E 53, 6144 (1996), 10.1103/PhysRevE.53.6144].

Delivery Path Length and Holding Tree Minimization Method of Securities Delivery among the Registration Agencies Connected as Non-Tree

NASA Astrophysics Data System (ADS)

Shimamura, Atsushi; Moritsu, Toshiyuki; Someya, Harushi

To dematerialize the securities such as stocks or cooporate bonds, the securities were registered to account in the registration agencies which were connected as tree. This tree structure had the advantage in the management of the securities those were issued large amount and number of brands of securities were limited. But when the securities such as account receivables or advance notes are dematerialized, number of brands of the securities increases extremely. In this case, the management of securities with tree structure becomes very difficult because of the concentration of information to root of the tree. To resolve this problem, using the graph structure is assumed instead of the tree structure. When the securities are kept with tree structure, the delivery path of securities is unique, but when securities are kept with graph structure, path of delivery is not unique. In this report, we describe the requirement of the delivery path of securities, and we describe selecting method of the path.

Classification of ligand molecules in PDB with fast heuristic graph match algorithm COMPLIG.

PubMed

Saito, Mihoko; Takemura, Naomi; Shirai, Tsuyoshi

2012-12-14

A fast heuristic graph-matching algorithm, COMPLIG, was devised to classify the small-molecule ligands in the Protein Data Bank (PDB), which are currently not properly classified on structure basis. By concurrently classifying proteins and ligands, we determined the most appropriate parameter for categorizing ligands to be more than 60% identity of atoms and bonds between molecules, and we classified 11,585 types of ligands into 1946 clusters. Although the large clusters were composed of nucleotides or amino acids, a significant presence of drug compounds was also observed. Application of the system to classify the natural ligand status of human proteins in the current database suggested that, at most, 37% of the experimental structures of human proteins were in complex with natural ligands. However, protein homology- and/or ligand similarity-based modeling was implied to provide models of natural interactions for an additional 28% of the total, which might be used to increase the knowledge of intrinsic protein-metabolite interactions. Copyright © 2012 Elsevier Ltd. All rights reserved.

Signalling Network Construction for Modelling Plant Defence Response

PubMed Central

Miljkovic, Dragana; Stare, Tjaša; Mozetič, Igor; Podpečan, Vid; Petek, Marko; Witek, Kamil; Dermastia, Marina; Lavrač, Nada; Gruden, Kristina

2012-01-01

Plant defence signalling response against various pathogens, including viruses, is a complex phenomenon. In resistant interaction a plant cell perceives the pathogen signal, transduces it within the cell and performs a reprogramming of the cell metabolism leading to the pathogen replication arrest. This work focuses on signalling pathways crucial for the plant defence response, i.e., the salicylic acid, jasmonic acid and ethylene signal transduction pathways, in the Arabidopsis thaliana model plant. The initial signalling network topology was constructed manually by defining the representation formalism, encoding the information from public databases and literature, and composing a pathway diagram. The manually constructed network structure consists of 175 components and 387 reactions. In order to complement the network topology with possibly missing relations, a new approach to automated information extraction from biological literature was developed. This approach, named Bio3graph, allows for automated extraction of biological relations from the literature, resulting in a set of (component1, reaction, component2) triplets and composing a graph structure which can be visualised, compared to the manually constructed topology and examined by the experts. Using a plant defence response vocabulary of components and reaction types, Bio3graph was applied to a set of 9,586 relevant full text articles, resulting in 137 newly detected reactions between the components. Finally, the manually constructed topology and the new reactions were merged to form a network structure consisting of 175 components and 524 reactions. The resulting pathway diagram of plant defence signalling represents a valuable source for further computational modelling and interpretation of omics data. The developed Bio3graph approach, implemented as an executable language processing and graph visualisation workflow, is publically available at http://ropot.ijs.si/bio3graph/and can be utilised for modelling other biological systems, given that an adequate vocabulary is provided. PMID:23272172

Adaptive Signal Recovery on Graphs via Harmonic Analysis for Experimental Design in Neuroimaging.

PubMed

Kim, Won Hwa; Hwang, Seong Jae; Adluru, Nagesh; Johnson, Sterling C; Singh, Vikas

2016-10-01

Consider an experimental design of a neuroimaging study, where we need to obtain p measurements for each participant in a setting where p ' (< p ) are cheaper and easier to acquire while the remaining ( p - p ') are expensive. For example, the p ' measurements may include demographics, cognitive scores or routinely offered imaging scans while the ( p - p ') measurements may correspond to more expensive types of brain image scans with a higher participant burden. In this scenario, it seems reasonable to seek an "adaptive" design for data acquisition so as to minimize the cost of the study without compromising statistical power. We show how this problem can be solved via harmonic analysis of a band-limited graph whose vertices correspond to participants and our goal is to fully recover a multi-variate signal on the nodes, given the full set of cheaper features and a partial set of more expensive measurements. This is accomplished using an adaptive query strategy derived from probing the properties of the graph in the frequency space. To demonstrate the benefits that this framework can provide, we present experimental evaluations on two independent neuroimaging studies and show that our proposed method can reliably recover the true signal with only partial observations directly yielding substantial financial savings.

Unsupervised Metric Fusion Over Multiview Data by Graph Random Walk-Based Cross-View Diffusion.

PubMed

Wang, Yang; Zhang, Wenjie; Wu, Lin; Lin, Xuemin; Zhao, Xiang

2017-01-01

Learning an ideal metric is crucial to many tasks in computer vision. Diverse feature representations may combat this problem from different aspects; as visual data objects described by multiple features can be decomposed into multiple views, thus often provide complementary information. In this paper, we propose a cross-view fusion algorithm that leads to a similarity metric for multiview data by systematically fusing multiple similarity measures. Unlike existing paradigms, we focus on learning distance measure by exploiting a graph structure of data samples, where an input similarity matrix can be improved through a propagation of graph random walk. In particular, we construct multiple graphs with each one corresponding to an individual view, and a cross-view fusion approach based on graph random walk is presented to derive an optimal distance measure by fusing multiple metrics. Our method is scalable to a large amount of data by enforcing sparsity through an anchor graph representation. To adaptively control the effects of different views, we dynamically learn view-specific coefficients, which are leveraged into graph random walk to balance multiviews. However, such a strategy may lead to an over-smooth similarity metric where affinities between dissimilar samples may be enlarged by excessively conducting cross-view fusion. Thus, we figure out a heuristic approach to controlling the iteration number in the fusion process in order to avoid over smoothness. Extensive experiments conducted on real-world data sets validate the effectiveness and efficiency of our approach.

Graph theory and the Virasoro master equation

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

Obers, N.A.J.

1991-04-01

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

Informative graphing of continuous safety variables relative to normal reference limits.

PubMed

Breder, Christopher D

2018-05-16

Interpreting graphs of continuous safety variables can be complicated because differences in age, gender, and testing site methodologies data may give rise to multiple reference limits. Furthermore, data below the lower limit of normal are compressed relative to those points above the upper limit of normal. The objective of this study is to develop a graphing technique that addresses these issues and is visually intuitive. A mock dataset with multiple reference ranges is initially used to develop the graphing technique. Formulas are developed for conditions where data are above the upper limit of normal, normal, below the lower limit of normal, and below the lower limit of normal when the data value equals zero. After the formulae are developed, an anonymized dataset from an actual set of trials for an approved drug is evaluated comparing the technique developed in this study to standard graphical methods. Formulas are derived for the novel graphing method based on multiples of the normal limits. The formula for values scaled between the upper and lower limits of normal is a novel application of a readily available scaling formula. The formula for the lower limit of normal is novel and addresses the issue of this value potentially being indeterminate when the result to be scaled as a multiple is zero. The formulae and graphing method described in this study provides a visually intuitive method to graph continuous safety data including laboratory values, vital sign data.

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.

Northwest Laboratory for Integrated Systems, University of Washington, Semiannual Technical Report Number 1, July 1-November 8, 1991

DTIC Science & Technology

1991-11-08

only simple bounds on delays but also relate the delays in linear inequalities so that tradeoffs are apparent. We model circuits as communicating...set of linear inequalities constraining the variables. These relations provide synthesis tools with information about tradeoffs between circuit delays...available to express the original circuit as a graph of elementary gates and then cover the graph’s fanout-free trees with collections of three-input

Graph Theory Meets Ab Initio Molecular Dynamics: Atomic Structures and Transformations at the Nanoscale

NASA Astrophysics Data System (ADS)

Pietrucci, Fabio; Andreoni, Wanda

2011-08-01

Social permutation invariant coordinates are introduced describing the bond network around a given atom. They originate from the largest eigenvalue and the corresponding eigenvector of the contact matrix, are invariant under permutation of identical atoms, and bear a clear signature of an order-disorder transition. Once combined with ab initio metadynamics, these coordinates are shown to be a powerful tool for the discovery of low-energy isomers of molecules and nanoclusters as well as for a blind exploration of isomerization, association, and dissociation reactions.

Vectorization of optically sectioned brain microvasculature: learning aids completion of vascular graphs by connecting gaps and deleting open-ended segments.

PubMed

Kaufhold, John P; Tsai, Philbert S; Blinder, Pablo; Kleinfeld, David

2012-08-01

A graph of tissue vasculature is an essential requirement to model the exchange of gasses and nutriments between the blood and cells in the brain. Such a graph is derived from a vectorized representation of anatomical data, provides a map of all vessels as vertices and segments, and may include the location of nonvascular components, such as neuronal and glial somata. Yet vectorized data sets typically contain erroneous gaps, spurious endpoints, and spuriously merged strands. Current methods to correct such defects only address the issue of connecting gaps and further require manual tuning of parameters in a high dimensional algorithm. To address these shortcomings, we introduce a supervised machine learning method that (1) connects vessel gaps by "learned threshold relaxation"; (2) removes spurious segments by "learning to eliminate deletion candidate strands"; and (3) enforces consistency in the joint space of learned vascular graph corrections through "consistency learning." Human operators are only required to label individual objects they recognize in a training set and are not burdened with tuning parameters. The supervised learning procedure examines the geometry and topology of features in the neighborhood of each vessel segment under consideration. We demonstrate the effectiveness of these methods on four sets of microvascular data, each with >800(3) voxels, obtained with all optical histology of mouse tissue and vectorization by state-of-the-art techniques in image segmentation. Through statistically validated sampling and analysis in terms of precision recall curves, we find that learning with bagged boosted decision trees reduces equal-error error rates for threshold relaxation by 5-21% and strand elimination performance by 18-57%. We benchmark generalization performance across datasets; while improvements vary between data sets, learning always leads to a useful reduction in error rates. Overall, learning is shown to more than halve the total error rate, and therefore, human time spent manually correcting such vectorizations. Copyright © 2012 Elsevier B.V. All rights reserved.

Vectorization of optically sectioned brain microvasculature: Learning aids completion of vascular graphs by connecting gaps and deleting open-ended segments

PubMed Central

Kaufhold, John P.; Tsai, Philbert S.; Blinder, Pablo; Kleinfeld, David

2012-01-01

A graph of tissue vasculature is an essential requirement to model the exchange of gasses and nutriments between the blood and cells in the brain. Such a graph is derived from a vectorized representation of anatomical data, provides a map of all vessels as vertices and segments, and may include the location of nonvascular components, such as neuronal and glial somata. Yet vectorized data sets typically contain erroneous gaps, spurious endpoints, and spuriously merged strands. Current methods to correct such defects only address the issue of connecting gaps and further require manual tuning of parameters in a high dimensional algorithm. To address these shortcomings, we introduce a supervised machine learning method that (1) connects vessel gaps by “learned threshold relaxation”; (2) removes spurious segments by “learning to eliminate deletion candidate strands”; and (3) enforces consistency in the joint space of learned vascular graph corrections through “consistency learning.” Human operators are only required to label individual objects they recognize in a training set and are not burdened with tuning parameters. The supervised learning procedure examines the geometry and topology of features in the neighborhood of each vessel segment under consideration. We demonstrate the effectiveness of these methods on four sets of microvascular data, each with > 8003 voxels, obtained with all optical histology of mouse tissue and vectorization by state-of-the-art techniques in image segmentation. Through statistically validated sampling and analysis in terms of precision recall curves, we find that learning with bagged boosted decision trees reduces equal-error error rates for threshold relaxation by 5 to 21 % and strand elimination performance by 18 to 57 %. We benchmark generalization performance across datasets; while improvements vary between data sets, learning always leads to a useful reduction in error rates. Overall, learning is shown to more than halve the total error rate, and therefore, human time spent manually correcting such vectorizations. PMID:22854035

Heuristic-driven graph wavelet modeling of complex terrain

NASA Astrophysics Data System (ADS)

Cioacǎ, Teodor; Dumitrescu, Bogdan; Stupariu, Mihai-Sorin; Pǎtru-Stupariu, Ileana; Nǎpǎrus, Magdalena; Stoicescu, Ioana; Peringer, Alexander; Buttler, Alexandre; Golay, François

2015-03-01

We present a novel method for building a multi-resolution representation of large digital surface models. The surface points coincide with the nodes of a planar graph which can be processed using a critically sampled, invertible lifting scheme. To drive the lazy wavelet node partitioning, we employ an attribute aware cost function based on the generalized quadric error metric. The resulting algorithm can be applied to multivariate data by storing additional attributes at the graph's nodes. We discuss how the cost computation mechanism can be coupled with the lifting scheme and examine the results by evaluating the root mean square error. The algorithm is experimentally tested using two multivariate LiDAR sets representing terrain surface and vegetation structure with different sampling densities.

Kernel approach to molecular similarity based on iterative graph similarity.

PubMed

Rupp, Matthias; Proschak, Ewgenij; Schneider, Gisbert

2007-01-01

Similarity measures for molecules are of basic importance in chemical, biological, and pharmaceutical applications. We introduce a molecular similarity measure defined directly on the annotated molecular graph, based on iterative graph similarity and optimal assignments. We give an iterative algorithm for the computation of the proposed molecular similarity measure, prove its convergence and the uniqueness of the solution, and provide an upper bound on the required number of iterations necessary to achieve a desired precision. Empirical evidence for the positive semidefiniteness of certain parametrizations of our function is presented. We evaluated our molecular similarity measure by using it as a kernel in support vector machine classification and regression applied to several pharmaceutical and toxicological data sets, with encouraging results.

Parasol: An Architecture for Cross-Cloud Federated Graph Querying

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

Lieberman, Michael; Choudhury, Sutanay; Hughes, Marisa

2014-06-22

Large scale data fusion of multiple datasets can often provide in- sights that examining datasets individually cannot. However, when these datasets reside in different data centers and cannot be collocated due to technical, administrative, or policy barriers, a unique set of problems arise that hamper querying and data fusion. To ad- dress these problems, a system and architecture named Parasol is presented that enables federated queries over graph databases residing in multiple clouds. Parasol’s design is flexible and requires only minimal assumptions for participant clouds. Query optimization techniques are also described that are compatible with Parasol’s lightweight architecture. Experiments onmore » a prototype implementation of Parasol indicate its suitability for cross-cloud federated graph queries.« less

Graph-theoretic approach to quantum correlations.

PubMed

Cabello, Adán; Severini, Simone; Winter, Andreas

2014-01-31

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

US GeoData Available Through the Internet

USGS Publications Warehouse

,

2000-01-01

The U.S. Geological Survey (USGS) offers certain US GeoData data sets through the Internet. They can be retrieved using the World Wide Web or anonymous File Transfer Protocol (FTP). The data bases and their directory paths are as follows: * 1:24,000-scale digital line graph data in SDTS format (/pub/data/DLG/24K) * 1:2,000,000-scale digital line graph data in SDTS format (/pub/data/DLG/2M) * 1:100,000-scale digital line graph data (/pub/data/DLG/100K) * 1:100,000-scale land use and land cover data (/pub/data/LULC/100K) * 1:250,000-scale land use and land cover data (/pub/data/LULC/250K) * 1-degree digital elevation model data (/pub/data/DEM/250)

Existence of infinitely many stationary solutions of the L2-subcritical and critical NLSE on compact metric graphs

NASA Astrophysics Data System (ADS)

Dovetta, Simone

2018-04-01

We investigate the existence of stationary solutions for the nonlinear Schrödinger equation on compact metric graphs. In the L2-subcritical setting, we prove the existence of an infinite number of such solutions, for every value of the mass. In the critical regime, the existence of infinitely many solutions is established if the mass is lower than a threshold value, while global minimizers of the NLS energy exist if and only if the mass is lower or equal to the threshold. Moreover, the relation between this threshold and the topology of the graph is characterized. The investigation is based on variational techniques and some new versions of Gagliardo-Nirenberg inequalities.

Exactly solvable random graph ensemble with extensively many short cycles

NASA Astrophysics Data System (ADS)

Aguirre López, Fabián; Barucca, Paolo; Fekom, Mathilde; Coolen, Anthony C. C.

2018-02-01

We introduce and analyse ensembles of 2-regular random graphs with a tuneable distribution of short cycles. The phenomenology of these graphs depends critically on the scaling of the ensembles’ control parameters relative to the number of nodes. A phase diagram is presented, showing a second order phase transition from a connected to a disconnected phase. We study both the canonical formulation, where the size is large but fixed, and the grand canonical formulation, where the size is sampled from a discrete distribution, and show their equivalence in the thermodynamical limit. We also compute analytically the spectral density, which consists of a discrete set of isolated eigenvalues, representing short cycles, and a continuous part, representing cycles of diverging size.

A Combined Approach to Cartographic Displacement for Buildings Based on Skeleton and Improved Elastic Beam Algorithm

PubMed Central

Liu, Yuangang; Guo, Qingsheng; Sun, Yageng; Ma, Xiaoya

2014-01-01

Scale reduction from source to target maps inevitably leads to conflicts of map symbols in cartography and geographic information systems (GIS). Displacement is one of the most important map generalization operators and it can be used to resolve the problems that arise from conflict among two or more map objects. In this paper, we propose a combined approach based on constraint Delaunay triangulation (CDT) skeleton and improved elastic beam algorithm for automated building displacement. In this approach, map data sets are first partitioned. Then the displacement operation is conducted in each partition as a cyclic and iterative process of conflict detection and resolution. In the iteration, the skeleton of the gap spaces is extracted using CDT. It then serves as an enhanced data model to detect conflicts and construct the proximity graph. Then, the proximity graph is adjusted using local grouping information. Under the action of forces derived from the detected conflicts, the proximity graph is deformed using the improved elastic beam algorithm. In this way, buildings are displaced to find an optimal compromise between related cartographic constraints. To validate this approach, two topographic map data sets (i.e., urban and suburban areas) were tested. The results were reasonable with respect to each constraint when the density of the map was not extremely high. In summary, the improvements include (1) an automated parameter-setting method for elastic beams, (2) explicit enforcement regarding the positional accuracy constraint, added by introducing drag forces, (3) preservation of local building groups through displacement over an adjusted proximity graph, and (4) an iterative strategy that is more likely to resolve the proximity conflicts than the one used in the existing elastic beam algorithm. PMID:25470727

Automatic segmentation of colon glands using object-graphs.

PubMed

Gunduz-Demir, Cigdem; Kandemir, Melih; Tosun, Akif Burak; Sokmensuer, Cenk

2010-02-01

Gland segmentation is an important step to automate the analysis of biopsies that contain glandular structures. However, this remains a challenging problem as the variation in staining, fixation, and sectioning procedures lead to a considerable amount of artifacts and variances in tissue sections, which may result in huge variances in gland appearances. In this work, we report a new approach for gland segmentation. This approach decomposes the tissue image into a set of primitive objects and segments glands making use of the organizational properties of these objects, which are quantified with the definition of object-graphs. As opposed to the previous literature, the proposed approach employs the object-based information for the gland segmentation problem, instead of using the pixel-based information alone. Working with the images of colon tissues, our experiments demonstrate that the proposed object-graph approach yields high segmentation accuracies for the training and test sets and significantly improves the segmentation performance of its pixel-based counterparts. The experiments also show that the object-based structure of the proposed approach provides more tolerance to artifacts and variances in tissues.

Exact sampling of graphs with prescribed degree correlations

NASA Astrophysics Data System (ADS)

Bassler, Kevin E.; Del Genio, Charo I.; Erdős, Péter L.; Miklós, István; Toroczkai, Zoltán

2015-08-01

Many real-world networks exhibit correlations between the node degrees. For instance, in social networks nodes tend to connect to nodes of similar degree and conversely, in biological and technological networks, high-degree nodes tend to be linked with low-degree nodes. Degree correlations also affect the dynamics of processes supported by a network structure, such as the spread of opinions or epidemics. The proper modelling of these systems, i.e., without uncontrolled biases, requires the sampling of networks with a specified set of constraints. We present a solution to the sampling problem when the constraints imposed are the degree correlations. In particular, we develop an exact method to construct and sample graphs with a specified joint-degree matrix, which is a matrix providing the number of edges between all the sets of nodes of a given degree, for all degrees, thus completely specifying all pairwise degree correlations, and additionally, the degree sequence itself. Our algorithm always produces independent samples without backtracking. The complexity of the graph construction algorithm is {O}({NM}) where N is the number of nodes and M is the number of edges.

Using a high-dimensional graph of semantic space to model relationships among words

PubMed Central

Jackson, Alice F.; Bolger, Donald J.

2014-01-01

The GOLD model (Graph Of Language Distribution) is a network model constructed based on co-occurrence in a large corpus of natural language that may be used to explore what information may be present in a graph-structured model of language, and what information may be extracted through theoretically-driven algorithms as well as standard graph analysis methods. The present study will employ GOLD to examine two types of relationship between words: semantic similarity and associative relatedness. Semantic similarity refers to the degree of overlap in meaning between words, while associative relatedness refers to the degree to which two words occur in the same schematic context. It is expected that a graph structured model of language constructed based on co-occurrence should easily capture associative relatedness, because this type of relationship is thought to be present directly in lexical co-occurrence. However, it is hypothesized that semantic similarity may be extracted from the intersection of the set of first-order connections, because two words that are semantically similar may occupy similar thematic or syntactic roles across contexts and thus would co-occur lexically with the same set of nodes. Two versions the GOLD model that differed in terms of the co-occurence window, bigGOLD at the paragraph level and smallGOLD at the adjacent word level, were directly compared to the performance of a well-established distributional model, Latent Semantic Analysis (LSA). The superior performance of the GOLD models (big and small) suggest that a single acquisition and storage mechanism, namely co-occurrence, can account for associative and conceptual relationships between words and is more psychologically plausible than models using singular value decomposition (SVD). PMID:24860525

Using a high-dimensional graph of semantic space to model relationships among words.

PubMed

Jackson, Alice F; Bolger, Donald J

2014-01-01

The GOLD model (Graph Of Language Distribution) is a network model constructed based on co-occurrence in a large corpus of natural language that may be used to explore what information may be present in a graph-structured model of language, and what information may be extracted through theoretically-driven algorithms as well as standard graph analysis methods. The present study will employ GOLD to examine two types of relationship between words: semantic similarity and associative relatedness. Semantic similarity refers to the degree of overlap in meaning between words, while associative relatedness refers to the degree to which two words occur in the same schematic context. It is expected that a graph structured model of language constructed based on co-occurrence should easily capture associative relatedness, because this type of relationship is thought to be present directly in lexical co-occurrence. However, it is hypothesized that semantic similarity may be extracted from the intersection of the set of first-order connections, because two words that are semantically similar may occupy similar thematic or syntactic roles across contexts and thus would co-occur lexically with the same set of nodes. Two versions the GOLD model that differed in terms of the co-occurence window, bigGOLD at the paragraph level and smallGOLD at the adjacent word level, were directly compared to the performance of a well-established distributional model, Latent Semantic Analysis (LSA). The superior performance of the GOLD models (big and small) suggest that a single acquisition and storage mechanism, namely co-occurrence, can account for associative and conceptual relationships between words and is more psychologically plausible than models using singular value decomposition (SVD).

A theoretical and experimental investigation of graph theoretical measures for land development in satellite imagery.

PubMed

Unsalan, Cem; Boyer, Kim L

2005-04-01

Today's commercial satellite images enable experts to classify region types in great detail. In previous work, we considered discriminating rural and urban regions [23]. However, a more detailed classification is required for many purposes. These fine classifications assist government agencies in many ways including urban planning, transportation management, and rescue operations. In a step toward the automation of the fine classification process, this paper explores graph theoretical measures over grayscale images. The graphs are constructed by assigning photometric straight line segments to vertices, while graph edges encode their spatial relationships. We then introduce a set of measures based on various properties of the graph. These measures are nearly monotonic (positively correlated) with increasing structure (organization) in the image. Thus, increased cultural activity and land development are indicated by increases in these measures-without explicit extraction of road networks, buildings, residences, etc. These latter, time consuming (and still only partially automated) tasks can be restricted only to "promising" image regions, according to our measures. In some applications our measures may suffice. We present a theoretical basis for the measures followed by extensive experimental results in which the measures are first compared to manual evaluations of land development. We then present and test a method to focus on, and (pre)extract, suburban-style residential areas. These are of particular importance in many applications, and are especially difficult to extract. In this work, we consider commercial IKONOS data. These images are orthorectified to provide a fixed resolution of 1 meter per pixel on the ground. They are, therefore, metric in the sense that ground distance is fixed in scale to pixel distance. Our data set is large and diverse, including sea and coastline, rural, forest, residential, industrial, and urban areas.

Unusual percolation in simple small-world networks.

PubMed

Cohen, Reuven; Dawid, Daryush Jonathan; Kardar, Mehran; Bar-Yam, Yaneer

2009-06-01

We present an exact solution of percolation in a generalized class of Watts-Strogatz graphs defined on a one-dimensional underlying lattice. We find a nonclassical critical point in the limit of the number of long-range bonds in the system going to zero, with a discontinuity in the percolation probability and a divergence in the mean finite-cluster size. We show that the critical behavior falls into one of three regimes depending on the proportion of occupied long-range to unoccupied nearest-neighbor bonds, with each regime being characterized by different critical exponents. The three regimes can be united by a single scaling function around the critical point. These results can be used to identify the number of long-range links necessary to secure connectivity in a communication or transportation chain. As an example, we can resolve the communication problem in a game of "telephone."

Spectrophotometric determination of 1-(3-dimethylaminopropyl)-3-ethylcarbodiimide hydrochloride by flow injection analysis.

PubMed

Seno, Kunihiko; Matumura, Kazuki; Oshima, Mitsuko; Motomizu, Shoji

2008-04-01

1-(3-dimethylaminopropyl)-3-ethylcarbodiimide hydrochloride (EDC.HCl) is a very useful agent to form amide bonds (peptide bonds) in an aqueous medium. A simple and fast detection system was developed using the reaction with pyridine and ethylenediamine in acidic aqueous solution and spectrophotometric flow injection analysis. The absorbances were measured at 400 nm and the reaction was accelerated at 40 degrees C. The calibration graph showed good linearity from 0 to 10% of EDC.HCl solutions: the regression equation was y=3.15x10(4)x (y, peak area; x, % concentration of EDC.HCl). The RSD was under 1.0%. Sample throughput was 15 h(-1). This method was applied to monitoring the EDC.HCl concentration that remained after the anhydration of phthalic acid in water, esterification of acetic acid in methanol or dehydration condensation of malonic acid and ethylenediamine in water.

Labeled Graph Kernel for Behavior Analysis.

PubMed

Zhao, Ruiqi; Martinez, Aleix M

2016-08-01

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

An efficient and scalable graph modeling approach for capturing information at different levels in next generation sequencing reads

PubMed Central

2013-01-01

Background Next generation sequencing technologies have greatly advanced many research areas of the biomedical sciences through their capability to generate massive amounts of genetic information at unprecedented rates. The advent of next generation sequencing has led to the development of numerous computational tools to analyze and assemble the millions to billions of short sequencing reads produced by these technologies. While these tools filled an important gap, current approaches for storing, processing, and analyzing short read datasets generally have remained simple and lack the complexity needed to efficiently model the produced reads and assemble them correctly. Results Previously, we presented an overlap graph coarsening scheme for modeling read overlap relationships on multiple levels. Most current read assembly and analysis approaches use a single graph or set of clusters to represent the relationships among a read dataset. Instead, we use a series of graphs to represent the reads and their overlap relationships across a spectrum of information granularity. At each information level our algorithm is capable of generating clusters of reads from the reduced graph, forming an integrated graph modeling and clustering approach for read analysis and assembly. Previously we applied our algorithm to simulated and real 454 datasets to assess its ability to efficiently model and cluster next generation sequencing data. In this paper we extend our algorithm to large simulated and real Illumina datasets to demonstrate that our algorithm is practical for both sequencing technologies. Conclusions Our overlap graph theoretic algorithm is able to model next generation sequencing reads at various levels of granularity through the process of graph coarsening. Additionally, our model allows for efficient representation of the read overlap relationships, is scalable for large datasets, and is practical for both Illumina and 454 sequencing technologies. PMID:24564333

Use of Time-Aware Language Model in Entity Driven Filtering System

DTIC Science & Technology

2014-11-01

knowledge graph explo- ration. In the case where no Wikipedia page were found for an entity, the set remains empty; - a set of surface forms found using...Interna- tional Conference on Weblogs and Social Media, Barcelona, Catalonia , Spain, July 17-21, 2011.

A new network representation of the metabolism to detect chemical transformation modules.

PubMed

Sorokina, Maria; Medigue, Claudine; Vallenet, David

2015-11-14

Metabolism is generally modeled by directed networks where nodes represent reactions and/or metabolites. In order to explore metabolic pathway conservation and divergence among organisms, previous studies were based on graph alignment to find similar pathways. Few years ago, the concept of chemical transformation modules, also called reaction modules, was introduced and correspond to sequences of chemical transformations which are conserved in metabolism. We propose here a novel graph representation of the metabolic network where reactions sharing a same chemical transformation type are grouped in Reaction Molecular Signatures (RMS). RMS were automatically computed for all reactions and encode changes in atoms and bonds. A reaction network containing all available metabolic knowledge was then reduced by an aggregation of reaction nodes and edges to obtain a RMS network. Paths in this network were explored and a substantial number of conserved chemical transformation modules was detected. Furthermore, this graph-based formalism allows us to define several path scores reflecting different biological conservation meanings. These scores are significantly higher for paths corresponding to known metabolic pathways and were used conjointly to build association rules that should predict metabolic pathway types like biosynthesis or degradation. This representation of metabolism in a RMS network offers new insights to capture relevant metabolic contexts. Furthermore, along with genomic context methods, it should improve the detection of gene clusters corresponding to new metabolic pathways.

Predictive Models for the Free Energy of Hydrogen Bonded Complexes with Single and Cooperative Hydrogen Bonds.

PubMed

Glavatskikh, Marta; Madzhidov, Timur; Solov'ev, Vitaly; Marcou, Gilles; Horvath, Dragos; Varnek, Alexandre

2016-12-01

In this work, we report QSPR modeling of the free energy ΔG of 1 : 1 hydrogen bond complexes of different H-bond acceptors and donors. The modeling was performed on a large and structurally diverse set of 3373 complexes featuring a single hydrogen bond, for which ΔG was measured at 298 K in CCl 4 . The models were prepared using Support Vector Machine and Multiple Linear Regression, with ISIDA fragment descriptors. The marked atoms strategy was applied at fragmentation stage, in order to capture the location of H-bond donor and acceptor centers. Different strategies of model validation have been suggested, including the targeted omission of individual H-bond acceptors and donors from the training set, in order to check whether the predictive ability of the model is not limited to the interpolation of H-bond strength between two already encountered partners. Successfully cross-validating individual models were combined into a consensus model, and challenged to predict external test sets of 629 and 12 complexes, in which donor and acceptor formed single and cooperative H-bonds, respectively. In all cases, SVM models outperform MLR. The SVM consensus model performs well both in 3-fold cross-validation (RMSE=1.50 kJ/mol), and on the external test sets containing complexes with single (RMSE=3.20 kJ/mol) and cooperative H-bonds (RMSE=1.63 kJ/mol). © 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

Layered data association using graph-theoretic formulation with applications to tennis ball tracking in monocular sequences.

PubMed

Yan, Fei; Christmas, William; Kittler, Josef

2008-10-01

In this paper, we propose a multilayered data association scheme with graph-theoretic formulation for tracking multiple objects that undergo switching dynamics in clutter. The proposed scheme takes as input object candidates detected in each frame. At the object candidate level, "tracklets'' are "grown'' from sets of candidates that have high probabilities of containing only true positives. At the tracklet level, a directed and weighted graph is constructed, where each node is a tracklet, and the edge weight between two nodes is defined according to the "compatibility'' of the two tracklets. The association problem is then formulated as an all-pairs shortest path (APSP) problem in this graph. Finally, at the path level, by analyzing the APSPs, all object trajectories are identified, and track initiation and track termination are automatically dealt with. By exploiting a special topological property of the graph, we have also developed a more efficient APSP algorithm than the general-purpose ones. The proposed data association scheme is applied to tennis sequences to track tennis balls. Experiments show that it works well on sequences where other data association methods perform poorly or fail completely.

Communication and complexity in a GRN-based multicellular system for graph colouring.

PubMed

Buck, Moritz; Nehaniv, Chrystopher L

2008-01-01

Artificial Genetic Regulatory Networks (GRNs) are interesting control models through their simplicity and versatility. They can be easily implemented, evolved and modified, and their similarity to their biological counterparts makes them interesting for simulations of life-like systems as well. These aspects suggest they may be perfect control systems for distributed computing in diverse situations, but to be usable for such applications the computational power and evolvability of GRNs need to be studied. In this research we propose a simple distributed system implementing GRNs to solve the well known NP-complete graph colouring problem. Every node (cell) of the graph to be coloured is controlled by an instance of the same GRN. All the cells communicate directly with their immediate neighbours in the graph so as to set up a good colouring. The quality of this colouring directs the evolution of the GRNs using a genetic algorithm. We then observe the quality of the colouring for two different graphs according to different communication protocols and the number of different proteins in the cell (a measure for the possible complexity of a GRN). Those two points, being the main scalability issues that any computational paradigm raises, will then be discussed.

Information extraction and knowledge graph construction from geoscience literature

NASA Astrophysics Data System (ADS)

Wang, Chengbin; Ma, Xiaogang; Chen, Jianguo; Chen, Jingwen

2018-03-01

Geoscience literature published online is an important part of open data, and brings both challenges and opportunities for data analysis. Compared with studies of numerical geoscience data, there are limited works on information extraction and knowledge discovery from textual geoscience data. This paper presents a workflow and a few empirical case studies for that topic, with a focus on documents written in Chinese. First, we set up a hybrid corpus combining the generic and geology terms from geology dictionaries to train Chinese word segmentation rules of the Conditional Random Fields model. Second, we used the word segmentation rules to parse documents into individual words, and removed the stop-words from the segmentation results to get a corpus constituted of content-words. Third, we used a statistical method to analyze the semantic links between content-words, and we selected the chord and bigram graphs to visualize the content-words and their links as nodes and edges in a knowledge graph, respectively. The resulting graph presents a clear overview of key information in an unstructured document. This study proves the usefulness of the designed workflow, and shows the potential of leveraging natural language processing and knowledge graph technologies for geoscience.

Incremental isometric embedding of high-dimensional data using connected neighborhood graphs.

PubMed

Zhao, Dongfang; Yang, Li

2009-01-01

Most nonlinear data embedding methods use bottom-up approaches for capturing the underlying structure of data distributed on a manifold in high dimensional space. These methods often share the first step which defines neighbor points of every data point by building a connected neighborhood graph so that all data points can be embedded to a single coordinate system. These methods are required to work incrementally for dimensionality reduction in many applications. Because input data stream may be under-sampled or skewed from time to time, building connected neighborhood graph is crucial to the success of incremental data embedding using these methods. This paper presents algorithms for updating $k$-edge-connected and $k$-connected neighborhood graphs after a new data point is added or an old data point is deleted. It further utilizes a simple algorithm for updating all-pair shortest distances on the neighborhood graph. Together with incremental classical multidimensional scaling using iterative subspace approximation, this paper devises an incremental version of Isomap with enhancements to deal with under-sampled or unevenly distributed data. Experiments on both synthetic and real-world data sets show that the algorithm is efficient and maintains low dimensional configurations of high dimensional data under various data distributions.

Minimum nonuniform graph partitioning with unrelated weights

NASA Astrophysics Data System (ADS)

Makarychev, K. S.; Makarychev, Yu S.

2017-12-01

We give a bi-criteria approximation algorithm for the Minimum Nonuniform Graph Partitioning problem, recently introduced by Krauthgamer, Naor, Schwartz and Talwar. In this problem, we are given a graph G=(V,E) and k numbers ρ_1,\\dots, ρ_k. The goal is to partition V into k disjoint sets (bins) P_1,\\dots, P_k satisfying \\vert P_i\\vert≤ ρi \\vert V\\vert for all i, so as to minimize the number of edges cut by the partition. Our bi-criteria algorithm gives an O(\\sqrt{log \\vert V\\vert log k}) approximation for the objective function in general graphs and an O(1) approximation in graphs excluding a fixed minor. The approximate solution satisfies the relaxed capacity constraints \\vert P_i\\vert ≤ (5+ \\varepsilon)ρi \\vert V\\vert. This algorithm is an improvement upon the O(log \\vert V\\vert)-approximation algorithm by Krauthgamer, Naor, Schwartz and Talwar. We extend our results to the case of 'unrelated weights' and to the case of 'unrelated d-dimensional weights'. A preliminary version of this work was presented at the 41st International Colloquium on Automata, Languages and Programming (ICALP 2014). Bibliography: 7 titles.

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

NASA Technical Reports Server (NTRS)

Gillan, Douglas J.; Lewis, Robert

1994-01-01

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

The Effects of Graphic Feedback, Goal-Setting, and Manager Praise on Customer Service Behaviors

ERIC Educational Resources Information Center

Loewy, Shannon; Bailey, Jon

2007-01-01

The current study used a multiple baseline design to investigate the effects of graphic feedback, goal setting, and manager praise on customer service behaviors in a large retail setting. Direct observation of customer greeting, eye contact, and smiling was used to collect data. After baseline data were collected feedback graphs were posted twice…

Classification of urine sediment based on convolution neural network

NASA Astrophysics Data System (ADS)

Pan, Jingjing; Jiang, Cunbo; Zhu, Tiantian

2018-04-01

By designing a new convolution neural network framework, this paper breaks the constraints of the original convolution neural network framework requiring large training samples and samples of the same size. Move and cropping the input images, generate the same size of the sub-graph. And then, the generated sub-graph uses the method of dropout, increasing the diversity of samples and preventing the fitting generation. Randomly select some proper subset in the sub-graphic set and ensure that the number of elements in the proper subset is same and the proper subset is not the same. The proper subsets are used as input layers for the convolution neural network. Through the convolution layer, the pooling, the full connection layer and output layer, we can obtained the classification loss rate of test set and training set. In the red blood cells, white blood cells, calcium oxalate crystallization classification experiment, the classification accuracy rate of 97% or more.

Studies with Laser Cooled Atoms and Single Molecules

DTIC Science & Technology

2007-09-01

between soda lime glass slides. The bond-setting time can be tailored to allow time for precision optical alignment. We also extended our previous single...This method achieves 100% successful bonding rates between soda lime glass slides. The bond-setting time and be can tailored to allow time for...simple method to bond optical components using silica nanoparticle sol-gel chemistry. The silica nanoparticles polymerize into highly branched

On extreme points of the diffusion polytope

DOE PAGES

Hay, M. J.; Schiff, J.; Fisch, N. J.

2017-01-04

Here, we consider a class of diffusion problems defined on simple graphs in which the populations at any two vertices may be averaged if they are connected by an edge. The diffusion polytope is the convex hull of the set of population vectors attainable using finite sequences of these operations. A number of physical problems have linear programming solutions taking the diffusion polytope as the feasible region, e.g. the free energy that can be removed from plasma using waves, so there is a need to describe and enumerate its extreme points. We also review known results for the case ofmore » the complete graph Kn, and study a variety of problems for the path graph Pn and the cyclic graph Cn. Finall, we describe the different kinds of extreme points that arise, and identify the diffusion polytope in a number of simple cases. In the case of increasing initial populations on Pn the diffusion polytope is topologically an n-dimensional hypercube.« less

Loops in hierarchical channel networks

NASA Astrophysics Data System (ADS)

Katifori, Eleni; Magnasco, Marcelo

2012-02-01

Nature provides us with many examples of planar distribution and structural networks having dense sets of closed loops. An archetype of this form of network organization is the vasculature of dicotyledonous leaves, which showcases a hierarchically-nested architecture. Although a number of methods have been proposed to measure aspects of the structure of such networks, a robust metric to quantify their hierarchical organization is still lacking. We present an algorithmic framework that allows mapping loopy networks to binary trees, preserving in the connectivity of the trees the architecture of the original graph. We apply this framework to investigate computer generated and natural graphs extracted from digitized images of dicotyledonous leaves and animal vasculature. We calculate various metrics on the corresponding trees and discuss the relationship of these quantities to the architectural organization of the original graphs. This algorithmic framework decouples the geometric information from the metric topology (connectivity and edge weight) and it ultimately allows us to perform a quantitative statistical comparison between predictions of theoretical models and naturally occurring loopy graphs.

Approximate ground states of the random-field Potts model from graph cuts

NASA Astrophysics Data System (ADS)

Kumar, Manoj; Kumar, Ravinder; Weigel, Martin; Banerjee, Varsha; Janke, Wolfhard; Puri, Sanjay

2018-05-01

While the ground-state problem for the random-field Ising model is polynomial, and can be solved using a number of well-known algorithms for maximum flow or graph cut, the analog random-field Potts model corresponds to a multiterminal flow problem that is known to be NP-hard. Hence an efficient exact algorithm is very unlikely to exist. As we show here, it is nevertheless possible to use an embedding of binary degrees of freedom into the Potts spins in combination with graph-cut methods to solve the corresponding ground-state problem approximately in polynomial time. We benchmark this heuristic algorithm using a set of quasiexact ground states found for small systems from long parallel tempering runs. For a not-too-large number q of Potts states, the method based on graph cuts finds the same solutions in a fraction of the time. We employ the new technique to analyze the breakup length of the random-field Potts model in two dimensions.

Constructing a Graph Database for Semantic Literature-Based Discovery.

PubMed

Hristovski, Dimitar; Kastrin, Andrej; Dinevski, Dejan; Rindflesch, Thomas C

2015-01-01

Literature-based discovery (LBD) generates discoveries, or hypotheses, by combining what is already known in the literature. Potential discoveries have the form of relations between biomedical concepts; for example, a drug may be determined to treat a disease other than the one for which it was intended. LBD views the knowledge in a domain as a network; a set of concepts along with the relations between them. As a starting point, we used SemMedDB, a database of semantic relations between biomedical concepts extracted with SemRep from Medline. SemMedDB is distributed as a MySQL relational database, which has some problems when dealing with network data. We transformed and uploaded SemMedDB into the Neo4j graph database, and implemented the basic LBD discovery algorithms with the Cypher query language. We conclude that storing the data needed for semantic LBD is more natural in a graph database. Also, implementing LBD discovery algorithms is conceptually simpler with a graph query language when compared with standard SQL.

Cluster Tails for Critical Power-Law Inhomogeneous Random Graphs

NASA Astrophysics Data System (ADS)

van der Hofstad, Remco; Kliem, Sandra; van Leeuwaarden, Johan S. H.

2018-04-01

Recently, the scaling limit of cluster sizes for critical inhomogeneous random graphs of rank-1 type having finite variance but infinite third moment degrees was obtained in Bhamidi et al. (Ann Probab 40:2299-2361, 2012). It was proved that when the degrees obey a power law with exponent τ \\in (3,4), the sequence of clusters ordered in decreasing size and multiplied through by n^{-(τ -2)/(τ -1)} converges as n→ ∞ to a sequence of decreasing non-degenerate random variables. Here, we study the tails of the limit of the rescaled largest cluster, i.e., the probability that the scaling limit of the largest cluster takes a large value u, as a function of u. This extends a related result of Pittel (J Combin Theory Ser B 82(2):237-269, 2001) for the Erdős-Rényi random graph to the setting of rank-1 inhomogeneous random graphs with infinite third moment degrees. We make use of delicate large deviations and weak convergence arguments.

Exploring the evolution of London's street network in the information space: A dual approach

NASA Astrophysics Data System (ADS)

Masucci, A. Paolo; Stanilov, Kiril; Batty, Michael

2014-01-01

We study the growth of London's street network in its dual representation, as the city has evolved over the past 224 years. The dual representation of a planar graph is a content-based network, where each node is a set of edges of the planar graph and represents a transportation unit in the so-called information space, i.e., the space where information is handled in order to navigate through the city. First, we discuss a novel hybrid technique to extract dual graphs from planar graphs, called the hierarchical intersection continuity negotiation principle. Then we show that the growth of the network can be analytically described by logistic laws and that the topological properties of the network are governed by robust log-normal distributions characterizing the network's connectivity and small-world properties that are consistent over time. Moreover, we find that the double-Pareto-like distributions for the connectivity emerge for major roads and can be modeled via a stochastic content-based network model using simple space-filling principles.

Network analysis for the visualization and analysis of qualitative data.

PubMed

Pokorny, Jennifer J; Norman, Alex; Zanesco, Anthony P; Bauer-Wu, Susan; Sahdra, Baljinder K; Saron, Clifford D

2018-03-01

We present a novel manner in which to visualize the coding of qualitative data that enables representation and analysis of connections between codes using graph theory and network analysis. Network graphs are created from codes applied to a transcript or audio file using the code names and their chronological location. The resulting network is a representation of the coding data that characterizes the interrelations of codes. This approach enables quantification of qualitative codes using network analysis and facilitates examination of associations of network indices with other quantitative variables using common statistical procedures. Here, as a proof of concept, we applied this method to a set of interview transcripts that had been coded in 2 different ways and the resultant network graphs were examined. The creation of network graphs allows researchers an opportunity to view and share their qualitative data in an innovative way that may provide new insights and enhance transparency of the analytical process by which they reach their conclusions. (PsycINFO Database Record (c) 2018 APA, all rights reserved).

27 CFR 25.98 - Surety or security.

Code of Federal Regulations, 2012 CFR

2012-04-01

... coverage. Bonds required by this part will be given with corporate surety or collateral security. (b... limitations set forth for corporate security by the Secretary which are set forth in the current revision of... penal sum of the bond. (e) Deposit of collateral securities in lieu of corporate surety. Bonds or notes...

27 CFR 25.98 - Surety or security.

Code of Federal Regulations, 2013 CFR

2013-04-01

... coverage. Bonds required by this part will be given with corporate surety or collateral security. (b... limitations set forth for corporate security by the Secretary which are set forth in the current revision of... penal sum of the bond. (e) Deposit of collateral securities in lieu of corporate surety. Bonds or notes...

27 CFR 25.98 - Surety or security.

Code of Federal Regulations, 2010 CFR

2010-04-01

... coverage. Bonds required by this part will be given with corporate surety or collateral security. (b... limitations set forth for corporate security by the Secretary which are set forth in the current revision of... penal sum of the bond. (e) Deposit of collateral securities in lieu of corporate surety. Bonds or notes...

27 CFR 25.98 - Surety or security.

Code of Federal Regulations, 2011 CFR

2011-04-01

... coverage. Bonds required by this part will be given with corporate surety or collateral security. (b... limitations set forth for corporate security by the Secretary which are set forth in the current revision of... penal sum of the bond. (e) Deposit of collateral securities in lieu of corporate surety. Bonds or notes...

27 CFR 25.98 - Surety or security.

Code of Federal Regulations, 2014 CFR

2014-04-01

... coverage. Bonds required by this part will be given with corporate surety or collateral security. (b... limitations set forth for corporate security by the Secretary which are set forth in the current revision of... penal sum of the bond. (e) Deposit of collateral securities in lieu of corporate surety. Bonds or notes...

Coverability graphs for a class of synchronously executed unbounded Petri net

NASA Technical Reports Server (NTRS)

Stotts, P. David; Pratt, Terrence W.

1990-01-01

After detailing a variant of the concurrent-execution rule for firing of maximal subsets, in which the simultaneous firing of conflicting transitions is prohibited, an algorithm is constructed for generating the coverability graph of a net executed under this synchronous firing rule. The omega insertion criteria in the algorithm are shown to be valid for any net on which the algorithm terminates. It is accordingly shown that the set of nets on which the algorithm terminates includes the 'conflict-free' class.

A graph-based approach to detect spatiotemporal dynamics in satellite image time series

NASA Astrophysics Data System (ADS)

Guttler, Fabio; Ienco, Dino; Nin, Jordi; Teisseire, Maguelonne; Poncelet, Pascal

2017-08-01

Enhancing the frequency of satellite acquisitions represents a key issue for Earth Observation community nowadays. Repeated observations are crucial for monitoring purposes, particularly when intra-annual process should be taken into account. Time series of images constitute a valuable source of information in these cases. The goal of this paper is to propose a new methodological framework to automatically detect and extract spatiotemporal information from satellite image time series (SITS). Existing methods dealing with such kind of data are usually classification-oriented and cannot provide information about evolutions and temporal behaviors. In this paper we propose a graph-based strategy that combines object-based image analysis (OBIA) with data mining techniques. Image objects computed at each individual timestamp are connected across the time series and generates a set of evolution graphs. Each evolution graph is associated to a particular area within the study site and stores information about its temporal evolution. Such information can be deeply explored at the evolution graph scale or used to compare the graphs and supply a general picture at the study site scale. We validated our framework on two study sites located in the South of France and involving different types of natural, semi-natural and agricultural areas. The results obtained from a Landsat SITS support the quality of the methodological approach and illustrate how the framework can be employed to extract and characterize spatiotemporal dynamics.

Route Network Construction with Location-Direction-Enabled Photographs

NASA Astrophysics Data System (ADS)

Fujita, Hideyuki; Sagara, Shota; Ohmori, Tadashi; Shintani, Takahiko

2018-05-01

We propose a method for constructing a geometric graph for generating routes that summarize a geographical area and also have visual continuity by using a set of location-direction-enabled photographs. A location- direction-enabled photograph is a photograph that has information about the location (position of the camera at the time of shooting) and the direction (direction of the camera at the time of shooting). Each nodes of the graph corresponds to a location-direction-enabled photograph. The location of each node is the location of the corresponding photograph, and a route on the graph corresponds to a route in the geographic area and a sequence of photographs. The proposed graph is constructed to represent characteristic spots and paths linking the spots, and it is assumed to be a kind of a spatial summarization of the area with the photographs. Therefore, we call the routes on the graph as spatial summary route. Each route on the proposed graph also has a visual continuity, which means that we can understand the spatial relationship among the continuous photographs on the route such as moving forward, backward, turning right, etc. In this study, when the changes in the shooting position and shooting direction satisfied a given threshold, the route was defined to have visual continuity. By presenting the photographs in order along the generated route, information can be presented sequentially, while maintaining visual continuity to a great extent.

Scalable Triadic Analysis of Large-Scale Graphs: Multi-Core vs. Multi-Processor vs. Multi-Threaded Shared Memory Architectures

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

Chin, George; Marquez, Andres; Choudhury, Sutanay

2012-09-01

Triadic analysis encompasses a useful set of graph mining methods that is centered on the concept of a triad, which is a subgraph of three nodes and the configuration of directed edges across the nodes. Such methods are often applied in the social sciences as well as many other diverse fields. Triadic methods commonly operate on a triad census that counts the number of triads of every possible edge configuration in a graph. Like other graph algorithms, triadic census algorithms do not scale well when graphs reach tens of millions to billions of nodes. To enable the triadic analysis ofmore » large-scale graphs, we developed and optimized a triad census algorithm to efficiently execute on shared memory architectures. We will retrace the development and evolution of a parallel triad census algorithm. Over the course of several versions, we continually adapted the code’s data structures and program logic to expose more opportunities to exploit parallelism on shared memory that would translate into improved computational performance. We will recall the critical steps and modifications that occurred during code development and optimization. Furthermore, we will compare the performances of triad census algorithm versions on three specific systems: Cray XMT, HP Superdome, and AMD multi-core NUMA machine. These three systems have shared memory architectures but with markedly different hardware capabilities to manage parallelism.« less

Visualization and recommendation of large image collections toward effective sensemaking

NASA Astrophysics Data System (ADS)

Gu, Yi; Wang, Chaoli; Nemiroff, Robert; Kao, David; Parra, Denis

2016-03-01

In our daily lives, images are among the most commonly found data which we need to handle. We present iGraph, a graph-based approach for visual analytics of large image collections and their associated text information. Given such a collection, we compute the similarity between images, the distance between texts, and the connection between image and text to construct iGraph, a compound graph representation which encodes the underlying relationships among these images and texts. To enable effective visual navigation and comprehension of iGraph with tens of thousands of nodes and hundreds of millions of edges, we present a progressive solution that offers collection overview, node comparison, and visual recommendation. Our solution not only allows users to explore the entire collection with representative images and keywords but also supports detailed comparison for understanding and intuitive guidance for navigation. The visual exploration of iGraph is further enhanced with the implementation of bubble sets to highlight group memberships of nodes, suggestion of abnormal keywords or time periods based on text outlier detection, and comparison of four different recommendation solutions. For performance speedup, multiple graphics processing units and central processing units are utilized for processing and visualization in parallel. We experiment with two image collections and leverage a cluster driving a display wall of nearly 50 million pixels. We show the effectiveness of our approach by demonstrating experimental results and conducting a user study.

A note on the stability and discriminability of graph-based features for classification problems in digital pathology

NASA Astrophysics Data System (ADS)

Cruz-Roa, Angel; Xu, Jun; Madabhushi, Anant

2015-01-01

Nuclear architecture or the spatial arrangement of individual cancer nuclei on histopathology images has been shown to be associated with different grades and differential risk for a number of solid tumors such as breast, prostate, and oropharyngeal. Graph-based representations of individual nuclei (nuclei representing the graph nodes) allows for mining of quantitative metrics to describe tumor morphology. These graph features can be broadly categorized into global and local depending on the type of graph construction method. While a number of local graph (e.g. Cell Cluster Graphs) and global graph (e.g. Voronoi, Delaunay Triangulation, Minimum Spanning Tree) features have been shown to associated with cancer grade, risk, and outcome for different cancer types, the sensitivity of the preceding segmentation algorithms in identifying individual nuclei can have a significant bearing on the discriminability of the resultant features. This therefore begs the question as to which features while being discriminative of cancer grade and aggressiveness are also the most resilient to the segmentation errors. These properties are particularly desirable in the context of digital pathology images, where the method of slide preparation, staining, and type of nuclear segmentation algorithm employed can all dramatically affect the quality of the nuclear graphs and corresponding features. In this paper we evaluated the trade off between discriminability and stability of both global and local graph-based features in conjunction with a few different segmentation algorithms and in the context of two different histopathology image datasets of breast cancer from whole-slide images (WSI) and tissue microarrays (TMA). Specifically in this paper we investigate a few different performance measures including stability, discriminability and stability vs discriminability trade off, all of which are based on p-values from the Kruskal-Wallis one-way analysis of variance for local and global graph features. Apart from identifying the set of local and global features that satisfied the trade off between stability and discriminability, our most interesting finding was that a simple segmentation method was sufficient to identify the most discriminant features for invasive tumour detection in TMAs, whereas for tumour grading in WSI, the graph based features were more sensitive to the accuracy of the segmentation algorithm employed.

A graph-based approach for the retrieval of multi-modality medical images.

PubMed

Kumar, Ashnil; Kim, Jinman; Wen, Lingfeng; Fulham, Michael; Feng, Dagan

2014-02-01

In this paper, we address the retrieval of multi-modality medical volumes, which consist of two different imaging modalities, acquired sequentially, from the same scanner. One such example, positron emission tomography and computed tomography (PET-CT), provides physicians with complementary functional and anatomical features as well as spatial relationships and has led to improved cancer diagnosis, localisation, and staging. The challenge of multi-modality volume retrieval for cancer patients lies in representing the complementary geometric and topologic attributes between tumours and organs. These attributes and relationships, which are used for tumour staging and classification, can be formulated as a graph. It has been demonstrated that graph-based methods have high accuracy for retrieval by spatial similarity. However, naïvely representing all relationships on a complete graph obscures the structure of the tumour-anatomy relationships. We propose a new graph structure derived from complete graphs that structurally constrains the edges connected to tumour vertices based upon the spatial proximity of tumours and organs. This enables retrieval on the basis of tumour localisation. We also present a similarity matching algorithm that accounts for different feature sets for graph elements from different imaging modalities. Our method emphasises the relationships between a tumour and related organs, while still modelling patient-specific anatomical variations. Constraining tumours to related anatomical structures improves the discrimination potential of graphs, making it easier to retrieve similar images based on tumour location. We evaluated our retrieval methodology on a dataset of clinical PET-CT volumes. Our results showed that our method enabled the retrieval of multi-modality images using spatial features. Our graph-based retrieval algorithm achieved a higher precision than several other retrieval techniques: gray-level histograms as well as state-of-the-art methods such as visual words using the scale- invariant feature transform (SIFT) and relational matrices representing the spatial arrangements of objects. Copyright © 2013 Elsevier B.V. All rights reserved.

Distance Magic-Type and Distance Antimagic-Type Labelings of Graphs

NASA Astrophysics Data System (ADS)

Freyberg, Bryan J.

Generally speaking, a distance magic-type labeling of a graph G of order n is a bijection l from the vertex set of the graph to the first n natural numbers or to the elements of a group of order n, with the property that the weight of each vertex is the same. The weight of a vertex x is defined as the sum (or appropriate group operation) of all the labels of vertices adjacent to x. If instead we require that all weights differ, then we refer to the labeling as a distance antimagic-type labeling. This idea can be generalized for directed graphs; the weight will take into consideration the direction of the arcs. In this manuscript, we provide new results for d-handicap labeling, a distance antimagic-type labeling, and introduce a new distance magic-type labeling called orientable Gamma-distance magic labeling. A d-handicap distance antimagic labeling (or just d-handicap labeling for short) of a graph G = ( V,E) of order n is a bijection l from V to the set {1,2,...,n} with induced weight function [special characters omitted]. such that l(xi) = i and the sequence of weights w(x 1),w(x2),...,w (xn) forms an arithmetic sequence with constant difference d at least 1. If a graph G admits a d-handicap labeling, we say G is a d-handicap graph. A d-handicap incomplete tournament, H(n,k,d ) is an incomplete tournament of n teams ranked with the first n natural numbers such that each team plays exactly k games and the strength of schedule of the ith ranked team is d more than the i + 1st ranked team. That is, strength of schedule increases arithmetically with strength of team. Constructing an H(n,k,d) is equivalent to finding a d-handicap labeling of a k-regular graph of order n.. In Chapter 2 we provide general constructions for every d for large classes of both n and k, providing breadfth and depth to the catalog of known H(n,k,d)'s. In Chapters 3 - 6, we introduce a new type of labeling called orientable Gamma-distance magic labeling. Let Gamma be an abelian group of order n. If for a graph G = (V,E) of order n there exists an orientation of the edges of G and a companion bijection from V to Gamma with the property that there is an element mu of Gamma (called the magic constant) such that [special characters omitted] where w(x) is the weight of vertex x, we say that G is orientable Gamma -distance magic. In addition to introducing the concept, we provide numerous results on orientable Zn-distance magic graphs, where Zn is the cyclic group of order n.. In Chapter 7, we summarize the results of this dissertation and provide suggestions for future work.

Can HN[double bond, length as m-dash]NH, FN[double bond, length as m-dash]NH, or HN[double bond, length as m-dash]CHOH bridge the σ-hole and the lone pair at P in binary complexes with H2XP, for X = F, Cl, NC, OH, CN, CCH, CH3, and H?

PubMed

Del Bene, Janet E; Alkorta, Ibon; Elguero, José

2015-11-11

Ab initio MP2/aug'-cc-pVTZ calculations have been carried out to investigate the properties of complexes formed between H2XP, for X = F, Cl, NC, OH, CN, CCH, CH3, and H, and the possible bridging molecules HN[double bond, length as m-dash]NH, FN[double bond, length as m-dash]NH, and HN[double bond, length as m-dash]CHOH. H2XP:HNNH and H2XP:FNNH complexes are stabilized by PN pnicogen bonds, except for H2(CH3)P:FNNH and H3P:FNNH which are stabilized by N-HP hydrogen bonds. H2XP:HNCHOH complexes are stabilized by PN pnicogen bonds and nonlinear O-HP hydrogen bonds. For a fixed H2XP molecule, binding energies decrease in the order HNCHOH > HNNH > FNNH, except for the binding energies of H2(CH3)P and H3P with HNNH and FNNH. Binding energies of complexes with HNCHOH and HNNH increase as the P-N1 distance decreases, but binding energies of complexes with FNNH show little dependence on this distance. The large binding energies of H2XP:HNCHOH complexes arise from a cooperative effect involving electron-pair acceptance by P to form a pnicogen bond, and electron-pair donation by P to form a hydrogen bond. The dominant charge-transfer interaction in these complexes involves electron-pair donation by N across the pnicogen bond, except for complexes in which X is one of the more electropositive substituents, CCH, CH3, and H. For these, lone-pair donation by P across the hydrogen bond dominates. AIM and NBO data for these complexes are consistent with their bonding characteristics, showing molecular graphs with bond critical points and charge-transfer interactions associated with hydrogen and pnicogen bonds. EOM-CCSD spin-spin coupling constants (1p)J(P-N) across the pnicogen bond for each series of complexes correlate with the P-N distance. In contrast, (2h)J(O-P) values for complexes H2XP:HNCHOH do not correlate with the O-P distance, a consequence of the nonlinearity of these hydrogen bonds.

Graph theory and the Virasoro master equation

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

Obers, N.A.J.

1991-01-01

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

Attribute-based Decision Graphs: A framework for multiclass data classification.

PubMed

Bertini, João Roberto; Nicoletti, Maria do Carmo; Zhao, Liang

2017-01-01

Graph-based algorithms have been successfully applied in machine learning and data mining tasks. A simple but, widely used, approach to build graphs from vector-based data is to consider each data instance as a vertex and connecting pairs of it using a similarity measure. Although this abstraction presents some advantages, such as arbitrary shape representation of the original data, it is still tied to some drawbacks, for example, it is dependent on the choice of a pre-defined distance metric and is biased by the local information among data instances. Aiming at exploring alternative ways to build graphs from data, this paper proposes an algorithm for constructing a new type of graph, called Attribute-based Decision Graph-AbDG. Given a vector-based data set, an AbDG is built by partitioning each data attribute range into disjoint intervals and representing each interval as a vertex. The edges are then established between vertices from different attributes according to a pre-defined pattern. Classification is performed through a matching process among the attribute values of the new instance and AbDG. Moreover, AbDG provides an inner mechanism to handle missing attribute values, which contributes for expanding its applicability. Results of classification tasks have shown that AbDG is a competitive approach when compared to well-known multiclass algorithms. The main contribution of the proposed framework is the combination of the advantages of attribute-based and graph-based techniques to perform robust pattern matching data classification, while permitting the analysis the input data considering only a subset of its attributes. Copyright © 2016 Elsevier Ltd. All rights reserved.

Multiple kernels learning-based biological entity relationship extraction method.

PubMed

Dongliang, Xu; Jingchang, Pan; Bailing, Wang

2017-09-20

Automatic extracting protein entity interaction information from biomedical literature can help to build protein relation network and design new drugs. There are more than 20 million literature abstracts included in MEDLINE, which is the most authoritative textual database in the field of biomedicine, and follow an exponential growth over time. This frantic expansion of the biomedical literature can often be difficult to absorb or manually analyze. Thus efficient and automated search engines are necessary to efficiently explore the biomedical literature using text mining techniques. The P, R, and F value of tag graph method in Aimed corpus are 50.82, 69.76, and 58.61%, respectively. The P, R, and F value of tag graph kernel method in other four evaluation corpuses are 2-5% higher than that of all-paths graph kernel. And The P, R and F value of feature kernel and tag graph kernel fuse methods is 53.43, 71.62 and 61.30%, respectively. The P, R and F value of feature kernel and tag graph kernel fuse methods is 55.47, 70.29 and 60.37%, respectively. It indicated that the performance of the two kinds of kernel fusion methods is better than that of simple kernel. In comparison with the all-paths graph kernel method, the tag graph kernel method is superior in terms of overall performance. Experiments show that the performance of the multi-kernels method is better than that of the three separate single-kernel method and the dual-mutually fused kernel method used hereof in five corpus sets.

Multi-objective optimal design of magnetorheological engine mount based on an improved non-dominated sorting genetic algorithm

NASA Astrophysics Data System (ADS)

Zheng, Ling; Duan, Xuwei; Deng, Zhaoxue; Li, Yinong

2014-03-01

A novel flow-mode magneto-rheological (MR) engine mount integrated a diaphragm de-coupler and the spoiler plate is designed and developed to isolate engine and the transmission from the chassis in a wide frequency range and overcome the stiffness in high frequency. A lumped parameter model of the MR engine mount in single degree of freedom system is further developed based on bond graph method to predict the performance of the MR engine mount accurately. The optimization mathematical model is established to minimize the total of force transmissibility over several frequency ranges addressed. In this mathematical model, the lumped parameters are considered as design variables. The maximum of force transmissibility and the corresponding frequency in low frequency range as well as individual lumped parameter are limited as constraints. The multiple interval sensitivity analysis method is developed to select the optimized variables and improve the efficiency of optimization process. An improved non-dominated sorting genetic algorithm (NSGA-II) is used to solve the multi-objective optimization problem. The synthesized distance between the individual in Pareto set and the individual in possible set in engineering is defined and calculated. A set of real design parameters is thus obtained by the internal relationship between the optimal lumped parameters and practical design parameters for the MR engine mount. The program flowchart for the improved non-dominated sorting genetic algorithm (NSGA-II) is given. The obtained results demonstrate the effectiveness of the proposed optimization approach in minimizing the total of force transmissibility over several frequency ranges addressed.

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.

Multigraph: Reusable Interactive Data Graphs

NASA Astrophysics Data System (ADS)

Phillips, M. B.

2010-12-01

There are surprisingly few good software tools available for presenting time series data on the internet. The most common practice is to use a desktop program such as Excel or Matlab to save a graph as an image which can be included in a web page like any other image. This disconnects the graph from the data in a way that makes updating a graph with new data a cumbersome manual process, and it limits the user to one particular view of the data. The Multigraph project defines an XML format for describing interactive data graphs, and software tools for creating and rendering those graphs in web pages and other internet connected applications. Viewing a Multigraph graph is extremely simple and intuitive, and requires no instructions; the user can pan and zoom by clicking and dragging, in a familiar "Google Maps" kind of way. Creating a new graph for inclusion in a web page involves writing a simple XML configuration file. Multigraph can read data in a variety of formats, and can display data from a web service, allowing users to "surf" through large data sets, downloading only those the parts of the data that are needed for display. The Multigraph XML format, or "MUGL" for short, provides a concise description of the visual properties of a graph, such as axes, plot styles, data sources, labels, etc, as well as interactivity properties such as how and whether the user can pan or zoom along each axis. Multigraph reads a file in this format, draws the described graph, and allows the user to interact with it. Multigraph software currently includes a Flash application for embedding graphs in web pages, a Flex component for embedding graphs in larger Flex/Flash applications, and a plugin for creating graphs in the WordPress content management system. Plans for the future include a Java version for desktop viewing and editing, a command line version for batch and server side rendering, and possibly Android and iPhone versions. Multigraph is currently in use on several web sites including the US Drought Portal (www.drought.gov), the NOAA Climate Services Portal (www.climate.gov), the Climate Reference Network (www.ncdc.noaa.gov/crn), NCDC's State of the Climate Report (www.ncdc.noaa.gov/sotc), and the US Forest Service's Forest Change Assessment Viewer (ews.forestthreats.org/NPDE/NPDE.html). More information about Multigraph is available from the web site www.multigraph.org. Interactive Multigraph Display of Real Time Weather Data

A Measure for the Cohesion of Weighted Networks.

ERIC Educational Resources Information Center

Egghe, Leo; Rousseau, Ronald

2003-01-01

Discusses graph theory in information science, focusing on measures for the cohesion of networks. Illustrates how a set of weights between connected nodes can be transformed into a set of dissimilarity measures and presents an example of the new compactness measures for a cocitation and a bibliographic coupling network. (Author/LRW)

Teaching the Assessment of Normality Using Large Easily-Generated Real Data Sets

ERIC Educational Resources Information Center

Kulp, Christopher W.; Sprechini, Gene D.

2016-01-01

A classroom activity is presented, which can be used in teaching students statistics with an easily generated, large, real world data set. The activity consists of analyzing a video recording of an object. The colour data of the recorded object can then be used as a data set to explore variation in the data using graphs including histograms,…

Markov models for fMRI correlation structure: Is brain functional connectivity small world, or decomposable into networks?

PubMed

Varoquaux, G; Gramfort, A; Poline, J B; Thirion, B

2012-01-01

Correlations in the signal observed via functional Magnetic Resonance Imaging (fMRI), are expected to reveal the interactions in the underlying neural populations through hemodynamic response. In particular, they highlight distributed set of mutually correlated regions that correspond to brain networks related to different cognitive functions. Yet graph-theoretical studies of neural connections give a different picture: that of a highly integrated system with small-world properties: local clustering but with short pathways across the complete structure. We examine the conditional independence properties of the fMRI signal, i.e. its Markov structure, to find realistic assumptions on the connectivity structure that are required to explain the observed functional connectivity. In particular we seek a decomposition of the Markov structure into segregated functional networks using decomposable graphs: a set of strongly-connected and partially overlapping cliques. We introduce a new method to efficiently extract such cliques on a large, strongly-connected graph. We compare methods learning different graph structures from functional connectivity by testing the goodness of fit of the model they learn on new data. We find that summarizing the structure as strongly-connected networks can give a good description only for very large and overlapping networks. These results highlight that Markov models are good tools to identify the structure of brain connectivity from fMRI signals, but for this purpose they must reflect the small-world properties of the underlying neural systems. Copyright © 2012 Elsevier Ltd. All rights reserved.

FTree query construction for virtual screening: a statistical analysis.

PubMed

Gerlach, Christof; Broughton, Howard; Zaliani, Andrea

2008-02-01

FTrees (FT) is a known chemoinformatic tool able to condense molecular descriptions into a graph object and to search for actives in large databases using graph similarity. The query graph is classically derived from a known active molecule, or a set of actives, for which a similar compound has to be found. Recently, FT similarity has been extended to fragment space, widening its capabilities. If a user were able to build a knowledge-based FT query from information other than a known active structure, the similarity search could be combined with other, normally separate, fields like de-novo design or pharmacophore searches. With this aim in mind, we performed a comprehensive analysis of several databases in terms of FT description and provide a basic statistical analysis of the FT spaces so far at hand. Vendors' catalogue collections and MDDR as a source of potential or known "actives", respectively, have been used. With the results reported herein, a set of ranges, mean values and standard deviations for several query parameters are presented in order to set a reference guide for the users. Applications on how to use this information in FT query building are also provided, using a newly built 3D-pharmacophore from 57 5HT-1F agonists and a published one which was used for virtual screening for tRNA-guanine transglycosylase (TGT) inhibitors.

FTree query construction for virtual screening: a statistical analysis

NASA Astrophysics Data System (ADS)

Gerlach, Christof; Broughton, Howard; Zaliani, Andrea

2008-02-01

FTrees (FT) is a known chemoinformatic tool able to condense molecular descriptions into a graph object and to search for actives in large databases using graph similarity. The query graph is classically derived from a known active molecule, or a set of actives, for which a similar compound has to be found. Recently, FT similarity has been extended to fragment space, widening its capabilities. If a user were able to build a knowledge-based FT query from information other than a known active structure, the similarity search could be combined with other, normally separate, fields like de-novo design or pharmacophore searches. With this aim in mind, we performed a comprehensive analysis of several databases in terms of FT description and provide a basic statistical analysis of the FT spaces so far at hand. Vendors' catalogue collections and MDDR as a source of potential or known "actives", respectively, have been used. With the results reported herein, a set of ranges, mean values and standard deviations for several query parameters are presented in order to set a reference guide for the users. Applications on how to use this information in FT query building are also provided, using a newly built 3D-pharmacophore from 57 5HT-1F agonists and a published one which was used for virtual screening for tRNA-guanine transglycosylase (TGT) inhibitors.

Different transport behaviors of NH4 (+) and NH3 in transmembrane cyclic peptide nanotubes.

PubMed

Zhang, Mingming; Fan, Jianfen; Xu, Jian; Weng, Peipei; Lin, Huifang

2016-10-01

Two water-filled transmembrane cyclic peptide nanotubes (CPNTs) of 8×cyclo-(WL)n=4,5/POPE were chosen to investigate the dependences of the transport properties of the positive NH4 (+) and neutral NH3 on the channel radius. Molecular dynamic simulations revealed that molecular charge, size, ability to form H-bonds and channel radius all significantly influence the behaviors of NH4 (+) and NH3 in a CPNT. Higher electrostatic interactions, more H-bonds, and water-bridges were found in the NH4 (+) system, resulting in NH4 (+) meeting higher energy barriers, while NH3 can enter, exit and permeate the channels effortlessly. This work sheds a first light on the differences between the mechanisms of NH4 (+) and NH3 moving in a CPNT at an atomic level. Graphical Abstract Snapshot of the simulation system of NH4 (+)_octa-CPNT with an NH4 (+) initially positioned at one mouth of the tube, PMF profiles for single NH4 (+) ion and NH3 molecule moving through water-filled transmembrane CPNTs of 8×cyclo-(WL)n=4,5/POPE and sketch graphs of the possible H-bond forms of NH3 and NH4 (+) with the neighboring water.

The Roadmaker's algorithm for the discrete pulse transform.

PubMed

Laurie, Dirk P

2011-02-01

The discrete pulse transform (DPT) is a decomposition of an observed signal into a sum of pulses, i.e., signals that are constant on a connected set and zero elsewhere. Originally developed for 1-D signal processing, the DPT has recently been generalized to more dimensions. Applications in image processing are currently being investigated. The time required to compute the DPT as originally defined via the successive application of LULU operators (members of a class of minimax filters studied by Rohwer) has been a severe drawback to its applicability. This paper introduces a fast method for obtaining such a decomposition, called the Roadmaker's algorithm because it involves filling pits and razing bumps. It acts selectively only on those features actually present in the signal, flattening them in order of increasing size by subtracing an appropriate positive or negative pulse, which is then appended to the decomposition. The implementation described here covers 1-D signal as well as two and 3-D image processing in a single framework. This is achieved by considering the signal or image as a function defined on a graph, with the geometry specified by the edges of the graph. Whenever a feature is flattened, nodes in the graph are merged, until eventually only one node remains. At that stage, a new set of edges for the same nodes as the graph, forming a tree structure, defines the obtained decomposition. The Roadmaker's algorithm is shown to be equivalent to the DPT in the sense of obtaining the same decomposition. However, its simpler operators are not in general equivalent to the LULU operators in situations where those operators are not applied successively. A by-product of the Roadmaker's algorithm is that it yields a proof of the so-called Highlight Conjecture, stated as an open problem in 2006. We pay particular attention to algorithmic details and complexity, including a demonstration that in the 1-D case, and also in the case of a complete graph, the Roadmaker's algorithm has optimal complexity: it runs in time O(m), where m is the number of arcs in the graph.