Girth 5 graphs from relative difference sets
Jørgensen, Leif Kjær
2005-01-01
We consider the problem of construction of graphs with given degree $k$ and girth 5 and as few vertices as possible. We give a construction of a family of girth 5 graphs based on relative difference sets. This family contains the smallest known graph of degree 8 and girth 5 which was constructed ...
Girth 5 graphs from relative difference sets
Jørgensen, Leif Kjær
We consider the problem of construction of graphs with given degree and girth 5 and as few vertices as possible. We give a construction of a family of girth 5 graphs based on relative difference sets. This family contains the smallest known graph of degree 8 and girth 5 which was constructed by G...
XML Graphs in Program Analysis
Møller, Anders; Schwartzbach, Michael I.
2011-01-01
of XML graphs against different XML schema languages, and provide a software package that enables others to make use of these ideas. We also survey the use of XML graphs for program analysis with four very different languages: XACT (XML in Java), Java Servlets (Web application programming), XSugar......XML graphs have shown to be a simple and effective formalism for representing sets of XML documents in program analysis. It has evolved through a six year period with variants tailored for a range of applications. We present a unified definition, outline the key properties including validation...
Maunz, Peter Lukas Wilhelm [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Sterk, Jonathan David [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Lobser, Daniel [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Parekh, Ojas D. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Ryan-Anderson, Ciaran [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2016-01-01
In recent years, advanced network analytics have become increasingly important to na- tional security with applications ranging from cyber security to detection and disruption of ter- rorist networks. While classical computing solutions have received considerable investment, the development of quantum algorithms to address problems, such as data mining of attributed relational graphs, is a largely unexplored space. Recent theoretical work has shown that quan- tum algorithms for graph analysis can be more efficient than their classical counterparts. Here, we have implemented a trapped-ion-based two-qubit quantum information proces- sor to address these goals. Building on Sandia's microfabricated silicon surface ion traps, we have designed, realized and characterized a quantum information processor using the hyperfine qubits encoded in two 171 Yb + ions. We have implemented single qubit gates using resonant microwave radiation and have employed Gate set tomography (GST) to characterize the quan- tum process. For the first time, we were able to prove that the quantum process surpasses the fault tolerance thresholds of some quantum codes by demonstrating a diamond norm distance of less than 1 . 9 x 10 [?] 4 . We used Raman transitions in order to manipulate the trapped ions' motion and realize two-qubit gates. We characterized the implemented motion sensitive and insensitive single qubit processes and achieved a maximal process infidelity of 6 . 5 x 10 [?] 5 . We implemented the two-qubit gate proposed by Molmer and Sorensen and achieved a fidelity of more than 97 . 7%.
XML Graphs in Program Analysis
Møller, Anders; Schwartzbach, Michael Ignatieff
2007-01-01
XML graphs have shown to be a simple and effective formalism for representing sets of XML documents in program analysis. It has evolved through a six year period with variants tailored for a range of applications. We present a unified definition, outline the key properties including validation...... of XML graphs against different XML schema languages, and provide a software package that enables others to make use of these ideas. We also survey four very different applications: XML in Java, Java Servlets and JSP, transformations between XML and non-XML data, and XSLT....
Decomposing a planar graph into an independent set and a 3-degenerate graph
Thomassen, Carsten
2001-01-01
We prove the conjecture made by O. V. Borodin in 1976 that the vertex set of every planar graph can be decomposed into an independent set and a set inducing a 3-degenerate graph. (C) 2001 Academic Press....
A Maximum Resonant Set of Polyomino Graphs
Zhang Heping
2016-05-01
Full Text Available A polyomino graph P is a connected finite subgraph of the infinite plane grid such that each finite face is surrounded by a regular square of side length one and each edge belongs to at least one square. A dimer covering of P corresponds to a perfect matching. Different dimer coverings can interact via an alternating cycle (or square with respect to them. A set of disjoint squares of P is a resonant set if P has a perfect matching M so that each one of those squares is M-alternating. In this paper, we show that if K is a maximum resonant set of P, then P − K has a unique perfect matching. We further prove that the maximum forcing number of a polyomino graph is equal to the cardinality of a maximum resonant set. This confirms a conjecture of Xu et al. [26]. We also show that if K is a maximal alternating set of P, then P − K has a unique perfect matching.
Tutte sets in graphs I: Maximal tutte sets and D-graphs
Bauer, D.; Broersma, Haitze J.; Morgana, A.; Schmeichel, E.
A well-known formula of Tutte and Berge expresses the size of a maximum matching in a graph $G$ in terms of what is usually called the deficiency of $G$. A subset $X$ of $V(G)$ for which this deficiency is attained is called a Tutte set of $G$. While much is known about maximum matchings, less is
The number of independent sets in unicyclic graphs
Pedersen, Anders Sune; Vestergaard, Preben Dahl
In this paper, we determine upper and lower bounds for the number of independent sets in a unicyclic graph in terms of its order. This gives an upper bound for the number of independent sets in a connected graph which contains at least one cycle. We also determine the upper bound for the number...
Connected feedback vertex set in planar graphs
Grigoriev, Alexander; Sitters, René
2010-01-01
We study the problem of finding a minimum tree spanning the faces of a given planar graph. We show that a constant factor approximation follows from the unconnected version if the minimum degree is 3. Moreover, we present a polynomial time approximation scheme for both the connected and unconnected
Application of Bipolar Fuzzy Sets in Graph Structures
Muhammad Akram
2016-01-01
Full Text Available A graph structure is a useful tool in solving the combinatorial problems in different areas of computer science and computational intelligence systems. In this paper, we apply the concept of bipolar fuzzy sets to graph structures. We introduce certain notions, including bipolar fuzzy graph structure (BFGS, strong bipolar fuzzy graph structure, bipolar fuzzy Ni-cycle, bipolar fuzzy Ni-tree, bipolar fuzzy Ni-cut vertex, and bipolar fuzzy Ni-bridge, and illustrate these notions by several examples. We study ϕ-complement, self-complement, strong self-complement, and totally strong self-complement in bipolar fuzzy graph structures, and we investigate some of their interesting properties.
Weighted Maximum-Clique Transversal Sets of Graphs
Chuan-Min Lee
2011-01-01
A maximum-clique transversal set of a graph G is a subset of vertices intersecting all maximum cliques of G. The maximum-clique transversal set problem is to find a maximum-clique transversal set of G of minimum cardinality. Motivated by the placement of transmitters for cellular telephones, Chang, Kloks, and Lee introduced the concept of maximum-clique transversal sets on graphs in 2001. In this paper, we study the weighted version of the maximum-clique transversal set problem for split grap...
Software for Graph Analysis and Visualization
M. I. Kolomeychenko
2014-01-01
Full Text Available This paper describes the software for graph storage, analysis and visualization. The article presents a comparative analysis of existing software for analysis and visualization of graphs, describes the overall architecture of application and basic principles of construction and operation of the main modules. Furthermore, a description of the developed graph storage oriented to storage and processing of large-scale graphs is presented. The developed algorithm for finding communities and implemented algorithms of autolayouts of graphs are the main functionality of the product. The main advantage of the developed software is high speed processing of large size networks (up to millions of nodes and links. Moreover, the proposed graph storage architecture is unique and has no analogues. The developed approaches and algorithms are optimized for operating with big graphs and have high productivity.
Attack Graph Construction for Security Events Analysis
Andrey Alexeevich Chechulin
2014-09-01
Full Text Available The paper is devoted to investigation of the attack graphs construction and analysis task for a network security evaluation and real-time security event processing. Main object of this research is the attack modeling process. The paper contains the description of attack graphs building, modifying and analysis technique as well as overview of implemented prototype for network security analysis based on attack graph approach.
Reconfiguring Independent Sets in Claw-Free Graphs
Bonsma, P.S.; Kamiński, Marcin; Wrochna, Marcin; Ravi, R.; Gørtz, Inge Li
We present a polynomial-time algorithm that, given two independent sets in a claw-free graph G, decides whether one can be transformed into the other by a sequence of elementary steps. Each elementary step is to remove a vertex v from the current independent set S and to add a new vertex w (not in
Applied and computational harmonic analysis on graphs and networks
Irion, Jeff; Saito, Naoki
2015-09-01
In recent years, the advent of new sensor technologies and social network infrastructure has provided huge opportunities and challenges for analyzing data recorded on such networks. In the case of data on regular lattices, computational harmonic analysis tools such as the Fourier and wavelet transforms have well-developed theories and proven track records of success. It is therefore quite important to extend such tools from the classical setting of regular lattices to the more general setting of graphs and networks. In this article, we first review basics of graph Laplacian matrices, whose eigenpairs are often interpreted as the frequencies and the Fourier basis vectors on a given graph. We point out, however, that such an interpretation is misleading unless the underlying graph is either an unweighted path or cycle. We then discuss our recent effort of constructing multiscale basis dictionaries on a graph, including the Hierarchical Graph Laplacian Eigenbasis Dictionary and the Generalized Haar-Walsh Wavelet Packet Dictionary, which are viewed as generalizations of the classical hierarchical block DCTs and the Haar-Walsh wavelet packets, respectively, to the graph setting. Finally, we demonstrate the usefulness of our dictionaries by using them to simultaneously segment and denoise 1-D noisy signals sampled on regular lattices, a problem where classical tools have difficulty.
Muhammad, Akram; Musavarah, Sarwar
2016-01-01
In this research study, we introduce the concept of bipolar neutrosophic graphs. We present the dominating and independent sets of bipolar neutrosophic graphs. We describe novel multiple criteria decision making methods based on bipolar neutrosophic sets and bipolar neutrosophic graphs. We also develop an algorithm for computing domination in bipolar neutrosophic graphs.
Partitioning the vertices of a graph into two total dominating sets ...
A total dominating set in a graph G is a set S of vertices of G such that every vertex in G is adjacent to a vertex of S. We study graphs whose vertex set can be partitioned into two total dominating sets. In particular, we develop several sufficient conditions for a graph to have a vertex partition into two total dominating sets.
Distributed Large Independent Sets in One Round On Bounded-independence Graphs
Halldorsson , Magnus M.; Konrad , Christian
2015-01-01
International audience; We present a randomized one-round, single-bit messages, distributed algorithm for the maximum independent set problem in polynomially bounded-independence graphs with poly-logarithmic approximation factor. Bounded-independence graphs capture various models of wireless networks such as the unit disc graphs model and the quasi unit disc graphs model. For instance, on unit disc graphs, our achieved approximation ratio is O((log(n)/log(log(n)))^2).A starting point of our w...
Some Results on the Graph Theory for Complex Neutrosophic Sets
Shio Gai Quek
2018-05-01
Full Text Available Fuzzy graph theory plays an important role in the study of the symmetry and asymmetry properties of fuzzy graphs. With this in mind, in this paper, we introduce new neutrosophic graphs called complex neutrosophic graphs of type 1 (abbr. CNG1. We then present a matrix representation for it and study some properties of this new concept. The concept of CNG1 is an extension of the generalized fuzzy graphs of type 1 (GFG1 and generalized single-valued neutrosophic graphs of type 1 (GSVNG1. The utility of the CNG1 introduced here are applied to a multi-attribute decision making problem related to Internet server selection.
SNAP: A General Purpose Network Analysis and Graph Mining Library.
Leskovec, Jure; Sosič, Rok
2016-10-01
Large networks are becoming a widely used abstraction for studying complex systems in a broad set of disciplines, ranging from social network analysis to molecular biology and neuroscience. Despite an increasing need to analyze and manipulate large networks, only a limited number of tools are available for this task. Here, we describe Stanford Network Analysis Platform (SNAP), a general-purpose, high-performance system that provides easy to use, high-level operations for analysis and manipulation of large networks. We present SNAP functionality, describe its implementational details, and give performance benchmarks. SNAP has been developed for single big-memory machines and it balances the trade-off between maximum performance, compact in-memory graph representation, and the ability to handle dynamic graphs where nodes and edges are being added or removed over time. SNAP can process massive networks with hundreds of millions of nodes and billions of edges. SNAP offers over 140 different graph algorithms that can efficiently manipulate large graphs, calculate structural properties, generate regular and random graphs, and handle attributes and meta-data on nodes and edges. Besides being able to handle large graphs, an additional strength of SNAP is that networks and their attributes are fully dynamic, they can be modified during the computation at low cost. SNAP is provided as an open source library in C++ as well as a module in Python. We also describe the Stanford Large Network Dataset, a set of social and information real-world networks and datasets, which we make publicly available. The collection is a complementary resource to our SNAP software and is widely used for development and benchmarking of graph analytics algorithms.
Cycles through all finite vertex sets in infinite graphs
Kundgen, Andre; Li, Binlong; Thomassen, Carsten
2017-01-01
is contained in a cycle of G. We apply this to extend a number of results and conjectures on finite graphs to Hamiltonian curves in infinite locally finite graphs. For example, Barnette’s conjecture (that every finite planar cubic 3-connected bipartite graph is Hamiltonian) is equivalent to the statement...
Tutte sets in graphs II: The complexity of finding maximum Tutte sets
Bauer, D.; Broersma, Haitze J.; Kahl, N.; Morgana, A.; Schmeichel, E.; Surowiec, T.
2007-01-01
A well-known formula of Tutte and Berge expresses the size of a maximum matching in a graph $G$ in terms of what is usually called the deficiency. A subset $X$ of $V(G)$ for which this deficiency is attained is called a Tutte set of $G$. While much is known about maximum matchings, less is known
On The Center Sets and Center Numbers of Some Graph Classes
R, Ram Kumar.; Balakrishnan, Kannan; Changat, Manoj; Sreekumar, A.; Narasimha-Shenoi, Prasanth G.
2013-01-01
For a set $S$ of vertices and the vertex $v$ in a connected graph $G$, $\\displaystyle\\max_{x \\in S}d(x,v)$ is called the $S$-eccentricity of $v$ in $G$. The set of vertices with minimum $S$-eccentricity is called the $S$-center of $G$. Any set $A$ of vertices of $G$ such that $A$ is an $S$-center for some set $S$ of vertices of $G$ is called a center set. We identify the center sets of certain classes of graphs namely, Block graphs, $K_{m,n}$, $K_n-e$, wheel graphs, odd cycles and symmetric e...
Vatrapu, Ravi; Hussain, Abid; Buus Lassen, Niels
2015-01-01
of Facebook or Twitter data. However, there exist no other holistic computational social science approach beyond the relational sociology and graph theory of SNA. To address this limitation, this paper presents an alternative holistic approach to Big Social Data analytics called Social Set Analysis (SSA......This paper argues that the basic premise of Social Network Analysis (SNA) -- namely that social reality is constituted by dyadic relations and that social interactions are determined by structural properties of networks-- is neither necessary nor sufficient, for Big Social Data analytics...
Strategic Port Graph Rewriting: An Interactive Modelling and Analysis Framework
Maribel Fernández
2014-07-01
Full Text Available We present strategic portgraph rewriting as a basis for the implementation of visual modelling and analysis tools. The goal is to facilitate the specification, analysis and simulation of complex systems, using port graphs. A system is represented by an initial graph and a collection of graph rewriting rules, together with a user-defined strategy to control the application of rules. The strategy language includes constructs to deal with graph traversal and management of rewriting positions in the graph. We give a small-step operational semantics for the language, and describe its implementation in the graph transformation and visualisation tool PORGY.
Material control study: a directed graph and fault tree procedure for adversary event set generation
Lambert, H.E.; Lim, J.J.; Gilman, F.M.
1978-01-01
In work for the United States Nuclear Regulatory Commission, Lawrence Livermore Laboratory is developing an assessment procedure to evaluate the effectiveness of a potential nuclear facility licensee's material control (MC) system. The purpose of an MC system is to prevent the theft of special nuclear material such as plutonium and highly enriched uranium. The key in the assessment procedure is the generation and analysis of the adversary event sets by a directed graph and fault-tree methodology
Application of graph theory to the morphological analysis of settlements
Szmytkie Robert
2017-01-01
In the following paper, the analyses of morphology of settlements were conducted using graph methods. The intention of the author was to create a quantifiable and simple measure, which, in a quantitative way, would express the degree of development of a graph (the spatial pattern of settlement). When analysing examples of graphs assigned to a set of small towns and large villages, it was noticed that the graph development index should depend on: a relative number of edges in relation to the n...
Multiscale weighted colored graphs for protein flexibility and rigidity analysis
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.
Text categorization of biomedical data sets using graph kernels and a controlled vocabulary.
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.
Almost all k-cop-win graphs contain a dominating set of cardinality k
Pralat, Pawel
2013-01-01
We consider $k$-cop-win graphs in the binomial random graph $G(n,1/2).$ It is known that almost all cop-win graphs contain a universal vertex. We generalize this result and prove that for every $k \\in N$, almost all $k$-cop-win graphs contain a dominating set of cardinality $k$. From this it follows that the asymptotic number of labelled $k$-cop-win graphs of order $n$ is equal to $(1+o(1)) (1-2^{-k})^{-k} {n \\choose k} 2^{n^2/2 - (1/2-\\log_2(1-2^{-k})) n}$.
Two-setting Bell inequalities for graph states
Toth, Geza; Guehne, Otfried; Briegel, Hans J.
2006-01-01
We present Bell inequalities for graph states with a high violation of local realism. In particular, we show that there is a basic Bell inequality for every nontrivial graph state which is violated by the state at least by a factor of 2. This inequality needs the measurement of, at most, two operators for each qubit and involves only some of the qubits. We also show that for some families of graph states composite Bell inequalities can be constructed such that the violation of local realism increases exponentially with the number of qubits. We prove that some of our inequalities are facets of the convex polytope containing the many-body correlations consistent with local hidden variable models. Our Bell inequalities are built from stabilizing operators of graph states
Refining intra-protein contact prediction by graph analysis
Eyal Eran
2007-05-01
Full Text Available Abstract Background Accurate prediction of intra-protein residue contacts from sequence information will allow the prediction of protein structures. Basic predictions of such specific contacts can be further refined by jointly analyzing predicted contacts, and by adding information on the relative positions of contacts in the protein primary sequence. Results We introduce a method for graph analysis refinement of intra-protein contacts, termed GARP. Our previously presented intra-contact prediction method by means of pair-to-pair substitution matrix (P2PConPred was used to test the GARP method. In our approach, the top contact predictions obtained by a basic prediction method were used as edges to create a weighted graph. The edges were scored by a mutual clustering coefficient that identifies highly connected graph regions, and by the density of edges between the sequence regions of the edge nodes. A test set of 57 proteins with known structures was used to determine contacts. GARP improves the accuracy of the P2PConPred basic prediction method in whole proteins from 12% to 18%. Conclusion Using a simple approach we increased the contact prediction accuracy of a basic method by 1.5 times. Our graph approach is simple to implement, can be used with various basic prediction methods, and can provide input for further downstream analyses.
Modular Environment for Graph Research and Analysis with a Persistent
2009-11-18
The MEGRAPHS software package provides a front-end to graphs and vectors residing on special-purpose computing resources. It allows these data objects to be instantiated, destroyed, and manipulated. A variety of primitives needed for typical graph analyses are provided. An example program illustrating how MEGRAPHS can be used to implement a PageRank computation is included in the distribution.The MEGRAPHS software package is targeted towards developers of graph algorithms. Programmers using MEGRAPHS would write graph analysis programs in terms of high-level graph and vector operations. These computations are transparently executed on the Cray XMT compute nodes.
Visibility Graph Based Time Series Analysis.
Stephen, Mutua; Gu, Changgui; Yang, Huijie
2015-01-01
Network based time series analysis has made considerable achievements in the recent years. By mapping mono/multivariate time series into networks, one can investigate both it's microscopic and macroscopic behaviors. However, most proposed approaches lead to the construction of static networks consequently providing limited information on evolutionary behaviors. In the present paper we propose a method called visibility graph based time series analysis, in which series segments are mapped to visibility graphs as being descriptions of the corresponding states and the successively occurring states are linked. This procedure converts a time series to a temporal network and at the same time a network of networks. Findings from empirical records for stock markets in USA (S&P500 and Nasdaq) and artificial series generated by means of fractional Gaussian motions show that the method can provide us rich information benefiting short-term and long-term predictions. Theoretically, we propose a method to investigate time series from the viewpoint of network of networks.
Visibility Graph Based Time Series Analysis.
Mutua Stephen
Full Text Available Network based time series analysis has made considerable achievements in the recent years. By mapping mono/multivariate time series into networks, one can investigate both it's microscopic and macroscopic behaviors. However, most proposed approaches lead to the construction of static networks consequently providing limited information on evolutionary behaviors. In the present paper we propose a method called visibility graph based time series analysis, in which series segments are mapped to visibility graphs as being descriptions of the corresponding states and the successively occurring states are linked. This procedure converts a time series to a temporal network and at the same time a network of networks. Findings from empirical records for stock markets in USA (S&P500 and Nasdaq and artificial series generated by means of fractional Gaussian motions show that the method can provide us rich information benefiting short-term and long-term predictions. Theoretically, we propose a method to investigate time series from the viewpoint of network of networks.
Visibility graph analysis on heartbeat dynamics of meditation training
Jiang, Sen; Bian, Chunhua; Ning, Xinbao; Ma, Qianli D. Y.
2013-06-01
We apply the visibility graph analysis to human heartbeat dynamics by constructing the complex networks of heartbeat interval time series and investigating the statistical properties of the network before and during chi and yoga meditation. The experiment results show that visibility graph analysis can reveal the dynamical changes caused by meditation training manifested as regular heartbeat, which is closely related to the adjustment of autonomous neural system, and visibility graph analysis is effective to evaluate the effect of meditation.
Zero Forcing Sets and Controllability of Dynamical Systems Defined on Graphs
Monshizadeh Naini, Nima; Zhang, Shuo; Camlibel, M. Kanat
In this technical note, controllability of systems defined on graphs is discussed. We consider the problem of controllability of the network for a family of matrices carrying the structure of an underlying directed graph. A one-to-one correspondence between the set of leaders rendering the network
Maximal independent set graph partitions for representations of body-centered cubic lattices
Erleben, Kenny
2009-01-01
corresponding to the leaves of a quad-tree thus has a smaller memory foot-print. The adjacency information in the graph relieves one from going up and down the quad-tree when searching for neighbors. This results in constant time complexities for refinement and coarsening operations.......A maximal independent set graph data structure for a body-centered cubic lattice is presented. Refinement and coarsening operations are defined in terms of set-operations resulting in robust and easy implementation compared to a quad-tree-based implementation. The graph only stores information...
Decomposing a planar graph of girth 5 into an independent set and a forest
Kawarabayashi, Ken-ichi; Thomassen, Carsten
2009-01-01
We use a list-color technique to extend the result of Borodin and Glebov that the vertex set of every planar graph of girth at least 5 can be partitioned into an independent set and a set which induces a forest. We apply this extension to also extend Grötzsch's theorem that every planar triangle-...
Application of graph theory to the morphological analysis of settlements
Szmytkie Robert
2017-12-01
Full Text Available In the following paper, the analyses of morphology of settlements were conducted using graph methods. The intention of the author was to create a quantifiable and simple measure, which, in a quantitative way, would express the degree of development of a graph (the spatial pattern of settlement. When analysing examples of graphs assigned to a set of small towns and large villages, it was noticed that the graph development index should depend on: a relative number of edges in relation to the number of nodes (β index, the number of cycles (urban blocks, which evidences the complexity of the spatial pattern of settlement, and the average rank of nodes of a graph, which expresses the degree of complexity of a street network.
GOGrapher: A Python library for GO graph representation and analysis.
Muller, Brian; Richards, Adam J; Jin, Bo; Lu, Xinghua
2009-07-07
The Gene Ontology is the most commonly used controlled vocabulary for annotating proteins. The concepts in the ontology are organized as a directed acyclic graph, in which a node corresponds to a biological concept and a directed edge denotes the parent-child semantic relationship between a pair of terms. A large number of protein annotations further create links between proteins and their functional annotations, reflecting the contemporary knowledge about proteins and their functional relationships. This leads to a complex graph consisting of interleaved biological concepts and their associated proteins. What is needed is a simple, open source library that provides tools to not only create and view the Gene Ontology graph, but to analyze and manipulate it as well. Here we describe the development and use of GOGrapher, a Python library that can be used for the creation, analysis, manipulation, and visualization of Gene Ontology related graphs. An object-oriented approach was adopted to organize the hierarchy of the graphs types and associated classes. An Application Programming Interface is provided through which different types of graphs can be pragmatically created, manipulated, and visualized. GOGrapher has been successfully utilized in multiple research projects, e.g., a graph-based multi-label text classifier for protein annotation. The GOGrapher project provides a reusable programming library designed for the manipulation and analysis of Gene Ontology graphs. The library is freely available for the scientific community to use and improve.
GOGrapher: A Python library for GO graph representation and analysis
Lu Xinghua
2009-07-01
Full Text Available Abstract Background The Gene Ontology is the most commonly used controlled vocabulary for annotating proteins. The concepts in the ontology are organized as a directed acyclic graph, in which a node corresponds to a biological concept and a directed edge denotes the parent-child semantic relationship between a pair of terms. A large number of protein annotations further create links between proteins and their functional annotations, reflecting the contemporary knowledge about proteins and their functional relationships. This leads to a complex graph consisting of interleaved biological concepts and their associated proteins. What is needed is a simple, open source library that provides tools to not only create and view the Gene Ontology graph, but to analyze and manipulate it as well. Here we describe the development and use of GOGrapher, a Python library that can be used for the creation, analysis, manipulation, and visualization of Gene Ontology related graphs. Findings An object-oriented approach was adopted to organize the hierarchy of the graphs types and associated classes. An Application Programming Interface is provided through which different types of graphs can be pragmatically created, manipulated, and visualized. GOGrapher has been successfully utilized in multiple research projects, e.g., a graph-based multi-label text classifier for protein annotation. Conclusion The GOGrapher project provides a reusable programming library designed for the manipulation and analysis of Gene Ontology graphs. The library is freely available for the scientific community to use and improve.
Analysis and enumeration algorithms for biological graphs
Marino, Andrea
2015-01-01
In this work we plan to revise the main techniques for enumeration algorithms and to show four examples of enumeration algorithms that can be applied to efficiently deal with some biological problems modelled by using biological networks: enumerating central and peripheral nodes of a network, enumerating stories, enumerating paths or cycles, and enumerating bubbles. Notice that the corresponding computational problems we define are of more general interest and our results hold in the case of arbitrary graphs. Enumerating all the most and less central vertices in a network according to their eccentricity is an example of an enumeration problem whose solutions are polynomial and can be listed in polynomial time, very often in linear or almost linear time in practice. Enumerating stories, i.e. all maximal directed acyclic subgraphs of a graph G whose sources and targets belong to a predefined subset of the vertices, is on the other hand an example of an enumeration problem with an exponential number of solutions...
Dynamic MLD analysis with flow graphs
Jenab, K.; Sarfaraz, A.; Dhillon, B.S.; Seyed Hosseini, S.M.
2012-01-01
Master Logic Diagram (MLD) depicts the interrelationships among the independent functions and dependent support functions. Using MLD, the manner in which all functions, sub-functions interact to achieve the overall system objective can be investigated. This paper reports a probabilistic model to analyze an MLD by translating the interrelationships to a graph model. The proposed model uses the flow-graph concept and Moment Generating Function (MGF) to analyze the dependency matrix representing the MLD with embedded self-healing function/sub-functions. The functions/sub-functions are featured by failure detection and recovery mechanisms. The newly developed model provides the probability of the system failure, and system mean and standard deviation time to failure in the MLD. An illustrative example is demonstrated to present the application of the model.
DNA microarray data and contextual analysis of correlation graphs
Hingamp Pascal
2003-04-01
Full Text Available Abstract Background DNA microarrays are used to produce large sets of expression measurements from which specific biological information is sought. Their analysis requires efficient and reliable algorithms for dimensional reduction, classification and annotation. Results We study networks of co-expressed genes obtained from DNA microarray experiments. The mathematical concept of curvature on graphs is used to group genes or samples into clusters to which relevant gene or sample annotations are automatically assigned. Application to publicly available yeast and human lymphoma data demonstrates the reliability of the method in spite of its simplicity, especially with respect to the small number of parameters involved. Conclusions We provide a method for automatically determining relevant gene clusters among the many genes monitored with microarrays. The automatic annotations and the graphical interface improve the readability of the data. A C++ implementation, called Trixy, is available from http://tagc.univ-mrs.fr/bioinformatics/trixy.html.
Discrete geometric analysis of message passing algorithm on graphs
Watanabe, Yusuke
2010-04-01
We often encounter probability distributions given as unnormalized products of non-negative functions. The factorization structures are represented by hypergraphs called factor graphs. Such distributions appear in various fields, including statistics, artificial intelligence, statistical physics, error correcting codes, etc. Given such a distribution, computations of marginal distributions and the normalization constant are often required. However, they are computationally intractable because of their computational costs. One successful approximation method is Loopy Belief Propagation (LBP) algorithm. The focus of this thesis is an analysis of the LBP algorithm. If the factor graph is a tree, i.e. having no cycle, the algorithm gives the exact quantities. If the factor graph has cycles, however, the LBP algorithm does not give exact results and possibly exhibits oscillatory and non-convergent behaviors. The thematic question of this thesis is "How the behaviors of the LBP algorithm are affected by the discrete geometry of the factor graph?" The primary contribution of this thesis is the discovery of a formula that establishes the relation between the LBP, the Bethe free energy and the graph zeta function. This formula provides new techniques for analysis of the LBP algorithm, connecting properties of the graph and of the LBP and the Bethe free energy. We demonstrate applications of the techniques to several problems including (non) convexity of the Bethe free energy, the uniqueness and stability of the LBP fixed point. We also discuss the loop series initiated by Chertkov and Chernyak. The loop series is a subgraph expansion of the normalization constant, or partition function, and reflects the graph geometry. We investigate theoretical natures of the series. Moreover, we show a partial connection between the loop series and the graph zeta function.
Network graph analysis and visualization with Gephi
Cherven, Ken
2013-01-01
A practical, hands-on guide, that provides you with all the tools you need to visualize and analyze your data using network graphs with Gephi.This book is for data analysts who want to intuitively reveal patterns and trends, highlight outliers, and tell stories with their data using Gephi. It is great for anyone looking to explore interactions within network datasets, whether the data comes from social media or elsewhere. It is also a valuable resource for those seeking to learn more about Gephi without being overwhelmed by technical details.
Political Discourse Analysis Through Solving Problems of Graph Theory
Monica Patrut
2010-03-01
Full Text Available In this article, we show how, using graph theory, we can make a content analysis of political discourse. Assumptions of this analysis are:
- we have a corpus of speech of each party or candidate;
- we consider that speech conveys economic, political, socio-cultural values, these taking the form of words or word families;
- we consider that there are interdependences between the values of a political discourse; they are given by the co-occurrence of two values, as words in the text, within a well defined fragment, or they are determined by the internal logic of political discourse;
- established links between values in a political speech have associated positive numbers indicating the "power" of those links; these "powers" are defined according to both the number of co-occurrences of values, and the internal logic of the discourse where they occur.
In this context we intend to highlight the following:
a which is the dominant value in a political speech;
b which groups of values have ties between them and have no connection with the rest;
c which is the order in which political values should be set in order to obtain an equivalent but more synthetic speech compared to the already given one;
d which are the links between values that form the "core" political speech.
To solve these problems, we shall use the Political Analyst program. After that, we shall present the concepts necessary to the understanding of the introductory graph theory, useful in understanding the analysis of the software and then the operation of the program. This paper extends the previous paper [6].
Graph based communication analysis for hardware/software codesign
Knudsen, Peter Voigt; Madsen, Jan
1999-01-01
In this paper we present a coarse grain CDFG (Control/Data Flow Graph) model suitable for hardware/software partitioning of single processes and demonstrate how it is necessary to perform various transformations on the graph structure before partitioning in order to achieve a structure that allows...... for accurate estimation of communication overhead between nodes mapped to different processors. In particular, we demonstrate how various transformations of control structures can lead to a more accurate communication analysis and more efficient implementations. The purpose of the transformations is to obtain...
Max-plus algebraic throughput analysis of synchronous dataflow graphs
de Groote, Robert; Kuper, Jan; Broersma, Haitze J.; Smit, Gerardus Johannes Maria
2012-01-01
In this paper we present a novel approach to throughput analysis of synchronous dataflow (SDF) graphs. Our approach is based on describing the evolution of actor firing times as a linear time-invariant system in max-plus algebra. Experimental results indicate that our approach is faster than
Trudeau, Richard J
1994-01-01
Preface1. Pure Mathematics Introduction; Euclidean Geometry as Pure Mathematics; Games; Why Study Pure Mathematics?; What's Coming; Suggested Reading2. Graphs Introduction; Sets; Paradox; Graphs; Graph diagrams; Cautions; Common Graphs; Discovery; Complements and Subgraphs; Isomorphism; Recognizing Isomorphic Graphs; Semantics The Number of Graphs Having a Given nu; Exercises; Suggested Reading3. Planar Graphs Introduction; UG, K subscript 5, and the Jordan Curve Theorem; Are there More Nonplanar Graphs?; Expansions; Kuratowski's Theorem; Determining Whether a Graph is Planar or
Vatrapu, Ravi; Mukkamala, Raghava Rao; Hussain, Abid
2016-01-01
, conceptual and formal models of social data, and an analytical framework for combining big social data sets with organizational and societal data sets. Three empirical studies of big social data are presented to illustrate and demonstrate social set analysis in terms of fuzzy set-theoretical sentiment...... automata and agent-based modeling). However, when it comes to organizational and societal units of analysis, there exists no approach to conceptualize, model, analyze, explain, and predict social media interactions as individuals' associations with ideas, values, identities, and so on. To address...... analysis, crisp set-theoretical interaction analysis, and event-studies-oriented set-theoretical visualizations. Implications for big data analytics, current limitations of the set-theoretical approach, and future directions are outlined....
Information Retrieval and Graph Analysis Approaches for Book Recommendation.
Benkoussas, Chahinez; Bellot, Patrice
2015-01-01
A combination of multiple information retrieval approaches is proposed for the purpose of book recommendation. In this paper, book recommendation is based on complex user's query. We used different theoretical retrieval models: probabilistic as InL2 (Divergence from Randomness model) and language model and tested their interpolated combination. Graph analysis algorithms such as PageRank have been successful in Web environments. We consider the application of this algorithm in a new retrieval approach to related document network comprised of social links. We called Directed Graph of Documents (DGD) a network constructed with documents and social information provided from each one of them. Specifically, this work tackles the problem of book recommendation in the context of INEX (Initiative for the Evaluation of XML retrieval) Social Book Search track. A series of reranking experiments demonstrate that combining retrieval models yields significant improvements in terms of standard ranked retrieval metrics. These results extend the applicability of link analysis algorithms to different environments.
Utilization of graph theory in security analysis of power grid
Dalibor Válek
2014-12-01
Full Text Available This paper describes way how to use graph theory in security analysis. As an environment is used network of power lines and devices which are included here. Power grid is considered as a system of nodes which make together graph (network. On the simple example is applied Fiedler´s theory which is able to select the most important power lines of whole network. Components related to these lines are logicly ordered and considered by author´s modified analysis. This method has been improved and optimalized for risks related with illegal acts. Each power grid component has been connected with possible kind of attack and every of this device was gradually evaluated by five coefficients which takes values from 1 to 10. On the coefficient basis was assessed the level of risk. In the last phase the most risky power grid components have been selected. On the selected devices have been proposed security measures.
High Performance Descriptive Semantic Analysis of Semantic Graph Databases
Joslyn, Cliff A.; Adolf, Robert D.; al-Saffar, Sinan; Feo, John T.; Haglin, David J.; Mackey, Greg E.; Mizell, David W.
2011-06-02
As semantic graph database technology grows to address components ranging from extant large triple stores to SPARQL endpoints over SQL-structured relational databases, it will become increasingly important to be able to understand their inherent semantic structure, whether codified in explicit ontologies or not. Our group is researching novel methods for what we call descriptive semantic analysis of RDF triplestores, to serve purposes of analysis, interpretation, visualization, and optimization. But data size and computational complexity makes it increasingly necessary to bring high performance computational resources to bear on this task. Our research group built a novel high performance hybrid system comprising computational capability for semantic graph database processing utilizing the large multi-threaded architecture of the Cray XMT platform, conventional servers, and large data stores. In this paper we describe that architecture and our methods, and present the results of our analyses of basic properties, connected components, namespace interaction, and typed paths such for the Billion Triple Challenge 2010 dataset.
Information Retrieval and Graph Analysis Approaches for Book Recommendation
Chahinez Benkoussas; Patrice Bellot
2015-01-01
A combination of multiple information retrieval approaches is proposed for the purpose of book recommendation. In this paper, book recommendation is based on complex user's query. We used different theoretical retrieval models: probabilistic as InL2 (Divergence from Randomness model) and language model and tested their interpolated combination. Graph analysis algorithms such as PageRank have been successful in Web environments. We consider the application of this algorithm in a new retrieval ...
Artistic image analysis using graph-based learning approaches.
Carneiro, Gustavo
2013-08-01
We introduce a new methodology for the problem of artistic image analysis, which among other tasks, involves the automatic identification of visual classes present in an art work. In this paper, we advocate the idea that artistic image analysis must explore a graph that captures the network of artistic influences by computing the similarities in terms of appearance and manual annotation. One of the novelties of our methodology is the proposed formulation that is a principled way of combining these two similarities in a single graph. Using this graph, we show that an efficient random walk algorithm based on an inverted label propagation formulation produces more accurate annotation and retrieval results compared with the following baseline algorithms: bag of visual words, label propagation, matrix completion, and structural learning. We also show that the proposed approach leads to a more efficient inference and training procedures. This experiment is run on a database containing 988 artistic images (with 49 visual classification problems divided into a multiclass problem with 27 classes and 48 binary problems), where we show the inference and training running times, and quantitative comparisons with respect to several retrieval and annotation performance measures.
Knowledge based analysis of radiology reports using conceptual graphs
Schroeder, M.
1992-07-01
The telegraphic language found in radiological reports can be well understood by a natrual language system using the underlying domain knowledge. We present the METEXA system, which emphasizes the use of radiological domain knowledge to determine the semantics of utterances. Syntactic and semantic analysis, lexical sematics and the structure of the domain model are described in some detail. A resolution-based inference engine answers relevant questions concerning the contents of the reports. As knowledge representation formalism the Conceptual Graph Theory by John Sowa has been chosen. (orig.)
High-performance analysis of filtered semantic graphs
Buluç, A; Fox, A; Gilbert, JR; Kamil, S; Lugowski, A; Oliker, L; Williams, S
2012-01-01
High performance is a crucial consideration when executing a complex analytic query on a massive semantic graph. In a semantic graph, vertices and edges carry \\attributes" of various types. Analytic queries on semantic graphs typically depend on the values of these attributes; thus, the computation must either view the graph through a filter that passes only those individual vertices and edges of interest, or else must first materialize a subgraph or subgraphs consisting of only the vertices ...
Graph-Based Analysis of Nuclear Smuggling Data
Cook, Diane; Holder, Larry; Thompson, Sandra E.; Whitney, Paul D.; Chilton, Lawrence
2009-01-01
Much of the data that is collected and analyzed today is structural, consisting not only of entities but also of relationships between the entities. As a result, analysis applications rely upon automated structural data mining approaches to find patterns and concepts of interest. This ability to analyze structural data has become a particular challenge in many security-related domains. In these domains, focusing on the relationships between entities in the data is critical to detect important underlying patterns. In this study we apply structural data mining techniques to automate analysis of nuclear smuggling data. In particular, we choose to model the data as a graph and use graph-based relational learning to identify patterns and concepts of interest in the data. In this paper, we identify the analysis questions that are of importance to security analysts and describe the knowledge representation and data mining approach that we adopt for this challenge. We analyze the results using the Russian nuclear smuggling event database.
Hendrix, William; Jenkins, John; Padmanabhan, Kanchana; Chakraborty, Arpan
2014-01-01
Practical Graph Mining with R presents a "do-it-yourself" approach to extracting interesting patterns from graph data. It covers many basic and advanced techniques for the identification of anomalous or frequently recurring patterns in a graph, the discovery of groups or clusters of nodes that share common patterns of attributes and relationships, the extraction of patterns that distinguish one category of graphs from another, and the use of those patterns to predict the category of new graphs. Hands-On Application of Graph Data Mining Each chapter in the book focuses on a graph mining task, such as link analysis, cluster analysis, and classification. Through applications using real data sets, the book demonstrates how computational techniques can help solve real-world problems. The applications covered include network intrusion detection, tumor cell diagnostics, face recognition, predictive toxicology, mining metabolic and protein-protein interaction networks, and community detection in social networks. De...
Information Retrieval and Graph Analysis Approaches for Book Recommendation
Chahinez Benkoussas
2015-01-01
Full Text Available A combination of multiple information retrieval approaches is proposed for the purpose of book recommendation. In this paper, book recommendation is based on complex user's query. We used different theoretical retrieval models: probabilistic as InL2 (Divergence from Randomness model and language model and tested their interpolated combination. Graph analysis algorithms such as PageRank have been successful in Web environments. We consider the application of this algorithm in a new retrieval approach to related document network comprised of social links. We called Directed Graph of Documents (DGD a network constructed with documents and social information provided from each one of them. Specifically, this work tackles the problem of book recommendation in the context of INEX (Initiative for the Evaluation of XML retrieval Social Book Search track. A series of reranking experiments demonstrate that combining retrieval models yields significant improvements in terms of standard ranked retrieval metrics. These results extend the applicability of link analysis algorithms to different environments.
Graph analysis of dream reports is especially informative about psychosis.
Mota, Natália B; Furtado, Raimundo; Maia, Pedro P C; Copelli, Mauro; Ribeiro, Sidarta
2014-01-15
Early psychiatry investigated dreams to understand psychopathologies. Contemporary psychiatry, which neglects dreams, has been criticized for lack of objectivity. In search of quantitative insight into the structure of psychotic speech, we investigated speech graph attributes (SGA) in patients with schizophrenia, bipolar disorder type I, and non-psychotic controls as they reported waking and dream contents. Schizophrenic subjects spoke with reduced connectivity, in tight correlation with negative and cognitive symptoms measured by standard psychometric scales. Bipolar and control subjects were undistinguishable by waking reports, but in dream reports bipolar subjects showed significantly less connectivity. Dream-related SGA outperformed psychometric scores or waking-related data for group sorting. Altogether, the results indicate that online and offline processing, the two most fundamental modes of brain operation, produce nearly opposite effects on recollections: While dreaming exposes differences in the mnemonic records across individuals, waking dampens distinctions. The results also demonstrate the feasibility of the differential diagnosis of psychosis based on the analysis of dream graphs, pointing to a fast, low-cost and language-invariant tool for psychiatric diagnosis and the objective search for biomarkers. The Freudian notion that "dreams are the royal road to the unconscious" is clinically useful, after all.
Graph analysis of dream reports is especially informative about psychosis
Mota, Natália B.; Furtado, Raimundo; Maia, Pedro P. C.; Copelli, Mauro; Ribeiro, Sidarta
2014-01-01
Early psychiatry investigated dreams to understand psychopathologies. Contemporary psychiatry, which neglects dreams, has been criticized for lack of objectivity. In search of quantitative insight into the structure of psychotic speech, we investigated speech graph attributes (SGA) in patients with schizophrenia, bipolar disorder type I, and non-psychotic controls as they reported waking and dream contents. Schizophrenic subjects spoke with reduced connectivity, in tight correlation with negative and cognitive symptoms measured by standard psychometric scales. Bipolar and control subjects were undistinguishable by waking reports, but in dream reports bipolar subjects showed significantly less connectivity. Dream-related SGA outperformed psychometric scores or waking-related data for group sorting. Altogether, the results indicate that online and offline processing, the two most fundamental modes of brain operation, produce nearly opposite effects on recollections: While dreaming exposes differences in the mnemonic records across individuals, waking dampens distinctions. The results also demonstrate the feasibility of the differential diagnosis of psychosis based on the analysis of dream graphs, pointing to a fast, low-cost and language-invariant tool for psychiatric diagnosis and the objective search for biomarkers. The Freudian notion that ``dreams are the royal road to the unconscious'' is clinically useful, after all.
Complexity Analysis of Precedence Terminating Infinite Graph Rewrite Systems
Naohi Eguchi
2015-05-01
Full Text Available The general form of safe recursion (or ramified recurrence can be expressed by an infinite graph rewrite system including unfolding graph rewrite rules introduced by Dal Lago, Martini and Zorzi, in which the size of every normal form by innermost rewriting is polynomially bounded. Every unfolding graph rewrite rule is precedence terminating in the sense of Middeldorp, Ohsaki and Zantema. Although precedence terminating infinite rewrite systems cover all the primitive recursive functions, in this paper we consider graph rewrite systems precedence terminating with argument separation, which form a subclass of precedence terminating graph rewrite systems. We show that for any precedence terminating infinite graph rewrite system G with a specific argument separation, both the runtime complexity of G and the size of every normal form in G can be polynomially bounded. As a corollary, we obtain an alternative proof of the original result by Dal Lago et al.
An Application of Graph Theory in Markov Chains Reliability Analysis
Pavel Skalny
2014-01-01
Full Text Available The paper presents reliability analysis which was realized for an industrial company. The aim of the paper is to present the usage of discrete time Markov chains and the flow in network approach. Discrete Markov chains a well-known method of stochastic modelling describes the issue. The method is suitable for many systems occurring in practice where we can easily distinguish various amount of states. Markov chains are used to describe transitions between the states of the process. The industrial process is described as a graph network. The maximal flow in the network corresponds to the production. The Ford-Fulkerson algorithm is used to quantify the production for each state. The combination of both methods are utilized to quantify the expected value of the amount of manufactured products for the given time period.
An Experiment on Graph Analysis Methodologies for Scenarios
Brothers, Alan J.; Whitney, Paul D.; Wolf, Katherine E.; Kuchar, Olga A.; Chin, George
2005-09-30
Visual graph representations are increasingly used to represent, display, and explore scenarios and the structure of organizations. The graph representations of scenarios are readily understood, and commercial software is available to create and manage these representations. The purpose of the research presented in this paper is to explore whether these graph representations support quantitative assessments of the underlying scenarios. The underlying structure of the scenarios is the information that is being targeted in the experiment and the extent to which the scenarios are similar in content. An experiment was designed that incorporated both the contents of the scenarios and analysts’ graph representations of the scenarios. The scenarios’ content was represented graphically by analysts, and both the structure and the semantics of the graph representation were attempted to be used to understand the content. The structure information was not found to be discriminating for the content of the scenarios in this experiment; but, the semantic information was discriminating.
EEG analysis of seizure patterns using visibility graphs for detection of generalized seizures.
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.
Viseur, Sophie; Chiaberge, Christophe; Rhomer, Jérémy; Audigane, Pascal
2015-04-01
computed for each reservoir rock geobody and studied through a graph spectral analysis. To achieve this, the skeleton is converted into a graph structure. The spectral analysis applied on this graph structure allows a distance to be defined between pairs of graphs. Therefore, this distance is used as support for clustering analysis to gather models that share the same reservoir rock topology. To show the ability of the defined distances to discriminate different types of reservoir connectivity, a synthetic data set of fluvial models with different geological settings was generated and studied using the proposed approach. The results of the clustering analysis are shown and discussed.
Overlapping communities detection based on spectral analysis of line graphs
Gui, Chun; Zhang, Ruisheng; Hu, Rongjing; Huang, Guoming; Wei, Jiaxuan
2018-05-01
Community in networks are often overlapping where one vertex belongs to several clusters. Meanwhile, many networks show hierarchical structure such that community is recursively grouped into hierarchical organization. In order to obtain overlapping communities from a global hierarchy of vertices, a new algorithm (named SAoLG) is proposed to build the hierarchical organization along with detecting the overlap of community structure. SAoLG applies the spectral analysis into line graphs to unify the overlap and hierarchical structure of the communities. In order to avoid the limitation of absolute distance such as Euclidean distance, SAoLG employs Angular distance to compute the similarity between vertices. Furthermore, we make a micro-improvement partition density to evaluate the quality of community structure and use it to obtain the more reasonable and sensible community numbers. The proposed SAoLG algorithm achieves a balance between overlap and hierarchy by applying spectral analysis to edge community detection. The experimental results on one standard network and six real-world networks show that the SAoLG algorithm achieves higher modularity and reasonable community number values than those generated by Ahn's algorithm, the classical CPM and GN ones.
Graph analysis of structural brain networks in Alzheimer's disease: beyond small world properties.
John, Majnu; Ikuta, Toshikazu; Ferbinteanu, Janina
2017-03-01
Changes in brain connectivity in patients with early Alzheimer's disease (AD) have been investigated using graph analysis. However, these studies were based on small data sets, explored a limited range of network parameters, and did not focus on more restricted sub-networks, where neurodegenerative processes may introduce more prominent alterations. In this study, we constructed structural brain networks out of 87 regions using data from 135 healthy elders and 100 early AD patients selected from the Open Access Series of Imaging Studies (OASIS) database. We evaluated the graph properties of these networks by investigating metrics of network efficiency, small world properties, segregation, product measures of complexity, and entropy. Because degenerative processes take place at different rates in different brain areas, analysis restricted to sub-networks may reveal changes otherwise undetected. Therefore, we first analyzed the graph properties of a network encompassing all brain areas considered together, and then repeated the analysis after dividing the brain areas into two sub-networks constructed by applying a clustering algorithm. At the level of large scale network, the analysis did not reveal differences between AD patients and controls. In contrast, the same analysis performed on the two sub-networks revealed that small worldness diminished with AD only in the sub-network containing the areas of medial temporal lobe known to be heaviest and earliest affected. The second sub-network, which did not present significant AD-induced modifications of 'classical' small world parameters, nonetheless showed a trend towards an increase in small world propensity, a novel metric that unbiasedly quantifies small world structure. Beyond small world properties, complexity and entropy measures indicated that the intricacy of connection patterns and structural diversity decreased in both sub-networks. These results show that neurodegenerative processes impact volumetric
On the graph and systems analysis of reversible chemical reaction networks with mass action kinetics
Rao, Shodhan; Jayawardhana, Bayu; Schaft, Arjan van der
2012-01-01
Motivated by the recent progresses on the interplay between the graph theory and systems theory, we revisit the analysis of reversible chemical reaction networks described by mass action kinetics by reformulating it using the graph knowledge of the underlying networks. Based on this formulation, we
Inference of Ancestral Recombination Graphs through Topological Data Analysis
Cámara, Pablo G.; Levine, Arnold J.; Rabadán, Raúl
2016-01-01
The recent explosion of genomic data has underscored the need for interpretable and comprehensive analyses that can capture complex phylogenetic relationships within and across species. Recombination, reassortment and horizontal gene transfer constitute examples of pervasive biological phenomena that cannot be captured by tree-like representations. Starting from hundreds of genomes, we are interested in the reconstruction of potential evolutionary histories leading to the observed data. Ancestral recombination graphs represent potential histories that explicitly accommodate recombination and mutation events across orthologous genomes. However, they are computationally costly to reconstruct, usually being infeasible for more than few tens of genomes. Recently, Topological Data Analysis (TDA) methods have been proposed as robust and scalable methods that can capture the genetic scale and frequency of recombination. We build upon previous TDA developments for detecting and quantifying recombination, and present a novel framework that can be applied to hundreds of genomes and can be interpreted in terms of minimal histories of mutation and recombination events, quantifying the scales and identifying the genomic locations of recombinations. We implement this framework in a software package, called TARGet, and apply it to several examples, including small migration between different populations, human recombination, and horizontal evolution in finches inhabiting the Galápagos Islands. PMID:27532298
Spectral analysis of growing graphs a quantum probability point of view
Obata, Nobuaki
2017-01-01
This book is designed as a concise introduction to the recent achievements on spectral analysis of graphs or networks from the point of view of quantum (or non-commutative) probability theory. The main topics are spectral distributions of the adjacency matrices of finite or infinite graphs and their limit distributions for growing graphs. The main vehicle is quantum probability, an algebraic extension of the traditional probability theory, which provides a new framework for the analysis of adjacency matrices revealing their non-commutative nature. For example, the method of quantum decomposition makes it possible to study spectral distributions by means of interacting Fock spaces or equivalently by orthogonal polynomials. Various concepts of independence in quantum probability and corresponding central limit theorems are used for the asymptotic study of spectral distributions for product graphs. This book is written for researchers, teachers, and students interested in graph spectra, their (asymptotic) spectr...
Analysis of successive data sets
Spreeuwers, Lieuwe Jan; Breeuwer, Marcel; Haselhoff, Eltjo Hans
2008-01-01
The invention relates to the analysis of successive data sets. A local intensity variation is formed from such successive data sets, that is, from data values in successive data sets at corresponding positions in each of the data sets. A region of interest is localized in the individual data sets on
Analysis of successive data sets
Spreeuwers, Lieuwe Jan; Breeuwer, Marcel; Haselhoff, Eltjo Hans
2002-01-01
The invention relates to the analysis of successive data sets. A local intensity variation is formed from such successive data sets, that is, from data values in successive data sets at corresponding positions in each of the data sets. A region of interest is localized in the individual data sets on
2015-01-01
Assistant for Calculus (winter 2011) xii CHAPTER 1 Introduction We present several methods, outlined in Chapters 3-5, for image processing and data...local calculus formulation [103] to generalize the continuous formulation to a (non-local) discrete setting, while other non-local versions for...graph-based model based on the Ginzburg-Landau functional in their work [9]. To define the functional on a graph, the spatial gradient is replaced by a
Lubna Moin
2009-04-01
Full Text Available This research paper basically explores and compares the different modeling and analysis techniques and than it also explores the model order reduction approach and significance. The traditional modeling and simulation techniques for dynamic systems are generally adequate for single-domain systems only, but the Bond Graph technique provides new strategies for reliable solutions of multi-domain system. They are also used for analyzing linear and non linear dynamic production system, artificial intelligence, image processing, robotics and industrial automation. This paper describes a unique technique of generating the Genetic design from the tree structured transfer function obtained from Bond Graph. This research work combines bond graphs for model representation with Genetic programming for exploring different ideas on design space tree structured transfer function result from replacing typical bond graph element with their impedance equivalent specifying impedance lows for Bond Graph multiport. This tree structured form thus obtained from Bond Graph is applied for generating the Genetic Tree. Application studies will identify key issues and importance for advancing this approach towards becoming on effective and efficient design tool for synthesizing design for Electrical system. In the first phase, the system is modeled using Bond Graph technique. Its system response and transfer function with conventional and Bond Graph method is analyzed and then a approach towards model order reduction is observed. The suggested algorithm and other known modern model order reduction techniques are applied to a 11th order high pass filter [1], with different approach. The model order reduction technique developed in this paper has least reduction errors and secondly the final model retains structural information. The system response and the stability analysis of the system transfer function taken by conventional and by Bond Graph method is compared and
Z. Qorbali
2013-12-01
.Conclusion: as a result of establishing the presented method, identical levels in conventional risk graph table are replaced with different sublevels that not only increases the accuracy in determining the SIL, but also elucidates the effective factor in improving the safety level and consequently saves time and cost significantly. The proposed technique has been employed to develop the SIL of Tehran Refinery ISOMAX Center. IRG and FIRG results have been compared to clarify the efficacy and importance of the proposed method
Bayesian analysis for exponential random graph models using the adaptive exchange sampler
Jin, Ick Hoon; Liang, Faming; Yuan, Ying
2013-01-01
Exponential random graph models have been widely used in social network analysis. However, these models are extremely difficult to handle from a statistical viewpoint, because of the existence of intractable normalizing constants. In this paper, we
Mladen Skelin
2014-03-01
Full Text Available Scenario-aware dataflow (SADF is a prominent tool for modeling and analysis of dynamic embedded dataflow applications. In SADF the application is represented as a finite collection of synchronous dataflow (SDF graphs, each of which represents one possible application behaviour or scenario. A finite state machine (FSM specifies the possible orders of scenario occurrences. The SADF model renders the tightest possible performance guarantees, but is limited by its finiteness. This means that from a practical point of view, it can only handle dynamic dataflow applications that are characterized by a reasonably sized set of possible behaviours or scenarios. In this paper we remove this limitation for a class of SADF graphs by means of SADF model parametrization in terms of graph port rates and actor execution times. First, we formally define the semantics of the model relevant for throughput analysis based on (max,+ linear system theory and (max,+ automata. Second, by generalizing some of the existing results, we give the algorithms for worst-case throughput analysis of parametric rate and parametric actor execution time acyclic SADF graphs with a fully connected, possibly infinite state transition system. Third, we demonstrate our approach on a few realistic applications from digital signal processing (DSP domain mapped onto an embedded multi-processor architecture.
Compilation of functional languages using flow graph analysis
Hartel, Pieter H.; Glaser, Hugh; Wild, John M.
A system based on the notion of a flow graph is used to specify formally and to implement a compiler for a lazy functional language. The compiler takes a simple functional language as input and generates C. The generated C program can then be compiled, and loaded with an extensive run-time system to
SpectralNET – an application for spectral graph analysis and visualization
Schreiber Stuart L
2005-10-01
Full Text Available Abstract Background Graph theory provides a computational framework for modeling a variety of datasets including those emerging from genomics, proteomics, and chemical genetics. Networks of genes, proteins, small molecules, or other objects of study can be represented as graphs of nodes (vertices and interactions (edges that can carry different weights. SpectralNET is a flexible application for analyzing and visualizing these biological and chemical networks. Results Available both as a standalone .NET executable and as an ASP.NET web application, SpectralNET was designed specifically with the analysis of graph-theoretic metrics in mind, a computational task not easily accessible using currently available applications. Users can choose either to upload a network for analysis using a variety of input formats, or to have SpectralNET generate an idealized random network for comparison to a real-world dataset. Whichever graph-generation method is used, SpectralNET displays detailed information about each connected component of the graph, including graphs of degree distribution, clustering coefficient by degree, and average distance by degree. In addition, extensive information about the selected vertex is shown, including degree, clustering coefficient, various distance metrics, and the corresponding components of the adjacency, Laplacian, and normalized Laplacian eigenvectors. SpectralNET also displays several graph visualizations, including a linear dimensionality reduction for uploaded datasets (Principal Components Analysis and a non-linear dimensionality reduction that provides an elegant view of global graph structure (Laplacian eigenvectors. Conclusion SpectralNET provides an easily accessible means of analyzing graph-theoretic metrics for data modeling and dimensionality reduction. SpectralNET is publicly available as both a .NET application and an ASP.NET web application from http://chembank.broad.harvard.edu/resources/. Source code is
Visibility graph approach to the analysis of ocean tidal records
Telesca, Luciano; Lovallo, Michele; Pierini, Jorge O.
2012-01-01
By using the recent method of the visibility graph, three time series of oceanic tide level in central Argentina were investigated. The degree distributions show a rich structure; in particular the maximum is due to the main periodic oscillations at 24 hours and 12 hours and higher harmonics. The degree distributions of the residuals (obtained removing from the original signals the cyclic components) suggest that the local effects, linked with the particular coastal conditions of the sites, are discernible for the degree k 100. Although a relationship between the spectral exponent α and the exponent of the degree distribution γ of tidal signals can be recognized, this cannot be simply stated due to the very rich and complex structure of time dynamics of tides. The present study, even if still preliminary, show the importance of the visibility graph method in investigating the complex time dynamics of observational and experimental signals.
Fubiao Feng
2017-03-01
Full Text Available Recently, graph embedding has drawn great attention for dimensionality reduction in hyperspectral imagery. For example, locality preserving projection (LPP utilizes typical Euclidean distance in a heat kernel to create an affinity matrix and projects the high-dimensional data into a lower-dimensional space. However, the Euclidean distance is not sufficiently correlated with intrinsic spectral variation of a material, which may result in inappropriate graph representation. In this work, a graph-based discriminant analysis with spectral similarity (denoted as GDA-SS measurement is proposed, which fully considers curves changing description among spectral bands. Experimental results based on real hyperspectral images demonstrate that the proposed method is superior to traditional methods, such as supervised LPP, and the state-of-the-art sparse graph-based discriminant analysis (SGDA.
Survey of Approaches to Generate Realistic Synthetic Graphs
Lim, Seung-Hwan [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Lee, Sangkeun [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Powers, Sarah S [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Shankar, Mallikarjun [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Imam, Neena [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
2016-10-01
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 broad 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.
Network graph analysis of gene-gene interactions in genome-wide association study data.
Lee, Sungyoung; Kwon, Min-Seok; Park, Taesung
2012-12-01
Most common complex traits, such as obesity, hypertension, diabetes, and cancers, are known to be associated with multiple genes, environmental factors, and their epistasis. Recently, the development of advanced genotyping technologies has allowed us to perform genome-wide association studies (GWASs). For detecting the effects of multiple genes on complex traits, many approaches have been proposed for GWASs. Multifactor dimensionality reduction (MDR) is one of the powerful and efficient methods for detecting high-order gene-gene (GxG) interactions. However, the biological interpretation of GxG interactions identified by MDR analysis is not easy. In order to aid the interpretation of MDR results, we propose a network graph analysis to elucidate the meaning of identified GxG interactions. The proposed network graph analysis consists of three steps. The first step is for performing GxG interaction analysis using MDR analysis. The second step is to draw the network graph using the MDR result. The third step is to provide biological evidence of the identified GxG interaction using external biological databases. The proposed method was applied to Korean Association Resource (KARE) data, containing 8838 individuals with 327,632 single-nucleotide polymorphisms, in order to perform GxG interaction analysis of body mass index (BMI). Our network graph analysis successfully showed that many identified GxG interactions have known biological evidence related to BMI. We expect that our network graph analysis will be helpful to interpret the biological meaning of GxG interactions.
Graph Grammar-Based Multi-Frontal Parallel Direct Solver for Two-Dimensional Isogeometric Analysis
Kuźnik, Krzysztof
2012-06-02
This paper introduces the graph grammar based model for developing multi-thread multi-frontal parallel direct solver for two dimensional isogeometric finite element method. Execution of the solver algorithm has been expressed as the sequence of graph grammar productions. At the beginning productions construct the elimination tree with leaves corresponding to finite elements. Following sequence of graph grammar productions generates element frontal matri-ces at leaf nodes, merges matrices at parent nodes and eliminates rows corresponding to fully assembled degrees of freedom. Finally, there are graph grammar productions responsible for root problem solution and recursive backward substitutions. Expressing the solver algorithm by graph grammar productions allows us to explore the concurrency of the algorithm. The graph grammar productions are grouped into sets of independent tasks that can be executed concurrently. The resulting concurrent multi-frontal solver algorithm is implemented and tested on NVIDIA GPU, providing O(NlogN) execution time complexity where N is the number of degrees of freedom. We have confirmed this complexity by solving up to 1 million of degrees of freedom with 448 cores GPU.
C. Dalfo
2015-10-01
Full Text Available We study a family of graphs related to the $n$-cube. The middle cube graph of parameter k is the subgraph of $Q_{2k-1}$ induced by the set of vertices whose binary representation has either $k-1$ or $k$ number of ones. The middle cube graphs can be obtained from the well-known odd graphs by doubling their vertex set. Here we study some of the properties of the middle cube graphs in the light of the theory of distance-regular graphs. In particular, we completely determine their spectra (eigenvalues and their multiplicities, and associated eigenvectors.
Ren, Jie
2017-12-01
The process by which a kinesin motor couples its ATPase activity with concerted mechanical hand-over-hand steps is a foremost topic of molecular motor physics. Two major routes toward elucidating kinesin mechanisms are the motility performance characterization of velocity and run length, and single-molecular state detection experiments. However, these two sets of experimental approaches are largely uncoupled to date. Here, we introduce an integrative motility state analysis based on a theorized kinetic graph theory for kinesin, which, on one hand, is validated by a wealth of accumulated motility data, and, on the other hand, allows for rigorous quantification of state occurrences and chemomechanical cycling probabilities. An interesting linear scaling for kinesin motility performance across species is discussed as well. An integrative kinetic graph theory analysis provides a powerful tool to bridge motility and state characterization experiments, so as to forge a unified effort for the elucidation of the working mechanisms of molecular motors.
Seiller, Thomas
2016-01-01
Interaction graphs were introduced as a general, uniform, construction of dynamic models of linear logic, encompassing all Geometry of Interaction (GoI) constructions introduced so far. This series of work was inspired from Girard's hyperfinite GoI, and develops a quantitative approach that should...... be understood as a dynamic version of weighted relational models. Until now, the interaction graphs framework has been shown to deal with exponentials for the constrained system ELL (Elementary Linear Logic) while keeping its quantitative aspect. Adapting older constructions by Girard, one can clearly define...... "full" exponentials, but at the cost of these quantitative features. We show here that allowing interpretations of proofs to use continuous (yet finite in a measure-theoretic sense) sets of states, as opposed to earlier Interaction Graphs constructions were these sets of states were discrete (and finite...
Faenza, Y.; Oriolo, G.; Stauffer, G.
2011-01-01
We propose an algorithm for solving the maximum weighted stable set problem on claw-free graphs that runs in O(n^3)-time, drastically improving the previous best known complexity bound. This algorithm is based on a novel decomposition theorem for claw-free graphs, which is also intioduced in the present paper. Despite being weaker than the well-known structure result for claw-free graphs given by Chudnovsky and Seymour, our decomposition theorem is, on the other hand, algorithmic, i.e. it is ...
Full Text Available List Contact us The Rice Growth Monitoring for The Phenotypic Functional Analysis Graph of growth data Data ...detail Data name Graph of growth data DOI 10.18908/lsdba.nbdc00945-003 Description of data contents The grap...h of chronological changes in root, coleoptile, the first leaf, and the second leaf. Data file File name: growth..._data_graph.zip File URL: ftp://ftp.biosciencedbc.jp/archive/agritogo-rice-phenome/LATEST/data/growth...e Update History of This Database Site Policy | Contact Us Graph of growth data -
Graph theoretical analysis of EEG functional connectivity during music perception.
Wu, Junjie; Zhang, Junsong; Liu, Chu; Liu, Dongwei; Ding, Xiaojun; Zhou, Changle
2012-11-05
The present study evaluated the effect of music on large-scale structure of functional brain networks using graph theoretical concepts. While most studies on music perception used Western music as an acoustic stimulus, Guqin music, representative of Eastern music, was selected for this experiment to increase our knowledge of music perception. Electroencephalography (EEG) was recorded from non-musician volunteers in three conditions: Guqin music, noise and silence backgrounds. Phase coherence was calculated in the alpha band and between all pairs of EEG channels to construct correlation matrices. Each resulting matrix was converted into a weighted graph using a threshold, and two network measures: the clustering coefficient and characteristic path length were calculated. Music perception was found to display a higher level mean phase coherence. Over the whole range of thresholds, the clustering coefficient was larger while listening to music, whereas the path length was smaller. Networks in music background still had a shorter characteristic path length even after the correction for differences in mean synchronization level among background conditions. This topological change indicated a more optimal structure under music perception. Thus, prominent small-world properties are confirmed in functional brain networks. Furthermore, music perception shows an increase of functional connectivity and an enhancement of small-world network organizations. Copyright © 2012 Elsevier B.V. All rights reserved.
Par@Graph - a parallel toolbox for the construction and analysis of large complex climate networks
Tantet, A.J.J.
2015-01-01
In this paper, we present Par@Graph, a software toolbox to reconstruct and analyze complex climate networks having a large number of nodes (up to at least 106) and edges (up to at least 1012). The key innovation is an efficient set of parallel software tools designed to leverage the inherited hybrid
Graph theoretical analysis of resting magnetoencephalographic functional connectivity networks
Lindsay eRutter
2013-07-01
Full Text Available Complex networks have been observed to comprise small-world properties, believed to represent an optimal organization of local specialization and global integration of information processing at reduced wiring cost. Here, we applied magnitude squared coherence to resting magnetoencephalographic time series in reconstructed source space, acquired from controls and patients with schizophrenia, and generated frequency-dependent adjacency matrices modeling functional connectivity between virtual channels. After configuring undirected binary and weighted graphs, we found that all human networks demonstrated highly localized clustering and short characteristic path lengths. The most conservatively thresholded networks showed efficient wiring, with topographical distance between connected vertices amounting to one-third as observed in surrogate randomized topologies. Nodal degrees of the human networks conformed to a heavy-tailed exponentially truncated power-law, compatible with the existence of hubs, which included theta and alpha bilateral cerebellar tonsil, beta and gamma bilateral posterior cingulate, and bilateral thalamus across all frequencies. We conclude that all networks showed small-worldness, minimal physical connection distance, and skewed degree distributions characteristic of physically-embedded networks, and that these calculations derived from graph theoretical mathematics did not quantifiably distinguish between subject populations, independent of bandwidth. However, post-hoc measurements of edge computations at the scale of the individual vertex revealed trends of reduced gamma connectivity across the posterior medial parietal cortex in patients, an observation consistent with our prior resting activation study that found significant reduction of synthetic aperture magnetometry gamma power across similar regions. The basis of these small differences remains unclear.
Global spectral graph wavelet signature for surface analysis of carpal bones
Masoumi, Majid; Rezaei, Mahsa; Ben Hamza, A.
2018-02-01
Quantitative shape comparison is a fundamental problem in computer vision, geometry processing and medical imaging. In this paper, we present a spectral graph wavelet approach for shape analysis of carpal bones of the human wrist. We employ spectral graph wavelets to represent the cortical surface of a carpal bone via the spectral geometric analysis of the Laplace-Beltrami operator in the discrete domain. We propose global spectral graph wavelet (GSGW) descriptor that is isometric invariant, efficient to compute, and combines the advantages of both low-pass and band-pass filters. We perform experiments on shapes of the carpal bones of ten women and ten men from a publicly-available database of wrist bones. Using one-way multivariate analysis of variance (MANOVA) and permutation testing, we show through extensive experiments that the proposed GSGW framework gives a much better performance compared to the global point signature embedding approach for comparing shapes of the carpal bones across populations.
Modal Analysis of In-Wheel Motor-Driven Electric Vehicle Based on Bond Graph Theory
Di Tan
2017-01-01
Full Text Available A half-car vibration model of an electric vehicle driven by rear in-wheel motors was developed using bond graph theory and the modular modeling method. Based on the bond graph model, modal analysis was carried out to study the vibration characteristics of the electric vehicle. To verify the effectiveness of the established model, the results were compared to ones computed on the ground of modal analysis and Newton equations. The comparison shows that the vibration model of the electric vehicle based on bond graph theory not only is able to better compute the natural frequency but also can easily determine the deformation mode, momentum mode, and other isomorphism modes and describe the dynamic characteristics of an electric vehicle driven by in-wheel motors more comprehensively than other modal analysis methods.
Tahmassebi, Amirhessam; Pinker-Domenig, Katja; Wengert, Georg; Lobbes, Marc; Stadlbauer, Andreas; Romero, Francisco J.; Morales, Diego P.; Castillo, Encarnacion; Garcia, Antonio; Botella, Guillermo; Meyer-Bäse, Anke
2017-05-01
Graph network models in dementia have become an important computational technique in neuroscience to study fundamental organizational principles of brain structure and function of neurodegenerative diseases such as dementia. The graph connectivity is reflected in the connectome, the complete set of structural and functional connections of the graph network, which is mostly based on simple Pearson correlation links. In contrast to simple Pearson correlation networks, the partial correlations (PC) only identify direct correlations while indirect associations are eliminated. In addition to this, the state-of-the-art techniques in brain research are based on static graph theory, which is unable to capture the dynamic behavior of the brain connectivity, as it alters with disease evolution. We propose a new research avenue in neuroimaging connectomics based on combining dynamic graph network theory and modeling strategies at different time scales. We present the theoretical framework for area aggregation and time-scale modeling in brain networks as they pertain to disease evolution in dementia. This novel paradigm is extremely powerful, since we can derive both static parameters pertaining to node and area parameters, as well as dynamic parameters, such as system's eigenvalues. By implementing and analyzing dynamically both disease driven PC-networks and regular concentration networks, we reveal differences in the structure of these network that play an important role in the temporal evolution of this disease. The described research is key to advance biomedical research on novel disease prediction trajectories and dementia therapies.
Mechanical system reliability analysis using a combination of graph theory and Boolean function
Tang, J.
2001-01-01
A new method based on graph theory and Boolean function for assessing reliability of mechanical systems is proposed. The procedure for this approach consists of two parts. By using the graph theory, the formula for the reliability of a mechanical system that considers the interrelations of subsystems or components is generated. Use of the Boolean function to examine the failure interactions of two particular elements of the system, followed with demonstrations of how to incorporate such failure dependencies into the analysis of larger systems, a constructive algorithm for quantifying the genuine interconnections between the subsystems or components is provided. The combination of graph theory and Boolean function provides an effective way to evaluate the reliability of a large, complex mechanical system. A numerical example demonstrates that this method an effective approaches in system reliability analysis
PyFolding: Open-Source Graphing, Simulation, and Analysis of the Biophysical Properties of Proteins.
Lowe, Alan R; Perez-Riba, Albert; Itzhaki, Laura S; Main, Ewan R G
2018-02-06
For many years, curve-fitting software has been heavily utilized to fit simple models to various types of biophysical data. Although such software packages are easy to use for simple functions, they are often expensive and present substantial impediments to applying more complex models or for the analysis of large data sets. One field that is reliant on such data analysis is the thermodynamics and kinetics of protein folding. Over the past decade, increasingly sophisticated analytical models have been generated, but without simple tools to enable routine analysis. Consequently, users have needed to generate their own tools or otherwise find willing collaborators. Here we present PyFolding, a free, open-source, and extensible Python framework for graphing, analysis, and simulation of the biophysical properties of proteins. To demonstrate the utility of PyFolding, we have used it to analyze and model experimental protein folding and thermodynamic data. Examples include: 1) multiphase kinetic folding fitted to linked equations, 2) global fitting of multiple data sets, and 3) analysis of repeat protein thermodynamics with Ising model variants. Moreover, we demonstrate how PyFolding is easily extensible to novel functionality beyond applications in protein folding via the addition of new models. Example scripts to perform these and other operations are supplied with the software, and we encourage users to contribute notebooks and models to create a community resource. Finally, we show that PyFolding can be used in conjunction with Jupyter notebooks as an easy way to share methods and analysis for publication and among research teams. Copyright © 2017 Biophysical Society. Published by Elsevier Inc. All rights reserved.
Network Graph Analysis of Gene-Gene Interactions in Genome-Wide Association Study Data
Sungyoung Lee
2012-12-01
Full Text Available Most common complex traits, such as obesity, hypertension, diabetes, and cancers, are known to be associated with multiple genes, environmental factors, and their epistasis. Recently, the development of advanced genotyping technologies has allowed us to perform genome-wide association studies (GWASs. For detecting the effects of multiple genes on complex traits, many approaches have been proposed for GWASs. Multifactor dimensionality reduction (MDR is one of the powerful and efficient methods for detecting high-order gene-gene (GxG interactions. However, the biological interpretation of GxG interactions identified by MDR analysis is not easy. In order to aid the interpretation of MDR results, we propose a network graph analysis to elucidate the meaning of identified GxG interactions. The proposed network graph analysis consists of three steps. The first step is for performing GxG interaction analysis using MDR analysis. The second step is to draw the network graph using the MDR result. The third step is to provide biological evidence of the identified GxG interaction using external biological databases. The proposed method was applied to Korean Association Resource (KARE data, containing 8838 individuals with 327,632 single-nucleotide polymorphisms, in order to perform GxG interaction analysis of body mass index (BMI. Our network graph analysis successfully showed that many identified GxG interactions have known biological evidence related to BMI. We expect that our network graph analysis will be helpful to interpret the biological meaning of GxG interactions.
Golino, Hudson F; Epskamp, Sacha
2017-01-01
The estimation of the correct number of dimensions is a long-standing problem in psychometrics. Several methods have been proposed, such as parallel analysis (PA), Kaiser-Guttman's eigenvalue-greater-than-one rule, multiple average partial procedure (MAP), the maximum-likelihood approaches that use fit indexes as BIC and EBIC and the less used and studied approach called very simple structure (VSS). In the present paper a new approach to estimate the number of dimensions will be introduced and compared via simulation to the traditional techniques pointed above. The approach proposed in the current paper is called exploratory graph analysis (EGA), since it is based on the graphical lasso with the regularization parameter specified using EBIC. The number of dimensions is verified using the walktrap, a random walk algorithm used to identify communities in networks. In total, 32,000 data sets were simulated to fit known factor structures, with the data sets varying across different criteria: number of factors (2 and 4), number of items (5 and 10), sample size (100, 500, 1000 and 5000) and correlation between factors (orthogonal, .20, .50 and .70), resulting in 64 different conditions. For each condition, 500 data sets were simulated using lavaan. The result shows that the EGA performs comparable to parallel analysis, EBIC, eBIC and to Kaiser-Guttman rule in a number of situations, especially when the number of factors was two. However, EGA was the only technique able to correctly estimate the number of dimensions in the four-factor structure when the correlation between factors were .7, showing an accuracy of 100% for a sample size of 5,000 observations. Finally, the EGA was used to estimate the number of factors in a real dataset, in order to compare its performance with the other six techniques tested in the simulation study.
Graph theory applied to noise and vibration control in statistical energy analysis models.
Guasch, Oriol; Cortés, Lluís
2009-06-01
A fundamental aspect of noise and vibration control in statistical energy analysis (SEA) models consists in first identifying and then reducing the energy flow paths between subsystems. In this work, it is proposed to make use of some results from graph theory to address both issues. On the one hand, linear and path algebras applied to adjacency matrices of SEA graphs are used to determine the existence of any order paths between subsystems, counting and labeling them, finding extremal paths, or determining the power flow contributions from groups of paths. On the other hand, a strategy is presented that makes use of graph cut algorithms to reduce the energy flow from a source subsystem to a receiver one, modifying as few internal and coupling loss factors as possible.
Powers, Sarah S. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Lothian, Joshua [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
2014-12-01
The benchmarking effort within the Extreme Scale Systems Center at Oak Ridge National Laboratory seeks to provide High Performance Computing benchmarks and test suites of interest to the DoD sponsor. The work described in this report is a part of the effort focusing on graph generation. A previously developed benchmark, SystemBurn, allows the emulation of a broad spectrum of application behavior profiles within a single framework. To complement this effort, similar capabilities are desired for graph-centric problems. This report described the in-depth analysis of the generated synthetic graphs' properties at a variety of scales using different generator implementations and examines their applicability to replicating real world datasets.
Visibility graph analysis on quarterly macroeconomic series of China based on complex network theory
Wang, Na; Li, Dong; Wang, Qiwen
2012-12-01
The visibility graph approach and complex network theory provide a new insight into time series analysis. The inheritance of the visibility graph from the original time series was further explored in the paper. We found that degree distributions of visibility graphs extracted from Pseudo Brownian Motion series obtained by the Frequency Domain algorithm exhibit exponential behaviors, in which the exponential exponent is a binomial function of the Hurst index inherited in the time series. Our simulations presented that the quantitative relations between the Hurst indexes and the exponents of degree distribution function are different for different series and the visibility graph inherits some important features of the original time series. Further, we convert some quarterly macroeconomic series including the growth rates of value-added of three industry series and the growth rates of Gross Domestic Product series of China to graphs by the visibility algorithm and explore the topological properties of graphs associated from the four macroeconomic series, namely, the degree distribution and correlations, the clustering coefficient, the average path length, and community structure. Based on complex network analysis we find degree distributions of associated networks from the growth rates of value-added of three industry series are almost exponential and the degree distributions of associated networks from the growth rates of GDP series are scale free. We also discussed the assortativity and disassortativity of the four associated networks as they are related to the evolutionary process of the original macroeconomic series. All the constructed networks have “small-world” features. The community structures of associated networks suggest dynamic changes of the original macroeconomic series. We also detected the relationship among government policy changes, community structures of associated networks and macroeconomic dynamics. We find great influences of government
Analysis of electrical penetration graph data: what to do with artificially terminated events?
Observing the durations of hemipteran feeding behaviors via Electrical Penetration Graph (EPG) results in situations where the duration of the last behavior is not ended by the insect under observation, but by the experimenter. These are artificially terminated events. In data analysis, one must ch...
A Qualitative Analysis Framework Using Natural Language Processing and Graph Theory
Tierney, Patrick J.
2012-01-01
This paper introduces a method of extending natural language-based processing of qualitative data analysis with the use of a very quantitative tool--graph theory. It is not an attempt to convert qualitative research to a positivist approach with a mathematical black box, nor is it a "graphical solution". Rather, it is a method to help qualitative…
Performance analysis of chi models using discrete-time probabilistic reward graphs
Trcka, N.; Georgievska, S.; Markovski, J.; Andova, S.; Vink, de E.P.
2008-01-01
We propose the model of discrete-time probabilistic reward graphs (DTPRGs) for performance analysis of systems exhibiting discrete deterministic time delays and probabilistic behavior, via their interpretation as discrete-time Markov reward chains, full-fledged platform for qualitative and
Tyner, Bryan C.; Fienup, Daniel M.
2016-01-01
Task analyses are ubiquitous to applied behavior analysis interventions, yet little is known about the factors that make them effective. Numerous task analyses have been published in behavior analytic journals for constructing single-subject design graphs; however, learner outcomes using these task analyses may fall short of what could be…
Debrabant, Birgit; Soerensen, Mette
2014-01-01
Abstract We discuss the use of modified Kolmogorov-Smirnov (KS) statistics in the context of gene set analysis and review corresponding null and alternative hypotheses. Especially, we show that, when enhancing the impact of highly significant genes in the calculation of the test statistic, the co...
Graph-based Data Modeling and Analysis for Data Fusion in Remote Sensing
Fan, Lei
., fusion of multi-source data can in principal produce more detailed information than each single source. On the other hand, besides the abundant spectral information contained in HSI data, features such as texture and shape may be employed to represent data points from a spatial perspective. Furthermore, feature fusion also includes the strategy of removing redundant and noisy features in the dataset. One of the major problems in machine learning and pattern recognition is to develop appropriate representations for complex nonlinear data. In HSI processing, a particular data point is usually described as a vector with coordinates corresponding to the intensities measured in the spectral bands. This vector representation permits the application of linear and nonlinear transformations with linear algebra to find an alternative representation of the data. More generally, HSI is multi-dimensional in nature and the vector representation may lose the contextual correlations. Tensor representation provides a more sophisticated modeling technique and a higher-order generalization to linear subspace analysis. In graph theory, data points can be generalized as nodes with connectivities measured from the proximity of a local neighborhood. The graph-based framework efficiently characterizes the relationships among the data and allows for convenient mathematical manipulation in many applications, such as data clustering, feature extraction, feature selection and data alignment. In this thesis, graph-based approaches applied in the field of multi-source feature and data fusion in remote sensing area are explored. We will mainly investigate the fusion of spatial, spectral and LiDAR information with linear and multilinear algebra under graph-based framework for data clustering and classification problems.
Analysis of the 2005-2016 Earthquake Sequence in Northern Iran Using the Visibility Graph Method
Khoshnevis, Naeem; Taborda, Ricardo; Azizzadeh-Roodpish, Shima; Telesca, Luciano
2017-11-01
We present an analysis of the seismicity of northern Iran in the period between 2005 and 2016 using a recently introduced method based on concepts of graph theory. The method relies on the inter-event visibility defined in terms of a connectivity degree parameter, k, which is correlated with the earthquake magnitude, M. Previous studies show that the slope m of the line fitting the k- M plot by the least squares method also observes a relationship with the b value from the Gutenberg-Richter law, thus rendering the graph analysis useful to examine the seismicity of a region. These correlations seem to hold for the analysis of relatively small sequences of earthquakes, offering the possibility of studying seismicity parameters in time. We apply this approach to the case of the seismicity of northern Iran, using an earthquake catalog for the tectonic seismic regions of Azerbaijan, Alborz, and Kopeh Dagh. We use results drawn for this region with the visibility graph approach in combination with results from other similar studies to further improve the universal relationship between m and b, and show that the visibility graph approach can be considered as a valid alternative for analyzing regional seismicity properties and earthquake sequences.
A method for independent component graph analysis of resting-state fMRI
de Paula, Demetrius Ribeiro; Ziegler, Erik; Abeyasinghe, Pubuditha M.
2017-01-01
Introduction Independent component analysis (ICA) has been extensively used for reducing task-free BOLD fMRI recordings into spatial maps and their associated time-courses. The spatially identified independent components can be considered as intrinsic connectivity networks (ICNs) of non-contiguou......Introduction Independent component analysis (ICA) has been extensively used for reducing task-free BOLD fMRI recordings into spatial maps and their associated time-courses. The spatially identified independent components can be considered as intrinsic connectivity networks (ICNs) of non......-contiguous regions. To date, the spatial patterns of the networks have been analyzed with techniques developed for volumetric data. Objective Here, we detail a graph building technique that allows these ICNs to be analyzed with graph theory. Methods First, ICA was performed at the single-subject level in 15 healthy...... parcellated regions. Third, between-node functional connectivity was established by building edge weights for each networks. Group-level graph analysis was finally performed for each network and compared to the classical network. Results Network graph comparison between the classically constructed network...
Stability analysis of switched linear systems defined by graphs
Athanasopoulos, Nikolaos; Lazar, Mircea
2015-01-01
We present necessary and sufficient conditions for global exponential stability for switched discrete-time linear systems, under arbitrary switching, which is constrained within a set of admissible transitions. The class of systems studied includes the family of systems under arbitrary switching, periodic systems, and systems with minimum and maximum dwell time specifications. To reach the result, we describe the set of rules that define the admissible transitions with a weighted directed gra...
Pseudo-Bond Graph model for the analysis of the thermal behavior of buildings
Merabtine Abdelatif
2013-01-01
Full Text Available In this work, a simplified graphical modeling tool, which in some extent can be considered in halfway between detailed physical and Data driven dynamic models, has been developed. This model is based on Bond Graphs approach. This approach has the potential to display explicitly the nature of power in a building system, such as a phenomenon of storage, processing and dissipating energy such as Heating, Ventilation and Air-Conditioning (HVAC systems. This paper represents the developed models of the two transient heat conduction problems corresponding to the most practical cases in building envelope, such as the heat transfer through vertical walls, roofs and slabs. The validation procedure consists of comparing the results obtained with this model with analytical solution. It has shown very good agreement between measured data and Bond Graphs model simulation. The Bond Graphs technique is then used to model the building dynamic thermal behavior over a single zone building structure and compared with a set of experimental data. An evaluation of indoor temperature was carried out in order to check our Bond Graphs model.
Screw-vector bond graphs for kinetic-static modelling and analysis of mechanisms
Bidard, Catherine
1994-01-01
This dissertation deals with the kinetic-static modelling and analysis of spatial mechanisms used in robotics systems. A framework is proposed, which embodies a geometrical and a network approach for kinetic-static modelling. For this purpose we use screw theory and bond graphs. A new form of bond graphs is introduced: the screw-vector bond graph, whose power variables are defined to be wrenches and twists expressed as intrinsic screw-vectors. The mechanism is then identified as a network, whose components are kinematic pairs and whose topology is described by a directed graph. A screw-vector Simple Junction Structure represents the topological constraints. Kinematic pairs are represented by one-port elements, defined by two reciprocal screw-vector spaces. Using dual bases of screw-vectors, a generic decomposition of kinematic pair elements is given. The reduction of kinetic-static models of series and parallel kinematic chains is used in order to derive kinetic-static functional models in geometric form. Thereupon, the computational causality assignment is adapted for the graphical analysis of the mobility and the functioning of spatial mechanisms, based on completely or incompletely specified models. (author) [fr
Collective Rationality in Graph Aggregation
Endriss, U.; Grandi, U.; Schaub, T.; Friedrich, G.; O'Sullivan, B.
2014-01-01
Suppose a number of agents each provide us with a directed graph over a common set of vertices. Graph aggregation is the problem of computing a single “collective” graph that best represents the information inherent in this profile of individual graphs. We consider this aggregation problem from the
Comparing Visual and Statistical Analysis of Multiple Baseline Design Graphs.
Wolfe, Katie; Dickenson, Tammiee S; Miller, Bridget; McGrath, Kathleen V
2018-04-01
A growing number of statistical analyses are being developed for single-case research. One important factor in evaluating these methods is the extent to which each corresponds to visual analysis. Few studies have compared statistical and visual analysis, and information about more recently developed statistics is scarce. Therefore, our purpose was to evaluate the agreement between visual analysis and four statistical analyses: improvement rate difference (IRD); Tau-U; Hedges, Pustejovsky, Shadish (HPS) effect size; and between-case standardized mean difference (BC-SMD). Results indicate that IRD and BC-SMD had the strongest overall agreement with visual analysis. Although Tau-U had strong agreement with visual analysis on raw values, it had poorer agreement when those values were dichotomized to represent the presence or absence of a functional relation. Overall, visual analysis appeared to be more conservative than statistical analysis, but further research is needed to evaluate the nature of these disagreements.
Stability analysis of switched linear systems defined by graphs
Athanasopoulos, N.; Lazar, M.
2014-01-01
We present necessary and sufficient conditions for global exponential stability for switched discrete-time linear systems, under arbitrary switching, which is constrained within a set of admissible transitions. The class of systems studied includes the family of systems under arbitrary switching,
Endriss, U.; Grandi, U.
Graph aggregation is the process of computing a single output graph that constitutes a good compromise between several input graphs, each provided by a different source. One needs to perform graph aggregation in a wide variety of situations, e.g., when applying a voting rule (graphs as preference
On an edge partition and root graphs of some classes of line graphs
K Pravas
2017-04-01
Full Text Available The Gallai and the anti-Gallai graphs of a graph $G$ are complementary pairs of spanning subgraphs of the line graph of $G$. In this paper we find some structural relations between these graph classes by finding a partition of the edge set of the line graph of a graph $G$ into the edge sets of the Gallai and anti-Gallai graphs of $G$. Based on this, an optimal algorithm to find the root graph of a line graph is obtained. Moreover, root graphs of diameter-maximal, distance-hereditary, Ptolemaic and chordal graphs are also discussed.
Graph Mining Meets the Semantic Web
Lee, Sangkeun (Matt) [ORNL; Sukumar, Sreenivas R [ORNL; Lim, Seung-Hwan [ORNL
2015-01-01
The Resource Description Framework (RDF) and SPARQL Protocol and RDF Query Language (SPARQL) were introduced about a decade ago to enable flexible schema-free data interchange on the Semantic Web. Today, data scientists use the framework as a scalable graph representation for integrating, querying, exploring and analyzing data sets hosted at different sources. With increasing adoption, the need for graph mining capabilities for the Semantic Web has emerged. We address that need through implementation of three popular iterative Graph Mining algorithms (Triangle count, Connected component analysis, and PageRank). We implement these algorithms as SPARQL queries, wrapped within Python scripts. We evaluate the performance of our implementation on 6 real world data sets and show graph mining algorithms (that have a linear-algebra formulation) can indeed be unleashed on data represented as RDF graphs using the SPARQL query interface.
Simplifying Scalable Graph Processing with a Domain-Specific Language
Hong, Sungpack; Salihoglu, Semih; Widom, Jennifer; Olukotun, Kunle
2014-01-01
Large-scale graph processing, with its massive data sets, requires distributed processing. However, conventional frameworks for distributed graph processing, such as Pregel, use non-traditional programming models that are well-suited for parallelism and scalability but inconvenient for implementing non-trivial graph algorithms. In this paper, we use Green-Marl, a Domain-Specific Language for graph analysis, to intuitively describe graph algorithms and extend its compiler to generate equivalent Pregel implementations. Using the semantic information captured by Green-Marl, the compiler applies a set of transformation rules that convert imperative graph algorithms into Pregel's programming model. Our experiments show that the Pregel programs generated by the Green-Marl compiler perform similarly to manually coded Pregel implementations of the same algorithms. The compiler is even able to generate a Pregel implementation of a complicated graph algorithm for which a manual Pregel implementation is very challenging.
Simplifying Scalable Graph Processing with a Domain-Specific Language
Hong, Sungpack
2014-01-01
Large-scale graph processing, with its massive data sets, requires distributed processing. However, conventional frameworks for distributed graph processing, such as Pregel, use non-traditional programming models that are well-suited for parallelism and scalability but inconvenient for implementing non-trivial graph algorithms. In this paper, we use Green-Marl, a Domain-Specific Language for graph analysis, to intuitively describe graph algorithms and extend its compiler to generate equivalent Pregel implementations. Using the semantic information captured by Green-Marl, the compiler applies a set of transformation rules that convert imperative graph algorithms into Pregel\\'s programming model. Our experiments show that the Pregel programs generated by the Green-Marl compiler perform similarly to manually coded Pregel implementations of the same algorithms. The compiler is even able to generate a Pregel implementation of a complicated graph algorithm for which a manual Pregel implementation is very challenging.
Mal-Netminer: Malware Classification Approach Based on Social Network Analysis of System Call Graph
Jae-wook Jang
2015-01-01
Full Text Available As the security landscape evolves over time, where thousands of species of malicious codes are seen every day, antivirus vendors strive to detect and classify malware families for efficient and effective responses against malware campaigns. To enrich this effort and by capitalizing on ideas from the social network analysis domain, we build a tool that can help classify malware families using features driven from the graph structure of their system calls. To achieve that, we first construct a system call graph that consists of system calls found in the execution of the individual malware families. To explore distinguishing features of various malware species, we study social network properties as applied to the call graph, including the degree distribution, degree centrality, average distance, clustering coefficient, network density, and component ratio. We utilize features driven from those properties to build a classifier for malware families. Our experimental results show that “influence-based” graph metrics such as the degree centrality are effective for classifying malware, whereas the general structural metrics of malware are less effective for classifying malware. Our experiments demonstrate that the proposed system performs well in detecting and classifying malware families within each malware class with accuracy greater than 96%.
Design of Graph Analysis Model to support Decision Making
An, Sang Ha; Lee, Sung Jin; Chang, Soon Heung; Kim, Sung Ho; Kim, Tae Woon
2005-01-01
Korea is meeting the growing electric power needs by using nuclear, fissile, hydro energy and so on. But we can not use fissile energy forever, and the people's consideration about nature has been changed. So we have to prepare appropriate energy by the conditions before people need more energy. And we should prepare dynamic response because people's need would be changed as the time goes on. So we designed graphic analysis model (GAM) for the dynamic analysis of decision on the energy sources. It can support Analytic Hierarchy Process (AHP) analysis based on Graphic User Interface
Simplicial complexes of graphs
Jonsson, Jakob
2008-01-01
A graph complex is a finite family of graphs closed under deletion of edges. Graph complexes show up naturally in many different areas of mathematics, including commutative algebra, geometry, and knot theory. Identifying each graph with its edge set, one may view a graph complex as a simplicial complex and hence interpret it as a geometric object. This volume examines topological properties of graph complexes, focusing on homotopy type and homology. Many of the proofs are based on Robin Forman's discrete version of Morse theory. As a byproduct, this volume also provides a loosely defined toolbox for attacking problems in topological combinatorics via discrete Morse theory. In terms of simplicity and power, arguably the most efficient tool is Forman's divide and conquer approach via decision trees; it is successfully applied to a large number of graph and digraph complexes.
Mining concepts of health responsibility using text mining and exploratory graph analysis.
Kjellström, Sofia; Golino, Hudson
2018-05-24
Occupational therapists need to know about people's beliefs about personal responsibility for health to help them pursue everyday activities. The study aims to employ state-of-the-art quantitative approaches to understand people's views of health and responsibility at different ages. A mixed method approach was adopted, using text mining to extract information from 233 interviews with participants aged 5 to 96 years, and then exploratory graph analysis to estimate the number of latent variables. The fit of the structure estimated via the exploratory graph analysis was verified using confirmatory factor analysis. Exploratory graph analysis estimated three dimensions of health responsibility: (1) creating good health habits and feeling good; (2) thinking about one's own health and wanting to improve it; and 3) adopting explicitly normative attitudes to take care of one's health. The comparison between the three dimensions among age groups showed, in general, that children and adolescents, as well as the old elderly (>73 years old) expressed ideas about personal responsibility for health less than young adults, adults and young elderly. Occupational therapists' knowledge of the concepts of health responsibility is of value when working with a patient's health, but an identified challenge is how to engage children and older persons.
Multiresolution analysis over graphs for a motor imagery based online BCI game.
Asensio-Cubero, Javier; Gan, John Q; Palaniappan, Ramaswamy
2016-01-01
Multiresolution analysis (MRA) over graph representation of EEG data has proved to be a promising method for offline brain-computer interfacing (BCI) data analysis. For the first time we aim to prove the feasibility of the graph lifting transform in an online BCI system. Instead of developing a pointer device or a wheel-chair controller as test bed for human-machine interaction, we have designed and developed an engaging game which can be controlled by means of imaginary limb movements. Some modifications to the existing MRA analysis over graphs for BCI have also been proposed, such as the use of common spatial patterns for feature extraction at the different levels of decomposition, and sequential floating forward search as a best basis selection technique. In the online game experiment we obtained for three classes an average classification rate of 63.0% for fourteen naive subjects. The application of a best basis selection method helps significantly decrease the computing resources needed. The present study allows us to further understand and assess the benefits of the use of tailored wavelet analysis for processing motor imagery data and contributes to the further development of BCI for gaming purposes. Copyright © 2015 Elsevier Ltd. All rights reserved.
Graph theoretical analysis and application of fMRI-based brain network in Alzheimer's disease
LIU Xue-na
2012-08-01
Full Text Available Alzheimer's disease (AD, a progressive neurodegenerative disease, is clinically characterized by impaired memory and many other cognitive functions. However, the pathophysiological mechanisms underlying the disease are not thoroughly understood. In recent years, using functional magnetic resonance imaging (fMRI as well as advanced graph theory based network analysis approach, several studies of patients with AD suggested abnormal topological organization in both global and regional properties of functional brain networks, specifically, as demonstrated by a loss of small-world network characteristics. These studies provide novel insights into the pathophysiological mechanisms of AD and could be helpful in developing imaging biomarkers for disease diagnosis. In this paper we introduce the essential concepts of complex brain networks theory, and review recent advances of the study on human functional brain networks in AD, especially focusing on the graph theoretical analysis of small-world network based on fMRI. We also propound the existent problems and research orientation.
Bayesian analysis for exponential random graph models using the adaptive exchange sampler
Jin, Ick Hoon
2013-01-01
Exponential random graph models have been widely used in social network analysis. However, these models are extremely difficult to handle from a statistical viewpoint, because of the existence of intractable normalizing constants. In this paper, we consider a fully Bayesian analysis for exponential random graph models using the adaptive exchange sampler, which solves the issue of intractable normalizing constants encountered in Markov chain Monte Carlo (MCMC) simulations. The adaptive exchange sampler can be viewed as a MCMC extension of the exchange algorithm, and it generates auxiliary networks via an importance sampling procedure from an auxiliary Markov chain running in parallel. The convergence of this algorithm is established under mild conditions. The adaptive exchange sampler is illustrated using a few social networks, including the Florentine business network, molecule synthetic network, and dolphins network. The results indicate that the adaptive exchange algorithm can produce more accurate estimates than approximate exchange algorithms, while maintaining the same computational efficiency.
Deptuła Adam
2017-01-01
Full Text Available Analysis and synthesis of mechanisms is one of the fundamental tasks of engineering. Mechanisms can suffer from errors due to versatile reasons. Graph-based methods of analysis and synthesis of planetary gears constitute an alternative method for checking their correctness. Previous applications of the graph theory concerned modelling gears for dynamic analysis, kinematic analysis, synthesis, structural analysis, gearshift optimization and automatic design based on so-called graph grammars. Some tasks may be performed only with the methods resulting from the graph theory, e.g. enumeration of structural solutions. The contour plot method consists in distinguishing a series of consecutive rigid units of the analysed mechanism, forming a closed loop (so-called contour. At a later stage, it is possible to analyze the obtained contour graph as a directed graph of dependence. This work presents an example of the application of game-tree structures in describing the contour graph of a planetary gear. In addition, complex parametric tree structures are included.
Graph analysis of cell clusters forming vascular networks
Alves, A. P.; Mesquita, O. N.; Gómez-Gardeñes, J.; Agero, U.
2018-03-01
This manuscript describes the experimental observation of vasculogenesis in chick embryos by means of network analysis. The formation of the vascular network was observed in the area opaca of embryos from 40 to 55 h of development. In the area opaca endothelial cell clusters self-organize as a primitive and approximately regular network of capillaries. The process was observed by bright-field microscopy in control embryos and in embryos treated with Bevacizumab (Avastin), an antibody that inhibits the signalling of the vascular endothelial growth factor (VEGF). The sequence of images of the vascular growth were thresholded, and used to quantify the forming network in control and Avastin-treated embryos. This characterization is made by measuring vessels density, number of cell clusters and the largest cluster density. From the original images, the topology of the vascular network was extracted and characterized by means of the usual network metrics such as: the degree distribution, average clustering coefficient, average short path length and assortativity, among others. This analysis allows to monitor how the largest connected cluster of the vascular network evolves in time and provides with quantitative evidence of the disruptive effects that Avastin has on the tree structure of vascular networks.
Modelling and analysis of distributed simulation protocols with distributed graph transformation
Lara, Juan de; Taentzer, Gabriele
2005-01-01
Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. J. de Lara, and G. Taentzer, "Modelling and analysis of distributed simulation protocols with distributed graph transformation...
Jonathan Laney
2015-01-01
Full Text Available The assessment of neuroplasticity after stroke through functional magnetic resonance imaging (fMRI analysis is a developing field where the objective is to better understand the neural process of recovery and to better target rehabilitation interventions. The challenge in this population stems from the large amount of individual spatial variability and the need to summarize entire brain maps by generating simple, yet discriminating features to highlight differences in functional connectivity. Independent vector analysis (IVA has been shown to provide superior performance in preserving subject variability when compared with widely used methods such as group independent component analysis. Hence, in this paper, graph-theoretical (GT analysis is applied to IVA-generated components to effectively exploit the individual subjects' connectivity to produce discriminative features. The analysis is performed on fMRI data collected from individuals with chronic stroke both before and after a 6-week arm and hand rehabilitation intervention. Resulting GT features are shown to capture connectivity changes that are not evident through direct comparison of the group t-maps. The GT features revealed increased small worldness across components and greater centrality in key motor networks as a result of the intervention, suggesting improved efficiency in neural communication. Clinically, these results bring forth new possibilities as a means to observe the neural processes underlying improvements in motor function.
The Stability Analysis Method of the Cohesive Granular Slope on the Basis of Graph Theory.
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.
Zhang, L.-C.; Patone, M.
2017-01-01
We synthesise the existing theory of graph sampling. We propose a formal definition of sampling in finite graphs, and provide a classification of potential graph parameters. We develop a general approach of Horvitz–Thompson estimation to T-stage snowball sampling, and present various reformulations of some common network sampling methods in the literature in terms of the outlined graph sampling theory.
Pogliani, Lionello
2010-01-30
Twelve properties of a highly heterogeneous class of organic solvents have been modeled with a graph-theoretical molecular connectivity modified (MC) method, which allows to encode the core electrons and the hydrogen atoms. The graph-theoretical method uses the concepts of simple, general, and complete graphs, where these last types of graphs are used to encode the core electrons. The hydrogen atoms have been encoded by the aid of a graph-theoretical perturbation parameter, which contributes to the definition of the valence delta, delta(v), a key parameter in molecular connectivity studies. The model of the twelve properties done with a stepwise search algorithm is always satisfactory, and it allows to check the influence of the hydrogen content of the solvent molecules on the choice of the type of descriptor. A similar argument holds for the influence of the halogen atoms on the type of core electron representation. In some cases the molar mass, and in a minor way, special "ad hoc" parameters have been used to improve the model. A very good model of the surface tension could be obtained by the aid of five experimental parameters. A mixed model method based on experimental parameters plus molecular connectivity indices achieved, instead, to consistently improve the model quality of five properties. To underline is the importance of the boiling point temperatures as descriptors in these last two model methodologies. Copyright 2009 Wiley Periodicals, Inc.
ON BIPOLAR SINGLE VALUED NEUTROSOPHIC GRAPHS
Said Broumi; Mohamed Talea; Assia Bakali; Florentin Smarandache
2016-01-01
In this article, we combine the concept of bipolar neutrosophic set and graph theory. We introduce the notions of bipolar single valued neutrosophic graphs, strong bipolar single valued neutrosophic graphs, complete bipolar single valued neutrosophic graphs, regular bipolar single valued neutrosophic graphs and investigate some of their related properties.
Ye, Zheng; Doñamayor, Nuria; Münte, Thomas F
2014-02-01
A set of cortical and sub-cortical brain structures has been linked with sentence-level semantic processes. However, it remains unclear how these brain regions are organized to support the semantic integration of a word into sentential context. To look into this issue, we conducted a functional magnetic resonance imaging (fMRI) study that required participants to silently read sentences with semantically congruent or incongruent endings and analyzed the network properties of the brain with two approaches, independent component analysis (ICA) and graph theoretical analysis (GTA). The GTA suggested that the whole-brain network is topologically stable across conditions. The ICA revealed a network comprising the supplementary motor area (SMA), left inferior frontal gyrus, left middle temporal gyrus, left caudate nucleus, and left angular gyrus, which was modulated by the incongruity of sentence ending. Furthermore, the GTA specified that the connections between the left SMA and left caudate nucleus as well as that between the left caudate nucleus and right thalamus were stronger in response to incongruent vs. congruent endings. Copyright © 2012 Wiley Periodicals, Inc.
Visibility graph network analysis of natural gas price: The case of North American market
Sun, Mei; Wang, Yaqi; Gao, Cuixia
2016-11-01
Fluctuations in prices of natural gas significantly affect global economy. Therefore, the research on the characteristics of natural gas price fluctuations, turning points and its influencing cycle on the subsequent price series is of great significance. Global natural gas trade concentrates on three regional markets: the North American market, the European market and the Asia-Pacific market, with North America having the most developed natural gas financial market. In addition, perfect legal supervision and coordinated regulations make the North American market more open and more competitive. This paper focuses on the North American natural gas market specifically. The Henry Hub natural gas spot price time series is converted to a visibility graph network which provides a new direction for macro analysis of time series, and several indicators are investigated: degree and degree distribution, the average shortest path length and community structure. The internal mechanisms underlying price fluctuations are explored through the indicators. The results show that the natural gas prices visibility graph network (NGP-VGN) is of small-world and scale-free properties simultaneously. After random rearrangement of original price time series, the degree distribution of network becomes exponential distribution, different from the original ones. This means that, the original price time series is of long-range negative correlation fractal characteristic. In addition, nodes with large degree correspond to significant geopolitical or economic events. Communities correspond to time cycles in visibility graph network. The cycles of time series and the impact scope of hubs can be found by community structure partition.
Mali, P.; Manna, S. K.; Mukhopadhyay, A.; Haldar, P. K.; Singh, G.
2018-03-01
Multiparticle emission data in nucleus-nucleus collisions are studied in a graph theoretical approach. The sandbox algorithm used to analyze complex networks is employed to characterize the multifractal properties of the visibility graphs associated with the pseudorapidity distribution of charged particles produced in high-energy heavy-ion collisions. Experimental data on 28Si+Ag/Br interaction at laboratory energy Elab = 14 . 5 A GeV, and 16O+Ag/Br and 32S+Ag/Br interactions both at Elab = 200 A GeV, are used in this analysis. We observe a scale free nature of the degree distributions of the visibility and horizontal visibility graphs associated with the event-wise pseudorapidity distributions. Equivalent event samples simulated by ultra-relativistic quantum molecular dynamics, produce degree distributions that are almost identical to the respective experiment. However, the multifractal variables obtained by using sandbox algorithm for the experiment to some extent differ from the respective simulated results.
Functional Multiple-Set Canonical Correlation Analysis
Hwang, Heungsun; Jung, Kwanghee; Takane, Yoshio; Woodward, Todd S.
2012-01-01
We propose functional multiple-set canonical correlation analysis for exploring associations among multiple sets of functions. The proposed method includes functional canonical correlation analysis as a special case when only two sets of functions are considered. As in classical multiple-set canonical correlation analysis, computationally, the…
de Mol, M.J.; Rensink, Arend; Hunt, James J.
This paper introduces an approach for adding graph transformation-based functionality to existing JAVA programs. The approach relies on a set of annotations to identify the intended graph structure, as well as on user methods to manipulate that structure, within the user’s own JAVA class
Cohen, A.M.; Beineke, L.W.; Wilson, R.J.; Cameron, P.J.
2004-01-01
In this chapter we investigate the classification of distance-transitive graphs: these are graphs whose automorphism groups are transitive on each of the sets of pairs of vertices at distance i, for i = 0, 1,.... We provide an introduction into the field. By use of the classification of finite
A first course in graph theory and combinatorics
Cioabă, Sebastian M
2009-01-01
The concept of a graph is fundamental in mathematics since it conveniently encodes diverse relations and facilitates combinatorial analysis of many complicated counting problems. In this book, the authors have traced the origins of graph theory from its humble beginnings of recreational mathematics to its modern setting for modeling communication networks as is evidenced by the World Wide Web graph used by many Internet search engines. This book is an introduction to graph theory and combinatorial analysis. It is based on courses given by the second author at Queen's University at Kingston, Ontario, Canada between 2002 and 2008. The courses were aimed at students in their final year of their undergraduate program.
Key Concept Identification: A Comprehensive Analysis of Frequency and Topical Graph-Based Approaches
Muhammad Aman
2018-05-01
Full Text Available Automatic key concept extraction from text is the main challenging task in information extraction, information retrieval and digital libraries, ontology learning, and text analysis. The statistical frequency and topical graph-based ranking are the two kinds of potentially powerful and leading unsupervised approaches in this area, devised to address the problem. To utilize the potential of these approaches and improve key concept identification, a comprehensive performance analysis of these approaches on datasets from different domains is needed. The objective of the study presented in this paper is to perform a comprehensive empirical analysis of selected frequency and topical graph-based algorithms for key concept extraction on three different datasets, to identify the major sources of error in these approaches. For experimental analysis, we have selected TF-IDF, KP-Miner and TopicRank. Three major sources of error, i.e., frequency errors, syntactical errors and semantical errors, and the factors that contribute to these errors are identified. Analysis of the results reveals that performance of the selected approaches is significantly degraded by these errors. These findings can help us develop an intelligent solution for key concept extraction in the future.
A comparison between fault tree analysis and reliability graph with general gates
Kim, Man Cheol; Seong, Poong Hyun; Jung, Woo Sik
2004-01-01
Currently, level-1 probabilistic safety assessment (PSA) is performed on the basis of event tree analysis and fault tree analysis. Kim and Seong developed a new method for system reliability analysis named reliability graph with general gates (RGGG). The RGGG is an extension of conventional reliability graph, and it utilizes the transformation of system structures to equivalent Bayesian networks for quantitative calculation. The RGGG is considered to be intuitive and easy-to-use while as powerful as fault tree analysis. As an example, Kim and Seong already showed that the Bayesian network model for digital plant protection system (DPPS), which is transformed from the RGGG model for DPPS, can be shown in 1 page, while the fault tree model for DPPS consists of 64 pages of fault trees. Kim and Seong also insisted that Bayesian network model for DPPS is more intuitive because the one-to-one matching between each node in the Bayesian network model and an actual component of DPPS is possible. In this paper, we are going to give a comparison between fault tree analysis and the RGGG method with two example systems. The two example systems are the recirculation of in Korean standard nuclear power plants (KSNP) and the fault tree model developed by Rauzy
Gilani, S. A. N.; Awrangjeb, M.; Lu, G.
2015-03-01
Building detection in complex scenes is a non-trivial exercise due to building shape variability, irregular terrain, shadows, and occlusion by highly dense vegetation. In this research, we present a graph based algorithm, which combines multispectral imagery and airborne LiDAR information to completely delineate the building boundaries in urban and densely vegetated area. In the first phase, LiDAR data is divided into two groups: ground and non-ground data, using ground height from a bare-earth DEM. A mask, known as the primary building mask, is generated from the non-ground LiDAR points where the black region represents the elevated area (buildings and trees), while the white region describes the ground (earth). The second phase begins with the process of Connected Component Analysis (CCA) where the number of objects present in the test scene are identified followed by initial boundary detection and labelling. Additionally, a graph from the connected components is generated, where each black pixel corresponds to a node. An edge of a unit distance is defined between a black pixel and a neighbouring black pixel, if any. An edge does not exist from a black pixel to a neighbouring white pixel, if any. This phenomenon produces a disconnected components graph, where each component represents a prospective building or a dense vegetation (a contiguous block of black pixels from the primary mask). In the third phase, a clustering process clusters the segmented lines, extracted from multispectral imagery, around the graph components, if possible. In the fourth step, NDVI, image entropy, and LiDAR data are utilised to discriminate between vegetation, buildings, and isolated building's occluded parts. Finally, the initially extracted building boundary is extended pixel-wise using NDVI, entropy, and LiDAR data to completely delineate the building and to maximise the boundary reach towards building edges. The proposed technique is evaluated using two Australian data sets
Graph processing platforms at scale: practices and experiences
Lim, Seung-Hwan [ORNL; Lee, Sangkeun (Matt) [ORNL; Brown, Tyler C [ORNL; Sukumar, Sreenivas R [ORNL; Ganesh, Gautam [ORNL
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, 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.
Raquel L. Costa
2017-07-01
Full Text Available There are many steps in analyzing transcriptome data, from the acquisition of raw data to the selection of a subset of representative genes that explain a scientific hypothesis. The data produced can be represented as networks of interactions among genes and these may additionally be integrated with other biological databases, such as Protein-Protein Interactions, transcription factors and gene annotation. However, the results of these analyses remain fragmented, imposing difficulties, either for posterior inspection of results, or for meta-analysis by the incorporation of new related data. Integrating databases and tools into scientific workflows, orchestrating their execution, and managing the resulting data and its respective metadata are challenging tasks. Additionally, a great amount of effort is equally required to run in-silico experiments to structure and compose the information as needed for analysis. Different programs may need to be applied and different files are produced during the experiment cycle. In this context, the availability of a platform supporting experiment execution is paramount. We present GeNNet, an integrated transcriptome analysis platform that unifies scientific workflows with graph databases for selecting relevant genes according to the evaluated biological systems. It includes GeNNet-Wf, a scientific workflow that pre-loads biological data, pre-processes raw microarray data and conducts a series of analyses including normalization, differential expression inference, clusterization and gene set enrichment analysis. A user-friendly web interface, GeNNet-Web, allows for setting parameters, executing, and visualizing the results of GeNNet-Wf executions. To demonstrate the features of GeNNet, we performed case studies with data retrieved from GEO, particularly using a single-factor experiment in different analysis scenarios. As a result, we obtained differentially expressed genes for which biological functions were
Graphing trillions of triangles.
Burkhardt, Paul
2017-07-01
The increasing size of Big Data is often heralded but how data are transformed and represented is also profoundly important to knowledge discovery, and this is exemplified in Big Graph analytics. Much attention has been placed on the scale of the input graph but the product of a graph algorithm can be many times larger than the input. This is true for many graph problems, such as listing all triangles in a graph. Enabling scalable graph exploration for Big Graphs requires new approaches to algorithms, architectures, and visual analytics. A brief tutorial is given to aid the argument for thoughtful representation of data in the context of graph analysis. Then a new algebraic method to reduce the arithmetic operations in counting and listing triangles in graphs is introduced. Additionally, a scalable triangle listing algorithm in the MapReduce model will be presented followed by a description of the experiments with that algorithm that led to the current largest and fastest triangle listing benchmarks to date. Finally, a method for identifying triangles in new visual graph exploration technologies is proposed.
Graphs of neutron cross sections in JSD1000 for radiation shielding safety analysis
Yamano, Naoki
1984-03-01
Graphs of neutron cross sections and self-shielding factors in the JSD1000 library are presented for radiation shielding safety analysis. The compilation contains various reaction cross sections for 42 nuclides from 1 H to 241 Am in the energy range from 3.51 x 10 -4 eV to 16.5 MeV. The Bondarenko-type self-shielding factors of each reaction are given by the background cross sections from σ 0 = 0 to σ 0 = 10000. (author)
Graph Grammar-Based Multi-Frontal Parallel Direct Solver for Two-Dimensional Isogeometric Analysis
Kuźnik, Krzysztof; Paszyński, Maciej; Calo, Victor M.
2012-01-01
at parent nodes and eliminates rows corresponding to fully assembled degrees of freedom. Finally, there are graph grammar productions responsible for root problem solution and recursive backward substitutions. Expressing the solver algorithm by graph grammar
Inferring ontology graph structures using OWL reasoning
Rodriguez-Garcia, Miguel Angel
2018-01-05
Ontologies are representations of a conceptualization of a domain. Traditionally, ontologies in biology were represented as directed acyclic graphs (DAG) which represent the backbone taxonomy and additional relations between classes. These graphs are widely exploited for data analysis in the form of ontology enrichment or computation of semantic similarity. More recently, ontologies are developed in a formal language such as the Web Ontology Language (OWL) and consist of a set of axioms through which classes are defined or constrained. While the taxonomy of an ontology can be inferred directly from the axioms of an ontology as one of the standard OWL reasoning tasks, creating general graph structures from OWL ontologies that exploit the ontologies\\' semantic content remains a challenge.We developed a method to transform ontologies into graphs using an automated reasoner while taking into account all relations between classes. Searching for (existential) patterns in the deductive closure of ontologies, we can identify relations between classes that are implied but not asserted and generate graph structures that encode for a large part of the ontologies\\' semantic content. We demonstrate the advantages of our method by applying it to inference of protein-protein interactions through semantic similarity over the Gene Ontology and demonstrate that performance is increased when graph structures are inferred using deductive inference according to our method. Our software and experiment results are available at http://github.com/bio-ontology-research-group/Onto2Graph .Onto2Graph is a method to generate graph structures from OWL ontologies using automated reasoning. The resulting graphs can be used for improved ontology visualization and ontology-based data analysis.
Inferring ontology graph structures using OWL reasoning.
Rodríguez-García, Miguel Ángel; Hoehndorf, Robert
2018-01-05
Ontologies are representations of a conceptualization of a domain. Traditionally, ontologies in biology were represented as directed acyclic graphs (DAG) which represent the backbone taxonomy and additional relations between classes. These graphs are widely exploited for data analysis in the form of ontology enrichment or computation of semantic similarity. More recently, ontologies are developed in a formal language such as the Web Ontology Language (OWL) and consist of a set of axioms through which classes are defined or constrained. While the taxonomy of an ontology can be inferred directly from the axioms of an ontology as one of the standard OWL reasoning tasks, creating general graph structures from OWL ontologies that exploit the ontologies' semantic content remains a challenge. We developed a method to transform ontologies into graphs using an automated reasoner while taking into account all relations between classes. Searching for (existential) patterns in the deductive closure of ontologies, we can identify relations between classes that are implied but not asserted and generate graph structures that encode for a large part of the ontologies' semantic content. We demonstrate the advantages of our method by applying it to inference of protein-protein interactions through semantic similarity over the Gene Ontology and demonstrate that performance is increased when graph structures are inferred using deductive inference according to our method. Our software and experiment results are available at http://github.com/bio-ontology-research-group/Onto2Graph . Onto2Graph is a method to generate graph structures from OWL ontologies using automated reasoning. The resulting graphs can be used for improved ontology visualization and ontology-based data analysis.
Brouwer, A.E.; Haemers, W.H.; Brouwer, A.E.; Haemers, W.H.
2012-01-01
This chapter presents some simple results on graph spectra.We assume the reader is familiar with elementary linear algebra and graph theory. Throughout, J will denote the all-1 matrix, and 1 is the all-1 vector.
Comparative analysis through probability distributions of a data set
Cristea, Gabriel; Constantinescu, Dan Mihai
2018-02-01
In practice, probability distributions are applied in such diverse fields as risk analysis, reliability engineering, chemical engineering, hydrology, image processing, physics, market research, business and economic research, customer support, medicine, sociology, demography etc. This article highlights important aspects of fitting probability distributions to data and applying the analysis results to make informed decisions. There are a number of statistical methods available which can help us to select the best fitting model. Some of the graphs display both input data and fitted distributions at the same time, as probability density and cumulative distribution. The goodness of fit tests can be used to determine whether a certain distribution is a good fit. The main used idea is to measure the "distance" between the data and the tested distribution, and compare that distance to some threshold values. Calculating the goodness of fit statistics also enables us to order the fitted distributions accordingly to how good they fit to data. This particular feature is very helpful for comparing the fitted models. The paper presents a comparison of most commonly used goodness of fit tests as: Kolmogorov-Smirnov, Anderson-Darling, and Chi-Squared. A large set of data is analyzed and conclusions are drawn by visualizing the data, comparing multiple fitted distributions and selecting the best model. These graphs should be viewed as an addition to the goodness of fit tests.
Graph embedding with rich information through heterogeneous graph
Sun, Guolei
2017-01-01
Graph embedding, aiming to learn low-dimensional representations for nodes in graphs, has attracted increasing attention due to its critical application including node classification, link prediction and clustering in social network analysis. Most
Gene set analysis of the EADGENE chicken data-set
Skarman, Axel; Jiang, Li; Hornshøj, Henrik
2009-01-01
Abstract Background: Gene set analysis is considered to be a way of improving our biological interpretation of the observed expression patterns. This paper describes different methods applied to analyse expression data from a chicken DNA microarray dataset. Results: Applying different gene set...... analyses to the chicken expression data led to different ranking of the Gene Ontology terms tested. A method for prediction of possible annotations was applied. Conclusion: Biological interpretation based on gene set analyses dependent on the statistical method used. Methods for predicting the possible...
Proxy Graph: Visual Quality Metrics of Big Graph Sampling.
Nguyen, Quan Hoang; Hong, Seok-Hee; Eades, Peter; Meidiana, Amyra
2017-06-01
Data sampling has been extensively studied for large scale graph mining. Many analyses and tasks become more efficient when performed on graph samples of much smaller size. The use of proxy objects is common in software engineering for analysis and interaction with heavy objects or systems. In this paper, we coin the term 'proxy graph' and empirically investigate how well a proxy graph visualization can represent a big graph. Our investigation focuses on proxy graphs obtained by sampling; this is one of the most common proxy approaches. Despite the plethora of data sampling studies, this is the first evaluation of sampling in the context of graph visualization. For an objective evaluation, we propose a new family of quality metrics for visual quality of proxy graphs. Our experiments cover popular sampling techniques. Our experimental results lead to guidelines for using sampling-based proxy graphs in visualization.
van der Flier Wiesje M
2009-08-01
Full Text Available Abstract Background Although a large body of knowledge about both brain structure and function has been gathered over the last decades, we still have a poor understanding of their exact relationship. Graph theory provides a method to study the relation between network structure and function, and its application to neuroscientific data is an emerging research field. We investigated topological changes in large-scale functional brain networks in patients with Alzheimer's disease (AD and frontotemporal lobar degeneration (FTLD by means of graph theoretical analysis of resting-state EEG recordings. EEGs of 20 patients with mild to moderate AD, 15 FTLD patients, and 23 non-demented individuals were recorded in an eyes-closed resting-state. The synchronization likelihood (SL, a measure of functional connectivity, was calculated for each sensor pair in 0.5–4 Hz, 4–8 Hz, 8–10 Hz, 10–13 Hz, 13–30 Hz and 30–45 Hz frequency bands. The resulting connectivity matrices were converted to unweighted graphs, whose structure was characterized with several measures: mean clustering coefficient (local connectivity, characteristic path length (global connectivity and degree correlation (network 'assortativity'. All results were normalized for network size and compared with random control networks. Results In AD, the clustering coefficient decreased in the lower alpha and beta bands (p Conclusion With decreasing local and global connectivity parameters, the large-scale functional brain network organization in AD deviates from the optimal 'small-world' network structure towards a more 'random' type. This is associated with less efficient information exchange between brain areas, supporting the disconnection hypothesis of AD. Surprisingly, FTLD patients show changes in the opposite direction, towards a (perhaps excessively more 'ordered' network structure, possibly reflecting a different underlying pathophysiological process.
Fuzzy-Set Based Sentiment Analysis of Big Social Data
Mukkamala, Raghava Rao; Hussain, Abid; Vatrapu, Ravi
2014-01-01
Computational approaches to social media analytics are largely limited to graph theoretical approaches such as social network analysis (SNA) informed by the social philosophical approach of relational sociology. There are no other unified modelling approaches to social data that integrate...... the conceptual, formal, software, analytical and empirical realms. In this paper, we first present and discuss a theory and conceptual model of social data. Second, we outline a formal model based on fuzzy set theory and describe the operational semantics of the formal model with a real-world social data example...... from Facebook. Third, we briefly present and discuss the Social Data Analytics Tool (SODATO) that realizes the conceptual model in software and provisions social data analysis based on the conceptual and formal models. Fourth, we use SODATO to fetch social data from the facebook wall of a global brand...
Graph Transformation and Designing Parallel Sparse Matrix Algorithms beyond Data Dependence Analysis
H.X. Lin
2004-01-01
Full Text Available Algorithms are often parallelized based on data dependence analysis manually or by means of parallel compilers. Some vector/matrix computations such as the matrix-vector products with simple data dependence structures (data parallelism can be easily parallelized. For problems with more complicated data dependence structures, parallelization is less straightforward. The data dependence graph is a powerful means for designing and analyzing parallel algorithms. However, for sparse matrix computations, parallelization based on solely exploiting the existing parallelism in an algorithm does not always give satisfactory results. For example, the conventional Gaussian elimination algorithm for the solution of a tri-diagonal system is inherently sequential, so algorithms specially for parallel computation has to be designed. After briefly reviewing different parallelization approaches, a powerful graph formalism for designing parallel algorithms is introduced. This formalism will be discussed using a tri-diagonal system as an example. Its application to general matrix computations is also discussed. Its power in designing parallel algorithms beyond the ability of data dependence analysis is shown by means of a new algorithm called ACER (Alternating Cyclic Elimination and Reduction algorithm.
Visibility graph analysis of heart rate time series and bio-marker of congestive heart failure
Bhaduri, Anirban; Bhaduri, Susmita; Ghosh, Dipak
2017-09-01
Study of RR interval time series for Congestive Heart Failure had been an area of study with different methods including non-linear methods. In this article the cardiac dynamics of heart beat are explored in the light of complex network analysis, viz. visibility graph method. Heart beat (RR Interval) time series data taken from Physionet database [46, 47] belonging to two groups of subjects, diseased (congestive heart failure) (29 in number) and normal (54 in number) are analyzed with the technique. The overall results show that a quantitative parameter can significantly differentiate between the diseased subjects and the normal subjects as well as different stages of the disease. Further, the data when split into periods of around 1 hour each and analyzed separately, also shows the same consistent differences. This quantitative parameter obtained using the visibility graph analysis thereby can be used as a potential bio-marker as well as a subsequent alarm generation mechanism for predicting the onset of Congestive Heart Failure.
Using Graph and Vertex Entropy to Compare Empirical Graphs with Theoretical Graph Models
Tomasz Kajdanowicz
2016-09-01
Full Text Available Over the years, several theoretical graph generation models have been proposed. Among the most prominent are: the Erdős–Renyi random graph model, Watts–Strogatz small world model, Albert–Barabási preferential attachment model, Price citation model, and many more. Often, researchers working with real-world data are interested in understanding the generative phenomena underlying their empirical graphs. They want to know which of the theoretical graph generation models would most probably generate a particular empirical graph. In other words, they expect some similarity assessment between the empirical graph and graphs artificially created from theoretical graph generation models. Usually, in order to assess the similarity of two graphs, centrality measure distributions are compared. For a theoretical graph model this means comparing the empirical graph to a single realization of a theoretical graph model, where the realization is generated from the given model using an arbitrary set of parameters. The similarity between centrality measure distributions can be measured using standard statistical tests, e.g., the Kolmogorov–Smirnov test of distances between cumulative distributions. However, this approach is both error-prone and leads to incorrect conclusions, as we show in our experiments. Therefore, we propose a new method for graph comparison and type classification by comparing the entropies of centrality measure distributions (degree centrality, betweenness centrality, closeness centrality. We demonstrate that our approach can help assign the empirical graph to the most similar theoretical model using a simple unsupervised learning method.
Analysis of the enzyme network involved in cattle milk production using graph theory.
Ghorbani, Sholeh; Tahmoorespur, Mojtaba; Masoudi Nejad, Ali; Nasiri, Mohammad; Asgari, Yazdan
2015-06-01
Understanding cattle metabolism and its relationship with milk products is important in bovine breeding. A systemic view could lead to consequences that will result in a better understanding of existing concepts. Topological indices and quantitative characterizations mostly result from the application of graph theory on biological data. In the present work, the enzyme network involved in cattle milk production was reconstructed and analyzed based on available bovine genome information using several public datasets (NCBI, Uniprot, KEGG, and Brenda). The reconstructed network consisted of 3605 reactions named by KEGG compound numbers and 646 enzymes that catalyzed the corresponding reactions. The characteristics of the directed and undirected network were analyzed using Graph Theory. The mean path length was calculated to be4.39 and 5.41 for directed and undirected networks, respectively. The top 11 hub enzymes whose abnormality could harm bovine health and reduce milk production were determined. Therefore, the aim of constructing the enzyme centric network was twofold; first to find out whether such network followed the same properties of other biological networks, and second, to find the key enzymes. The results of the present study can improve our understanding of milk production in cattle. Also, analysis of the enzyme network can help improve the modeling and simulation of biological systems and help design desired phenotypes to increase milk production quality or quantity.
Du, Lei; Huang, Heng; Yan, Jingwen; Kim, Sungeun; Risacher, Shannon L; Inlow, Mark; Moore, Jason H; Saykin, Andrew J; Shen, Li
2016-05-15
Structured sparse canonical correlation analysis (SCCA) models have been used to identify imaging genetic associations. These models either use group lasso or graph-guided fused lasso to conduct feature selection and feature grouping simultaneously. The group lasso based methods require prior knowledge to define the groups, which limits the capability when prior knowledge is incomplete or unavailable. The graph-guided methods overcome this drawback by using the sample correlation to define the constraint. However, they are sensitive to the sign of the sample correlation, which could introduce undesirable bias if the sign is wrongly estimated. We introduce a novel SCCA model with a new penalty, and develop an efficient optimization algorithm. Our method has a strong upper bound for the grouping effect for both positively and negatively correlated features. We show that our method performs better than or equally to three competing SCCA models on both synthetic and real data. In particular, our method identifies stronger canonical correlations and better canonical loading patterns, showing its promise for revealing interesting imaging genetic associations. The Matlab code and sample data are freely available at http://www.iu.edu/∼shenlab/tools/angscca/ shenli@iu.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.
Hart, Michael G; Ypma, Rolf J F; Romero-Garcia, Rafael; Price, Stephen J; Suckling, John
2016-06-01
Neuroanatomy has entered a new era, culminating in the search for the connectome, otherwise known as the brain's wiring diagram. While this approach has led to landmark discoveries in neuroscience, potential neurosurgical applications and collaborations have been lagging. In this article, the authors describe the ideas and concepts behind the connectome and its analysis with graph theory. Following this they then describe how to form a connectome using resting state functional MRI data as an example. Next they highlight selected insights into healthy brain function that have been derived from connectome analysis and illustrate how studies into normal development, cognitive function, and the effects of synthetic lesioning can be relevant to neurosurgery. Finally, they provide a précis of early applications of the connectome and related techniques to traumatic brain injury, functional neurosurgery, and neurooncology.
Lin, Po-Chuan; Chen, Bo-Wei; Chang, Hangbae
2016-07-01
This study presents a human-centric technique for social video expansion based on semantic processing and graph analysis. The objective is to increase metadata of an online video and to explore related information, thereby facilitating user browsing activities. To analyze the semantic meaning of a video, shots and scenes are firstly extracted from the video on the server side. Subsequently, this study uses annotations along with ConceptNet to establish the underlying framework. Detailed metadata, including visual objects and audio events among the predefined categories, are indexed by using the proposed method. Furthermore, relevant online media associated with each category are also analyzed to enrich the existing content. With the above-mentioned information, users can easily browse and search the content according to the link analysis and its complementary knowledge. Experiments on a video dataset are conducted for evaluation. The results show that our system can achieve satisfactory performance, thereby demonstrating the feasibility of the proposed idea.
Kumar, Abhishek; Clement, Shibu; Agrawal, V P
2010-07-15
An attempt is made to address a few ecological and environment issues by developing different structural models for effluent treatment system for electroplating. The effluent treatment system is defined with the help of different subsystems contributing to waste minimization. Hierarchical tree and block diagram showing all possible interactions among subsystems are proposed. These non-mathematical diagrams are converted into mathematical models for design improvement, analysis, comparison, storage retrieval and commercially off-the-shelf purchases of different subsystems. This is achieved by developing graph theoretic model, matrix models and variable permanent function model. Analysis is carried out by permanent function, hierarchical tree and block diagram methods. Storage and retrieval is done using matrix models. The methodology is illustrated with the help of an example. Benefits to the electroplaters/end user are identified. 2010 Elsevier B.V. All rights reserved.
Graph mining for next generation sequencing: leveraging the assembly graph for biological insights.
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
Cécile Bordier
2017-08-01
Full Text Available Neuroimaging data can be represented as networks of nodes and edges that capture the topological organization of the brain connectivity. Graph theory provides a general and powerful framework to study these networks and their structure at various scales. By way of example, community detection methods have been widely applied to investigate the modular structure of many natural networks, including brain functional connectivity networks. Sparsification procedures are often applied to remove the weakest edges, which are the most affected by experimental noise, and to reduce the density of the graph, thus making it theoretically and computationally more tractable. However, weak links may also contain significant structural information, and procedures to identify the optimal tradeoff are the subject of active research. Here, we explore the use of percolation analysis, a method grounded in statistical physics, to identify the optimal sparsification threshold for community detection in brain connectivity networks. By using synthetic networks endowed with a ground-truth modular structure and realistic topological features typical of human brain functional connectivity networks, we show that percolation analysis can be applied to identify the optimal sparsification threshold that maximizes information on the networks' community structure. We validate this approach using three different community detection methods widely applied to the analysis of brain connectivity networks: Newman's modularity, InfoMap and Asymptotical Surprise. Importantly, we test the effects of noise and data variability, which are critical factors to determine the optimal threshold. This data-driven method should prove particularly useful in the analysis of the community structure of brain networks in populations characterized by different connectivity strengths, such as patients and controls.
Well-covered graphs and factors
Randerath, Bert; Vestergaard, Preben D.
2006-01-01
A maximum independent set of vertices in a graph is a set of pairwise nonadjacent vertices of largest cardinality α. Plummer defined a graph to be well-covered, if every independent set is contained in a maximum independent set of G. Every well-covered graph G without isolated vertices has a perf...
Resting-state theta band connectivity and graph analysis in generalized social anxiety disorder.
Xing, Mengqi; Tadayonnejad, Reza; MacNamara, Annmarie; Ajilore, Olusola; DiGangi, Julia; Phan, K Luan; Leow, Alex; Klumpp, Heide
2017-01-01
Functional magnetic resonance imaging (fMRI) resting-state studies show generalized social anxiety disorder (gSAD) is associated with disturbances in networks involved in emotion regulation, emotion processing, and perceptual functions, suggesting a network framework is integral to elucidating the pathophysiology of gSAD. However, fMRI does not measure the fast dynamic interconnections of functional networks. Therefore, we examined whole-brain functional connectomics with electroencephalogram (EEG) during resting-state. Resting-state EEG data was recorded for 32 patients with gSAD and 32 demographically-matched healthy controls (HC). Sensor-level connectivity analysis was applied on EEG data by using Weighted Phase Lag Index (WPLI) and graph analysis based on WPLI was used to determine clustering coefficient and characteristic path length to estimate local integration and global segregation of networks. WPLI results showed increased oscillatory midline coherence in the theta frequency band indicating higher connectivity in the gSAD relative to HC group during rest. Additionally, WPLI values positively correlated with state anxiety levels within the gSAD group but not the HC group. Our graph theory based connectomics analysis demonstrated increased clustering coefficient and decreased characteristic path length in theta-based whole brain functional organization in subjects with gSAD compared to HC. Theta-dependent interconnectivity was associated with state anxiety in gSAD and an increase in information processing efficiency in gSAD (compared to controls). Results may represent enhanced baseline self-focused attention, which is consistent with cognitive models of gSAD and fMRI studies implicating emotion dysregulation and disturbances in task negative networks (e.g., default mode network) in gSAD.
Vecchio, Fabrizio; Miraglia, Francesca; Bramanti, Placido; Rossini, Paolo Maria
2014-01-01
Modern analysis of electroencephalographic (EEG) rhythms provides information on dynamic brain connectivity. To test the hypothesis that aging processes modulate the brain connectivity network, EEG recording was conducted on 113 healthy volunteers. They were divided into three groups in accordance with their ages: 36 Young (15-45 years), 46 Adult (50-70 years), and 31 Elderly (>70 years). To evaluate the stability of the investigated parameters, a subgroup of 10 subjects underwent a second EEG recording two weeks later. Graph theory functions were applied to the undirected and weighted networks obtained by the lagged linear coherence evaluated by eLORETA on cortical sources. EEG frequency bands of interest were: delta (2-4 Hz), theta (4-8 Hz), alpha1 (8-10.5 Hz), alpha2 (10.5-13 Hz), beta1 (13-20 Hz), beta2 (20-30 Hz), and gamma (30-40 Hz). The spectral connectivity analysis of cortical sources showed that the normalized Characteristic Path Length (λ) presented the pattern Young > Adult>Elderly in the higher alpha band. Elderly also showed a greater increase in delta and theta bands than Young. The correlation between age and λ showed that higher ages corresponded to higher λ in delta and theta and lower in the alpha2 band; this pattern reflects the age-related modulation of higher (alpha) and decreased (delta) connectivity. The Normalized Clustering coefficient (γ) and small-world network modeling (σ) showed non-significant age-modulation. Evidence from the present study suggests that graph theory can aid in the analysis of connectivity patterns estimated from EEG and can facilitate the study of the physiological and pathological brain aging features of functional connectivity networks.
Ali Dashti
Full Text Available This paper presents an implementation of the brute-force exact k-Nearest Neighbor Graph (k-NNG construction for ultra-large high-dimensional data cloud. The proposed method uses Graphics Processing Units (GPUs and is scalable with multi-levels of parallelism (between nodes of a cluster, between different GPUs on a single node, and within a GPU. The method is applicable to homogeneous computing clusters with a varying number of nodes and GPUs per node. We achieve a 6-fold speedup in data processing as compared with an optimized method running on a cluster of CPUs and bring a hitherto impossible [Formula: see text]-NNG generation for a dataset of twenty million images with 15 k dimensionality into the realm of practical possibility.
Temporal Representation in Semantic Graphs
Levandoski, J J; Abdulla, G M
2007-08-07
A wide range of knowledge discovery and analysis applications, ranging from business to biological, make use of semantic graphs when modeling relationships and concepts. Most of the semantic graphs used in these applications are assumed to be static pieces of information, meaning temporal evolution of concepts and relationships are not taken into account. Guided by the need for more advanced semantic graph queries involving temporal concepts, this paper surveys the existing work involving temporal representations in semantic graphs.
Extracting Loop Bounds for WCET Analysis Using the Instrumentation Point Graph
Betts, A.; Bernat, G.
2009-05-01
Every calculation engine proposed in the literature of Worst-Case Execution Time (WCET) analysis requires upper bounds on loop iterations. Existing mechanisms to procure this information are either error prone, because they are gathered from the end-user, or limited in scope, because automatic analyses target very specific loop structures. In this paper, we present a technique that obtains bounds completely automatically for arbitrary loop structures. In particular, we show how to employ the Instrumentation Point Graph (IPG) to parse traces of execution (generated by an instrumented program) in order to extract bounds relative to any loop-nesting level. With this technique, therefore, non-rectangular dependencies between loops can be captured, allowing more accurate WCET estimates to be calculated. We demonstrate the improvement in accuracy by comparing WCET estimates computed through our HMB framework against those computed with state-of-the-art techniques.
Domination criticality in product graphs
M.R. Chithra
2015-07-01
Full Text Available A connected dominating set is an important notion and has many applications in routing and management of networks. Graph products have turned out to be a good model of interconnection networks. This motivated us to study the Cartesian product of graphs G with connected domination number, γc(G=2,3 and characterize such graphs. Also, we characterize the k−γ-vertex (edge critical graphs and k−γc-vertex (edge critical graphs for k=2,3 where γ denotes the domination number of G. We also discuss the vertex criticality in grids.
Generalized connectivity of graphs
Li, Xueliang
2016-01-01
Noteworthy results, proof techniques, open problems and conjectures in generalized (edge-) connectivity are discussed in this book. Both theoretical and practical analyses for generalized (edge-) connectivity of graphs are provided. Topics covered in this book include: generalized (edge-) connectivity of graph classes, algorithms, computational complexity, sharp bounds, Nordhaus-Gaddum-type results, maximum generalized local connectivity, extremal problems, random graphs, multigraphs, relations with the Steiner tree packing problem and generalizations of connectivity. This book enables graduate students to understand and master a segment of graph theory and combinatorial optimization. Researchers in graph theory, combinatorics, combinatorial optimization, probability, computer science, discrete algorithms, complexity analysis, network design, and the information transferring models will find this book useful in their studies.
Joyner, W David
2017-01-01
This textbook acts as a pathway to higher mathematics by seeking and illuminating the connections between graph theory and diverse fields of mathematics, such as calculus on manifolds, group theory, algebraic curves, Fourier analysis, cryptography and other areas of combinatorics. An overview of graph theory definitions and polynomial invariants for graphs prepares the reader for the subsequent dive into the applications of graph theory. To pique the reader’s interest in areas of possible exploration, recent results in mathematics appear throughout the book, accompanied with examples of related graphs, how they arise, and what their valuable uses are. The consequences of graph theory covered by the authors are complicated and far-reaching, so topics are always exhibited in a user-friendly manner with copious graphs, exercises, and Sage code for the computation of equations. Samples of the book’s source code can be found at github.com/springer-math/adventures-in-graph-theory. The text is geared towards ad...
Vestergaard, Preben Dahl; Hartnell, Bert L.
2006-01-01
There are many results dealing with the problem of decomposing a fixed graph into isomorphic subgraphs. There has also been work on characterizing graphs with the property that one can delete the edges of a number of edge disjoint copies of the subgraph and, regardless of how that is done, the gr...
PAGANI Toolkit: Parallel graph-theoretical analysis package for brain network big data.
Du, Haixiao; Xia, Mingrui; Zhao, Kang; Liao, Xuhong; Yang, Huazhong; Wang, Yu; He, Yong
2018-05-01
The recent collection of unprecedented quantities of neuroimaging data with high spatial resolution has led to brain network big data. However, a toolkit for fast and scalable computational solutions is still lacking. Here, we developed the PArallel Graph-theoretical ANalysIs (PAGANI) Toolkit based on a hybrid central processing unit-graphics processing unit (CPU-GPU) framework with a graphical user interface to facilitate the mapping and characterization of high-resolution brain networks. Specifically, the toolkit provides flexible parameters for users to customize computations of graph metrics in brain network analyses. As an empirical example, the PAGANI Toolkit was applied to individual voxel-based brain networks with ∼200,000 nodes that were derived from a resting-state fMRI dataset of 624 healthy young adults from the Human Connectome Project. Using a personal computer, this toolbox completed all computations in ∼27 h for one subject, which is markedly less than the 118 h required with a single-thread implementation. The voxel-based functional brain networks exhibited prominent small-world characteristics and densely connected hubs, which were mainly located in the medial and lateral fronto-parietal cortices. Moreover, the female group had significantly higher modularity and nodal betweenness centrality mainly in the medial/lateral fronto-parietal and occipital cortices than the male group. Significant correlations between the intelligence quotient and nodal metrics were also observed in several frontal regions. Collectively, the PAGANI Toolkit shows high computational performance and good scalability for analyzing connectome big data and provides a friendly interface without the complicated configuration of computing environments, thereby facilitating high-resolution connectomics research in health and disease. © 2018 Wiley Periodicals, Inc.
2011-01-01
Enerdata analyses 4 future energy scenarios accounting for 2 economic growth assumptions combined with 2 alternative carbon emission mitigation policies. In this study, a series of analyses supported by graphs assess the energy consumption and intensity forecasts in emerging and developed markets. In particular, one analysis is dedicated to energies competition, including gas, coal and renewable energies. (authors)
Error analysis of terrestrial laser scanning data by means of spherical statistics and 3D graphs.
Cuartero, Aurora; Armesto, Julia; Rodríguez, Pablo G; Arias, Pedro
2010-01-01
This paper presents a complete analysis of the positional errors of terrestrial laser scanning (TLS) data based on spherical statistics and 3D graphs. Spherical statistics are preferred because of the 3D vectorial nature of the spatial error. Error vectors have three metric elements (one module and two angles) that were analyzed by spherical statistics. A study case has been presented and discussed in detail. Errors were calculating using 53 check points (CP) and CP coordinates were measured by a digitizer with submillimetre accuracy. The positional accuracy was analyzed by both the conventional method (modular errors analysis) and the proposed method (angular errors analysis) by 3D graphics and numerical spherical statistics. Two packages in R programming language were performed to obtain graphics automatically. The results indicated that the proposed method is advantageous as it offers a more complete analysis of the positional accuracy, such as angular error component, uniformity of the vector distribution, error isotropy, and error, in addition the modular error component by linear statistics.
Rashno, Abdolreza; Koozekanani, Dara D; Drayna, Paul M; Nazari, Behzad; Sadri, Saeed; Rabbani, Hossein; Parhi, Keshab K
2018-05-01
This paper presents a fully automated algorithm to segment fluid-associated (fluid-filled) and cyst regions in optical coherence tomography (OCT) retina images of subjects with diabetic macular edema. The OCT image is segmented using a novel neutrosophic transformation and a graph-based shortest path method. In neutrosophic domain, an image is transformed into three sets: (true), (indeterminate) that represents noise, and (false). This paper makes four key contributions. First, a new method is introduced to compute the indeterminacy set , and a new -correction operation is introduced to compute the set in neutrosophic domain. Second, a graph shortest-path method is applied in neutrosophic domain to segment the inner limiting membrane and the retinal pigment epithelium as regions of interest (ROI) and outer plexiform layer and inner segment myeloid as middle layers using a novel definition of the edge weights . Third, a new cost function for cluster-based fluid/cyst segmentation in ROI is presented which also includes a novel approach in estimating the number of clusters in an automated manner. Fourth, the final fluid regions are achieved by ignoring very small regions and the regions between middle layers. The proposed method is evaluated using two publicly available datasets: Duke, Optima, and a third local dataset from the UMN clinic which is available online. The proposed algorithm outperforms the previously proposed Duke algorithm by 8% with respect to the dice coefficient and by 5% with respect to precision on the Duke dataset, while achieving about the same sensitivity. Also, the proposed algorithm outperforms a prior method for Optima dataset by 6%, 22%, and 23% with respect to the dice coefficient, sensitivity, and precision, respectively. Finally, the proposed algorithm also achieves sensitivity of 67.3%, 88.8%, and 76.7%, for the Duke, Optima, and the university of minnesota (UMN) datasets, respectively.
Set theoretical aspects of real analysis
Kharazishvili, Alexander B
2014-01-01
This book addresses a number of questions in real analysis and classical measure theory that are of a set-theoretic flavor. Accessible to graduate students, the beginning of the book presents introductory topics on real analysis and Lebesque measure theory. These topics highlight the boundary between fundamental concepts of measurability and non-measurability for point sets and functions. The remainder of the book deals with more specialized material on set-theoretical real analysis. Problems are included at the end of each chapter.
Haynes Teresa W.
2014-08-01
Full Text Available A path π = (v1, v2, . . . , vk+1 in a graph G = (V,E is a downhill path if for every i, 1 ≤ i ≤ k, deg(vi ≥ deg(vi+1, where deg(vi denotes the degree of vertex vi ∈ V. The downhill domination number equals the minimum cardinality of a set S ⊆ V having the property that every vertex v ∈ V lies on a downhill path originating from some vertex in S. We investigate downhill domination numbers of graphs and give upper bounds. In particular, we show that the downhill domination number of a graph is at most half its order, and that the downhill domination number of a tree is at most one third its order. We characterize the graphs obtaining each of these bounds
Cytoscape.js: a graph theory library for visualisation and analysis.
Franz, Max; Lopes, Christian T; Huck, Gerardo; Dong, Yue; Sumer, Onur; Bader, Gary D
2016-01-15
Cytoscape.js is an open-source JavaScript-based graph library. Its most common use case is as a visualization software component, so it can be used to render interactive graphs in a web browser. It also can be used in a headless manner, useful for graph operations on a server, such as Node.js. Cytoscape.js is implemented in JavaScript. Documentation, downloads and source code are available at http://js.cytoscape.org. gary.bader@utoronto.ca. © The Author 2015. Published by Oxford University Press.
Jha, Mayank Shekhar; Chatti, Nizar; Declerck, Philippe
2017-09-01
This paper addresses the fault diagnosis problem of uncertain systems in the context of Bond Graph modelling technique. The main objective is to enhance the fault detection step based on Interval valued Analytical Redundancy Relations (named I-ARR) in order to overcome the problems related to false alarms, missed alarms and robustness issues. These I-ARRs are a set of fault indicators that generate the interval bounds called thresholds. A fault is detected once the nominal residuals (point valued part of I-ARRs) exceed the thresholds. However, the existing fault detection method is limited to parametric faults and it presents various limitations with regards to estimation of measurement signal derivatives, to which I-ARRs are sensitive. The novelties and scientific interest of the proposed methodology are: (1) to improve the accuracy of the measurements derivatives estimation by using a dedicated sliding mode differentiator proposed in this work, (2) to suitably integrate the Fourier-Motzkin Elimination (FME) technique within the I-ARRs based diagnosis so that measurements faults can be detected successfully. The latter provides interval bounds over the derivatives which are included in the thresholds. The proposed methodology is studied under various scenarios (parametric and measurement faults) via simulations over a mechatronic torsion bar system.
Decomposing Oriented Graphs into Six Locally Irregular Oriented Graphs
Bensmail, Julien; Renault, Gabriel
2016-01-01
An undirected graph G is locally irregular if every two of its adjacent vertices have distinct degrees. We say that G is decomposable into k locally irregular graphs if there exists a partition E1∪E2∪⋯∪Ek of the edge set E(G) such that each Ei induces a locally irregular graph. It was recently co...
An Analysis of the Influence of Graph Theory When Preparing for Programming Contests
Cristina Jordán
2017-01-01
Full Text Available The subject known as Programming Contests in the Bachelor’s Degree in Computer Engineering course focuses on solving programming problems frequently met within contests such as the Southwest Europe Regional Contest (SWERC. In order to solve these problems one first needs to model the problem correctly, find the ideal solution, and then be able to program it without making any mistakes in a very short period of time. Leading multinationals such as Google, Apple, IBM, Facebook and Microsoft place a very high value on these abilities when selecting candidates for posts in their companies. In this communication we present some preliminary results of an analysis of the interaction between two optional subjects in the Computer Science Degree course: Programming Contests (PC and Graphs, Models and Applications (GMA. The results of this analysis enabled us to make changes to some of the contents in GMA in order to better prepare the students to deal with the challenges they have to face in programming contests.
Abnormal brain white matter network in young smokers: a graph theory analysis study.
Zhang, Yajuan; Li, Min; Wang, Ruonan; Bi, Yanzhi; Li, Yangding; Yi, Zhang; Liu, Jixin; Yu, Dahua; Yuan, Kai
2018-04-01
Previous diffusion tensor imaging (DTI) studies had investigated the white matter (WM) integrity abnormalities in some specific fiber bundles in smokers. However, little is known about the changes in topological organization of WM structural network in young smokers. In current study, we acquired DTI datasets from 58 male young smokers and 51 matched nonsmokers and constructed the WM networks by the deterministic fiber tracking approach. Graph theoretical analysis was used to compare the topological parameters of WM network (global and nodal) and the inter-regional fractional anisotropy (FA) weighted WM connections between groups. The results demonstrated that both young smokers and nonsmokers had small-world topology in WM network. Further analysis revealed that the young smokers exhibited the abnormal topological organization, i.e., increased network strength, global efficiency, and decreased shortest path length. In addition, the increased nodal efficiency predominately was located in frontal cortex, striatum and anterior cingulate gyrus (ACG) in smokers. Moreover, based on network-based statistic (NBS) approach, the significant increased FA-weighted WM connections were mainly found in the PFC, ACG and supplementary motor area (SMA) regions. Meanwhile, the network parameters were correlated with the nicotine dependence severity (FTND) scores, and the nodal efficiency of orbitofrontal cortex was positive correlation with the cigarette per day (CPD) in young smokers. We revealed the abnormal topological organization of WM network in young smokers, which may improve our understanding of the neural mechanism of young smokers form WM topological organization level.
Ponten, S.C.; Daffertshofer, A.; Hillebrand, A.; Stam, C.J.
2010-01-01
We investigated the relationship between structural network properties and both synchronization strength and functional characteristics in a combined neural mass and graph theoretical model of the electroencephalogram (EEG). Thirty-two neural mass models (NMMs), each representing the lump activity
Summary: beyond fault trees to fault graphs
Alesso, H.P.; Prassinos, P.; Smith, C.F.
1984-09-01
Fault Graphs are the natural evolutionary step over a traditional fault-tree model. A Fault Graph is a failure-oriented directed graph with logic connectives that allows cycles. We intentionally construct the Fault Graph to trace the piping and instrumentation drawing (P and ID) of the system, but with logical AND and OR conditions added. Then we evaluate the Fault Graph with computer codes based on graph-theoretic methods. Fault Graph computer codes are based on graph concepts, such as path set (a set of nodes traveled on a path from one node to another) and reachability (the complete set of all possible paths between any two nodes). These codes are used to find the cut-sets (any minimal set of component failures that will fail the system) and to evaluate the system reliability
Graph Theoretical Analysis Reveals: Women's Brains Are Better Connected than Men's.
Balázs Szalkai
Full Text Available Deep graph-theoretic ideas in the context with the graph of the World Wide Web led to the definition of Google's PageRank and the subsequent rise of the most popular search engine to date. Brain graphs, or connectomes, are being widely explored today. We believe that non-trivial graph theoretic concepts, similarly as it happened in the case of the World Wide Web, will lead to discoveries enlightening the structural and also the functional details of the animal and human brains. When scientists examine large networks of tens or hundreds of millions of vertices, only fast algorithms can be applied because of the size constraints. In the case of diffusion MRI-based structural human brain imaging, the effective vertex number of the connectomes, or brain graphs derived from the data is on the scale of several hundred today. That size facilitates applying strict mathematical graph algorithms even for some hard-to-compute (or NP-hard quantities like vertex cover or balanced minimum cut. In the present work we have examined brain graphs, computed from the data of the Human Connectome Project, recorded from male and female subjects between ages 22 and 35. Significant differences were found between the male and female structural brain graphs: we show that the average female connectome has more edges, is a better expander graph, has larger minimal bisection width, and has more spanning trees than the average male connectome. Since the average female brain weighs less than the brain of males, these properties show that the female brain has better graph theoretical properties, in a sense, than the brain of males. It is known that the female brain has a smaller gray matter/white matter ratio than males, that is, a larger white matter/gray matter ratio than the brain of males; this observation is in line with our findings concerning the number of edges, since the white matter consists of myelinated axons, which, in turn, roughly correspond to the connections
Liu, Yuelu; Hong, Xiangfei; Bengson, Jesse J; Kelley, Todd A; Ding, Mingzhou; Mangun, George R
2017-08-15
The neural mechanisms by which intentions are transformed into actions remain poorly understood. We investigated the network mechanisms underlying spontaneous voluntary decisions about where to focus visual-spatial attention (willed attention). Graph-theoretic analysis of two independent datasets revealed that regions activated during willed attention form a set of functionally-distinct networks corresponding to the frontoparietal network, the cingulo-opercular network, and the dorsal attention network. Contrasting willed attention with instructed attention (where attention is directed by external cues), we observed that the dorsal anterior cingulate cortex was allied with the dorsal attention network in instructed attention, but shifted connectivity during willed attention to interact with the cingulo-opercular network, which then mediated communications between the frontoparietal network and the dorsal attention network. Behaviorally, greater connectivity in network hubs, including the dorsolateral prefrontal cortex, the dorsal anterior cingulate cortex, and the inferior parietal lobule, was associated with faster reaction times. These results, shown to be consistent across the two independent datasets, uncover the dynamic organization of functionally-distinct networks engaged to support intentional acts. Copyright © 2017 Elsevier Inc. All rights reserved.
Orgeta Gjermëni
2017-10-01
Full Text Available This article aims to provide new results about the intraday degree sequence distribution considering phone call network graph evolution in time. More specifically, it tackles the following problem. Given a large amount of landline phone call data records, what is the best way to summarize the distinct number of calling partners per client per day? In order to answer this question, a series of undirected phone call network graphs is constructed based on data from a local telecommunication source in Albania. All network graphs of the series are simplified. Further, a longitudinal temporal study is made on this network graphs series related to the degree distributions. Power law and log-normal distribution fittings on the degree sequence are compared on each of the network graphs of the series. The maximum likelihood method is used to estimate the parameters of the distributions, and a Kolmogorov–Smirnov test associated with a p-value is used to define the plausible models. A direct distribution comparison is made through a Vuong test in the case that both distributions are plausible. Another goal was to describe the parameters’ distributions’ shape. A Shapiro-Wilk test is used to test the normality of the data, and measures of shape are used to define the distributions’ shape. Study findings suggested that log-normal distribution models better the intraday degree sequence data of the network graphs. It is not possible to say that the distributions of log-normal parameters are normal.
Common-cause analysis using sets
Worrell, R.B.; Stack, D.W.
1977-12-01
Common-cause analysis was developed at the Aerojet Nuclear Company for studying the behavior of a system that is affected by special conditions and secondary causes. Common-cause analysis is related to fault tree analysis. Common-cause candidates are minimal cut sets whose primary events are closely linked by a special condition or are susceptible to the same secondary cause. It is shown that common-cause candidates can be identified using the Set Equation Transformation System (SETS). A Boolean equation is used to establish the special conditions and secondary cause susceptibilities for each primary event in the fault tree. A transformation of variables (substituting equals for equals), executed on a minimal cut set equation, results in replacing each primary event by the right side of its special condition/secondary cause equation and leads to the identification of the common-cause candidates
Intrinsic functional brain architecture derived from graph theoretical analysis in the human fetus.
Moriah E Thomason
Full Text Available The human brain undergoes dramatic maturational changes during late stages of fetal and early postnatal life. The importance of this period to the establishment of healthy neural connectivity is apparent in the high incidence of neural injury in preterm infants, in whom untimely exposure to ex-uterine factors interrupts neural connectivity. Though the relevance of this period to human neuroscience is apparent, little is known about functional neural networks in human fetal life. Here, we apply graph theoretical analysis to examine human fetal brain connectivity. Utilizing resting state functional magnetic resonance imaging (fMRI data from 33 healthy human fetuses, 19 to 39 weeks gestational age (GA, our analyses reveal that the human fetal brain has modular organization and modules overlap functional systems observed postnatally. Age-related differences between younger (GA <31 weeks and older (GA≥31 weeks fetuses demonstrate that brain modularity decreases, and connectivity of the posterior cingulate to other brain networks becomes more negative, with advancing GA. By mimicking functional principles observed postnatally, these results support early emerging capacity for information processing in the human fetal brain. Current technical limitations, as well as the potential for fetal fMRI to one day produce major discoveries about fetal origins or antecedents of neural injury or disease are discussed.
Haraldsdóttir, Hulda S.; Fleming, Ronan M. T.
2016-01-01
Conserved moieties are groups of atoms that remain intact in all reactions of a metabolic network. Identification of conserved moieties gives insight into the structure and function of metabolic networks and facilitates metabolic modelling. All moiety conservation relations can be represented as nonnegative integer vectors in the left null space of the stoichiometric matrix corresponding to a biochemical network. Algorithms exist to compute such vectors based only on reaction stoichiometry but their computational complexity has limited their application to relatively small metabolic networks. Moreover, the vectors returned by existing algorithms do not, in general, represent conservation of a specific moiety with a defined atomic structure. Here, we show that identification of conserved moieties requires data on reaction atom mappings in addition to stoichiometry. We present a novel method to identify conserved moieties in metabolic networks by graph theoretical analysis of their underlying atom transition networks. Our method returns the exact group of atoms belonging to each conserved moiety as well as the corresponding vector in the left null space of the stoichiometric matrix. It can be implemented as a pipeline of polynomial time algorithms. Our implementation completes in under five minutes on a metabolic network with more than 4,000 mass balanced reactions. The scalability of the method enables extension of existing applications for moiety conservation relations to genome-scale metabolic networks. We also give examples of new applications made possible by elucidating the atomic structure of conserved moieties. PMID:27870845
MACCIA, ELIZABETH S.; AND OTHERS
AN ANNOTATED BIBLIOGRAPHY OF 20 ITEMS AND A DISCUSSION OF ITS SIGNIFICANCE WAS PRESENTED TO DESCRIBE CURRENT UTILIZATION OF SUBJECT THEORIES IN THE CONSTRUCTION OF AN EDUCATIONAL THEORY. ALSO, A THEORY MODEL WAS USED TO DEMONSTRATE CONSTRUCTION OF A SCIENTIFIC EDUCATIONAL THEORY. THE THEORY MODEL INCORPORATED SET THEORY (S), INFORMATION THEORY…
Gene set analysis using variance component tests.
Huang, Yen-Tsung; Lin, Xihong
2013-06-28
Gene set analyses have become increasingly important in genomic research, as many complex diseases are contributed jointly by alterations of numerous genes. Genes often coordinate together as a functional repertoire, e.g., a biological pathway/network and are highly correlated. However, most of the existing gene set analysis methods do not fully account for the correlation among the genes. Here we propose to tackle this important feature of a gene set to improve statistical power in gene set analyses. We propose to model the effects of an independent variable, e.g., exposure/biological status (yes/no), on multiple gene expression values in a gene set using a multivariate linear regression model, where the correlation among the genes is explicitly modeled using a working covariance matrix. We develop TEGS (Test for the Effect of a Gene Set), a variance component test for the gene set effects by assuming a common distribution for regression coefficients in multivariate linear regression models, and calculate the p-values using permutation and a scaled chi-square approximation. We show using simulations that type I error is protected under different choices of working covariance matrices and power is improved as the working covariance approaches the true covariance. The global test is a special case of TEGS when correlation among genes in a gene set is ignored. Using both simulation data and a published diabetes dataset, we show that our test outperforms the commonly used approaches, the global test and gene set enrichment analysis (GSEA). We develop a gene set analyses method (TEGS) under the multivariate regression framework, which directly models the interdependence of the expression values in a gene set using a working covariance. TEGS outperforms two widely used methods, GSEA and global test in both simulation and a diabetes microarray data.
PERSEUS-HUB: Interactive and Collective Exploration of Large-Scale Graphs
Di Jin
2017-07-01
Full Text Available Graphs emerge naturally in many domains, such as social science, neuroscience, transportation engineering, and more. In many cases, such graphs have millions or billions of nodes and edges, and their sizes increase daily at a fast pace. How can researchers from various domains explore large graphs interactively and efficiently to find out what is ‘important’? How can multiple researchers explore a new graph dataset collectively and “help” each other with their findings? In this article, we present Perseus-Hub, a large-scale graph mining tool that computes a set of graph properties in a distributed manner, performs ensemble, multi-view anomaly detection to highlight regions that are worth investigating, and provides users with uncluttered visualization and easy interaction with complex graph statistics. Perseus-Hub uses a Spark cluster to calculate various statistics of large-scale graphs efficiently, and aggregates the results in a summary on the master node to support interactive user exploration. In Perseus-Hub, the visualized distributions of graph statistics provide preliminary analysis to understand a graph. To perform a deeper analysis, users with little prior knowledge can leverage patterns (e.g., spikes in the power-law degree distribution marked by other users or experts. Moreover, Perseus-Hub guides users to regions of interest by highlighting anomalous nodes and helps users establish a more comprehensive understanding about the graph at hand. We demonstrate our system through the case study on real, large-scale networks.
Andoulsi, R.
2001-12-01
We present in this thesis a study of a class of photovoltaic system by a bond graph approach. This study concerns the modelling, the analysis and the control of some configurations including PV generator, DC/DC converters and DC motor-pumps. The modelling of the different elements of a photovoltaic system is an indispensable stage that must precede all application of sizing, identification or simulation. However, theses PV systems are of hybrid type and their modelling is complex. It is why we use a unified modelling approach based on the bond graph technique. This methodology is completely systematic and has a sufficient flexibility for allowing the introduction of different components in the system. In the first chapter, we recall the principle of functioning of a photovoltaic generator and we treat mainly the MPPT (Maximum Power Point Tracking) working. In the second chapter, we elaborate bond graph models of various photovoltaic system configurations. For the PV source, we elaborate, in a first stage, a complete model taking into account the various physical phenomena influencing the quality of the PV source. In a second stage, we deduce a reduced bond graph model more easy to use for analysis and control purposes. For the DC/DC converters, we recall the bond graph modelling of switching elements and the average bond graph of the DC/DC converters developed in the literature. Thus, we deduce the bond graphs models of the various DC/DC converters to be used. The third chapter presents a dynamic study of some configurations stability in linear procedure. In the fourth chapter, we study the feasibility of non linear controllers by input/output linearization for some configurations of PV systems. In this study, we use the concept of inverse bond graph to determine, by a bond graph approach, the expression of the control input and the nature of the stability of the internal dynamics (dynamics of zeros). The fifth chapter is dedicated for the presentation of some
Graph theoretical analysis of functional network for comprehension of sign language.
Liu, Lanfang; Yan, Xin; Liu, Jin; Xia, Mingrui; Lu, Chunming; Emmorey, Karen; Chu, Mingyuan; Ding, Guosheng
2017-09-15
Signed languages are natural human languages using the visual-motor modality. Previous neuroimaging studies based on univariate activation analysis show that a widely overlapped cortical network is recruited regardless whether the sign language is comprehended (for signers) or not (for non-signers). Here we move beyond previous studies by examining whether the functional connectivity profiles and the underlying organizational structure of the overlapped neural network may differ between signers and non-signers when watching sign language. Using graph theoretical analysis (GTA) and fMRI, we compared the large-scale functional network organization in hearing signers with non-signers during the observation of sentences in Chinese Sign Language. We found that signed sentences elicited highly similar cortical activations in the two groups of participants, with slightly larger responses within the left frontal and left temporal gyrus in signers than in non-signers. Crucially, further GTA revealed substantial group differences in the topologies of this activation network. Globally, the network engaged by signers showed higher local efficiency (t (24) =2.379, p=0.026), small-worldness (t (24) =2.604, p=0.016) and modularity (t (24) =3.513, p=0.002), and exhibited different modular structures, compared to the network engaged by non-signers. Locally, the left ventral pars opercularis served as a network hub in the signer group but not in the non-signer group. These findings suggest that, despite overlap in cortical activation, the neural substrates underlying sign language comprehension are distinguishable at the network level from those for the processing of gestural action. Copyright © 2017 Elsevier B.V. All rights reserved.
Wang, Chao; Xu, Jin; Zhao, Songzhen; Lou, Wutao
2016-01-01
The study was dedicated to investigating the change in information processing in brain networks of vascular dementia (VaD) patients during the process of decision making. EEG was recorded from 18 VaD patients and 19 healthy controls when subjects were performing a visual oddball task. The whole task was divided into several stages by using global field power analysis. In the stage related to the decision-making process, graph theoretical analysis was applied to the binary directed network derived from EEG signals at nine electrodes in the frontal, central, and parietal regions in δ (0.5-3.5Hz), θ (4-7Hz), α1 (8-10Hz), α2 (11-13Hz), and β (14-30Hz) frequency bands based on directed transfer function. A weakened outgoing information flow, a decrease in out-degree, and an increase in in-degree were found in the parietal region in VaD patients, compared to healthy controls. In VaD patients, the parietal region may also lose its hub status in brain networks. In addition, the clustering coefficient was significantly lower in VaD patients. Impairment might be present in the parietal region or its connections with other regions, and it may serve as one of the causes for cognitive decline in VaD patients. The brain networks of VaD patients were significantly altered toward random networks. The present study extended our understanding of VaD from the perspective of brain functional networks, and it provided possible interpretations for cognitive deficits in VaD patients. Copyright © 2015 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved.
Multifractal analysis of visibility graph-based Ito-related connectivity time series.
Czechowski, Zbigniew; Lovallo, Michele; Telesca, Luciano
2016-02-01
In this study, we investigate multifractal properties of connectivity time series resulting from the visibility graph applied to normally distributed time series generated by the Ito equations with multiplicative power-law noise. We show that multifractality of the connectivity time series (i.e., the series of numbers of links outgoing any node) increases with the exponent of the power-law noise. The multifractality of the connectivity time series could be due to the width of connectivity degree distribution that can be related to the exit time of the associated Ito time series. Furthermore, the connectivity time series are characterized by persistence, although the original Ito time series are random; this is due to the procedure of visibility graph that, connecting the values of the time series, generates persistence but destroys most of the nonlinear correlations. Moreover, the visibility graph is sensitive for detecting wide "depressions" in input time series.
Time series analysis of the developed financial markets' integration using visibility graphs
Zhuang, Enyu; Small, Michael; Feng, Gang
2014-09-01
A time series representing the developed financial markets' segmentation from 1973 to 2012 is studied. The time series reveals an obvious market integration trend. To further uncover the features of this time series, we divide it into seven windows and generate seven visibility graphs. The measuring capabilities of the visibility graphs provide means to quantitatively analyze the original time series. It is found that the important historical incidents that influenced market integration coincide with variations in the measured graphical node degree. Through the measure of neighborhood span, the frequencies of the historical incidents are disclosed. Moreover, it is also found that large "cycles" and significant noise in the time series are linked to large and small communities in the generated visibility graphs. For large cycles, how historical incidents significantly affected market integration is distinguished by density and compactness of the corresponding communities.
On some covering graphs of a graph
Shariefuddin Pirzada
2016-10-01
Full Text Available For a graph $G$ with vertex set $V(G=\\{v_1, v_2, \\dots, v_n\\}$, let $S$ be the covering set of $G$ having the maximum degree over all the minimum covering sets of $G$. Let $N_S[v]=\\{u\\in S : uv \\in E(G \\}\\cup \\{v\\}$ be the closed neighbourhood of the vertex $v$ with respect to $S.$ We define a square matrix $A_S(G= (a_{ij},$ by $a_{ij}=1,$ if $\\left |N_S[v_i]\\cap N_S[v_j] \\right| \\geq 1, i\
Graph Theoretical Analysis of Developmental Patterns of the White Matter Network
Zhang eChen
2013-11-01
Full Text Available Understanding the development of human brain organization is critical for gaining insight into how the enhancement of cognitive processes is related to the fine-tuning of the brain network. However, the developmental trajectory of the large-scale white matter (WM network is not fully understood. Here, using graph theory, we examine developmental changes in the organization of WM networks in 180 typically-developing participants. WM networks were constructed using whole brain tractography and 78 cortical regions of interest were extracted from each participant. The subjects were first divided into 5 equal sample size (n=36 groups (early childhood: 6.0-9.7 years; late childhood: 9.8-12.7 years; adolescence: 12.9-17.5 years; young adult: 17.6-21.8 years; adult: 21.9-29.6 years. Most prominent changes in the topological properties of developing brain networks occur at late childhood and adolescence. During late childhood period, the structural brain network showed significant increase in the global efficiency but decrease in modularity, suggesting a shift of topological organization toward a more randomized configuration. However, while preserving most topological features, there was a significant increase in the local efficiency at adolescence, suggesting the dynamic process of rewiring and rebalancing brain connections at different growth stages. In addition, several pivotal hubs were identified that are vital for the global coordination of information flow over the whole brain network across all age groups. Significant increases of nodal efficiency were present in several regions such as precuneus at late childhood. Finally, a stable and functionally/anatomically related modular organization was identified throughout the development of the WM network. This study used network analysis to elucidate the topological changes in brain maturation, paving the way for developing novel methods for analyzing disrupted brain connectivity in
Jun Lv
Full Text Available Functional brain networks of human have been revealed to have small-world properties by both analyzing electroencephalogram (EEG and functional magnetic resonance imaging (fMRI time series.In our study, by using graph theoretical analysis, we attempted to investigate the changes of paralimbic-limbic cortex between wake and sleep states. Ten healthy young people were recruited to our experiment. Data from 2 subjects were excluded for the reason that they had not fallen asleep during the experiment. For each subject, blood oxygen level dependency (BOLD images were acquired to analyze brain network, and peripheral pulse signals were obtained continuously to identify if the subject was in sleep periods. Results of fMRI showed that brain networks exhibited stronger small-world characteristics during sleep state as compared to wake state, which was in consistent with previous studies using EEG synchronization. Moreover, we observed that compared with wake state, paralimbic-limbic cortex had less connectivity with neocortical system and centrencephalic structure in sleep.In conclusion, this is the first study, to our knowledge, has observed that small-world properties of brain functional networks altered when human sleeps without EEG synchronization. Moreover, we speculate that paralimbic-limbic cortex organization owns an efficient defense mechanism responsible for suppressing the external environment interference when humans sleep, which is consistent with the hypothesis that the paralimbic-limbic cortex may be functionally disconnected from brain regions which directly mediate their interactions with the external environment. Our findings also provide a reasonable explanation why stable sleep exhibits homeostasis which is far less susceptible to outside world.
Gene set analysis for interpreting genetic studies
Pers, Tune H
2016-01-01
Interpretation of genome-wide association study (GWAS) results is lacking behind the discovery of new genetic associations. Consequently, there is an urgent need for data-driven methods for interpreting genetic association studies. Gene set analysis (GSA) can identify aetiologic pathways...
Graph Structure in Three National Academic Webs: Power Laws with Anomalies.
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)
Zhang, Guo-Qiang; Luo, Lingyun; Ogbuji, Chime; Joslyn, Cliff; Mejino, Jose; Sahoo, Satya S
2012-01-01
The interaction of multiple types of relationships among anatomical classes in the Foundational Model of Anatomy (FMA) can provide inferred information valuable for quality assurance. This paper introduces a method called Motif Checking (MOCH) to study the effects of such multi-relation type interactions for detecting logical inconsistencies as well as other anomalies represented by the motifs. MOCH represents patterns of multi-type interaction as small labeled (with multiple types of edges) sub-graph motifs, whose nodes represent class variables, and labeled edges represent relational types. By representing FMA as an RDF graph and motifs as SPARQL queries, fragments of FMA are automatically obtained as auditing candidates. Leveraging the scalability and reconfigurability of Semantic Web Technology, we performed exhaustive analyses of a variety of labeled sub-graph motifs. The quality assurance feature of MOCH comes from the distinct use of a subset of the edges of the graph motifs as constraints for disjointness, whereby bringing in rule-based flavor to the approach as well. With possible disjointness implied by antonyms, we performed manual inspection of the resulting FMA fragments and tracked down sources of abnormal inferred conclusions (logical inconsistencies), which are amendable for programmatic revision of the FMA. Our results demonstrate that MOCH provides a unique source of valuable information for quality assurance. Since our approach is general, it is applicable to any ontological system with an OWL representation. PMID:23304382
Zhang, Guo-Qiang; Luo, Lingyun; Ogbuji, Chime; Joslyn, Cliff; Mejino, Jose; Sahoo, Satya S
2012-01-01
The interaction of multiple types of relationships among anatomical classes in the Foundational Model of Anatomy (FMA) can provide inferred information valuable for quality assurance. This paper introduces a method called Motif Checking (MOCH) to study the effects of such multi-relation type interactions for detecting logical inconsistencies as well as other anomalies represented by the motifs. MOCH represents patterns of multi-type interaction as small labeled (with multiple types of edges) sub-graph motifs, whose nodes represent class variables, and labeled edges represent relational types. By representing FMA as an RDF graph and motifs as SPARQL queries, fragments of FMA are automatically obtained as auditing candidates. Leveraging the scalability and reconfigurability of Semantic Web Technology, we performed exhaustive analyses of a variety of labeled sub-graph motifs. The quality assurance feature of MOCH comes from the distinct use of a subset of the edges of the graph motifs as constraints for disjointness, whereby bringing in rule-based flavor to the approach as well. With possible disjointness implied by antonyms, we performed manual inspection of the resulting FMA fragments and tracked down sources of abnormal inferred conclusions (logical inconsistencies), which are amendable for programmatic revision of the FMA. Our results demonstrate that MOCH provides a unique source of valuable information for quality assurance. Since our approach is general, it is applicable to any ontological system with an OWL representation.
Analysis of protein-protein interaction networks by means of annotated graph mining algorithms
Rahmani, Hossein
2012-01-01
This thesis discusses solutions to several open problems in Protein-Protein Interaction (PPI) networks with the aid of Knowledge Discovery. PPI networks are usually represented as undirected graphs, with nodes corresponding to proteins and edges representing interactions among protein pairs. A large
The Mathematics of Networks Science: Scale-Free, Power-Law Graphs and Continuum Theoretical Analysis
Padula, Janice
2012-01-01
When hoping to initiate or sustain students' interest in mathematics teachers should always consider relevance, relevance to students' lives and in the middle and later years of instruction in high school and university, accessibility. A topic such as the mathematics behind networks science, more specifically scale-free graphs, is up-to-date,…
Diestel, Reinhard
2017-01-01
This standard textbook of modern graph theory, now in its fifth edition, combines the authority of a classic with the engaging freshness of style that is the hallmark of active mathematics. It covers the core material of the subject with concise yet reliably complete proofs, while offering glimpses of more advanced methods in each field by one or two deeper results, again with proofs given in full detail. The book can be used as a reliable text for an introductory course, as a graduate text, and for self-study. From the reviews: “This outstanding book cannot be substituted with any other book on the present textbook market. It has every chance of becoming the standard textbook for graph theory.”Acta Scientiarum Mathematiciarum “Deep, clear, wonderful. This is a serious book about the heart of graph theory. It has depth and integrity. ”Persi Diaconis & Ron Graham, SIAM Review “The book has received a very enthusiastic reception, which it amply deserves. A masterly elucidation of modern graph theo...
A characterization of horizontal visibility graphs and combinatorics on words
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.
Human Error Analysis by Fuzzy-Set
Situmorang, Johnny
1996-01-01
In conventional HRA the probability of Error is treated as a single and exact value through constructing even tree, but in this moment the Fuzzy-Set Theory is used. Fuzzy set theory treat the probability of error as a plausibility which illustrate a linguistic variable. Most parameter or variable in human engineering been defined verbal good, fairly good, worst etc. Which describe a range of any value of probability. For example this analysis is quantified the human error in calibration task, and the probability of miscalibration is very low
A graph model for opportunistic network coding
Sorour, Sameh
2015-08-12
© 2015 IEEE. Recent advancements in graph-based analysis and solutions of instantly decodable network coding (IDNC) trigger the interest to extend them to more complicated opportunistic network coding (ONC) scenarios, with limited increase in complexity. In this paper, we design a simple IDNC-like graph model for a specific subclass of ONC, by introducing a more generalized definition of its vertices and the notion of vertex aggregation in order to represent the storage of non-instantly-decodable packets in ONC. Based on this representation, we determine the set of pairwise vertex adjacency conditions that can populate this graph with edges so as to guarantee decodability or aggregation for the vertices of each clique in this graph. We then develop the algorithmic procedures that can be applied on the designed graph model to optimize any performance metric for this ONC subclass. A case study on reducing the completion time shows that the proposed framework improves on the performance of IDNC and gets very close to the optimal performance.
Distorted Pattern Recognition and Analysis with the Help of IEf Graph Representation
Adam Sedziwy
2002-01-01
Full Text Available An algorithm for distorted pattern recognition is presented. lt's generalization of M Flasinski results (Pattern Recognition, 27, 1-16, 1992. A new formalism allows to make both qualitative and quantitive distortion analysis. It also enlarges parser flexibility by extending the set of patterns which may be recognized.
Cheung, King Sing
2014-01-01
Petri nets are a formal and theoretically rich model for the modelling and analysis of systems. A subclass of Petri nets, augmented marked graphs possess a structure that is especially desirable for the modelling and analysis of systems with concurrent processes and shared resources.This monograph consists of three parts: Part I provides the conceptual background for readers who have no prior knowledge on Petri nets; Part II elaborates the theory of augmented marked graphs; finally, Part III discusses the application to system integration. The book is suitable as a first self-contained volume
The groupies of random multipartite graphs
Portmann, Marius; Wang, Hongyun
2012-01-01
If a vertex $v$ in a graph $G$ has degree larger than the average of the degrees of its neighbors, we call it a groupie in $G$. In the current work, we study the behavior of groupie in random multipartite graphs with the link probability between sets of nodes fixed. Our results extend the previous ones on random (bipartite) graphs.
Alliances and Bisection Width for Planar Graphs
Olsen, Martin; Revsbæk, Morten
2013-01-01
An alliance in a graph is a set of vertices (allies) such that each vertex in the alliance has at least as many allies (counting the vertex itself) as non-allies in its neighborhood of the graph. We show that any planar graph with minimum degree at least 4 can be split into two alliances in polyn...
A new characterization of trivially perfect graphs
Christian Rubio Montiel
2015-03-01
Full Text Available A graph $G$ is \\emph{trivially perfect} if for every induced subgraph the cardinality of the largest set of pairwise nonadjacent vertices (the stability number $\\alpha(G$ equals the number of (maximal cliques $m(G$. We characterize the trivially perfect graphs in terms of vertex-coloring and we extend some definitions to infinite graphs.
ANALYSIS OF FORMING TREAD WHEEL SETS
Igor IVANOV
2017-09-01
Full Text Available This paper shows the results of a theoretical study of profile high-speed grinding (PHSG for forming tread wheel sets during repair instead of turning and mold-milling. Significant disadvantages of these methods are low capacity to adapt to the tool and inhomogeneous structure of the wheel material. This leads to understated treatment regimens and difficulties in recovering wheel sets with thermal and mechanical defects. This study carried out modeling and analysis of emerging cutting forces. Proposed algorithms describe the random occurrence of the components of the cutting forces in the restoration profile of wheel sets with an inhomogeneous structure of the material. To identify the statistical features of randomly generated structures fractal dimension and the method of random additions were used. The multifractal spectrum formed is decomposed into monofractals by wavelet transform. The proposed method allows you to create the preconditions for controlling the parameters of the treatment process.
SETS, Boolean Manipulation for Network Analysis and Fault Tree Analysis
Worrell, R.B.
1985-01-01
Description of problem or function - SETS is used for symbolic manipulation of set (or Boolean) equations, particularly the reduction of set equations by the application of set identities. It is a flexible and efficient tool for performing probabilistic risk analysis (PRA), vital area analysis, and common cause analysis. The equation manipulation capabilities of SETS can also be used to analyze non-coherent fault trees and determine prime implicants of Boolean functions, to verify circuit design implementation, to determine minimum cost fire protection requirements for nuclear reactor plants, to obtain solutions to combinatorial optimization problems with Boolean constraints, and to determine the susceptibility of a facility to unauthorized access through nullification of sensors in its protection system. 4. Method of solution - The SETS program is used to read, interpret, and execute the statements of a SETS user program which is an algorithm that specifies the particular manipulations to be performed and the order in which they are to occur. 5. Restrictions on the complexity of the problem - Any properly formed set equation involving the set operations of union, intersection, and complement is acceptable for processing by the SETS program. Restrictions on the size of a set equation that can be processed are not absolute but rather are related to the number of terms in the disjunctive normal form of the equation, the number of literals in the equation, etc. Nevertheless, set equations involving thousands and even hundreds of thousands of terms can be processed successfully
Graph Theory. 2. Vertex Descriptors and Graph Coloring
Lorentz JÄNTSCHI
2002-12-01
Full Text Available This original work presents the construction of a set of ten sequence matrices and their applications for ordering vertices in graphs. For every sequence matrix three ordering criteria are applied: lexicographic ordering, based on strings of numbers, corresponding to every vertex, extracted as rows from sequence matrices; ordering by the sum of path lengths from a given vertex; and ordering by the sum of paths, starting from a given vertex. We also examine a graph that has different orderings for the above criteria. We then proceed to demonstrate that every criterion induced its own partition of graph vertex. We propose the following theoretical result: both LAVS and LVDS criteria generate identical partitioning of vertices in any graph. Finally, a coloring of graph vertices according to introduced ordering criteria was proposed.
Hermann, Frank; Ehrig, Hartmut; Orejas, Fernando; Ulrike, Golas
2010-01-01
Triple Graph Grammars (TGGs) are a well-established concept for the specification of model transformations. In previous work we have formalized and analyzed already crucial properties of model transformations like termination, correctness and completeness, but functional behaviour - especially local confluence - is missing up to now. In order to close this gap we generate forward translation rules, which extend standard forward rules by translation attributes keeping track of the elements whi...
Static and dynamic analysis of beam assemblies using a differential system on an oriented graph
Náprstek, Jiří; Fischer, Cyril
2015-01-01
Roč. 155, July (2015), s. 28-41 ISSN 0045-7949 R&D Projects: GA ČR(CZ) GA15-01035S Institutional support: RVO:68378297 Keywords : symmetric operators * oriented graph * dynamic stiffness matrix * slope deflection method * finite element method Subject RIV: JM - Building Engineering Impact factor: 2.425, year: 2015 http://www.sciencedirect.com/science/article/pii/S0045794915000590#
Design of application for graph's handling with heuristic algorithms of analysis
López, Carlos Andrés; Ardila Urueña, William
2008-01-01
El siguiente artículo muestra la manera de desarrollar una sencilla aplicación de entorno grafico sobre la cual se puede experimentar diversas técnicas, desde algoritmos de resolución de grafos hasta heurísticas empleadas en inteligencia artificial. The next section shows how to develop a simple graphical application environment on which to experiment with various techniques, from algorithms resolution graph until heuristics used in artificial intelligence.
Gyori, Ervin; Lovasz, Laszlo
2006-01-01
This volume honours the eminent mathematicians Vera Sos and Andras Hajnal. The book includes survey articles reviewing classical theorems, as well as new, state-of-the-art results. Also presented are cutting edge expository research papers with new theorems and proofs in the area of the classical Hungarian subjects, like extremal combinatorics, colorings, combinatorial number theory, etc. The open problems and the latest results in the papers are sure to inspire further research.
Gould, Ronald
2012-01-01
This introduction to graph theory focuses on well-established topics, covering primary techniques and including both algorithmic and theoretical problems. The algorithms are presented with a minimum of advanced data structures and programming details. This thoroughly corrected 1988 edition provides insights to computer scientists as well as advanced undergraduates and graduate students of topology, algebra, and matrix theory. Fundamental concepts and notation and elementary properties and operations are the first subjects, followed by examinations of paths and searching, trees, and networks. S
Chartrand, Gary; Zhang, Ping
2010-01-01
Gary Chartrand has influenced the world of Graph Theory for almost half a century. He has supervised more than a score of Ph.D. dissertations and written several books on the subject. The most widely known of these texts, Graphs and Digraphs, … has much to recommend it, with clear exposition, and numerous challenging examples [that] make it an ideal textbook for the advanced undergraduate or beginning graduate course. The authors have updated their notation to reflect the current practice in this still-growing area of study. By the authors' estimation, the 5th edition is approximately 50% longer than the 4th edition. … the legendary Frank Harary, author of the second graph theory text ever produced, is one of the figures profiled. His book was the standard in the discipline for several decades. Chartrand, Lesniak and Zhang have produced a worthy successor.-John T. Saccoman, MAA Reviews, June 2012 (This book is in the MAA's basic library list.)As with the earlier editions, the current text emphasizes clear...
The planar cubic Cayley graphs
Georgakopoulos, Agelos
2018-01-01
The author obtains a complete description of the planar cubic Cayley graphs, providing an explicit presentation and embedding for each of them. This turns out to be a rich class, comprising several infinite families. He obtains counterexamples to conjectures of Mohar, Bonnington and Watkins. The author's analysis makes the involved graphs accessible to computation, corroborating a conjecture of Droms.
Planar graphs theory and algorithms
Nishizeki, T
1988-01-01
Collected in this volume are most of the important theorems and algorithms currently known for planar graphs, together with constructive proofs for the theorems. Many of the algorithms are written in Pidgin PASCAL, and are the best-known ones; the complexities are linear or 0(nlogn). The first two chapters provide the foundations of graph theoretic notions and algorithmic techniques. The remaining chapters discuss the topics of planarity testing, embedding, drawing, vertex- or edge-coloring, maximum independence set, subgraph listing, planar separator theorem, Hamiltonian cycles, and single- or multicommodity flows. Suitable for a course on algorithms, graph theory, or planar graphs, the volume will also be useful for computer scientists and graph theorists at the research level. An extensive reference section is included.
Krieger, M; Schwabenbauer, E-M; Hoischen-Taubner, S; Emanuelson, U; Sundrum, A
2018-03-01
Production diseases in dairy cows are multifactorial, which means they emerge from complex interactions between many different farm variables. Variables with a large impact on production diseases can be identified for groups of farms using statistical models, but these methods cannot be used to identify highly influential variables in individual farms. This, however, is necessary for herd health planning, because farm conditions and associated health problems vary largely between farms. The aim of this study was to rank variables according to their anticipated effect on production diseases on the farm level by applying a graph-based impact analysis on 192 European organic dairy farms. Direct impacts between 13 pre-defined variables were estimated for each farm during a round-table discussion attended by practitioners, that is farmer, veterinarian and herd advisor. Indirect impacts were elaborated through graph analysis taking into account impact strengths. Across farms, factors supposedly exerting the most influence on production diseases were 'feeding', 'hygiene' and 'treatment' (direct impacts), as well as 'knowledge and skills' and 'herd health monitoring' (indirect impacts). Factors strongly influenced by production diseases were 'milk performance', 'financial resources' and 'labour capacity' (directly and indirectly). Ranking of variables on the farm level revealed considerable differences between farms in terms of their most influential and most influenced farm factors. Consequently, very different strategies may be required to reduce production diseases in these farms. The method is based on perceptions and estimations and thus prone to errors. From our point of view, however, this weakness is clearly outweighed by the ability to assess and to analyse farm-specific relationships and thus to complement general knowledge with contextual knowledge. Therefore, we conclude that graph-based impact analysis represents a promising decision support tool for herd
Campolongo, Francesca; Braddock, Roger
1999-01-01
Sensitivity analysis screening methods aim to isolate the most important factors in experiments involving a large number of significant factors and interactions. This paper extends the one-factor-at-a-time screening method proposed by Morris. The new method, in addition to the 'overall' sensitivity measures already provided by the traditional Morris method, offers estimates of the two-factor interaction effects. The number of model evaluations required is O(k 2 ), where k is the number of model input factors. The efficient sampling strategy in the parameter space is based on concepts of graph theory and on the solution of the 'handcuffed prisoner problem'
Bell inequalities for graph states
Toth, G.; Hyllus, P.; Briegel, H.J.; Guehne, O.
2005-01-01
Full text: In the last years graph states have attracted an increasing interest in the field of quantum information theory. Graph states form a family of multi-qubit states which comprises many popular states such as the GHZ states and the cluster states. They also play an important role in applications. For instance, measurement based quantum computation uses graph states as resources. From a theoretical point of view, it is remarkable that graph states allow for a simple description in terms of stabilizing operators. In this contribution, we investigate the non-local properties of graph states. We derive a family of Bell inequalities which require three measurement settings for each party and are maximally violated by graph states. In turn, any graph state violates at least one of the inequalities. We show that for certain types of graph states the violation of these inequalities increases exponentially with the number of qubits. We also discuss connections to other entanglement properties such as the positively of the partial transpose or the geometric measure of entanglement. (author)
Analysis of the real EADGENE data set:
Jaffrézic, Florence; de Koning, Dirk-Jan; Boettcher, Paul J
2007-01-01
A large variety of methods has been proposed in the literature for microarray data analysis. The aim of this paper was to present techniques used by the EADGENE (European Animal Disease Genomics Network of Excellence) WP1.4 participants for data quality control, normalisation and statistical...... methods for the detection of differentially expressed genes in order to provide some more general data analysis guidelines. All the workshop participants were given a real data set obtained in an EADGENE funded microarray study looking at the gene expression changes following artificial infection with two...... quarters. Very little transcriptional variation was observed for the bacteria S. aureus. Lists of differentially expressed genes found by the different research teams were, however, quite dependent on the method used, especially concerning the data quality control step. These analyses also emphasised...
Music analysis and point-set compression
Meredith, David
A musical analysis represents a particular way of understanding certain aspects of the structure of a piece of music. The quality of an analysis can be evaluated to some extent by the degree to which knowledge of it improves performance on tasks such as mistake spotting, memorising a piece...... as the minimum description length principle and relates closely to certain ideas in the theory of Kolmogorov complexity. Inspired by this general principle, the hypothesis explored in this paper is that the best ways of understanding (or explanations for) a piece of music are those that are represented...... by the shortest possible descriptions of the piece. With this in mind, two compression algorithms are presented, COSIATEC and SIATECCompress. Each of these algorithms takes as input an in extenso description of a piece of music as a set of points in pitch-time space representing notes. Each algorithm...
Graph-based network analysis of resting-state functional MRI
Jinhui Wang
2010-06-01
Full Text Available In the past decade, resting-state functional MRI (R-fMRI measures of brain activity have attracted considerable attention. Based on changes in the blood oxygen level-dependent signal, R-fMRI offers a novel way to assess the brain’s spontaneous or intrinsic (i.e., task-free activity with both high spatial and temporal resolutions. The properties of both the intra- and inter-regional connectivity of resting-state brain activity have been well documented, promoting our understanding of the brain as a complex network. Specifically, the topological organization of brain networks has been recently studied with graph theory. In this review, we will summarize the recent advances in graph-based brain network analyses of R-fMRI signals, both in typical and atypical populations. Application of these approaches to R-fMRI data has demonstrated non-trivial topological properties of functional networks in the human brain. Among these is the knowledge that the brain’s intrinsic activity is organized as a small-world, highly efficient network, with significant modularity and highly connected hub regions. These network properties have also been found to change throughout normal development, aging and in various pathological conditions. The literature reviewed here suggests that graph-based network analyses are capable of uncovering system-level changes associated with different processes in the resting brain, which could provide novel insights into the understanding of the underlying physiological mechanisms of brain function. We also highlight several potential research topics in the future.
Graph-based network analysis of resting-state functional MRI.
Wang, Jinhui; Zuo, Xinian; He, Yong
2010-01-01
In the past decade, resting-state functional MRI (R-fMRI) measures of brain activity have attracted considerable attention. Based on changes in the blood oxygen level-dependent signal, R-fMRI offers a novel way to assess the brain's spontaneous or intrinsic (i.e., task-free) activity with both high spatial and temporal resolutions. The properties of both the intra- and inter-regional connectivity of resting-state brain activity have been well documented, promoting our understanding of the brain as a complex network. Specifically, the topological organization of brain networks has been recently studied with graph theory. In this review, we will summarize the recent advances in graph-based brain network analyses of R-fMRI signals, both in typical and atypical populations. Application of these approaches to R-fMRI data has demonstrated non-trivial topological properties of functional networks in the human brain. Among these is the knowledge that the brain's intrinsic activity is organized as a small-world, highly efficient network, with significant modularity and highly connected hub regions. These network properties have also been found to change throughout normal development, aging, and in various pathological conditions. The literature reviewed here suggests that graph-based network analyses are capable of uncovering system-level changes associated with different processes in the resting brain, which could provide novel insights into the understanding of the underlying physiological mechanisms of brain function. We also highlight several potential research topics in the future.
Domination versus disjunctive domination in graphs | Henning ...
Domination versus disjunctive domination in graphs. Michael A Henning, Sinclair A Marcon. Abstract. A dominating set in a graph G is a set S of vertices of G such that every vertex not in S is adjacent to a vertex of S. The domination number of G is the minimum cardinality of a dominating set of G. For a positive integer b, ...
Asymptote Misconception on Graphing Functions: Does Graphing Software Resolve It?
Mehmet Fatih Öçal
2017-01-01
Full Text Available Graphing function is an important issue in mathematics education due to its use in various areas of mathematics and its potential roles for students to enhance learning mathematics. The use of some graphing software assists students’ learning during graphing functions. However, the display of graphs of functions that students sketched by hand may be relatively different when compared to the correct forms sketched using graphing software. The possible misleading effects of this situation brought a discussion of a misconception (asymptote misconception on graphing functions. The purpose of this study is two- fold. First of all, this study investigated whether using graphing software (GeoGebra in this case helps students to determine and resolve this misconception in calculus classrooms. Second, the reasons for this misconception are sought. The multiple case study was utilized in this study. University students in two calculus classrooms who received instructions with (35 students or without GeoGebra assisted instructions (32 students were compared according to whether they fell into this misconception on graphing basic functions (1/x, lnx, ex. In addition, students were interviewed to reveal the reasons behind this misconception. Data were analyzed by means of descriptive and content analysis methods. The findings indicated that those who received GeoGebra assisted instruction were better in resolving it. In addition, the reasons behind this misconception were found to be teacher-based, exam-based and some other factors.
Quantum walk on a chimera graph
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.
Zhang, Yongping; Shang, Pengjian; Xiong, Hui; Xia, Jianan
Time irreversibility is an important property of nonequilibrium dynamic systems. A visibility graph approach was recently proposed, and this approach is generally effective to measure time irreversibility of time series. However, its result may be unreliable when dealing with high-dimensional systems. In this work, we consider the joint concept of time irreversibility and adopt the phase-space reconstruction technique to improve this visibility graph approach. Compared with the previous approach, the improved approach gives a more accurate estimate for the irreversibility of time series, and is more effective to distinguish irreversible and reversible stochastic processes. We also use this approach to extract the multiscale irreversibility to account for the multiple inherent dynamics of time series. Finally, we apply the approach to detect the multiscale irreversibility of financial time series, and succeed to distinguish the time of financial crisis and the plateau. In addition, Asian stock indexes away from other indexes are clearly visible in higher time scales. Simulations and real data support the effectiveness of the improved approach when detecting time irreversibility.
Intraplate seismicity in Canada: a graph theoretic approach to data analysis and interpretation
K. Vasudevan
2010-10-01
Full Text Available Intraplate seismicity occurs in central and northern Canada, but the underlying origin and dynamics remain poorly understood. Here, we apply a graph theoretic approach to characterize the statistical structure of spatiotemporal clustering exhibited by intraplate seismicity, a direct consequence of the underlying nonlinear dynamics. Using a recently proposed definition of "recurrences" based on record breaking processes (Davidsen et al., 2006, 2008, we have constructed directed graphs using catalogue data for three selected regions (Region 1: 45°−48° N/74°−80° W; Region 2: 51°−55° N/77°−83° W; and Region 3: 56°−70° N/65°−95° W, with attributes drawn from the location, origin time and the magnitude of the events. Based on comparisons with a null model derived from Poisson distribution or Monte Carlo shuffling of the catalogue data, our results provide strong evidence in support of spatiotemporal correlations of seismicity in all three regions considered. Similar evidence for spatiotemporal clustering has been documented using seismicity catalogues for southern California, suggesting possible similarities in underlying earthquake dynamics of both regions despite huge differences in the variability of seismic activity.
Pattern analysis of directed graphs using DEDICOM: an application to Enron email.
Bader, Brett William; Harshman, Richard A. (University of Western Ontario London, Ontario, Canada); Kolda, Tamara Gibson (Sandia National Labs, Livermore, CA)
2006-12-01
DEDICOM is a linear algebra model for analyzing intrinsically asymmetric relationships, such as trade among nations or the exchange of emails among individuals. DEDICOM decomposes a complex pattern of observed relations among objects into a sum of simpler patterns of inferred relations among latent components of the objects. Three-way DEDICOM is a higher-order extension of the model that incorporates a third mode of the data, such as time, giving it stronger uniqueness properties and consequently enhancing interpretability of solutions. In this paper, we present algorithms for computing these decompositions on large, sparse data as well as a variant for computing an asymmetric nonnegative factorization. When we apply these techniques to adjacency arrays arising from directed graphs with edges labeled by time, we obtain a smaller graph on latent semantic dimensions and gain additional information about their changing relationships over time. We demonstrate these techniques on the Enron email corpus to learn about the social networks and their transient behavior. The mixture of roles assigned to individuals by DEDICOM showed strong correspondence with known job classifications and revealed the patterns of communication between these roles. Changes in the communication pattern over time, e.g., between top executives and the legal department, were also apparent in the solutions.
Comparison of university students’ understanding of graphs in different contexts
Maja Planinic
2013-07-01
Full Text Available 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.
Vecchio, Fabrizio; Di Iorio, Riccardo; Miraglia, Francesca; Granata, Giuseppe; Romanello, Roberto; Bramanti, Placido; Rossini, Paolo Maria
2018-04-01
Transcranial direct current stimulation (tDCS) is a non-invasive technique able to modulate cortical excitability in a polarity-dependent way. At present, only few studies investigated the effects of tDCS on the modulation of functional connectivity between remote cortical areas. The aim of this study was to investigate-through graph theory analysis-how bipolar tDCS modulate cortical networks high-density EEG recordings were acquired before and after bipolar cathodal, anodal and sham tDCS involving the primary motor and pre-motor cortices of the dominant hemispherein 14 healthy subjects. Results showed that, after bipolar anodal tDCS stimulation, brain networks presented a less evident "small world" organization with a global tendency to be more random in its functional connections with respect to prestimulus condition in both hemispheres. Results suggest that tDCS globally modulates the cortical connectivity of the brain, modifying the underlying functional organization of the stimulated networks, which might be related to changes in synaptic efficiency of the motor network and related brain areas. This study demonstrated that graph analysis approach to EEG recordings is able to intercept changes in cortical functions mediated by bipolar anodal tDCS mainly involving the dominant M1 and related motor areas. Concluding, tDCS could be an useful technique to help understanding brain rhythms and their topographic functional organization and specificity.
On characterizing terrain visibility graphs
William Evans
2015-06-01
Full Text Available A terrain is an $x$-monotone polygonal line in the $xy$-plane. Two vertices of a terrain are mutually visible if and only if there is no terrain vertex on or above the open line segment connecting them. A graph whose vertices represent terrain vertices and whose edges represent mutually visible pairs of terrain vertices is called a terrain visibility graph. We would like to find properties that are both necessary and sufficient for a graph to be a terrain visibility graph; that is, we would like to characterize terrain visibility graphs.Abello et al. [Discrete and Computational Geometry, 14(3:331--358, 1995] showed that all terrain visibility graphs are “persistent”. They showed that the visibility information of a terrain point set implies some ordering requirements on the slopes of the lines connecting pairs of points in any realization, and as a step towards showing sufficiency, they proved that for any persistent graph $M$ there is a total order on the slopes of the (pseudo lines in a generalized configuration of points whose visibility graph is $M$.We give a much simpler proof of this result by establishing an orientation to every triple of vertices, reflecting some slope ordering requirements that are consistent with $M$ being the visibility graph, and prove that these requirements form a partial order. We give a faster algorithm to construct a total order on the slopes. Our approach attempts to clarify the implications of the graph theoretic properties on the ordering of the slopes, and may be interpreted as defining properties on an underlying oriented matroid that we show is a restricted type of $3$-signotope.
Network reconstruction via graph blending
Estrada, Rolando
2016-05-01
Graphs estimated from empirical data are often noisy and incomplete due to the difficulty of faithfully observing all the components (nodes and edges) of the true graph. This problem is particularly acute for large networks where the number of components may far exceed available surveillance capabilities. Errors in the observed graph can render subsequent analyses invalid, so it is vital to develop robust methods that can minimize these observational errors. Errors in the observed graph may include missing and spurious components, as well fused (multiple nodes are merged into one) and split (a single node is misinterpreted as many) nodes. Traditional graph reconstruction methods are only able to identify missing or spurious components (primarily edges, and to a lesser degree nodes), so we developed a novel graph blending framework that allows us to cast the full estimation problem as a simple edge addition/deletion problem. Armed with this framework, we systematically investigate the viability of various topological graph features, such as the degree distribution or the clustering coefficients, and existing graph reconstruction methods for tackling the full estimation problem. Our experimental results suggest that incorporating any topological feature as a source of information actually hinders reconstruction accuracy. We provide a theoretical analysis of this phenomenon and suggest several avenues for improving this estimation problem.
Quantum centrality testing on directed graphs via P T -symmetric quantum walks
Izaac, J. A.; Wang, J. B.; Abbott, P. C.; Ma, X. S.
2017-09-01
Various quantum-walk-based algorithms have been proposed to analyze and rank the centrality of graph vertices. However, issues arise when working with directed graphs: the resulting non-Hermitian Hamiltonian leads to nonunitary dynamics, and the total probability of the quantum walker is no longer conserved. In this paper, we discuss a method for simulating directed graphs using P T -symmetric quantum walks, allowing probability-conserving nonunitary evolution. This method is equivalent to mapping the directed graph to an undirected, yet weighted, complete graph over the same vertex set, and can be extended to cover interdependent networks of directed graphs. Previous work has shown centrality measures based on the continuous-time quantum walk provide an eigenvectorlike quantum centrality; using the P T -symmetric framework, we extend these centrality algorithms to directed graphs with a significantly reduced Hilbert space compared to previous proposals. In certain cases, this centrality measure provides an advantage over classical algorithms used in network analysis, for example, by breaking vertex rank degeneracy. Finally, we perform a statistical analysis over ensembles of random graphs, and show strong agreement with the classical PageRank measure on directed acyclic graphs.
EAGLE: 'EAGLE'Is an' Algorithmic Graph Library for Exploration
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, 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.'
Using OWL reasoning to support the generation of novel gene sets for enrichment analysis.
Osumi-Sutherland, David J; Ponta, Enrico; Courtot, Melanie; Parkinson, Helen; Badi, Laura
2018-02-14
The Gene Ontology (GO) consists of over 40,000 terms for biological processes, cell components and gene product activities linked into a graph structure by over 90,000 relationships. It has been used to annotate the functions and cellular locations of several million gene products. The graph structure is used by a variety of tools to group annotated genes into sets whose products share function or location. These gene sets are widely used to interpret the results of genomics experiments by assessing which sets are significantly over- or under-represented in results lists. F Hoffmann-La Roche Ltd. has developed a bespoke, manually maintained controlled vocabulary (RCV) for use in over-representation analysis. Many terms in this vocabulary group GO terms in novel ways that cannot easily be derived using the graph structure of the GO. For example, some RCV terms group GO terms by the cell, chemical or tissue type they refer to. Recent improvements in the content and formal structure of the GO make it possible to use logical queries in Web Ontology Language (OWL) to automatically map these cross-cutting classifications to sets of GO terms. We used this approach to automate mapping between RCV and GO, largely replacing the increasingly unsustainable manual mapping process. We then tested the utility of the resulting groupings for over-representation analysis. We successfully mapped 85% of RCV terms to logical OWL definitions and showed that these could be used to recapitulate and extend manual mappings between RCV terms and the sets of GO terms subsumed by them. We also show that gene sets derived from the resulting GO terms sets can be used to detect the signatures of cell and tissue types in whole genome expression data. The rich formal structure of the GO makes it possible to use reasoning to dynamically generate novel, biologically relevant groupings of GO terms. GO term groupings generated with this approach can be used in. over-representation analysis to detect
Visibility graph analysis of very short-term heart rate variability during sleep
Hou, F. Z.; Li, F. W.; Wang, J.; Yan, F. R.
2016-09-01
Based on a visibility-graph algorithm, complex networks were constructed from very short-term heart rate variability (HRV) during different sleep stages. Network measurements progressively changed from rapid eye movement (REM) sleep to light sleep and then deep sleep, exhibiting promising ability for sleep assessment. Abnormal activation of the cardiovascular controls with enhanced 'small-world' couplings and altered fractal organization during REM sleep indicates that REM could be a potential risk factor for adverse cardiovascular event, especially in males, older individuals, and people who are overweight. Additionally, an apparent influence of gender, aging, and obesity on sleep was demonstrated in healthy adults, which may be helpful for establishing expected sleep-HRV patterns in different populations.
Time series analysis of S&P 500 index: A horizontal visibility graph approach
Vamvakaris, Michail D.; Pantelous, Athanasios A.; Zuev, Konstantin M.
2018-05-01
The behavior of stock prices has been thoroughly studied throughout the last century, and contradictory results have been reported in the corresponding literature. In this paper, a network theoretical approach is provided to investigate how crises affected the behavior of US stock prices. We analyze high frequency data from S&P500 via the Horizontal Visibility Graph method, and find that all major crises that took place worldwide in the last twenty years, affected significantly the behavior of the price-index. Nevertheless, we observe that each of those crises impacted the index in a different way and magnitude. Interestingly, our results suggest that the predictability of the price-index series increases during the periods of crises.
Delmotte, A; Barahona, M; Tate, E W; Yaliraki, S N
2011-01-01
Despite the recognized importance of the multi-scale spatio-temporal organization of proteins, most computational tools can only access a limited spectrum of time and spatial scales, thereby ignoring the effects on protein behavior of the intricate coupling between the different scales. Starting from a physico-chemical atomistic network of interactions that encodes the structure of the protein, we introduce a methodology based on multi-scale graph partitioning that can uncover partitions and levels of organization of proteins that span the whole range of scales, revealing biological features occurring at different levels of organization and tracking their effect across scales. Additionally, we introduce a measure of robustness to quantify the relevance of the partitions through the generation of biochemically-motivated surrogate random graph models. We apply the method to four distinct conformations of myosin tail interacting protein, a protein from the molecular motor of the malaria parasite, and study properties that have been experimentally addressed such as the closing mechanism, the presence of conserved clusters, and the identification through computational mutational analysis of key residues for binding
Winlaw, Manda [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); De Sterck, Hans [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Sanders, Geoffrey [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2015-10-26
In very simple terms a network can be de ned as a collection of points joined together by lines. Thus, networks can be used to represent connections between entities in a wide variety of elds including engi- neering, science, medicine, and sociology. Many large real-world networks share a surprising number of properties, leading to a strong interest in model development research and techniques for building synthetic networks have been developed, that capture these similarities and replicate real-world graphs. Modeling these real-world networks serves two purposes. First, building models that mimic the patterns and prop- erties of real networks helps to understand the implications of these patterns and helps determine which patterns are important. If we develop a generative process to synthesize real networks we can also examine which growth processes are plausible and which are not. Secondly, high-quality, large-scale network data is often not available, because of economic, legal, technological, or other obstacles [7]. Thus, there are many instances where the systems of interest cannot be represented by a single exemplar network. As one example, consider the eld of cybersecurity, where systems require testing across diverse threat scenarios and validation across diverse network structures. In these cases, where there is no single exemplar network, the systems must instead be modeled as a collection of networks in which the variation among them may be just as important as their common features. By developing processes to build synthetic models, so-called graph generators, we can build synthetic networks that capture both the essential features of a system and realistic variability. Then we can use such synthetic graphs to perform tasks such as simulations, analysis, and decision making. We can also use synthetic graphs to performance test graph analysis algorithms, including clustering algorithms and anomaly detection algorithms.
A characterization of graphs with disjoint dominating and total ...
A dominating set of a graph is a set of vertices such that every vertex not in the set is adjacent to a vertex in the set, while a total dominating set of a graph is a set of vertices such that every vertex is adjacent to a vertex in the set. In this paper, we provide a constructive characterization of graphs whose vertex set can be ...
Chartrand, Gary; Rosen, Kenneth H
2008-01-01
Beginning with the origin of the four color problem in 1852, the field of graph colorings has developed into one of the most popular areas of graph theory. Introducing graph theory with a coloring theme, Chromatic Graph Theory explores connections between major topics in graph theory and graph colorings as well as emerging topics. This self-contained book first presents various fundamentals of graph theory that lie outside of graph colorings, including basic terminology and results, trees and connectivity, Eulerian and Hamiltonian graphs, matchings and factorizations, and graph embeddings. The remainder of the text deals exclusively with graph colorings. It covers vertex colorings and bounds for the chromatic number, vertex colorings of graphs embedded on surfaces, and a variety of restricted vertex colorings. The authors also describe edge colorings, monochromatic and rainbow edge colorings, complete vertex colorings, several distinguishing vertex and edge colorings, and many distance-related vertex coloring...
Community detection by graph Voronoi diagrams
Deritei, Dávid; Lázár, Zsolt I.; Papp, István; Járai-Szabó, Ferenc; Sumi, Róbert; Varga, Levente; Ravasz Regan, Erzsébet; Ercsey-Ravasz, Mária
2014-06-01
Accurate and efficient community detection in networks is a key challenge for complex network theory and its applications. The problem is analogous to cluster analysis in data mining, a field rich in metric space-based methods. Common to these methods is a geometric, distance-based definition of clusters or communities. Here we propose a new geometric approach to graph community detection based on graph Voronoi diagrams. Our method serves as proof of principle that the definition of appropriate distance metrics on graphs can bring a rich set of metric space-based clustering methods to network science. We employ a simple edge metric that reflects the intra- or inter-community character of edges, and a graph density-based rule to identify seed nodes of Voronoi cells. Our algorithm outperforms most network community detection methods applicable to large networks on benchmark as well as real-world networks. In addition to offering a computationally efficient alternative for community detection, our method opens new avenues for adapting a wide range of data mining algorithms to complex networks from the class of centroid- and density-based clustering methods.
Genus Ranges of 4-Regular Rigid Vertex Graphs.
Buck, Dorothy; Dolzhenko, Egor; Jonoska, Nataša; Saito, Masahico; Valencia, Karin
2015-01-01
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 2 n vertices ( n > 1), we prove that all intervals [ a, b ] for all a genus ranges. For graphs with 2 n - 1 vertices ( n ≥ 1), we prove that all intervals [ a, b ] for all a genus ranges. We also provide constructions of graphs that realize these ranges.
Analysis of Business Connections Utilizing Theory of Topology of Random Graphs
Trelewicz, Jennifer Q.; Volovich, Igor V.
2006-03-01
A business ecosystem is a system that describes interactions between organizations. In this paper, we build a theoretical framework that defines a model which can be used to analyze the business ecosystem. The basic concepts within the framework are organizations, business connections, and market, that are all defined in the paper. Many researchers analyze the performance and structure of business using the workflow of the business. Our work in business connections answers a different set of questions, concerning the monetary value in the business ecosystem, rather than the task-interaction view that is provided by workflow analysis. We apply methods for analysis of the topology of complex networks, characterized by the concepts of small path length, clustering, and scale-free degree distributions. To model the dynamics of the business ecosystem we analyze the notion of the state of an organization at a given instant of time. We point out that the notion of state in this case is fundamentally different from the concept of state of the system which is used in classical or quantum physics. To describe the state of the organization at a given time one has to know the probability of payments to contracts which in fact depend on the future behavior of the agents on the market. Therefore methods of p-adic analysis are appropriate to explore such a behavior. Microeconomic and macroeconomic factors are indivisible and moreover the actual state of the organization depends on the future. In this framework some simple models are analyzed in detail. Company strategy can be influenced by analysis of models, which can provide a probabilistic understanding of the market, giving degrees of predictability.
Fibonacci number of the tadpole graph
Joe DeMaio
2014-10-01
Full Text Available In 1982, Prodinger and Tichy defined the Fibonacci number of a graph G to be the number of independent sets of the graph G. They did so since the Fibonacci number of the path graph Pn is the Fibonacci number F(n+2 and the Fibonacci number of the cycle graph Cn is the Lucas number Ln. The tadpole graph Tn,k is the graph created by concatenating Cn and Pk with an edge from any vertex of Cn to a pendant of Pk for integers n=3 and k=0. This paper establishes formulae and identities for the Fibonacci number of the tadpole graph via algebraic and combinatorial methods.
Edge compression techniques for visualization of dense directed graphs.
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.
Graph embedding with rich information through heterogeneous graph
Sun, Guolei
2017-11-12
Graph embedding, aiming to learn low-dimensional representations for nodes in graphs, has attracted increasing attention due to its critical application including node classification, link prediction and clustering in social network analysis. Most existing algorithms for graph embedding only rely on the topology information and fail to use the copious information in nodes as well as edges. As a result, their performance for many tasks may not be satisfactory. In this thesis, we proposed a novel and general framework for graph embedding with rich text information (GERI) through constructing a heterogeneous network, in which we integrate node and edge content information with graph topology. Specially, we designed a novel biased random walk to explore the constructed heterogeneous network with the notion of flexible neighborhood. Our sampling strategy can compromise between BFS and DFS local search on heterogeneous graph. To further improve our algorithm, we proposed semi-supervised GERI (SGERI), which learns graph embedding in an discriminative manner through heterogeneous network with label information. The efficacy of our method is demonstrated by extensive comparison experiments with 9 baselines over multi-label and multi-class classification on various datasets including Citeseer, Cora, DBLP and Wiki. It shows that GERI improves the Micro-F1 and Macro-F1 of node classification up to 10%, and SGERI improves GERI by 5% in Wiki.
Open Graphs and Computational Reasoning
Lucas Dixon
2010-06-01
Full Text Available We present a form of algebraic reasoning for computational objects which are expressed as graphs. Edges describe the flow of data between primitive operations which are represented by vertices. These graphs have an interface made of half-edges (edges which are drawn with an unconnected end and enjoy rich compositional principles by connecting graphs along these half-edges. In particular, this allows equations and rewrite rules to be specified between graphs. Particular computational models can then be encoded as an axiomatic set of such rules. Further rules can be derived graphically and rewriting can be used to simulate the dynamics of a computational system, e.g. evaluating a program on an input. Examples of models which can be formalised in this way include traditional electronic circuits as well as recent categorical accounts of quantum information.
Orientations of infinite graphs with prescribed edge-connectivity
Thomassen, Carsten
2016-01-01
We prove a decomposition result for locally finite graphs which can be used to extend results on edge-connectivity from finite to infinite graphs. It implies that every 4k-edge-connected graph G contains an immersion of some finite 2k-edge-connected Eulerian graph containing any prescribed vertex...... set (while planar graphs show that G need not containa subdivision of a simple finite graph of large edge-connectivity). Also, every 8k-edge connected infinite graph has a k-arc-connected orientation, as conjectured in 1989....
DIMENSI METRIK GRAPH LOBSTER Ln (q;r
PANDE GDE DONY GUMILAR
2013-05-01
Full Text Available The metric dimension of connected graph G is the cardinality of minimum resolving set in graph G. In this research, we study how to find the metric dimension of lobster graph Ln (q;r. Lobster graph Ln (q;r is a regular lobster graph with vertices backbone on the main path, every backbone vertex is connected to q hand vertices and every hand vertex is connected to r finger vertices, with n, q, r element of N. We obtain the metric dimension of lobster graph L2 (1;1 is 1, the metric dimension of lobster graph L2 (1;1 for n > 2 is 2.
Learning heat diffusion graphs
Thanou, Dorina; Dong, Xiaowen; Kressner, Daniel; Frossard, Pascal
2016-01-01
Effective information analysis generally boils down to properly identifying the structure or geometry of the data, which is often represented by a graph. In some applications, this structure may be partly determined by design constraints or pre-determined sensing arrangements, like in road transportation networks for example. In general though, the data structure is not readily available and becomes pretty difficult to define. In particular, the global smoothness assumptions, that most of the...
EnsembleGraph: Interactive Visual Analysis of Spatial-Temporal Behavior for Ensemble Simulation Data
Shu, Qingya; Guo, Hanqi; Che, Limei; Yuan, Xiaoru; Liu, Junfeng; Liang, Jie
2016-04-19
We present a novel visualization framework—EnsembleGraph— for analyzing ensemble simulation data, in order to help scientists understand behavior similarities between ensemble members over space and time. A graph-based representation is used to visualize individual spatiotemporal regions with similar behaviors, which are extracted by hierarchical clustering algorithms. A user interface with multiple-linked views is provided, which enables users to explore, locate, and compare regions that have similar behaviors between and then users can investigate and analyze the selected regions in detail. The driving application of this paper is the studies on regional emission influences over tropospheric ozone, which is based on ensemble simulations conducted with different anthropogenic emission absences using the MOZART-4 (model of ozone and related tracers, version 4) model. We demonstrate the effectiveness of our method by visualizing the MOZART-4 ensemble simulation data and evaluating the relative regional emission influences on tropospheric ozone concentrations. Positive feedbacks from domain experts and two case studies prove efficiency of our method.
Partitioning graphs into connected parts
Hof, van 't P.; Paulusma, D.; Woeginger, G.J.; Frid, A.; Morozov, A.S.; Rybalchenko, A.; Wagner, K.W.
2009-01-01
The 2-DISJOINT CONNECTED SUBGRAPHS problem asks if a given graph has two vertex-disjoint connected subgraphs containing pre-specified sets of vertices. We show that this problem is NP-complete even if one of the sets has cardinality 2. The LONGEST PATH CONTRACTIBILITY problem asks for the largest
Wi Hoon eJung
2013-10-01
Full Text Available One major characteristic of experts is intuitive judgment, which is an automatic process whereby patterns stored in memory through long-term training are recognized. Indeed, long-term training may influence brain structure and function. A recent study revealed that chess experts at rest showed differences in structure and functional connectivity (FC in the head of caudate, which is associated with rapid best next-move generation. However, less is known about the structure and function of the brains of Baduk experts compared with those of experts in other strategy games. Therefore, we performed voxel-based morphometry and FC analyses in Baduk experts to investigate structural brain differences and to clarify the influence of these differences on functional interactions. We also conducted graph theoretical analysis to explore the topological organization of whole-brain functional networks. Compared to novices, Baduk experts exhibited decreased and increased gray matter volume in the amygdala and nucleus accumbens, respectively. We also found increased FC between the amygdala and medial orbitofrontal cortex and decreased FC between the nucleus accumbens and medial prefrontal cortex. Further graph theoretical analysis revealed differences in measures of the integration of the network and in the regional nodal characteristics of various brain regions activated during Baduk. This study provides evidence for structural and functional differences as well as altered topological organization of the whole-brain functional networks in Baduk experts. Our findings also offer novel suggestions about the cognitive mechanisms behind Baduk expertise, which involves intuitive decision-making mediated by somatic marker circuitry and visuospatial processing.
Comparative analysis among several cross section sets
Caldeira, A.D.
1983-01-01
Critical parameters were calculated using the one dimensional multigroup transport theory for several cross section sets. Calculations have been performed for water mixtures of uranium metal, plutonium metal and uranium-thorium oxide, and for metallics systems, to determine the critical dimensions of geometries (sphere and cylinder). For this aim, the following cross section sets were employed: 1) multigroup cross section sets obtained from the GAMTEC-II code; 2) the HANSEN-ROACH cross section sets; 3) cross section sets from the ENDF/B-IV, processed by the NJOY code. Finally, we have also calculated the corresponding critical radius using the one dimensional multigroup transport DTF-IV code. The numerical results agree within a few percent with the critical values obtained in the literature (where the greatest discrepancy occured in the critical dimensions of water mixtures calculated with the values generated by the NJOY code), a very good results in comparison with similar works. (Author) [pt
Lung vessel segmentation in CT images using graph-cuts
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.
A Field-Tested Task Analysis for Creating Single-Subject Graphs Using Microsoft[R] Office Excel
Lo, Ya-yu; Konrad, Moira
2007-01-01
Creating single-subject (SS) graphs is challenging for many researchers and practitioners because it is a complex task with many steps. Although several authors have introduced guidelines for creating SS graphs, many users continue to experience frustration. The purpose of this article is to minimize these frustrations by providing a field-tested…
Graph visualization (Invited talk)
Wijk, van J.J.; Kreveld, van M.J.; Speckmann, B.
2012-01-01
Black and white node link diagrams are the classic method to depict graphs, but these often fall short to give insight in large graphs or when attributes of nodes and edges play an important role. Graph visualization aims obtaining insight in such graphs using interactive graphical representations.
On path hypercompositions in graphs and automata
Massouros Christos G.
2016-01-01
Full Text Available The paths in graphs define hypercompositions in the set of their vertices and therefore it is feasible to associate hypercompositional structures to each graph. Similarly, the strings of letters from their alphabet, define hypercompositions in the automata, which in turn define the associated hypergroups to the automata. The study of the associated hypercompositional structures gives results in both, graphs and automata theory.
Steiner Distance in Graphs--A Survey
Mao, Yaping
2017-01-01
For a connected graph $G$ of order at least $2$ and $S\\subseteq V(G)$, the \\emph{Steiner distance} $d_G(S)$ among the vertices of $S$ is the minimum size among all connected subgraphs whose vertex sets contain $S$. In this paper, we summarize the known results on the Steiner distance parameters, including Steiner distance, Steiner diameter, Steiner center, Steiner median, Steiner interval, Steiner distance hereditary graph, Steiner distance stable graph, average Steiner distance, and Steiner ...
On the centrality of some graphs
Vecdi Aytac
2017-10-01
Full Text Available A central issue in the analysis of complex networks is the assessment of their stability and vulnerability. A variety of measures have been proposed in the literature to quantify the stability of networks and a number of graph-theoretic parameters have been used to derive formulas for calculating network reliability. Different measures for graph vulnerability have been introduced so far to study different aspects of the graph behavior after removal of vertices or links such as connectivity, toughness, scattering number, binding number, residual closeness and integrity. In this paper, we consider betweenness centrality of a graph. Betweenness centrality of a vertex of a graph is portion of the shortest paths all pairs of vertices passing through a given vertex. In this paper, we obtain exact values for betweenness centrality for some wheel related graphs namely gear, helm, sunflower and friendship graphs.
Triangle-free graphs whose independence number equals the degree
Brandt, Stephan
2010-01-01
In a triangle-free graph, the neighbourhood of every vertex is an independent set. We investigate the class S of triangle-free graphs where the neighbourhoods of vertices are maximum independent sets. Such a graph G must be regular of degree d = α (G) and the fractional chromatic number must sati...
Multi-Level Anomaly Detection on Time-Varying Graph Data
Bridges, Robert A [ORNL; Collins, John P [ORNL; Ferragut, Erik M [ORNL; Laska, Jason A [ORNL; Sullivan, Blair D [ORNL
2015-01-01
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 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, this 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.
Pragmatic Graph Rewriting Modifications
Rodgers, Peter; Vidal, Natalia
1999-01-01
We present new pragmatic constructs for easing programming in visual graph rewriting programming languages. The first is a modification to the rewriting process for nodes the host graph, where nodes specified as 'Once Only' in the LHS of a rewrite match at most once with a corresponding node in the host graph. This reduces the previously common use of tags to indicate the progress of matching in the graph. The second modification controls the application of LHS graphs, where those specified a...
Music analysis and point-set compression
Meredith, David
2015-01-01
COSIATEC, SIATECCompress and Forth’s algorithm are point-set compression algorithms developed for discovering repeated patterns in music, such as themes and motives that would be of interest to a music analyst. To investigate their effectiveness and versatility, these algorithms were evaluated...... on three analytical tasks that depend on the discovery of repeated patterns: classifying folk song melodies into tune families, discovering themes and sections in polyphonic music, and discovering subject and countersubject entries in fugues. Each algorithm computes a compressed encoding of a point......-set representation of a musical object in the form of a list of compact patterns, each pattern being given with a set of vectors indicating its occurrences. However, the algorithms adopt different strategies in their attempts to discover encodings that maximize compression.The best-performing algorithm on the folk...
Generating random networks and graphs
Coolen, Ton; Roberts, Ekaterina
2017-01-01
This book supports researchers who need to generate random networks, or who are interested in the theoretical study of random graphs. The coverage includes exponential random graphs (where the targeted probability of each network appearing in the ensemble is specified), growth algorithms (i.e. preferential attachment and the stub-joining configuration model), special constructions (e.g. geometric graphs and Watts Strogatz models) and graphs on structured spaces (e.g. multiplex networks). The presentation aims to be a complete starting point, including details of both theory and implementation, as well as discussions of the main strengths and weaknesses of each approach. It includes extensive references for readers wishing to go further. The material is carefully structured to be accessible to researchers from all disciplines while also containing rigorous mathematical analysis (largely based on the techniques of statistical mechanics) to support those wishing to further develop or implement the theory of rand...
Optimizing graph algorithms on pregel-like systems
Salihoglu, Semih; Widom, Jennifer
2014-01-01
We study the problem of implementing graph algorithms efficiently on Pregel-like systems, which can be surprisingly challenging. Standard graph algorithms in this setting can incur unnecessary inefficiencies such as slow convergence or high
Daniel-Petru GHENCEA
2017-06-01
Full Text Available The paper proposes a prediction model of behavior spindle from the point of view of the thermal deformations and the level of the vibrations by highlighting and processing the characteristic equations. This is a model analysis for the shaft with similar electro-mechanical characteristics can be achieved using a hybrid analysis based on artificial intelligence (genetic algorithms - artificial neural networks - fuzzy logic. The paper presents a prediction mode obtaining valid range of values for spindles with similar characteristics based on measured data sets from a few spindles test without additional measures being required. Extracting polynomial functions of graphs resulting from simultaneous measurements and predict the dynamics of the two features with multi-objective criterion is the main advantage of this method.
An Association-Oriented Partitioning Approach for Streaming Graph Query
Yun Hao
2017-01-01
Full Text Available The volumes of real-world graphs like knowledge graph are increasing rapidly, which makes streaming graph processing a hot research area. Processing graphs in streaming setting poses significant challenges from different perspectives, among which graph partitioning method plays a key role. Regarding graph query, a well-designed partitioning method is essential for achieving better performance. Existing offline graph partitioning methods often require full knowledge of the graph, which is not possible during streaming graph processing. In order to handle this problem, we propose an association-oriented streaming graph partitioning method named Assc. This approach first computes the rank values of vertices with a hybrid approximate PageRank algorithm. After splitting these vertices with an adapted variant affinity propagation algorithm, the process order on vertices in the sliding window can be determined. Finally, according to the level of these vertices and their association, the partition where the vertices should be distributed is decided. We compare its performance with a set of streaming graph partition methods and METIS, a widely adopted offline approach. The results show that our solution can partition graphs with hundreds of millions of vertices in streaming setting on a large collection of graph datasets and our approach outperforms other graph partitioning methods.
Graph algorithms in the titan toolkit.
McLendon, William Clarence, III; Wylie, Brian Neil
2009-10-01
Graph algorithms are a key component in a wide variety of intelligence analysis activities. The Graph-Based Informatics for Non-Proliferation and Counter-Terrorism project addresses the critical need of making these graph algorithms accessible to Sandia analysts in a manner that is both intuitive and effective. Specifically we describe the design and implementation of an open source toolkit for doing graph analysis, informatics, and visualization that provides Sandia with novel analysis capability for non-proliferation and counter-terrorism.
Tetravalent one-regular graphs of order 4p2
Feng, Yan-Quan; Kutnar, Klavdija; Marusic, Dragan
2014-01-01
A graph is one-regular if its automorphism group acts regularly on the set of its arcs. In this paper tetravalent one-regular graphs of order 4p2, where p is a prime, are classified.......A graph is one-regular if its automorphism group acts regularly on the set of its arcs. In this paper tetravalent one-regular graphs of order 4p2, where p is a prime, are classified....
Analyzing and synthesizing phylogenies using tree alignment graphs.
Stephen A Smith
Full Text Available 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
Analyzing and synthesizing phylogenies using tree alignment graphs.
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.
Blockchain Transaction Analysis Using Dominant Sets
Awan , Malik ,; Cortesi , Agostino
2017-01-01
Part 4: Engineering of Enterprise Software Products; International audience; Blockchain is an emerging backbone technology behind different crypto-currencies. It can also be used for other purposes and areas. There are different scalability issues associated with blockchain. It is important to know the in depth structure of blockchain by identifying common behaviors of the transactions and the effect of these behaviors on the nodes of the network. Dominant set approach can categorize the bloc...
Wang, Yishu; Zhao, Hongyu; Deng, Minghua; Fang, Huaying; Yang, Dejie
2017-08-24
Epistatic miniarrary profile (EMAP) studies have enabled the mapping of large-scale genetic interaction networks and generated large amounts of data in model organisms. It provides an incredible set of molecular tools and advanced technologies that should be efficiently understanding the relationship between the genotypes and phenotypes of individuals. However, the network information gained from EMAP cannot be fully exploited using the traditional statistical network models. Because the genetic network is always heterogeneous, for example, the network structure features for one subset of nodes are different from those of the left nodes. Exponentialfamily random graph models (ERGMs) are a family of statistical models, which provide a principled and flexible way to describe the structural features (e.g. the density, centrality and assortativity) of an observed network. However, the single ERGM is not enough to capture this heterogeneity of networks. In this paper, we consider a mixture ERGM (MixtureEGRM) networks, which model a network with several communities, where each community is described by a single EGRM.
Grimm, Guido W.; Renner, Susanne S.; Stamatakis, Alexandros; Hemleben, Vera
2007-01-01
The multi-copy internal transcribed spacer (ITS) region of nuclear ribosomal DNA is widely used to infer phylogenetic relationships among closely related taxa. Here we use maximum likelihood (ML) and splits graph analyses to extract phylogenetic information from ~ 600 mostly cloned ITS sequences, representing 81 species and subspecies of Acer, and both species of its sister Dipteronia. Additional analyses compared sequence motifs in Acer and several hundred Anacardiaceae, Burseraceae, Meliaceae, Rutaceae, and Sapindaceae ITS sequences in GenBank. We also assessed the effects of using smaller data sets of consensus sequences with ambiguity coding (accounting for within-species variation) instead of the full (partly redundant) original sequences. Neighbor-nets and bipartition networks were used to visualize conflict among character state patterns. Species clusters observed in the trees and networks largely agree with morphology-based classifications; of de Jong’s (1994) 16 sections, nine are supported in neighbor-net and bipartition networks, and ten by sequence motifs and the ML tree; of his 19 series, 14 are supported in networks, motifs, and the ML tree. Most nodes had higher bootstrap support with matrices of 105 or 40 consensus sequences than with the original matrix. Within-taxon ITS divergence did not differ between diploid and polyploid Acer, and there was little evidence of differentiated parental ITS haplotypes, suggesting that concerted evolution in Acer acts rapidly. PMID:19455198
Guido W. Grimm
2006-01-01
Full Text Available The multi-copy internal transcribed spacer (ITS region of nuclear ribosomal DNA is widely used to infer phylogenetic relationships among closely related taxa. Here we use maximum likelihood (ML and splits graph analyses to extract phylogenetic information from ~ 600 mostly cloned ITS sequences, representing 81 species and subspecies of Acer, and both species of its sister Dipteronia. Additional analyses compared sequence motifs in Acer and several hundred Anacardiaceae, Burseraceae, Meliaceae, Rutaceae, and Sapindaceae ITS sequences in GenBank. We also assessed the effects of using smaller data sets of consensus sequences with ambiguity coding (accounting for within-species variation instead of the full (partly redundant original sequences. Neighbor-nets and bipartition networks were used to visualize conflict among character state patterns. Species clusters observed in the trees and networks largely agree with morphology-based classifications; of de Jong’s (1994 16 sections, nine are supported in neighbor-net and bipartition networks, and ten by sequence motifs and the ML tree; of his 19 series, 14 are supported in networks, motifs, and the ML tree. Most nodes had higher bootstrap support with matrices of 105 or 40 consensus sequences than with the original matrix. Within-taxon ITS divergence did not differ between diploid and polyploid Acer, and there was little evidence of differentiated parental ITS haplotypes, suggesting that concerted evolution in Acer acts rapidly.
Quantum information processing with graph states
Schlingemann, Dirk-Michael
2005-04-01
Graph states are multiparticle states which are associated with graphs. Each vertex of the graph corresponds to a single system or particle. The links describe quantum correlations (entanglement) between pairs of connected particles. Graph states were initiated independently by two research groups: On the one hand, graph states were introduced by Briegel and Raussendorf as a resource for a new model of one-way quantum computing, where algorithms are implemented by a sequence of measurements at single particles. On the other hand, graph states were developed by the author of this thesis and ReinhardWerner in Braunschweig, as a tool to build quantum error correcting codes, called graph codes. The connection between the two approaches was fully realized in close cooperation of both research groups. This habilitation thesis provides a survey of the theory of graph codes, focussing mainly, but not exclusively on the author's own research work. We present the theoretical and mathematical background for the analysis of graph codes. The concept of one-way quantum computing for general graph states is discussed. We explicitly show how to realize the encoding and decoding device of a graph code on a one-way quantum computer. This kind of implementation is to be seen as a mathematical description of a quantum memory device. In addition to that, we investigate interaction processes, which enable the creation of graph states on very large systems. Particular graph states can be created, for instance, by an Ising type interaction between next neighbor particles which sits at the points of an infinitely extended cubic lattice. Based on the theory of quantum cellular automata, we give a constructive characterization of general interactions which create a translationally invariant graph state. (orig.)
Zabiniako Vitaly
2014-12-01
Full Text Available In this article, the authors perform an analysis in order to assess adaptation of magnetic force-directed algorithms for context-based information extraction from multi-attributed graphs during visualization sessions. Theoretic standings behind magnetic force-directed approach are stated together with review on how particular features of respective algorithms in combination with appropriate visual techniques are especially suitable for improved processing and presenting of knowledge that is captured in form of graphs. The complexity of retrieving multi-attributed information within the proposed approach is handled with dedicated tools, such as selective attraction of nodes to MFE (Magnetic Force Emitter based on search criteria, localization of POI (Point of Interest regions, graph node anchoring, etc. Implicit compatibility of aforementioned tools with interactive nature of data exploration is distinguished. Description of case study, based on bibliometric network analysis is given, which is followed by the review of existing related works in this field. Conclusions are made and further studies in the field of visualization of multi-attributed graphs are defined.
Bapat, Ravindra B
2014-01-01
This new edition illustrates the power of linear algebra in the study of graphs. The emphasis on matrix techniques is greater than in other texts on algebraic graph theory. Important matrices associated with graphs (for example, incidence, adjacency and Laplacian matrices) are treated in detail. Presenting a useful overview of selected topics in algebraic graph theory, early chapters of the text focus on regular graphs, algebraic connectivity, the distance matrix of a tree, and its generalized version for arbitrary graphs, known as the resistance matrix. Coverage of later topics include Laplacian eigenvalues of threshold graphs, the positive definite completion problem and matrix games based on a graph. Such an extensive coverage of the subject area provides a welcome prompt for further exploration. The inclusion of exercises enables practical learning throughout the book. In the new edition, a new chapter is added on the line graph of a tree, while some results in Chapter 6 on Perron-Frobenius theory are reo...
Nonlinear canonical correlation analysis with k sets of variables
van der Burg, Eeke; de Leeuw, Jan
1987-01-01
The multivariate technique OVERALS is introduced as a non-linear generalization of canonical correlation analysis (CCA). First, two sets CCA is introduced. Two sets CCA is a technique that computes linear combinations of sets of variables that correlate in an optimal way. Two sets CCA is then
Declarative Process Mining for DCR Graphs
Debois, Søren; Hildebrandt, Thomas T.; Laursen, Paw Høvsgaard
2017-01-01
We investigate process mining for the declarative Dynamic Condition Response (DCR) graphs process modelling language. We contribute (a) a process mining algorithm for DCR graphs, (b) a proposal for a set of metrics quantifying output model quality, and (c) a preliminary example-based comparison...
Equitable Colorings Of Corona Multiproducts Of Graphs
Furmánczyk Hanna
2017-11-01
Full Text Available A graph is equitably k-colorable if its vertices can be partitioned into k independent sets in such a way that the numbers of vertices in any two sets differ by at most one. The smallest k for which such a coloring exists is known as the equitable chromatic number of G and denoted by =(G. It is known that the problem of computation of =(G is NP-hard in general and remains so for corona graphs. In this paper we consider the same model of coloring in the case of corona multiproducts of graphs. In particular, we obtain some results regarding the equitable chromatic number for the l-corona product G ◦l H, where G is an equitably 3- or 4-colorable graph and H is an r-partite graph, a cycle or a complete graph. Our proofs are mostly constructive in that they lead to polynomial algorithms for equitable coloring of such graph products provided that there is given an equitable coloring of G. Moreover, we confirm the Equitable Coloring Conjecture for corona products of such graphs. This paper extends the results from [H. Furmánczyk, K. Kaliraj, M. Kubale and V.J. Vivin, Equitable coloring of corona products of graphs, Adv. Appl. Discrete Math. 11 (2013 103–120].
Vincze, Arpad; Nemeth, Andras
2013-01-01
According to a recent statement, the IAEA seeks to develop a more effective safeguards system to achieve greater deterrence, because deterrence of proliferation is much more effective than detection. To achieve this goal, a less predictive safeguards system is being developed based on the advanced state-level approach that is driven by all available safeguards-relevant information. The 'directed graph analysis' is recommended as a possible methodology to implement acquisition path analysis by the IAEA to support the State evaluation process. The basic methodology is simple, well established, powerful, and its adaptation to the modelling of the nuclear profile of a State requires minimum software development. Based on this methodology the material flow network model has been developed under the Hungarian Support Programme to the IAEA, which is described in detail. In the proposed model, materials in different chemical and physical form can flow through pipes representing declared processes, material transports, diversions or undeclared processes. The nodes of the network are the material types, while the edges of the network are the pipes. A state parameter (p) is assigned to each node and edge representing the probability of their existence in the State. The possible application of this model in the State-level analytical approach will be discussed and outlook for further work will be given. The paper is followed by the slides of the presentation
Adaptive Graph Convolutional Neural Networks
Li, Ruoyu; Wang, Sheng; Zhu, Feiyun; Huang, Junzhou
2018-01-01
Graph Convolutional Neural Networks (Graph CNNs) are generalizations of classical CNNs to handle graph data such as molecular data, point could and social networks. Current filters in graph CNNs are built for fixed and shared graph structure. However, for most real data, the graph structures varies in both size and connectivity. The paper proposes a generalized and flexible graph CNN taking data of arbitrary graph structure as input. In that way a task-driven adaptive graph is learned for eac...
Analysis of the Westland Data Set
Wen, Fang; Willett, Peter; Deb, Somnath
2001-01-01
The "Westland" set of empirical accelerometer helicopter data with seeded and labeled faults is analyzed with the aim of condition monitoring. The autoregressive (AR) coefficients from a simple linear model encapsulate a great deal of information in a relatively few measurements; and it has also been found that augmentation of these by harmonic and other parameters call improve classification significantly. Several techniques have been explored, among these restricted Coulomb energy (RCE) networks, learning vector quantization (LVQ), Gaussian mixture classifiers and decision trees. A problem with these approaches, and in common with many classification paradigms, is that augmentation of the feature dimension can degrade classification ability. Thus, we also introduce the Bayesian data reduction algorithm (BDRA), which imposes a Dirichlet prior oil training data and is thus able to quantify probability of error in all exact manner, such that features may be discarded or coarsened appropriately.
Sparse geometric graphs with small dilation
Aronov, B.; Berg, de M.; Cheong, O.; Gudmundsson, J.; Haverkort, H.J.; Vigneron, A.; Deng, X.; Du, D.
2005-01-01
Given a set S of n points in the plane, and an integer k such that 0 = k
A Characterization of 2-Tree Probe Interval Graphs
Brown David E.
2014-08-01
Full Text Available A graph is a probe interval graph if its vertices correspond to some set of intervals of the real line and can be partitioned into sets P and N so that vertices are adjacent if and only if their corresponding intervals intersect and at least one belongs to P. We characterize the 2-trees which are probe interval graphs and extend a list of forbidden induced subgraphs for such graphs created by Pržulj and Corneil in [2-tree probe interval graphs have a large obstruction set, Discrete Appl. Math. 150 (2005 216-231
Efficient dynamic graph construction for inductive semi-supervised learning.
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.
MAGMA: generalized gene-set analysis of GWAS data.
de Leeuw, C.A.; Mooij, J.M.; Heskes, T.; Posthuma, D.
2015-01-01
By aggregating data for complex traits in a biologically meaningful way, gene and gene-set analysis constitute a valuable addition to single-marker analysis. However, although various methods for gene and gene-set analysis currently exist, they generally suffer from a number of issues. Statistical
MAGMA: Generalized Gene-Set Analysis of GWAS Data
de Leeuw, C.A.; Mooij, J.M.; Heskes, T.; Posthuma, D.
2015-01-01
By aggregating data for complex traits in a biologically meaningful way, gene and gene-set analysis constitute a valuable addition to single-marker analysis. However, although various methods for gene and gene-set analysis currently exist, they generally suffer from a number of issues. Statistical
Wang, Jieqiong; Li, Ting; Xian, Junfang; Wang, Ningli; He, Huiguang
2016-01-01
Most previous glaucoma studies with resting-state fMRI have focused on the neuronal activity in the individual structure of the brain, yet ignored the functional communication of anatomically separated structures. The purpose of this study is to investigate the efficiency of the functional communication change or not in glaucoma patients. We applied the resting-state fMRI data to construct the connectivity network of 25 normal controls and 25 age-gender-matched primary open angle glaucoma patients. Graph theoretical analysis was performed to assess brain network pattern differences between the two groups. No significant differences of the global network measures were found between the two groups. However, the local measures were radically reorganized in glaucoma patients. Comparing with the hub regions in normal controls' network, we found that six hub regions disappeared and nine hub regions appeared in the network of patients. In addition, the betweenness centralities of two altered hub regions, right fusiform gyrus and right lingual gyrus, were significantly correlated with the visual field mean deviation. Although the efficiency of functional communication is preserved in the brain network of the glaucoma at the global level, the efficiency of functional communication is altered in some specialized regions of the glaucoma. (orig.)
Wang, Jieqiong [Chinese Academy of Sciences, State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Beijing (China); Li, Ting; Xian, Junfang [Capital Medical University, Department of Radiology, Beijing Tongren Hospital, Beijing (China); Wang, Ningli [Capital Medical University, Department of Ophthalmology, Beijing Tongren Hospital, Beijing (China); He, Huiguang [Chinese Academy of Sciences, State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Beijing (China); Chinese Academy of Sciences, Research Center for Brain-Inspired Intelligence, Institute of Automation, Beijing (China)
2016-11-15
Most previous glaucoma studies with resting-state fMRI have focused on the neuronal activity in the individual structure of the brain, yet ignored the functional communication of anatomically separated structures. The purpose of this study is to investigate the efficiency of the functional communication change or not in glaucoma patients. We applied the resting-state fMRI data to construct the connectivity network of 25 normal controls and 25 age-gender-matched primary open angle glaucoma patients. Graph theoretical analysis was performed to assess brain network pattern differences between the two groups. No significant differences of the global network measures were found between the two groups. However, the local measures were radically reorganized in glaucoma patients. Comparing with the hub regions in normal controls' network, we found that six hub regions disappeared and nine hub regions appeared in the network of patients. In addition, the betweenness centralities of two altered hub regions, right fusiform gyrus and right lingual gyrus, were significantly correlated with the visual field mean deviation. Although the efficiency of functional communication is preserved in the brain network of the glaucoma at the global level, the efficiency of functional communication is altered in some specialized regions of the glaucoma. (orig.)
Citation graph based ranking in Invenio
Marian, Ludmila; Rajman, Martin; Vesely, Martin
2010-01-01
Invenio is the web-based integrated digital library system developed at CERN. Within this framework, we present four types of ranking models based on the citation graph that complement the simple approach based on citation counts: time-dependent citation counts, a relevancy ranking which extends the PageRank model, a time-dependent ranking which combines the freshness of citations with PageRank and a ranking that takes into consideration the external citations. We present our analysis and results obtained on two main data sets: Inspire and CERN Document Server. Our main contributions are: (i) a study of the currently available ranking methods based on the citation graph; (ii) the development of new ranking methods that correct some of the identified limitations of the current methods such as treating all citations of equal importance, not taking time into account or considering the citation graph complete; (iii) a detailed study of the key parameters for these ranking methods. (The original publication is ava...
Hosseini, S M Hadi; Hoeft, Fumiko; Kesler, Shelli R
2012-01-01
In recent years, graph theoretical analyses of neuroimaging data have increased our understanding of the organization of large-scale structural and functional brain networks. However, tools for pipeline application of graph theory for analyzing topology of brain networks is still lacking. In this report, we describe the development of a graph-analysis toolbox (GAT) that facilitates analysis and comparison of structural and functional network brain networks. GAT provides a graphical user interface (GUI) that facilitates construction and analysis of brain networks, comparison of regional and global topological properties between networks, analysis of network hub and modules, and analysis of resilience of the networks to random failure and targeted attacks. Area under a curve (AUC) and functional data analyses (FDA), in conjunction with permutation testing, is employed for testing the differences in network topologies; analyses that are less sensitive to the thresholding process. We demonstrated the capabilities of GAT by investigating the differences in the organization of regional gray-matter correlation networks in survivors of acute lymphoblastic leukemia (ALL) and healthy matched Controls (CON). The results revealed an alteration in small-world characteristics of the brain networks in the ALL survivors; an observation that confirm our hypothesis suggesting widespread neurobiological injury in ALL survivors. Along with demonstration of the capabilities of the GAT, this is the first report of altered large-scale structural brain networks in ALL survivors.
S M Hadi Hosseini
Full Text Available In recent years, graph theoretical analyses of neuroimaging data have increased our understanding of the organization of large-scale structural and functional brain networks. However, tools for pipeline application of graph theory for analyzing topology of brain networks is still lacking. In this report, we describe the development of a graph-analysis toolbox (GAT that facilitates analysis and comparison of structural and functional network brain networks. GAT provides a graphical user interface (GUI that facilitates construction and analysis of brain networks, comparison of regional and global topological properties between networks, analysis of network hub and modules, and analysis of resilience of the networks to random failure and targeted attacks. Area under a curve (AUC and functional data analyses (FDA, in conjunction with permutation testing, is employed for testing the differences in network topologies; analyses that are less sensitive to the thresholding process. We demonstrated the capabilities of GAT by investigating the differences in the organization of regional gray-matter correlation networks in survivors of acute lymphoblastic leukemia (ALL and healthy matched Controls (CON. The results revealed an alteration in small-world characteristics of the brain networks in the ALL survivors; an observation that confirm our hypothesis suggesting widespread neurobiological injury in ALL survivors. Along with demonstration of the capabilities of the GAT, this is the first report of altered large-scale structural brain networks in ALL survivors.
Degree-based graph construction
Kim, Hyunju; Toroczkai, Zoltan; Erdos, Peter L; Miklos, Istvan; Szekely, Laszlo A
2009-01-01
Degree-based graph construction is a ubiquitous problem in network modelling (Newman et al 2006 The Structure and Dynamics of Networks (Princeton Studies in Complexity) (Princeton, NJ: Princeton University Press), Boccaletti et al 2006 Phys. Rep. 424 175), ranging from social sciences to chemical compounds and biochemical reaction networks in the cell. This problem includes existence, enumeration, exhaustive construction and sampling questions with aspects that are still open today. Here we give necessary and sufficient conditions for a sequence of nonnegative integers to be realized as a simple graph's degree sequence, such that a given (but otherwise arbitrary) set of connections from an arbitrarily given node is avoided. We then use this result to present a swap-free algorithm that builds all simple graphs realizing a given degree sequence. In a wider context, we show that our result provides a greedy construction method to build all the f-factor subgraphs (Tutte 1952 Can. J. Math. 4 314) embedded within K n setmn S k , where K n is the complete graph and S k is a star graph centred on one of the nodes. (fast track communication)
Peterlin, Primoz
2010-01-01
Two methods of data analysis are compared: spreadsheet software and a statistics software suite. Their use is compared analysing data collected in three selected experiments taken from an introductory physics laboratory, which include a linear dependence, a nonlinear dependence and a histogram. The merits of each method are compared. (Contains 7…
Golino, H.F.; Epskamp, S.
2017-01-01
The estimation of the correct number of dimensions is a long-standing problem in psychometrics. Several methods have been proposed, such as parallel analysis (PA), Kaiser-Guttman’s eigenvalue-greater-than-one rule, multiple average partial procedure (MAP), the maximum-likelihood approaches that use
Peterlin, Primoz
2010-01-01
Two methods of data analysis are compared: spreadsheet software and a statistics software suite. Their use is compared analysing data collected in three selected experiments taken from an introductory physics laboratory, which include a linear dependence, a nonlinear dependence and a histogram. The merits of each method are compared.
Replica methods for loopy sparse random graphs
Coolen, ACC
2016-01-01
I report on the development of a novel statistical mechanical formalism for the analysis of random graphs with many short loops, and processes on such graphs. The graphs are defined via maximum entropy ensembles, in which both the degrees (via hard constraints) and the adjacency matrix spectrum (via a soft constraint) are prescribed. The sum over graphs can be done analytically, using a replica formalism with complex replica dimensions. All known results for tree-like graphs are recovered in a suitable limit. For loopy graphs, the emerging theory has an appealing and intuitive structure, suggests how message passing algorithms should be adapted, and what is the structure of theories describing spin systems on loopy architectures. However, the formalism is still largely untested, and may require further adjustment and refinement. (paper)
Joint Graph Layouts for Visualizing Collections of Segmented Meshes
Ren, Jing; Schneider, Jens; Ovsjanikov, Maks; Wonka, Peter
2017-01-01
We present a novel and efficient approach for computing joint graph layouts and then use it to visualize collections of segmented meshes. Our joint graph layout algorithm takes as input the adjacency matrices for a set of graphs along with partial, possibly soft, correspondences between nodes of different graphs. We then use a two stage procedure, where in the first step, we extend spectral graph drawing to include a consistency term so that a collection of graphs can be handled jointly. Our second step extends metric multi-dimensional scaling with stress majorization to the joint layout setting, while using the output of the spectral approach as initialization. Further, we discuss a user interface for exploring a collection of graphs. Finally, we show multiple example visualizations of graphs stemming from collections of segmented meshes and we present qualitative and quantitative comparisons with previous work.
Joint Graph Layouts for Visualizing Collections of Segmented Meshes
Ren, Jing
2017-09-12
We present a novel and efficient approach for computing joint graph layouts and then use it to visualize collections of segmented meshes. Our joint graph layout algorithm takes as input the adjacency matrices for a set of graphs along with partial, possibly soft, correspondences between nodes of different graphs. We then use a two stage procedure, where in the first step, we extend spectral graph drawing to include a consistency term so that a collection of graphs can be handled jointly. Our second step extends metric multi-dimensional scaling with stress majorization to the joint layout setting, while using the output of the spectral approach as initialization. Further, we discuss a user interface for exploring a collection of graphs. Finally, we show multiple example visualizations of graphs stemming from collections of segmented meshes and we present qualitative and quantitative comparisons with previous work.
Soetevent, A.R.
2010-01-01
This paper extends Hotelling's model of price competition with quadratic transportation costs from a line to graphs. I propose an algorithm to calculate firm-level demand for any given graph, conditional on prices and firm locations. One feature of graph models of price competition is that spatial
Graphing Inequalities, Connecting Meaning
Switzer, J. Matt
2014-01-01
Students often have difficulty with graphing inequalities (see Filloy, Rojano, and Rubio 2002; Drijvers 2002), and J. Matt Switzer's students were no exception. Although students can produce graphs for simple inequalities, they often struggle when the format of the inequality is unfamiliar. Even when producing a correct graph of an…
Amine Labriji
2017-07-01
Full Text Available The topic of identifying the similarity of graphs was considered as highly recommended research field in the Web semantic, artificial intelligence, the shape recognition and information research. One of the fundamental problems of graph databases is finding similar graphs to a graph query. Existing approaches dealing with this problem are usually based on the nodes and arcs of the two graphs, regardless of parental semantic links. For instance, a common connection is not identified as being part of the similarity of two graphs in cases like two graphs without common concepts, the measure of similarity based on the union of two graphs, or the one based on the notion of maximum common sub-graph (SCM, or the distance of edition of graphs. This leads to an inadequate situation in the context of information research. To overcome this problem, we suggest a new measure of similarity between graphs, based on the similarity measure of Wu and Palmer. We have shown that this new measure satisfies the properties of a measure of similarities and we applied this new measure on examples. The results show that our measure provides a run time with a gain of time compared to existing approaches. In addition, we compared the relevance of the similarity values obtained, it appears that this new graphs measure is advantageous and offers a contribution to solving the problem mentioned above.
van Dam, Edwin R.; Koolen, Jack H.; Tanaka, Hajime
2016-01-01
This is a survey of distance-regular graphs. We present an introduction to distance-regular graphs for the reader who is unfamiliar with the subject, and then give an overview of some developments in the area of distance-regular graphs since the monograph 'BCN'[Brouwer, A.E., Cohen, A.M., Neumaier,
Fuzzy Graph Language Recognizability
Kalampakas , Antonios; Spartalis , Stefanos; Iliadis , Lazaros
2012-01-01
Part 5: Fuzzy Logic; International audience; Fuzzy graph language recognizability is introduced along the lines of the established theory of syntactic graph language recognizability by virtue of the algebraic structure of magmoids. The main closure properties of the corresponding class are investigated and several interesting examples of fuzzy graph languages are examined.
Brouwer, A.E.; Haemers, W.H.
2012-01-01
This book gives an elementary treatment of the basic material about graph spectra, both for ordinary, and Laplace and Seidel spectra. The text progresses systematically, by covering standard topics before presenting some new material on trees, strongly regular graphs, two-graphs, association
Characterizing graphs of maximum matching width at most 2
Jeong, Jisu; Ok, Seongmin; Suh, Geewon
2017-01-01
The maximum matching width is a width-parameter that is de ned on a branch-decomposition over the vertex set of a graph. The size of a maximum matching in the bipartite graph is used as a cut-function. In this paper, we characterize the graphs of maximum matching width at most 2 using the minor o...
Comparing Internet Probing Methodologies Through an Analysis of Large Dynamic Graphs
2014-06-01
System Number CAIDA Cooperative Association of Internet Data Analysis GB gigabyte IETF IPv4 IP IPv6 ISP NPS NTC RFC RTT TTL ICMP NPS ESD VSD TCP UDP DoS...including, DIMES, IPlane, Ark IPv4 All Prefix /24 and recently NPS probing methodol- ogy. NPS probing methodology is different from the others because it...trace, a history of the forward interface-level path and time to send and acknowledge are available to analyze. However, traceroute may not return
MAGMA: generalized gene-set analysis of GWAS data.
de Leeuw, Christiaan A; Mooij, Joris M; Heskes, Tom; Posthuma, Danielle
2015-04-01
By aggregating data for complex traits in a biologically meaningful way, gene and gene-set analysis constitute a valuable addition to single-marker analysis. However, although various methods for gene and gene-set analysis currently exist, they generally suffer from a number of issues. Statistical power for most methods is strongly affected by linkage disequilibrium between markers, multi-marker associations are often hard to detect, and the reliance on permutation to compute p-values tends to make the analysis computationally very expensive. To address these issues we have developed MAGMA, a novel tool for gene and gene-set analysis. The gene analysis is based on a multiple regression model, to provide better statistical performance. The gene-set analysis is built as a separate layer around the gene analysis for additional flexibility. This gene-set analysis also uses a regression structure to allow generalization to analysis of continuous properties of genes and simultaneous analysis of multiple gene sets and other gene properties. Simulations and an analysis of Crohn's Disease data are used to evaluate the performance of MAGMA and to compare it to a number of other gene and gene-set analysis tools. The results show that MAGMA has significantly more power than other tools for both the gene and the gene-set analysis, identifying more genes and gene sets associated with Crohn's Disease while maintaining a correct type 1 error rate. Moreover, the MAGMA analysis of the Crohn's Disease data was found to be considerably faster as well.
Integer Flows and Circuit Covers of Graphs and Signed Graphs
Cheng, Jian
The work in Chapter 2 is motivated by Tutte and Jaeger's pioneering work on converting modulo flows into integer-valued flows for ordinary graphs. For a signed graphs (G, sigma), we first prove that for each k ∈ {2, 3}, if (G, sigma) is (k - 1)-edge-connected and contains an even number of negative edges when k = 2, then every modulo k-flow of (G, sigma) can be converted into an integer-valued ( k + 1)-ow with a larger or the same support. We also prove that if (G, sigma) is odd-(2p+1)-edge-connected, then (G, sigma) admits a modulo circular (2 + 1/ p)-flows if and only if it admits an integer-valued circular (2 + 1/p)-flows, which improves all previous result by Xu and Zhang (DM2005), Schubert and Steffen (EJC2015), and Zhu (JCTB2015). Shortest circuit cover conjecture is one of the major open problems in graph theory. It states that every bridgeless graph G contains a set of circuits F such that each edge is contained in at least one member of F and the length of F is at most 7/5∥E(G)∥. This concept was recently generalized to signed graphs by Macajova et al. (JGT2015). In Chapter 3, we improve their upper bound from 11∥E( G)∥ to 14/3 ∥E(G)∥, and if G is 2-edgeconnected and has even negativeness, then it can be further reduced to 11/3 ∥E(G)∥. Tutte's 3-flow conjecture has been studied by many graph theorists in the last several decades. As a new approach to this conjecture, DeVos and Thomassen considered the vectors as ow values and found that there is a close relation between vector S1-flows and integer 3-NZFs. Motivated by their observation, in Chapter 4, we prove that if a graph G admits a vector S1-flow with rank at most two, then G admits an integer 3-NZF. The concept of even factors is highly related to the famous Four Color Theorem. We conclude this dissertation in Chapter 5 with an improvement of a recent result by Chen and Fan (JCTB2016) on the upperbound of even factors. We show that if a graph G contains an even factor, then it
PRIVATE GRAPHS – ACCESS RIGHTS ON GRAPHS FOR SEAMLESS NAVIGATION
W. Dorner
2016-06-01
Full Text Available After the success of GNSS (Global Navigational Satellite Systems and navigation services for public streets, indoor seems to be the next big development in navigational services, relying on RTLS – Real Time Locating Services (e.g. WIFI and allowing seamless navigation. In contrast to navigation and routing services on public streets, seamless navigation will cause an additional challenge: how to make routing data accessible to defined users or restrict access rights for defined areas or only to parts of the graph to a defined user group? The paper will present case studies and data from literature, where seamless and especially indoor navigation solutions are presented (hospitals, industrial complexes, building sites, but the problem of restricted access rights was only touched from a real world, but not a technical perspective. The analysis of case studies will show, that the objective of navigation and the different target groups for navigation solutions will demand well defined access rights and require solutions, how to make only parts of a graph to a user or application available to solve a navigational task. The paper will therefore introduce the concept of private graphs, which is defined as a graph for navigational purposes covering the street, road or floor network of an area behind a public street and suggest different approaches how to make graph data for navigational purposes available considering access rights and data protection, privacy and security issues as well.
Huang, Yun-An; Jastorff, Jan; Van den Stock, Jan; Van de Vliet, Laura; Dupont, Patrick; Vandenbulcke, Mathieu
2018-05-15
Psychological construction models of emotion state that emotions are variable concepts constructed by fundamental psychological processes, whereas according to basic emotion theory, emotions cannot be divided into more fundamental units and each basic emotion is represented by a unique and innate neural circuitry. In a previous study, we found evidence for the psychological construction account by showing that several brain regions were commonly activated when perceiving different emotions (i.e. a general emotion network). Moreover, this set of brain regions included areas associated with core affect, conceptualization and executive control, as predicted by psychological construction models. Here we investigate directed functional brain connectivity in the same dataset to address two questions: 1) is there a common pathway within the general emotion network for the perception of different emotions and 2) if so, does this common pathway contain information to distinguish between different emotions? We used generalized psychophysiological interactions and information flow indices to examine the connectivity within the general emotion network. The results revealed a general emotion pathway that connects neural nodes involved in core affect, conceptualization, language and executive control. Perception of different emotions could not be accurately classified based on the connectivity patterns from the nodes of the general emotion pathway. Successful classification was achieved when connections outside the general emotion pathway were included. We propose that the general emotion pathway functions as a common pathway within the general emotion network and is involved in shared basic psychological processes across emotions. However, additional connections within the general emotion network are required to classify different emotions, consistent with a constructionist account. Copyright © 2018 Elsevier Inc. All rights reserved.
Park, Bong Soo; Lee, Yoo Jin; Park, Jin-Han; Kim, Il Hwan; Park, Si Hyung; Lee, Ho-Joon; Park, Kang Min
2018-06-01
We evaluated global topology and organization of regional hubs in the brain networks and microstructural abnormalities in the white matter of patients with reflex syncope. Twenty patients with reflex syncope and thirty healthy subjects were recruited, and they underwent diffusion tensor imaging (DTI) scans. Graph theory was applied to obtain network measures based on extracted DTI data, using DSI Studio. We then investigated differences in the network measures between the patients with reflex syncope and the healthy subjects. We also analyzed microstructural abnormalities of white matter using tract-based spatial statistics analysis (TBSS). Measures of global topology were not different between patients with reflex syncope and healthy subjects. However, in reflex syncope patients, the strength measures of the right angular, left inferior frontal, left middle orbitofrontal, left superior medial frontal, and left middle temporal gyrus were lower than in healthy subjects. The betweenness centrality measures of the left middle orbitofrontal, left fusiform, and left lingual gyrus in patients were lower than those in healthy subjects. The PageRank centrality measures of the right angular, left middle orbitofrontal, and left superior medial frontal gyrus in patients were lower than those in healthy subjects. Regarding the analysis of the white matter microstructure, there were no differences in the fractional anisotropy and mean diffusivity values between the two groups. We have identified a reorganization of network hubs in the brain network of patients with reflex syncope. These alterations in brain network may play a role in the pathophysiologic mechanism underlying reflex syncope. © 2018 The Authors. Brain and Behavior published by Wiley Periodicals, Inc.
Genus of total graphs from rings: A survey
T. Tamizh Chelvam
2018-04-01
Full Text Available Let R be a commutative ring. The total graph T Γ ( R of R is the undirected graph with vertex set R and two distinct vertices x and y are adjacent if x + y is a zero divisor in R . In this paper, we present a survey of results on the genus of T Γ ( R and three of its generalizations. Keywords: Commutative ring, Total graph, Cayley graph, Genus, Planar
Connectivity: Performance Portable Algorithms for graph connectivity v. 0.1
2017-09-21
Graphs occur in several places in real world from road networks, social networks and scientific simulations. Connectivity is a graph analysis software to graph connectivity in modern architectures like multicore CPUs, Xeon Phi and GPUs.
Komachi, Mamoru; Kudo, Taku; Shimbo, Masashi; Matsumoto, Yuji
Bootstrapping has a tendency, called semantic drift, to select instances unrelated to the seed instances as the iteration proceeds. We demonstrate the semantic drift of Espresso-style bootstrapping has the same root as the topic drift of Kleinberg's HITS, using a simplified graph-based reformulation of bootstrapping. We confirm that two graph-based algorithms, the von Neumann kernels and the regularized Laplacian, can reduce the effect of semantic drift in the task of word sense disambiguation (WSD) on Senseval-3 English Lexical Sample Task. Proposed algorithms achieve superior performance to Espresso and previous graph-based WSD methods, even though the proposed algorithms have less parameters and are easy to calibrate.
Hell, Pavol
2004-01-01
This is a book about graph homomorphisms. Graph theory is now an established discipline but the study of graph homomorphisms has only recently begun to gain wide acceptance and interest. The subject gives a useful perspective in areas such as graph reconstruction, products, fractional and circular colourings, and has applications in complexity theory, artificial intelligence, telecommunication, and, most recently, statistical physics.Based on the authors' lecture notes for graduate courses, this book can be used as a textbook for a second course in graph theory at 4th year or master's level an
Field programmable gate array reliability analysis using the dynamic flow graph methodology
McNelles, Phillip; Lu, Lixuan [Faculty of Energy Systems and Nuclear Science, University of Ontario Institute of Technology (UOIT), Ontario (Canada)
2016-10-15
Field programmable gate array (FPGA)-based systems are thought to be a practical option to replace certain obsolete instrumentation and control systems in nuclear power plants. An FPGA is a type of integrated circuit, which is programmed after being manufactured. FPGAs have some advantages over other electronic technologies, such as analog circuits, microprocessors, and Programmable Logic Controllers (PLCs), for nuclear instrumentation and control, and safety system applications. However, safety-related issues for FPGA-based systems remain to be verified. Owing to this, modeling FPGA-based systems for safety assessment has now become an important point of research. One potential methodology is the dynamic flowgraph methodology (DFM). It has been used for modeling software/hardware interactions in modern control systems. In this paper, FPGA logic was analyzed using DFM. Four aspects of FPGAs are investigated: the 'IEEE 1164 standard', registers (D flip-flops), configurable logic blocks, and an FPGA-based signal compensator. The ModelSim simulations confirmed that DFM was able to accurately model those four FPGA properties, proving that DFM has the potential to be used in the modeling of FPGA-based systems. Furthermore, advantages of DFM over traditional reliability analysis methods and FPGA simulators are presented, along with a discussion of potential issues with using DFM for FPGA-based system modeling.
On a Fuzzy Algebra for Querying Graph Databases
Pivert , Olivier; Thion , Virginie; Jaudoin , Hélène; Smits , Grégory
2014-01-01
International audience; This paper proposes a notion of fuzzy graph database and describes a fuzzy query algebra that makes it possible to handle such database, which may be fuzzy or not, in a flexible way. The algebra, based on fuzzy set theory and the concept of a fuzzy graph, is composed of a set of operators that can be used to express preference queries on fuzzy graph databases. The preferences concern i) the content of the vertices of the graph and ii) the structure of the graph. In a s...
Introduction to quantum graphs
Berkolaiko, Gregory
2012-01-01
A "quantum graph" is a graph considered as a one-dimensional complex and equipped with a differential operator ("Hamiltonian"). Quantum graphs arise naturally as simplified models in mathematics, physics, chemistry, and engineering when one considers propagation of waves of various nature through a quasi-one-dimensional (e.g., "meso-" or "nano-scale") system that looks like a thin neighborhood of a graph. Works that currently would be classified as discussing quantum graphs have been appearing since at least the 1930s, and since then, quantum graphs techniques have been applied successfully in various areas of mathematical physics, mathematics in general and its applications. One can mention, for instance, dynamical systems theory, control theory, quantum chaos, Anderson localization, microelectronics, photonic crystals, physical chemistry, nano-sciences, superconductivity theory, etc. Quantum graphs present many non-trivial mathematical challenges, which makes them dear to a mathematician's heart. Work on qu...
Wang, Junjing; Qiu, Shijun; Xu, Yong; Liu, Zhenyin; Wen, Xue; Hu, Xiangshu; Zhang, Ruibin; Li, Meng; Wang, Wensheng; Huang, Ruiwang
2014-09-01
Temporal lobe epilepsy (TLE) is one of the most common forms of drug-resistant epilepsy. Previous studies have indicated that the TLE-related impairments existed in extensive local functional networks. However, little is known about the alterations in the topological properties of whole brain functional networks. In this study, we acquired resting-state BOLD-fMRI (rsfMRI) data from 26 TLE patients and 25 healthy controls, constructed their whole brain functional networks, compared the differences in topological parameters between the TLE patients and the controls, and analyzed the correlation between the altered topological properties and the epilepsy duration. The TLE patients showed significant increases in clustering coefficient and characteristic path length, but significant decrease in global efficiency compared to the controls. We also found altered nodal parameters in several regions in the TLE patients, such as the bilateral angular gyri, left middle temporal gyrus, right hippocampus, triangular part of left inferior frontal gyrus, left inferior parietal but supramarginal and angular gyri, and left parahippocampus gyrus. Further correlation analysis showed that the local efficiency of the TLE patients correlated positively with the epilepsy duration. Our results indicated the disrupted topological properties of whole brain functional networks in TLE patients. Our findings indicated the TLE-related impairments in the whole brain functional networks, which may help us to understand the clinical symptoms of TLE patients and offer a clue for the diagnosis and treatment of the TLE patients. Copyright © 2014 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved.
Eigenfunction statistics on quantum graphs
Gnutzmann, S.; Keating, J.P.; Piotet, F.
2010-01-01
We investigate the spatial statistics of the energy eigenfunctions on large quantum graphs. It has previously been conjectured that these should be described by a Gaussian Random Wave Model, by analogy with quantum chaotic systems, for which such a model was proposed by Berry in 1977. The autocorrelation functions we calculate for an individual quantum graph exhibit a universal component, which completely determines a Gaussian Random Wave Model, and a system-dependent deviation. This deviation depends on the graph only through its underlying classical dynamics. Classical criteria for quantum universality to be met asymptotically in the large graph limit (i.e. for the non-universal deviation to vanish) are then extracted. We use an exact field theoretic expression in terms of a variant of a supersymmetric σ model. A saddle-point analysis of this expression leads to the estimates. In particular, intensity correlations are used to discuss the possible equidistribution of the energy eigenfunctions in the large graph limit. When equidistribution is asymptotically realized, our theory predicts a rate of convergence that is a significant refinement of previous estimates. The universal and system-dependent components of intensity correlation functions are recovered by means of an exact trace formula which we analyse in the diagonal approximation, drawing in this way a parallel between the field theory and semiclassics. Our results provide the first instance where an asymptotic Gaussian Random Wave Model has been established microscopically for eigenfunctions in a system with no disorder.
Amedeo Ganciu
2018-02-01
Full Text Available The distribution of services across a territory generates daily commuting flows, which have a significant influence on the development of the territory and often causes congestion in large areas. This negatively affects the environmental, economic and social components of the metropolitan landscape. Using the graph theory, we constructed and analyzed various (in typologies of transportation and moving time flow networks in the two main Italian metropolitan areas: Rome (MCR and Milan (MCM. The analysis of these networks provided us with strategic information on the dynamics of the two urban macro-systems. In particular, the aim of our study was to: (i identify the characteristics, distribution and direction of the main attractive forces within the regional systems under study; (ii identify the main differences in size and structure of commuter networks between the two metropolitan areas and between the two regional systems that include the two mother cities; and, (iii identify the main differences in the size and structure of the two commuting networks by transport modes (private, public, non-motorized mobility and the travel time. The results highlighted significant differences between the two case studies regarding volume flows, complexity and structure networks, and the spatial extension of the territories that are governed by the two metropolitan areas. MCR is a strongly monocentric urban system with a regional influence centred on the mother city of Rome, while MCM is a diffused polycentric regional metropolitan system centred on multiple mother cities. The findings many have a role in urban planning choices and in the evaluation of policies aimed to favor sustainable mobility.
A model of language inflection graphs
Fukś, Henryk; Farzad, Babak; Cao, Yi
2014-01-01
Inflection graphs are highly complex networks representing relationships between inflectional forms of words in human languages. For so-called synthetic languages, such as Latin or Polish, they have particularly interesting structure due to the abundance of inflectional forms. We construct the simplest form of inflection graphs, namely a bipartite graph in which one group of vertices corresponds to dictionary headwords and the other group to inflected forms encountered in a given text. We, then, study projection of this graph on the set of headwords. The projection decomposes into a large number of connected components, to be called word groups. Distribution of sizes of word group exhibits some remarkable properties, resembling cluster distribution in a lattice percolation near the critical point. We propose a simple model which produces graphs of this type, reproducing the desired component distribution and other topological features.
Enabling Graph Appliance for Genome Assembly
Singh, Rina [ORNL; Graves, Jeffrey A [ORNL; Lee, Sangkeun (Matt) [ORNL; Sukumar, Sreenivas R [ORNL; Shankar, Mallikarjun [ORNL
2015-01-01
In recent years, there has been a huge growth in the amount of genomic data available as reads generated from various genome sequencers. The number of reads generated can be huge, ranging from hundreds to billions of nucleotide, each varying in size. Assembling such large amounts of data is one of the challenging computational problems for both biomedical and data scientists. Most of the genome assemblers developed have used de Bruijn graph techniques. A de Bruijn graph represents a collection of read sequences by billions of vertices and edges, which require large amounts of memory and computational power to store and process. This is the major drawback to de Bruijn graph assembly. Massively parallel, multi-threaded, shared memory systems can be leveraged to overcome some of these issues. The objective of our research is to investigate the feasibility and scalability issues of de Bruijn graph assembly on Cray s Urika-GD system; Urika-GD is a high performance graph appliance with a large shared memory and massively multithreaded custom processor designed for executing SPARQL queries over large-scale RDF data sets. However, to the best of our knowledge, there is no research on representing a de Bruijn graph as an RDF graph or finding Eulerian paths in RDF graphs using SPARQL for potential genome discovery. In this paper, we address the issues involved in representing a de Bruin graphs as RDF graphs and propose an iterative querying approach for finding Eulerian paths in large RDF graphs. We evaluate the performance of our implementation on real world ebola genome datasets and illustrate how genome assembly can be accomplished with Urika-GD using iterative SPARQL queries.
Identification of noise in linear data sets by factor analysis
Roscoe, B.A.; Hopke, Ph.K.
1982-01-01
A technique which has the ability to identify bad data points, after the data has been generated, is classical factor analysis. The ability of classical factor analysis to identify two different types of data errors make it ideally suited for scanning large data sets. Since the results yielded by factor analysis indicate correlations between parameters, one must know something about the nature of the data set and the analytical techniques used to obtain it to confidentially isolate errors. (author)
Graph-theoretical concepts and physicochemical data
Lionello Pogliani
2003-02-01
Full Text Available Graph theoretical concepts have been used to model the molecular polarizabilities of fifty-four organic derivatives, and the induced dipole moment of a set of fifty-seven organic compounds divided into three subsets. The starting point of these modeling strategies is the hydrogen-suppressed chemical graph and pseudograph of a molecule, which works very well for second row atoms. From these types of graphs a set of graph-theoretical basis indices, the molecular connectivity indices, can be derived and used to model properties and activities of molecules. With the aid of the molecular connectivity basis indices it is then possible to build higher-order descriptors. The problem of 'graph' encoding the contribution of the inner-core electrons of heteroatoms can here be solved with the aid of odd complete graphs, Kp-(p-odd. The use of these graph tools allow to draw an optimal modeling of the molecular polarizabilities and a satisfactory modeling of the induced dipole moment of a wide set of organic derivatives.
Nekrasov, A M; Lazarenko, T V; Zlatopol' skiy, A N
1982-01-01
The dynamics for the indicators of daily graphs of consumption of electricity in the USSR is the result of interaction of a large number of different-directed factors. Among them in recent years relatively greater influence has come from a change in the structure of consumers of each unified energy system and especially the USSR energy system with the unified energy systems with inclusion in it of large unified energy systems, whose time is shifted on time zones, and intensification of electrical bonds between the unified energy systems. The factor of expansion of the USSR energy system on the territory of the country because of the inclusion of new unified energy systems resulted in condensation of the daily graphs for consumption of electricity of the USSR energy system: increase in the coefficient of filling the daily graphs, their peak and semipeak parts, as well as coefficient of minimum consumption. Taking into consideration the program for further development of the country presented in the main trends for economic and social development of the USSR for 1981-1985 and for the period up to the year 1990, for the current and the near five-year plan, one can expect preservation of the revealed trends for dynamics of the indicators of the daily graphs for electricity consumption of the USSR energy system.
Constructing Knowledge Graphs of Depression
Huang, Zhisheng; Yang, Jie; van Harmelen, Frank; Hu, Qing
2017-01-01
Knowledge Graphs have been shown to be useful tools for integrating multiple medical knowledge sources, and to support such tasks as medical decision making, literature retrieval, determining healthcare quality indicators, co-morbodity analysis and many others. A large number of medical knowledge
Khakzad, Nima; Reniers, Genserik
2015-01-01
Dealing with large quantities of flammable and explosive materials, usually at high-pressure high-temperature conditions, makes process plants very vulnerable to cascading effects compared with other infrastructures. The combination of the extremely low frequency of cascading effects and the high complexity and interdependencies of process plants makes risk assessment and vulnerability analysis of process plants very challenging in the context of such events. In the present study, cascading effects were represented as a directed graph; accordingly, the efficacy of a set of graph metrics and measurements was examined in both unit and plant-wide vulnerability analysis of process plants. We demonstrated that vertex-level closeness and betweenness can be used in the unit vulnerability analysis of process plants for the identification of critical units within a process plant. Furthermore, the graph-level closeness metric can be used in the plant-wide vulnerability analysis for the identification of the most vulnerable plant layout with respect to the escalation of cascading effects. Furthermore, the results from the application of the graph metrics have been verified using a Bayesian network methodology. - Highlights: • Graph metrics can effectively be employed to identify vulnerable units and layouts in process plants. • Units with larger vertex-level closeness result in more probable and severe cascading effects. • Units with larger vertex-level betweenness contribute more to the escalation of cascading effects. • Layouts with larger graph-level closeness are more vulnerable to the escalation of cascading effects
Delve: A Data Set Retrieval and Document Analysis System
Akujuobi, Uchenna Thankgod
2017-12-29
Academic search engines (e.g., Google scholar or Microsoft academic) provide a medium for retrieving various information on scholarly documents. However, most of these popular scholarly search engines overlook the area of data set retrieval, which should provide information on relevant data sets used for academic research. Due to the increasing volume of publications, it has become a challenging task to locate suitable data sets on a particular research area for benchmarking or evaluations. We propose Delve, a web-based system for data set retrieval and document analysis. This system is different from other scholarly search engines as it provides a medium for both data set retrieval and real time visual exploration and analysis of data sets and documents.
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.
Analysis of operation events for HFETR emergency diesel generator set
Li Zhiqiang; Ji Xifang; Deng Hong
2015-01-01
By the statistic analysis of the historical failure data of the emergency diesel generator set, the specific mode, the attribute, and the direct and root origin for each failure are reviewed and summarized. Considering the current status of the emergency diesel generator set, the preventive measures and solutions in terms of operation, handling and maintenance are proposed, and the potential events for the emergency diesel generator set are analyzed. (authors)
Gene set analysis of purine and pyrimidine antimetabolites cancer therapies.
Fridley, Brooke L; Batzler, Anthony; Li, Liang; Li, Fang; Matimba, Alice; Jenkins, Gregory D; Ji, Yuan; Wang, Liewei; Weinshilboum, Richard M
2011-11-01
Responses to therapies, either with regard to toxicities or efficacy, are expected to involve complex relationships of gene products within the same molecular pathway or functional gene set. Therefore, pathways or gene sets, as opposed to single genes, may better reflect the true underlying biology and may be more appropriate units for analysis of pharmacogenomic studies. Application of such methods to pharmacogenomic studies may enable the detection of more subtle effects of multiple genes in the same pathway that may be missed by assessing each gene individually. A gene set analysis of 3821 gene sets is presented assessing the association between basal messenger RNA expression and drug cytotoxicity using ethnically defined human lymphoblastoid cell lines for two classes of drugs: pyrimidines [gemcitabine (dFdC) and arabinoside] and purines [6-thioguanine and 6-mercaptopurine]. The gene set nucleoside-diphosphatase activity was found to be significantly associated with both dFdC and arabinoside, whereas gene set γ-aminobutyric acid catabolic process was associated with dFdC and 6-thioguanine. These gene sets were significantly associated with the phenotype even after adjusting for multiple testing. In addition, five associated gene sets were found in common between the pyrimidines and two gene sets for the purines (3',5'-cyclic-AMP phosphodiesterase activity and γ-aminobutyric acid catabolic process) with a P value of less than 0.0001. Functional validation was attempted with four genes each in gene sets for thiopurine and pyrimidine antimetabolites. All four genes selected from the pyrimidine gene sets (PSME3, CANT1, ENTPD6, ADRM1) were validated, but only one (PDE4D) was validated for the thiopurine gene sets. In summary, results from the gene set analysis of pyrimidine and purine therapies, used often in the treatment of various cancers, provide novel insight into the relationship between genomic variation and drug response.
Chartrand, Gary
1984-01-01
Graph theory is used today in the physical sciences, social sciences, computer science, and other areas. Introductory Graph Theory presents a nontechnical introduction to this exciting field in a clear, lively, and informative style. Author Gary Chartrand covers the important elementary topics of graph theory and its applications. In addition, he presents a large variety of proofs designed to strengthen mathematical techniques and offers challenging opportunities to have fun with mathematics. Ten major topics - profusely illustrated - include: Mathematical Models, Elementary Concepts of Grap
3-biplacement of bipartite graphs
Lech Adamus
2008-01-01
Full Text Available Let \\(G=(L,R;E\\ be a bipartite graph with color classes \\(L\\ and \\(R\\ and edge set \\(E\\. A set of two bijections \\(\\{\\varphi_1 , \\varphi_2\\}\\, \\(\\varphi_1 , \\varphi_2 :L \\cup R \\to L \\cup R\\, is said to be a \\(3\\-biplacement of \\(G\\ if \\(\\varphi_1(L= \\varphi_2(L = L\\ and \\(E \\cap \\varphi_1^*(E=\\emptyset\\, \\(E \\cap \\varphi_2^*(E=\\emptyset\\, \\(\\varphi_1^*(E \\cap \\varphi_2^*(E=\\emptyset\\, where \\(\\varphi_1^*\\, \\(\\varphi_2^*\\ are the maps defined on \\(E\\, induced by \\(\\varphi_1\\, \\(\\varphi_2\\, respectively. We prove that if \\(|L| = p\\, \\(|R| = q\\, \\(3 \\leq p \\leq q\\, then every graph \\(G=(L,R;E\\ of size at most \\(p\\ has a \\(3\\-biplacement.
Adaptable Value-Set Analysis for Low-Level Code
Brauer, Jörg; Hansen, René Rydhof; Kowalewski, Stefan; Larsen, Kim G.; Olesen, Mads Chr.
2012-01-01
This paper presents a framework for binary code analysis that uses only SAT-based algorithms. Within the framework, incremental SAT solving is used to perform a form of weakly relational value-set analysis in a novel way, connecting the expressiveness of the value sets to computational complexity. Another key feature of our framework is that it translates the semantics of binary code into an intermediate representation. This allows for a straightforward translation of the program semantics in...
Adriaan R. Soetevent
2010-01-01
This paper extends Hotelling's model of price competition with quadratic transportation costs from a line to graphs. I propose an algorithm to calculate firm-level demand for any given graph, conditional on prices and firm locations. One feature of graph models of price competition is that spatial discontinuities in firm-level demand may occur. I show that the existence result of D'Aspremont et al. (1979) does not extend to simple star graphs. I conjecture that this non-existence result holds...
Pim Heijnen; Adriaan Soetevent
2014-01-01
This paper extends Hotelling's model of price competition with quadratic transportation costs from a line to graphs. We derive an algorithm to calculate firm-level demand for any given graph, conditional on prices and firm locations. These graph models of price competition may lead to spatial discontinuities in firm-level demand. We show that the existence result of D'Aspremont et al. (1979) does not extend to simple star graphs and conjecture that this non-existence result holds more general...
Aleks Kissinger
2014-03-01
Full Text Available String diagrams are a powerful tool for reasoning about physical processes, logic circuits, tensor networks, and many other compositional structures. Dixon, Duncan and Kissinger introduced string graphs, which are a combinatoric representations of string diagrams, amenable to automated reasoning about diagrammatic theories via graph rewrite systems. In this extended abstract, we show how the power of such rewrite systems can be greatly extended by introducing pattern graphs, which provide a means of expressing infinite families of rewrite rules where certain marked subgraphs, called !-boxes ("bang boxes", on both sides of a rule can be copied any number of times or removed. After reviewing the string graph formalism, we show how string graphs can be extended to pattern graphs and how pattern graphs and pattern rewrite rules can be instantiated to concrete string graphs and rewrite rules. We then provide examples demonstrating the expressive power of pattern graphs and how they can be applied to study interacting algebraic structures that are central to categorical quantum mechanics.
Gelfand, I M; Shnol, E E
1969-01-01
The second in a series of systematic studies by a celebrated mathematician I. M. Gelfand and colleagues, this volume presents students with a well-illustrated sequence of problems and exercises designed to illuminate the properties of functions and graphs. Since readers do not have the benefit of a blackboard on which a teacher constructs a graph, the authors abandoned the customary use of diagrams in which only the final form of the graph appears; instead, the book's margins feature step-by-step diagrams for the complete construction of each graph. The first part of the book employs simple fu
Creating more effective graphs
Robbins, Naomi B
2012-01-01
A succinct and highly readable guide to creating effective graphs The right graph can be a powerful tool for communicating information, improving a presentation, or conveying your point in print. If your professional endeavors call for you to present data graphically, here's a book that can help you do it more effectively. Creating More Effective Graphs gives you the basic knowledge and techniques required to choose and create appropriate graphs for a broad range of applications. Using real-world examples everyone can relate to, the author draws on her years of experience in gr
Lothian, Joshua [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Powers, Sarah S. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Sullivan, Blair D. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Baker, Matthew B. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Schrock, Jonathan [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Poole, Stephen W. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
2013-10-01
The benchmarking effort within the Extreme Scale Systems Center at Oak Ridge National Laboratory seeks to provide High Performance Computing benchmarks and test suites of interest to the DoD sponsor. The work described in this report is a part of the effort focusing on graph generation. A previously developed benchmark, SystemBurn, allowed the emulation of different application behavior profiles within a single framework. To complement this effort, similar capabilities are desired for graph-centric problems. This report examines existing synthetic graph generator implementations in preparation for further study on the properties of their generated synthetic graphs.
Mansutti, Alessio; Miculan, Marino; Peressotti, Marco
2017-01-01
We introduce loose graph simulations (LGS), a new notion about labelled graphs which subsumes in an intuitive and natural way subgraph isomorphism (SGI), regular language pattern matching (RLPM) and graph simulation (GS). Being a unification of all these notions, LGS allows us to express directly...... also problems which are “mixed” instances of previous ones, and hence which would not fit easily in any of them. After the definition and some examples, we show that the problem of finding loose graph simulations is NP-complete, we provide formal translation of SGI, RLPM, and GS into LGSs, and we give...
Alberto Apostolico
2009-08-01
Full Text Available The Web Graph is a large-scale graph that does not fit in main memory, so that lossless compression methods have been proposed for it. This paper introduces a compression scheme that combines efficient storage with fast retrieval for the information in a node. The scheme exploits the properties of the Web Graph without assuming an ordering of the URLs, so that it may be applied to more general graphs. Tests on some datasets of use achieve space savings of about 10% over existing methods.
Low-Rank Matrix Factorization With Adaptive Graph Regularizer.
Lu, Gui-Fu; Wang, Yong; Zou, Jian
2016-05-01
In this paper, we present a novel low-rank matrix factorization algorithm with adaptive graph regularizer (LMFAGR). We extend the recently proposed low-rank matrix with manifold regularization (MMF) method with an adaptive regularizer. Different from MMF, which constructs an affinity graph in advance, LMFAGR can simultaneously seek graph weight matrix and low-dimensional representations of data. That is, graph construction and low-rank matrix factorization are incorporated into a unified framework, which results in an automatically updated graph rather than a predefined one. The experimental results on some data sets demonstrate that the proposed algorithm outperforms the state-of-the-art low-rank matrix factorization methods.
BACFIRE, Minimal Cut Sets Common Cause Failure Fault Tree Analysis
Fussell, J.B.
1983-01-01
1 - Description of problem or function: BACFIRE, designed to aid in common cause failure analysis, searches among the basic events of a minimal cut set of the system logic model for common potential causes of failure. The potential cause of failure is called a qualitative failure characteristics. The algorithm searches qualitative failure characteristics (that are part of the program input) of the basic events contained in a set to find those characteristics common to all basic events. This search is repeated for all cut sets input to the program. Common cause failure analysis is thereby performed without inclusion of secondary failure in the system logic model. By using BACFIRE, a common cause failure analysis can be added to an existing system safety and reliability analysis. 2 - Method of solution: BACFIRE searches the qualitative failure characteristics of the basic events contained in the fault tree minimal cut set to find those characteristics common to all basic events by either of two criteria. The first criterion can be met if all the basic events in a minimal cut set are associated by a condition which alone may increase the probability of multiple component malfunction. The second criterion is met if all the basic events in a minimal cut set are susceptible to the same secondary failure cause and are located in the same domain for that cause of secondary failure. 3 - Restrictions on the complexity of the problem - Maxima of: 1001 secondary failure maps, 101 basic events, 10 cut sets
Graph Theory. 1. Fragmentation of Structural Graphs
Lorentz JÄNTSCHI
2002-12-01
Full Text Available The investigation of structural graphs has many fields of applications in engineering, especially in applied sciences like as applied chemistry and physics, computer sciences and automation, electronics and telecommunication. The main subject of the paper is to express fragmentation criteria in graph using a new method of investigation: terminal paths. Using terminal paths are defined most of the fragmentation criteria that are in use in molecular topology, but the fields of applications are more generally than that, as I mentioned before. Graphical examples of fragmentation are given for every fragmentation criteria. Note that all fragmentation is made with a computer program that implements a routine for every criterion.[1] A web routine for tracing all terminal paths in graph can be found at the address: http://vl.academicdirect.ro/molecular_topology/tpaths/ [1] M. V. Diudea, I. Gutman, L. Jäntschi, Molecular Topology, Nova Science, Commack, New York, 2001, 2002.
A graph rewriting programming language for graph drawing
Rodgers, Peter
1998-01-01
This paper describes Grrr, a prototype visual graph drawing tool. Previously there were no visual languages for programming graph drawing algorithms despite the inherently visual nature of the process. The languages which gave a diagrammatic view of graphs were not computationally complete and so could not be used to implement complex graph drawing algorithms. Hence current graph drawing tools are all text based. Recent developments in graph rewriting systems have produced computationally com...
Perepelitsa, VA; Sergienko, [No Value; Kochkarov, AM
1999-01-01
Definitions of prefractal and fractal graphs are introduced, and they are used to formulate mathematical models in different fields of knowledge. The topicality of fractal-graph recognition from the point of view, of fundamental improvement in the efficiency of the solution of algorithmic problems
Husfeldt, Thore
2015-01-01
This chapter presents an introduction to graph colouring algorithms. The focus is on vertex-colouring algorithms that work for general classes of graphs with worst-case performance guarantees in a sequential model of computation. The presentation aims to demonstrate the breadth of available...
Packing Degenerate Graphs Greedily
Allen, P.; Böttcher, J.; Hladký, J.; Piguet, Diana
2017-01-01
Roč. 61, August (2017), s. 45-51 ISSN 1571-0653 R&D Projects: GA ČR GJ16-07822Y Institutional support: RVO:67985807 Keywords : tree packing conjecture * graph packing * graph processes Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics
A graph model for opportunistic network coding
Sorour, Sameh; Aboutoraby, Neda; Al-Naffouri, Tareq Y.; Alouini, Mohamed-Slim
2015-01-01
© 2015 IEEE. Recent advancements in graph-based analysis and solutions of instantly decodable network coding (IDNC) trigger the interest to extend them to more complicated opportunistic network coding (ONC) scenarios, with limited increase
Kuramoto model for infinite graphs with kernels
Canale, Eduardo; Tembine, Hamidou; Tempone, Raul; Zouraris, Georgios E.
2015-01-01
. We focus on circulant graphs which have enough symmetries to make the computations easier. We then focus on the asymptotic regime where an integro-partial differential equation is derived. Numerical analysis and convergence proofs of the Fokker
David ePeebles
2015-10-01
Full Text Available The distinction between informational and computational equivalence of representations, first articulated by Larkin and Simon (1987 has been a fundamental principle in the analysis of diagrammatic reasoning which has been supported empirically on numerous occasions. We present an experiment that investigates this principle in relation to the performance of expert graph users of 2 x 2 'interaction' bar and line graphs. The study sought to determine whether expert interpretation is affected by graph format in the same way that novice interpretations are. The findings revealed that, unlike novices - and contrary to the assumptions of several graph comprehension models - experts' performance was the same for both graph formats, with their interpretation of bar graphs being no worse than that for line graphs. We discuss the implications of the study for guidelines for presenting such data and for models of expert graph comprehension.
Applications of Graph Spectral Techniques to Water Distribution Network Management
Armando di Nardo
2018-01-01
Full Text Available Cities depend on multiple heterogeneous, interconnected infrastructures to provide safe water to consumers. Given this complexity, efficient numerical techniques are needed to support optimal control and management of a water distribution network (WDN. This paper introduces a holistic analysis framework to support water utilities on the decision making process for an efficient supply management. The proposal is based on graph spectral techniques that take advantage of eigenvalues and eigenvectors properties of matrices that are associated with graphs. Instances of these matrices are the adjacency matrix and the Laplacian, among others. The interest for this application is to work on a graph that specifically represents a WDN. This is a complex network that is made by nodes corresponding to water sources and consumption points and links corresponding to pipes and valves. The aim is to face new challenges on urban water supply, ranging from computing approximations for network performance assessment to setting device positioning for efficient and automatic WDN division into district metered areas. It is consequently created a novel tool-set of graph spectral techniques adapted to improve main water management tasks and to simplify the identification of water losses through the definition of an optimal network partitioning. Two WDNs are used to analyze the proposed methodology. Firstly, the well-known network of C-Town is investigated for benchmarking of the proposed graph spectral framework. This allows for comparing the obtained results with others coming from previously proposed approaches in literature. The second case-study corresponds to an operational network. It shows the usefulness and optimality of the proposal to effectively manage a WDN.
Information extraction and knowledge graph construction from geoscience literature
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.
Perfect secure domination in graphs
S.V. Divya Rashmi
2017-07-01
Full Text Available Let $G=(V,E$ be a graph. A subset $S$ of $V$ is a dominating set of $G$ if every vertex in $Vsetminus S$ is adjacent to a vertex in $S.$ A dominating set $S$ is called a secure dominating set if for each $vin Vsetminus S$ there exists $uin S$ such that $v$ is adjacent to $u$ and $S_1=(Ssetminus{u}cup {v}$ is a dominating set. If further the vertex $uin S$ is unique, then $S$ is called a perfect secure dominating set. The minimum cardinality of a perfect secure dominating set of $G$ is called the perfect secure domination number of $G$ and is denoted by $gamma_{ps}(G.$ In this paper we initiate a study of this parameter and present several basic results.
Autoregressive Moving Average Graph Filtering
Isufi, Elvin; Loukas, Andreas; Simonetto, Andrea; Leus, Geert
2016-01-01
One of the cornerstones of the field of signal processing on graphs are graph filters, direct analogues of classical filters, but intended for signals defined on graphs. This work brings forth new insights on the distributed graph filtering problem. We design a family of autoregressive moving average (ARMA) recursions, which (i) are able to approximate any desired graph frequency response, and (ii) give exact solutions for tasks such as graph signal denoising and interpolation. The design phi...
Diallel analysis of fruit set in Hevea brasiliensis Muell. Arg.
Kenneth O. Omokhafe
2007-03-01
Full Text Available The clonal and inter-clonal combining ability of fruit set in a Hevea brasiliensis four-parent diallel mating was evaluated using a randomized complete block experimental design with three replicates. Twelve main and reciprocal crosses were hand pollinated and percentage fruit set was recorded. The raw data were subjected to an arc-sine transformation for analysis of variance, and general and specific combining ability. There was significant variation of each of fruit set for the various crosses, general combining ability and reciprocal effect. The breeding implications of these results are also discussed.
Subgraph detection using graph signals
Chepuri, Sundeep Prabhakar
2017-03-06
In this paper we develop statistical detection theory for graph signals. In particular, given two graphs, namely, a background graph that represents an usual activity and an alternative graph that represents some unusual activity, we are interested in answering the following question: To which of the two graphs does the observed graph signal fit the best? To begin with, we assume both the graphs are known, and derive an optimal Neyman-Pearson detector. Next, we derive a suboptimal detector for the case when the alternative graph is not known. The developed theory is illustrated with numerical experiments.
Subgraph detection using graph signals
Chepuri, Sundeep Prabhakar; Leus, Geert
2017-01-01
In this paper we develop statistical detection theory for graph signals. In particular, given two graphs, namely, a background graph that represents an usual activity and an alternative graph that represents some unusual activity, we are interested in answering the following question: To which of the two graphs does the observed graph signal fit the best? To begin with, we assume both the graphs are known, and derive an optimal Neyman-Pearson detector. Next, we derive a suboptimal detector for the case when the alternative graph is not known. The developed theory is illustrated with numerical experiments.
Hively, Lee M.
2014-09-16
Data collected from devices and human condition may be used to forewarn of critical events such as machine/structural failure or events from brain/heart wave data stroke. By monitoring the data, and determining what values are indicative of a failure forewarning, one can provide adequate notice of the impending failure in order to take preventive measures. This disclosure teaches a computer-based method to convert dynamical numeric data representing physical objects (unstructured data) into discrete-phase-space states, and hence into a graph (structured data) for extraction of condition change.
IGSA: Individual Gene Sets Analysis, including Enrichment and Clustering.
Wu, Lingxiang; Chen, Xiujie; Zhang, Denan; Zhang, Wubing; Liu, Lei; Ma, Hongzhe; Yang, Jingbo; Xie, Hongbo; Liu, Bo; Jin, Qing
2016-01-01
Analysis of gene sets has been widely applied in various high-throughput biological studies. One weakness in the traditional methods is that they neglect the heterogeneity of genes expressions in samples which may lead to the omission of some specific and important gene sets. It is also difficult for them to reflect the severities of disease and provide expression profiles of gene sets for individuals. We developed an application software called IGSA that leverages a powerful analytical capacity in gene sets enrichment and samples clustering. IGSA calculates gene sets expression scores for each sample and takes an accumulating clustering strategy to let the samples gather into the set according to the progress of disease from mild to severe. We focus on gastric, pancreatic and ovarian cancer data sets for the performance of IGSA. We also compared the results of IGSA in KEGG pathways enrichment with David, GSEA, SPIA, ssGSEA and analyzed the results of IGSA clustering and different similarity measurement methods. Notably, IGSA is proved to be more sensitive and specific in finding significant pathways, and can indicate related changes in pathways with the severity of disease. In addition, IGSA provides with significant gene sets profile for each sample.
Some Results on the Independence Polynomial of Unicyclic Graphs
Oboudi Mohammad Reza
2018-05-01
Full Text Available Let G be a simple graph on n vertices. An independent set in a graph is a set of pairwise non-adjacent vertices. The independence polynomial of G is the polynomial I(G,x=∑k=0ns(G,kxk$I(G,x = \\sum\
Determining X-chains in graph states
Wu, Jun-Yi; Kampermann, Hermann; Bruß, Dagmar
2016-01-01
The representation of graph states in the X-basis as well as the calculation of graph state overlaps can efficiently be performed by using the concept of X-chains (Wu et al 2015 Phys. Rev. A 92 012322). We present a necessary and sufficient criterion for X-chains and show that they can efficiently be determined by the Bareiss algorithm. An analytical approach for searching X-chain groups of a graph state is proposed. Furthermore we generalize the concept of X-chains to so-called Euler chains, whose induced subgraphs are Eulerian. This approach helps to determine if a given vertex set is an X-chain and we show how Euler chains can be used in the construction of multipartite Bell inequalities for graph states. (paper)
Use of graph algorithms in the processing and analysis of images with focus on the biomedical data.
Zdimalova, M; Roznovjak, R; Weismann, P; El Falougy, H; Kubikova, E
2017-01-01
Image segmentation is a known problem in the field of image processing. A great number of methods based on different approaches to this issue was created. One of these approaches utilizes the findings of the graph theory. Our work focuses on segmentation using shortest paths in a graph. Specifically, we deal with methods of "Intelligent Scissors," which use Dijkstra's algorithm to find the shortest paths. We created a new software in Microsoft Visual Studio 2013 integrated development environment Visual C++ in the language C++/CLI. We created a format application with a graphical users development environment for system Windows, with using the platform .Net (version 4.5). The program was used for handling and processing the original medical data. The major disadvantage of the method of "Intelligent Scissors" is the computational time length of Dijkstra's algorithm. However, after the implementation of a more efficient priority queue, this problem could be alleviated. The main advantage of this method we see in training that enables to adapt to a particular kind of edge, which we need to segment. The user involvement has a significant influence on the process of segmentation, which enormously aids to achieve high-quality results (Fig. 7, Ref. 13).
Bollobas, Bela
2004-01-01
The ever-expanding field of extremal graph theory encompasses a diverse array of problem-solving methods, including applications to economics, computer science, and optimization theory. This volume, based on a series of lectures delivered to graduate students at the University of Cambridge, presents a concise yet comprehensive treatment of extremal graph theory.Unlike most graph theory treatises, this text features complete proofs for almost all of its results. Further insights into theory are provided by the numerous exercises of varying degrees of difficulty that accompany each chapter. A
Pui Shan Wong
Full Text Available Fistulifera sp. strain JPCC DA0580 is a newly sequenced pennate diatom that is capable of simultaneously growing and accumulating lipids. This is a unique trait, not found in other related microalgae so far. It is able to accumulate between 40 to 60% of its cell weight in lipids, making it a strong candidate for the production of biofuel. To investigate this characteristic, we used RNA-Seq data gathered at four different times while Fistulifera sp. strain JPCC DA0580 was grown in oil accumulating and non-oil accumulating conditions. We then adapted gene set enrichment analysis (GSEA to investigate the relationship between the difference in gene expression of 7,822 genes and metabolic functions in our data. We utilized information in the KEGG pathway database to create the gene sets and changed GSEA to use re-sampling so that data from the different time points could be included in the analysis. Our GSEA method identified photosynthesis, lipid synthesis and amino acid synthesis related pathways as processes that play a significant role in oil production and growth in Fistulifera sp. strain JPCC DA0580. In addition to GSEA, we visualized the results by creating a network of compounds and reactions, and plotted the expression data on top of the network. This made existing graph algorithms available to us which we then used to calculate a path that metabolizes glucose into triacylglycerol (TAG in the smallest number of steps. By visualizing the data this way, we observed a separate up-regulation of genes at different times instead of a concerted response. We also identified two metabolic paths that used less reactions than the one shown in KEGG and showed that the reactions were up-regulated during the experiment. The combination of analysis and visualization methods successfully analyzed time-course data, identified important metabolic pathways and provided new hypotheses for further research.
Variable precision rough set for multiple decision attribute analysis
Lai; Kin; Keung
2008-01-01
A variable precision rough set (VPRS) model is used to solve the multi-attribute decision analysis (MADA) problem with multiple conflicting decision attributes and multiple condition attributes. By introducing confidence measures and a β-reduct, the VPRS model can rationally solve the conflicting decision analysis problem with multiple decision attributes and multiple condition attributes. For illustration, a medical diagnosis example is utilized to show the feasibility of the VPRS model in solving the MADA...
A static analysis tool set for assembler code verification
Dhodapkar, S.D.; Bhattacharjee, A.K.; Sen, Gopa
1991-01-01
Software Verification and Validation (V and V) is an important step in assuring reliability and quality of the software. The verification of program source code forms an important part of the overall V and V activity. The static analysis tools described here are useful in verification of assembler code. The tool set consists of static analysers for Intel 8086 and Motorola 68000 assembly language programs. The analysers examine the program source code and generate information about control flow within the program modules, unreachable code, well-formation of modules, call dependency between modules etc. The analysis of loops detects unstructured loops and syntactically infinite loops. Software metrics relating to size and structural complexity are also computed. This report describes the salient features of the design, implementation and the user interface of the tool set. The outputs generated by the analyser are explained using examples taken from some projects analysed by this tool set. (author). 7 refs., 17 figs
Outer-2-independent domination in graphs
independent dominating set of a graph is a set of vertices of such that every vertex of ()\\ has a neighbor in and the maximum vertex degree of the subgraph induced by ()\\ is at most one. The outer-2-independent domination ...
A Molecular Iodine Spectral Data Set for Rovibronic Analysis
Williamson, J. Charles; Kuntzleman, Thomas S.; Kafader, Rachael A.
2013-01-01
A data set of 7,381 molecular iodine vapor rovibronic transitions between the X and B electronic states has been prepared for an advanced undergraduate spectroscopic analysis project. Students apply standard theoretical techniques to these data and determine the values of three X-state constants (image omitted) and four B-state constants (image…
Optical generation of matter qubit graph states
Benjamin, S C; Eisert, J; Stace, T M
2005-01-01
We present a scheme for rapidly entangling matter qubits in order to create graph states for one-way quantum computing. The qubits can be simple three-level systems in separate cavities. Coupling involves only local fields and a static (unswitched) linear optics network. Fusion of graph-state sections occurs with, in principle, zero probability of damaging the nascent graph state. We avoid the finite thresholds of other schemes by operating on two entangled pairs, so that each generates exactly one photon. We do not require the relatively slow single qubit local flips to be applied during the growth phase: growth of the graph state can then become a purely optical process. The scheme naturally generates graph states with vertices of high degree and so is easily able to construct minimal graph states, with consequent resource savings. The most efficient approach will be to create new graph-state edges even as qubits elsewhere are measured, in a 'just in time' approach. An error analysis indicates that the scheme is relatively robust against imperfections in the apparatus
Huang, Xiaoke; Zhao, Ye; Yang, Jing; Zhang, Chong; Ma, Chao; Ye, Xinyue
2016-01-01
We propose TrajGraph, a new visual analytics method, for studying urban mobility patterns by integrating graph modeling and visual analysis with taxi trajectory data. A special graph is created to store and manifest real traffic information recorded by taxi trajectories over city streets. It conveys urban transportation dynamics which can be discovered by applying graph analysis algorithms. To support interactive, multiscale visual analytics, a graph partitioning algorithm is applied to create region-level graphs which have smaller size than the original street-level graph. Graph centralities, including Pagerank and betweenness, are computed to characterize the time-varying importance of different urban regions. The centralities are visualized by three coordinated views including a node-link graph view, a map view and a temporal information view. Users can interactively examine the importance of streets to discover and assess city traffic patterns. We have implemented a fully working prototype of this approach and evaluated it using massive taxi trajectories of Shenzhen, China. TrajGraph's capability in revealing the importance of city streets was evaluated by comparing the calculated centralities with the subjective evaluations from a group of drivers in Shenzhen. Feedback from a domain expert was collected. The effectiveness of the visual interface was evaluated through a formal user study. We also present several examples and a case study to demonstrate the usefulness of TrajGraph in urban transportation analysis.
Some Results on the Intersection Graphs of Ideals of Rings
Akbari, S.; Nikandish, R.; Nikmehr, M.J.
2010-08-01
Let R be a ring with unity and I(R)* be the set of all non-trivial left ideals of R. The intersection graph of ideals of R, denoted by G(R), is a graph with the vertex set I(R)* and two distinct vertices I and J are adjacent if and only if I intersection J ≠ 0. In this paper, we study some connections between the graph-theoretic properties of this graph and some algebraic properties of rings. We characterize all rings whose intersection graphs of ideals are not connected. Also we determine all rings whose clique number of the intersection graphs of ideals are finite. Among other results, it is shown that for every ring, if the clique number of G(R) is finite, then the chromatic number is finite too and if R is a reduced ring both are equal. (author)
Tailored Random Graph Ensembles
Roberts, E S; Annibale, A; Coolen, A C C
2013-01-01
Tailored graph ensembles are a developing bridge between biological networks and statistical mechanics. The aim is to use this concept to generate a suite of rigorous tools that can be used to quantify and compare the topology of cellular signalling networks, such as protein-protein interaction networks and gene regulation networks. We calculate exact and explicit formulae for the leading orders in the system size of the Shannon entropies of random graph ensembles constrained with degree distribution and degree-degree correlation. We also construct an ergodic detailed balance Markov chain with non-trivial acceptance probabilities which converges to a strictly uniform measure and is based on edge swaps that conserve all degrees. The acceptance probabilities can be generalized to define Markov chains that target any alternative desired measure on the space of directed or undirected graphs, in order to generate graphs with more sophisticated topological features.
Alspach, BR
1985-01-01
This volume deals with a variety of problems involving cycles in graphs and circuits in digraphs. Leading researchers in this area present here 3 survey papers and 42 papers containing new results. There is also a collection of unsolved problems.
Wilson, Robin J
1985-01-01
Graph Theory has recently emerged as a subject in its own right, as well as being an important mathematical tool in such diverse subjects as operational research, chemistry, sociology and genetics. This book provides a comprehensive introduction to the subject.
Hyperbolicity in median graphs
mic problems in hyperbolic spaces and hyperbolic graphs have been .... that in general the main obstacle is that we do not know the location of ...... [25] Jonckheere E and Lohsoonthorn P, A hyperbolic geometry approach to multipath routing,.
Cluster analysis by optimal decomposition of induced fuzzy sets
Backer, E
1978-01-01
Nonsupervised pattern recognition is addressed and the concept of fuzzy sets is explored in order to provide the investigator (data analyst) additional information supplied by the pattern class membership values apart from the classical pattern class assignments. The basic ideas behind the pattern recognition problem, the clustering problem, and the concept of fuzzy sets in cluster analysis are discussed, and a brief review of the literature of the fuzzy cluster analysis is given. Some mathematical aspects of fuzzy set theory are briefly discussed; in particular, a measure of fuzziness is suggested. The optimization-clustering problem is characterized. Then the fundamental idea behind affinity decomposition is considered. Next, further analysis takes place with respect to the partitioning-characterization functions. The iterative optimization procedure is then addressed. The reclassification function is investigated and convergence properties are examined. Finally, several experiments in support of the method suggested are described. Four object data sets serve as appropriate test cases. 120 references, 70 figures, 11 tables. (RWR)
Uniform Single Valued Neutrosophic Graphs
S. Broumi
2017-09-01
Full Text Available In this paper, we propose a new concept named the uniform single valued neutrosophic graph. An illustrative example and some properties are examined. Next, we develop an algorithmic approach for computing the complement of the single valued neutrosophic graph. A numerical example is demonstrated for computing the complement of single valued neutrosophic graphs and uniform single valued neutrosophic graph.
Seismic analysis for conceptual design of HCCR TBM-set
Lee, Dong Won, E-mail: dwlee@kaeri.re.kr [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of); Park, Seong Dae; Jin, Hyung Gon; Lee, Eo Hwak; Kim, Suk-Kwon; Yoon, Jae Sung [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of); Shin, Kyu In [Gentec Co., Daejeon, Republic of Korea (Korea, Republic of); Cho, Seungyon [National Fusion Research Institute, Daejeon (Korea, Republic of)
2016-11-01
Highlights: • The seismic analysis of KO HCCR TBM-set are performed. • The seismic envents like SL-1, SL-2, and SMHV are selected and evaluated with FEM code (ANSYS). • The results of the stresses and deformations are confirmed to meet the design criteria. - Abstract: Using the conceptual design of the Korean helium cooled ceramic reflector (HCCR) test blanket module (TBM) including the TBM-shield for testing in ITER, a seismic analysis is performed. According to the ITER TBM port plug (TBM PP) system load specifications, seismic events are selected as SL-1 (seismic level-1), SL-2 (seismic level-2), and SMHV (seismes maximaux historiquement vraisemblables, Maximum Histroically Probable Earthquakes). In a modal analysis a total of 50 modes are obtained. Then, a spectra response analysis for each seismic event is carried out using ANSYS based on the modal analysis results. For each event, the obtained Tresca stress is evaluated to confirm the design integrity, by comparing the resulting stress to the design criteria. The Tresca strain and displacement are also estimated for the HCCR TBM-set. From the analysis, it was concluded that the maximum stresses by the seismic events meet the design criteria, and the displacements are lower than the designed gap from the TBM PP frame. The results are provided to a load combination analysis.
Barra, F.; Gaspard, P.
2001-01-01
We consider the classical evolution of a particle on a graph by using a time-continuous Frobenius-Perron operator that generalizes previous propositions. In this way, the relaxation rates as well as the chaotic properties can be defined for the time-continuous classical dynamics on graphs. These properties are given as the zeros of some periodic-orbit zeta functions. We consider in detail the case of infinite periodic graphs where the particle undergoes a diffusion process. The infinite spatial extension is taken into account by Fourier transforms that decompose the observables and probability densities into sectors corresponding to different values of the wave number. The hydrodynamic modes of diffusion are studied by an eigenvalue problem of a Frobenius-Perron operator corresponding to a given sector. The diffusion coefficient is obtained from the hydrodynamic modes of diffusion and has the Green-Kubo form. Moreover, we study finite but large open graphs that converge to the infinite periodic graph when their size goes to infinity. The lifetime of the particle on the open graph is shown to correspond to the lifetime of a system that undergoes a diffusion process before it escapes
Bollobás, Béla
1998-01-01
The time has now come when graph theory should be part of the education of every serious student of mathematics and computer science, both for its own sake and to enhance the appreciation of mathematics as a whole. This book is an in-depth account of graph theory, written with such a student in mind; it reflects the current state of the subject and emphasizes connections with other branches of pure mathematics. The volume grew out of the author's earlier book, Graph Theory -- An Introductory Course, but its length is well over twice that of its predecessor, allowing it to reveal many exciting new developments in the subject. Recognizing that graph theory is one of several courses competing for the attention of a student, the book contains extensive descriptive passages designed to convey the flavor of the subject and to arouse interest. In addition to a modern treatment of the classical areas of graph theory such as coloring, matching, extremal theory, and algebraic graph theory, the book presents a detailed ...
Parameterized Verification of Graph Transformation Systems with Whole Neighbourhood Operations
Delzanno, Giorgio; Stückrath, Jan
2014-01-01
We introduce a new class of graph transformation systems in which rewrite rules can be guarded by universally quantified conditions on the neighbourhood of nodes. These conditions are defined via special graph patterns which may be transformed by the rule as well. For the new class for graph rewrite rules, we provide a symbolic procedure working on minimal representations of upward closed sets of configurations. We prove correctness and effectiveness of the procedure by a categorical presenta...
Ayu Cyntya Dewi, Dyah; Shaufiah; Asror, Ibnu
2018-03-01
SMS (Short Message Service) is on e of the communication services that still be the main choice, although now the phone grow with various applications. Along with the development of various other communication media, some countries lowered SMS rates to keep the interest of mobile users. It resulted in increased spam SMS that used by several parties, one of them for advertisement. Given the kind of multi-lingual documents in a message SMS, the Web, and others, necessary for effective multilingual or cross-lingual processing techniques is becoming increasingly important. The steps that performed in this research is data / messages first preprocessing then represented into a graph model. Then calculated using GKNN method. From this research we get the maximum accuracy is 98.86 with training data in Indonesian language and testing data in indonesian language with K 10 and threshold 0.001.
Groups, graphs and random walks
Salvatori, Maura; Sava-Huss, Ecaterina
2017-01-01
An accessible and panoramic account of the theory of random walks on groups and graphs, stressing the strong connections of the theory with other branches of mathematics, including geometric and combinatorial group theory, potential analysis, and theoretical computer science. This volume brings together original surveys and research-expository papers from renowned and leading experts, many of whom spoke at the workshop 'Groups, Graphs and Random Walks' celebrating the sixtieth birthday of Wolfgang Woess in Cortona, Italy. Topics include: growth and amenability of groups; Schrödinger operators and symbolic dynamics; ergodic theorems; Thompson's group F; Poisson boundaries; probability theory on buildings and groups of Lie type; structure trees for edge cuts in networks; and mathematical crystallography. In what is currently a fast-growing area of mathematics, this book provides an up-to-date and valuable reference for both researchers and graduate students, from which future research activities will undoubted...
Flux networks in metabolic graphs
Warren, P B; Queiros, S M Duarte; Jones, J L
2009-01-01
A metabolic model can be represented as a bipartite graph comprising linked reaction and metabolite nodes. Here it is shown how a network of conserved fluxes can be assigned to the edges of such a graph by combining the reaction fluxes with a conserved metabolite property such as molecular weight. A similar flux network can be constructed by combining the primal and dual solutions to the linear programming problem that typically arises in constraint-based modelling. Such constructions may help with the visualization of flux distributions in complex metabolic networks. The analysis also explains the strong correlation observed between metabolite shadow prices (the dual linear programming variables) and conserved metabolite properties. The methods were applied to recent metabolic models for Escherichia coli, Saccharomyces cerevisiae and Methanosarcina barkeri. Detailed results are reported for E. coli; similar results were found for other organisms
Ranking metrics in gene set enrichment analysis: do they matter?
Zyla, Joanna; Marczyk, Michal; Weiner, January; Polanska, Joanna
2017-05-12
There exist many methods for describing the complex relation between changes of gene expression in molecular pathways or gene ontologies under different experimental conditions. Among them, Gene Set Enrichment Analysis seems to be one of the most commonly used (over 10,000 citations). An important parameter, which could affect the final result, is the choice of a metric for the ranking of genes. Applying a default ranking metric may lead to poor results. In this work 28 benchmark data sets were used to evaluate the sensitivity and false positive rate of gene set analysis for 16 different ranking metrics including new proposals. Furthermore, the robustness of the chosen methods to sample size was tested. Using k-means clustering algorithm a group of four metrics with the highest performance in terms of overall sensitivity, overall false positive rate and computational load was established i.e. absolute value of Moderated Welch Test statistic, Minimum Significant Difference, absolute value of Signal-To-Noise ratio and Baumgartner-Weiss-Schindler test statistic. In case of false positive rate estimation, all selected ranking metrics were robust with respect to sample size. In case of sensitivity, the absolute value of Moderated Welch Test statistic and absolute value of Signal-To-Noise ratio gave stable results, while Baumgartner-Weiss-Schindler and Minimum Significant Difference showed better results for larger sample size. Finally, the Gene Set Enrichment Analysis method with all tested ranking metrics was parallelised and implemented in MATLAB, and is available at https://github.com/ZAEDPolSl/MrGSEA . Choosing a ranking metric in Gene Set Enrichment Analysis has critical impact on results of pathway enrichment analysis. The absolute value of Moderated Welch Test has the best overall sensitivity and Minimum Significant Difference has the best overall specificity of gene set analysis. When the number of non-normally distributed genes is high, using Baumgartner
Classification of user interfaces for graph-based online analytical processing
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.
Probabilistic Graph Layout for Uncertain Network Visualization.
Schulz, Christoph; Nocaj, Arlind; Goertler, Jochen; Deussen, Oliver; Brandes, Ulrik; Weiskopf, Daniel
2017-01-01
We present a novel uncertain network visualization technique based on node-link diagrams. Nodes expand spatially in our probabilistic graph layout, depending on the underlying probability distributions of edges. The visualization is created by computing a two-dimensional graph embedding that combines samples from the probabilistic graph. A Monte Carlo process is used to decompose a probabilistic graph into its possible instances and to continue with our graph layout technique. Splatting and edge bundling are used to visualize point clouds and network topology. The results provide insights into probability distributions for the entire network-not only for individual nodes and edges. We validate our approach using three data sets that represent a wide range of network types: synthetic data, protein-protein interactions from the STRING database, and travel times extracted from Google Maps. Our approach reveals general limitations of the force-directed layout and allows the user to recognize that some nodes of the graph are at a specific position just by chance.
Quantum complexity of graph and algebraic problems
Doern, Sebastian
2008-01-01
This thesis is organized as follows: In Chapter 2 we give some basic notations, definitions and facts from linear algebra, graph theory, group theory and quantum computation. In Chapter 3 we describe three important methods for the construction of quantum algorithms. We present the quantum search algorithm by Grover, the quantum amplitude amplification and the quantum walk search technique by Magniez et al. These three tools are the basis for the development of our new quantum algorithms for graph and algebra problems. In Chapter 4 we present two tools for proving quantum query lower bounds. We present the quantum adversary method by Ambainis and the polynomial method introduced by Beals et al. The quantum adversary tool is very useful to prove good lower bounds for many graph and algebra problems. The part of the thesis containing the original results is organized in two parts. In the first part we consider the graph problems. In Chapter 5 we give a short summary of known quantum graph algorithms. In Chapter 6 to 8 we study the complexity of our new algorithms for matching problems, graph traversal and independent set problems on quantum computers. In the second part of our thesis we present new quantum algorithms for algebraic problems. In Chapter 9 to 10 we consider group testing problems and prove quantum complexity bounds for important problems from linear algebra. (orig.)
Multiple graph regularized nonnegative matrix factorization
Wang, Jim Jing-Yan
2013-10-01
Non-negative matrix factorization (NMF) has been widely used as a data representation method based on components. To overcome the disadvantage of NMF in failing to consider the manifold structure of a data set, graph regularized NMF (GrNMF) has been proposed by Cai et al. by constructing an affinity graph and searching for a matrix factorization that respects graph structure. Selecting a graph model and its corresponding parameters is critical for this strategy. This process is usually carried out by cross-validation or discrete grid search, which are time consuming and prone to overfitting. In this paper, we propose a GrNMF, called MultiGrNMF, in which the intrinsic manifold is approximated by a linear combination of several graphs with different models and parameters inspired by ensemble manifold regularization. Factorization metrics and linear combination coefficients of graphs are determined simultaneously within a unified object function. They are alternately optimized in an iterative algorithm, thus resulting in a novel data representation algorithm. Extensive experiments on a protein subcellular localization task and an Alzheimer\\'s disease diagnosis task demonstrate the effectiveness of the proposed algorithm. © 2013 Elsevier Ltd. All rights reserved.
Quantum complexity of graph and algebraic problems
Doern, Sebastian
2008-02-04
This thesis is organized as follows: In Chapter 2 we give some basic notations, definitions and facts from linear algebra, graph theory, group theory and quantum computation. In Chapter 3 we describe three important methods for the construction of quantum algorithms. We present the quantum search algorithm by Grover, the quantum amplitude amplification and the quantum walk search technique by Magniez et al. These three tools are the basis for the development of our new quantum algorithms for graph and algebra problems. In Chapter 4 we present two tools for proving quantum query lower bounds. We present the quantum adversary method by Ambainis and the polynomial method introduced by Beals et al. The quantum adversary tool is very useful to prove good lower bounds for many graph and algebra problems. The part of the thesis containing the original results is organized in two parts. In the first part we consider the graph problems. In Chapter 5 we give a short summary of known quantum graph algorithms. In Chapter 6 to 8 we study the complexity of our new algorithms for matching problems, graph traversal and independent set problems on quantum computers. In the second part of our thesis we present new quantum algorithms for algebraic problems. In Chapter 9 to 10 we consider group testing problems and prove quantum complexity bounds for important problems from linear algebra. (orig.)
Distances in zero-divisor and total graphs from commutative rings–A survey
T. Tamizh Chelvam
2016-12-01
Full Text Available There are so many ways to construct graphs from algebraic structures. Most popular constructions are Cayley graphs, commuting graphs and non-commuting graphs from finite groups and zero-divisor graphs and total graphs from commutative rings. For a commutative ring R with non-zero identity, we denote the set of zero-divisors and unit elements of R by Z(R and U(R, respectively. One of the associated graphs to a ring R is the zero-divisor graph; it is a simple graph with vertex set Z(R∖{0}, and two vertices x and y are adjacent if and only if xy=0. This graph was first introduced by Beck, where all the elements of R are considered as the vertices. Anderson and Badawi, introduced the total graph of R, as the simple graph with all elements of R as vertices, and two distinct vertices x and y are adjacent if and only if x+y∈Z(R. For a given graph G, the concept of connectedness, diameter and girth are always of great interest. Several authors extensively studied about the zero-divisor and total graphs from commutative rings. In this paper, we present a survey of results obtained with regard to distances in zero-divisor and total graphs.
Tracking Research Data Footprints via Integration with Research Graph
Evans, B. J. K.; Wang, J.; Aryani, A.; Conlon, M.; Wyborn, L. A.; Choudhury, S. A.
2017-12-01
The researcher of today is likely to be part of a team that will use subsets of data from at least one, if not more external repositories, and that same data could be used by multiple researchers for many different purposes. At best, the repositories that host this data will know who is accessing their data, but rarely what they are using it for, resulting in funders of data collecting programs and data repositories that store the data unlikely to know: 1) which research funding contributed to the collection and preservation of a dataset, and 2) which data contributed to high impact research and publications. In days of funding shortages there is a growing need to be able to trace the footprint a data set from the originator that collected the data to the repository that stores the data and ultimately to any derived publications. The Research Data Alliance's Data Description Registry Interoperability Working Group (DDRIWG) has addressed this problem through the development of a distributed graph, called Research Graph that can map each piece of the research interaction puzzle by building aggregated graphs. It can connect datasets on the basis of co-authorship or other collaboration models such as joint funding and grants and can connect research datasets, publications, grants and researcher profiles across research repositories and infrastructures such as DataCite and ORCID. National Computational Infrastructure (NCI) in Australia is one of the early adopters of Research Graph. The graphic view and quantitative analysis helps NCI track the usage of their National reference data collections thus quantifying the role that these NCI-hosted data assets play within the funding-researcher-data-publication-cycle. The graph can unlock the complex interactions of the research projects by tracking the contribution of datasets, the various funding bodies and the downstream data users. RMap Project is a similar initiative which aims to solve complex relationships among
Use of Attack Graphs in Security Systems
Vivek Shandilya
2014-01-01
Full Text Available Attack graphs have been used to model the vulnerabilities of the systems and their potential exploits. The successful exploits leading to the partial/total failure of the systems are subject of keen security interest. Considerable effort has been expended in exhaustive modeling, analyses, detection, and mitigation of attacks. One prominent methodology involves constructing attack graphs of the pertinent system for analysis and response strategies. This not only gives the simplified representation of the system, but also allows prioritizing the security properties whose violations are of greater concern, for both detection and repair. We present a survey and critical study of state-of-the-art technologies in attack graph generation and use in security system. Based on our research, we identify the potential, challenges, and direction of the current research in using attack graphs.
Reconstructing Topological Graphs and Continua
Gartside, Paul; Pitz, Max F.; Suabedissen, Rolf
2015-01-01
The deck of a topological space $X$ is the set $\\mathcal{D}(X)=\\{[X \\setminus \\{x\\}] \\colon x \\in X\\}$, where $[Z]$ denotes the homeomorphism class of $Z$. A space $X$ is topologically reconstructible if whenever $\\mathcal{D}(X)=\\mathcal{D}(Y)$ then $X$ is homeomorphic to $Y$. It is shown that all metrizable compact connected spaces are reconstructible. It follows that all finite graphs, when viewed as a 1-dimensional cell-complex, are reconstructible in the topological sense, and more genera...
Decomposing a graph into bistars
Thomassen, Carsten
2013-01-01
Bárat and the present author conjectured that, for each tree T, there exists a natural number kT such that the following holds: If G is a kT-edge-connected graph such that |E(T)| divides |E(G)|, then G has a T-decomposition, that is, a decomposition of the edge set into trees each of which...... is isomorphic to T. The conjecture has been verified for infinitely many paths and for each star. In this paper we verify the conjecture for an infinite family of trees that are neither paths nor stars, namely all the bistars S(k,k+1)....
Setting Standards for Medically-Based Running Analysis
Vincent, Heather K.; Herman, Daniel C.; Lear-Barnes, Leslie; Barnes, Robert; Chen, Cong; Greenberg, Scott; Vincent, Kevin R.
2015-01-01
Setting standards for medically based running analyses is necessary to ensure that runners receive a high-quality service from practitioners. Medical and training history, physical and functional tests, and motion analysis of running at self-selected and faster speeds are key features of a comprehensive analysis. Self-reported history and movement symmetry are critical factors that require follow-up therapy or long-term management. Pain or injury is typically the result of a functional deficit above or below the site along the kinematic chain. PMID:25014394
Stochastic analysis in discrete and continuous settings with normal martingales
Privault, Nicolas
2009-01-01
This volume gives a unified presentation of stochastic analysis for continuous and discontinuous stochastic processes, in both discrete and continuous time. It is mostly self-contained and accessible to graduate students and researchers having already received a basic training in probability. The simultaneous treatment of continuous and jump processes is done in the framework of normal martingales; that includes the Brownian motion and compensated Poisson processes as specific cases. In particular, the basic tools of stochastic analysis (chaos representation, gradient, divergence, integration by parts) are presented in this general setting. Applications are given to functional and deviation inequalities and mathematical finance.
spa: Semi-Supervised Semi-Parametric Graph-Based Estimation in R
Mark Culp
2011-04-01
Full Text Available In this paper, we present an R package that combines feature-based (X data and graph-based (G data for prediction of the response Y . In this particular case, Y is observed for a subset of the observations (labeled and missing for the remainder (unlabeled. We examine an approach for fitting Y = Xβ + f(G where β is a coefficient vector and f is a function over the vertices of the graph. The procedure is semi-supervised in nature (trained on the labeled and unlabeled sets, requiring iterative algorithms for fitting this estimate. The package provides several key functions for fitting and evaluating an estimator of this type. The package is illustrated on a text analysis data set, where the observations are text documents (papers, the response is the category of paper (either applied or theoretical statistics, the X information is the name of the journal in which the paper resides, and the graph is a co-citation network, with each vertex an observation and each edge the number of times that the two papers cite a common paper. An application involving classification of protein location using a protein interaction graph and an application involving classification on a manifold with part of the feature data converted to a graph are also presented.
Model-based gene set analysis for Bioconductor.
Bauer, Sebastian; Robinson, Peter N; Gagneur, Julien
2011-07-01
Gene Ontology and other forms of gene-category analysis play a major role in the evaluation of high-throughput experiments in molecular biology. Single-category enrichment analysis procedures such as Fisher's exact test tend to flag large numbers of redundant categories as significant, which can complicate interpretation. We have recently developed an approach called model-based gene set analysis (MGSA), that substantially reduces the number of redundant categories returned by the gene-category analysis. In this work, we present the Bioconductor package mgsa, which makes the MGSA algorithm available to users of the R language. Our package provides a simple and flexible application programming interface for applying the approach. The mgsa package has been made available as part of Bioconductor 2.8. It is released under the conditions of the Artistic license 2.0. peter.robinson@charite.de; julien.gagneur@embl.de.
Wada, Akihiko; Shizukuishi, Takashi; Kikuta, Junko; Yamada, Haruyasu; Watanabe, Yusuke; Imamura, Yoshiki; Shinozaki, Takahiro; Dezawa, Ko; Haradome, Hiroki; Abe, Osamu
2017-05-01
Burning mouth syndrome (BMS) is a chronic intraoral pain syndrome featuring idiopathic oral pain and burning discomfort despite clinically normal oral mucosa. The etiology of chronic pain syndrome is unclear, but preliminary neuroimaging research has suggested the alteration of volume, metabolism, blood flow, and diffusion at multiple brain regions. According to the neuromatrix theory of Melzack, pain sense is generated in the brain by the network of multiple pain-related brain regions. Therefore, the alteration of pain-related network is also assumed as an etiology of chronic pain. In this study, we investigated the brain network of BMS brain by using probabilistic tractography and graph analysis. Fourteen BMS patients and 14 age-matched healthy controls underwent 1.5T MRI. Structural connectivity was calculated in 83 anatomically defined regions with probabilistic tractography of 60-axis diffusion tensor imaging and 3D T1-weighted imaging. Graph theory network analysis was used to evaluate the brain network at local and global connectivity. In BMS brain, a significant difference of local brain connectivity was recognized at the bilateral rostral anterior cingulate cortex, right medial orbitofrontal cortex, and left pars orbitalis which belong to the medial pain system; however, no significant difference was recognized at the lateral system including the somatic sensory cortex. A strengthened connection of the anterior cingulate cortex and medial prefrontal cortex with the basal ganglia, thalamus, and brain stem was revealed. Structural brain network analysis revealed the alteration of the medial system of the pain-related brain network in chronic pain syndrome.
On some interconnections between combinatorial optimization and extremal graph theory
Cvetković Dragoš M.
2004-01-01
Full Text Available The uniting feature of combinatorial optimization and extremal graph theory is that in both areas one should find extrema of a function defined in most cases on a finite set. While in combinatorial optimization the point is in developing efficient algorithms and heuristics for solving specified types of problems, the extremal graph theory deals with finding bounds for various graph invariants under some constraints and with constructing extremal graphs. We analyze by examples some interconnections and interactions of the two theories and propose some conclusions.
Graph-based clustering and data visualization algorithms
Vathy-Fogarassy, Ágnes
2013-01-01
This work presents a data visualization technique that combines graph-based topology representation and dimensionality reduction methods to visualize the intrinsic data structure in a low-dimensional vector space. The application of graphs in clustering and visualization has several advantages. A graph of important edges (where edges characterize relations and weights represent similarities or distances) provides a compact representation of the entire complex data set. This text describes clustering and visualization methods that are able to utilize information hidden in these graphs, based on
Optimizing graph algorithms on pregel-like systems
Salihoglu, Semih
2014-03-01
We study the problem of implementing graph algorithms efficiently on Pregel-like systems, which can be surprisingly challenging. Standard graph algorithms in this setting can incur unnecessary inefficiencies such as slow convergence or high communication or computation cost, typically due to structural properties of the input graphs such as large diameters or skew in component sizes. We describe several optimization techniques to address these inefficiencies. Our most general technique is based on the idea of performing some serial computation on a tiny fraction of the input graph, complementing Pregel\\'s vertex-centric parallelism. We base our study on thorough implementations of several fundamental graph algorithms, some of which have, to the best of our knowledge, not been implemented on Pregel-like systems before. The algorithms and optimizations we describe are fully implemented in our open-source Pregel implementation. We present detailed experiments showing that our optimization techniques improve runtime significantly on a variety of very large graph datasets.
Generating Realistic Labelled, Weighted Random Graphs
Michael Charles Davis
2015-12-01
Full Text Available Generative algorithms for random graphs have yielded insights into the structure and evolution of real-world networks. Most networks exhibit a well-known set of properties, such as heavy-tailed degree distributions, clustering and community formation. Usually, random graph models consider only structural information, but many real-world networks also have labelled vertices and weighted edges. In this paper, we present a generative model for random graphs with discrete vertex labels and numeric edge weights. The weights are represented as a set of Beta Mixture Models (BMMs with an arbitrary number of mixtures, which are learned from real-world networks. We propose a Bayesian Variational Inference (VI approach, which yields an accurate estimation while keeping computation times tractable. We compare our approach to state-of-the-art random labelled graph generators and an earlier approach based on Gaussian Mixture Models (GMMs. Our results allow us to draw conclusions about the contribution of vertex labels and edge weights to graph structure.
Fundamentals of algebraic graph transformation
Ehrig, Hartmut; Prange, Ulrike; Taentzer, Gabriele
2006-01-01
Graphs are widely used to represent structural information in the form of objects and connections between them. Graph transformation is the rule-based manipulation of graphs, an increasingly important concept in computer science and related fields. This is the first textbook treatment of the algebraic approach to graph transformation, based on algebraic structures and category theory. Part I is an introduction to the classical case of graph and typed graph transformation. In Part II basic and advanced results are first shown for an abstract form of replacement systems, so-called adhesive high-level replacement systems based on category theory, and are then instantiated to several forms of graph and Petri net transformation systems. Part III develops typed attributed graph transformation, a technique of key relevance in the modeling of visual languages and in model transformation. Part IV contains a practical case study on model transformation and a presentation of the AGG (attributed graph grammar) tool envir...
The STAPL Parallel Graph Library
Harshvardhan,
2013-01-01
This paper describes the stapl Parallel Graph Library, a high-level framework that abstracts the user from data-distribution and parallelism details and allows them to concentrate on parallel graph algorithm development. It includes a customizable distributed graph container and a collection of commonly used parallel graph algorithms. The library introduces pGraph pViews that separate algorithm design from the container implementation. It supports three graph processing algorithmic paradigms, level-synchronous, asynchronous and coarse-grained, and provides common graph algorithms based on them. Experimental results demonstrate improved scalability in performance and data size over existing graph libraries on more than 16,000 cores and on internet-scale graphs containing over 16 billion vertices and 250 billion edges. © Springer-Verlag Berlin Heidelberg 2013.
Geodetic achievement and avoidance games for graphs | Haynes ...
Let G = (V,E) be a nontrivial connected graph. For a subset S ⊆ V, the geodesic closure (S) of S is the set of all vertices on geodesics (shortest paths) between two vertices of S. We study the geodetic achievement and avoidance games defined by Buckley and Harary (Geodetic games for graphs, Quaestiones Math.
On Merrifield-Simmons index of molecular graphs
Gutman Ivan
2016-01-01
Full Text Available The Merrifield-Simmons index σ = σ(G of a graph G is the number of independent vertex sets of G. This index can be calculated recursively and expressed in terms of Fibonacci numbers. We determine the molecular graphs for which σ can be recursively calculated in a single step.
Bipartite Diametrical Graphs of Diameter 4 and Extreme Orders
Salah Al-Addasi
2008-01-01
in which this upper bound is attained, this graph can be viewed as a generalization of the Rhombic Dodecahedron. Then we show that for any ≥2, the graph (2,2 is the unique (up to isomorphism bipartite diametrical graph of diameter 4 and partite sets of cardinalities 2 and 2, and hence in particular, for =3, the graph (6,8 which is just the Rhombic Dodecahedron is the unique (up to isomorphism bipartite diametrical graph of such a diameter and cardinalities of partite sets. Thus we complete a characterization of -graphs of diameter 4 and cardinality of the smaller partite set not exceeding 6. We prove that the neighborhoods of vertices of the larger partite set of (2,2 form a matroid whose basis graph is the hypercube . We prove that any -graph of diameter 4 is bipartite self complementary, thus in particular (2,2. Finally, we study some additional properties of (2,2 concerning the order of its automorphism group, girth, domination number, and when being Eulerian.
Wang, Jin-Hui; Zuo, Xi-Nian; Gohel, Suril; Milham, Michael P.; Biswal, Bharat B.; He, Yong
2011-01-01
Graph-based computational network analysis has proven a powerful tool to quantitatively characterize functional architectures of the brain. However, the test-retest (TRT) reliability of graph metrics of functional networks has not been systematically examined. Here, we investigated TRT reliability of topological metrics of functional brain networks derived from resting-state functional magnetic resonance imaging data. Specifically, we evaluated both short-term (5 months apart) TRT reliability for 12 global and 6 local nodal network metrics. We found that reliability of global network metrics was overall low, threshold-sensitive and dependent on several factors of scanning time interval (TI, long-term>short-term), network membership (NM, networks excluding negative correlations>networks including negative correlations) and network type (NT, binarized networks>weighted networks). The dependence was modulated by another factor of node definition (ND) strategy. The local nodal reliability exhibited large variability across nodal metrics and a spatially heterogeneous distribution. Nodal degree was the most reliable metric and varied the least across the factors above. Hub regions in association and limbic/paralimbic cortices showed moderate TRT reliability. Importantly, nodal reliability was robust to above-mentioned four factors. Simulation analysis revealed that global network metrics were extremely sensitive (but varying degrees) to noise in functional connectivity and weighted networks generated numerically more reliable results in compared with binarized networks. For nodal network metrics, they showed high resistance to noise in functional connectivity and no NT related differences were found in the resistance. These findings provide important implications on how to choose reliable analytical schemes and network metrics of interest. PMID:21818285
White, AT
1985-01-01
The field of topological graph theory has expanded greatly in the ten years since the first edition of this book appeared. The original nine chapters of this classic work have therefore been revised and updated. Six new chapters have been added, dealing with: voltage graphs, non-orientable imbeddings, block designs associated with graph imbeddings, hypergraph imbeddings, map automorphism groups and change ringing.Thirty-two new problems have been added to this new edition, so that there are now 181 in all; 22 of these have been designated as ``difficult'''' and 9 as ``unsolved''''. Three of the four unsolved problems from the first edition have been solved in the ten years between editions; they are now marked as ``difficult''''.
Ribes, Luis
2017-01-01
This book offers a detailed introduction to graph theoretic methods in profinite groups and applications to abstract groups. It is the first to provide a comprehensive treatment of the subject. The author begins by carefully developing relevant notions in topology, profinite groups and homology, including free products of profinite groups, cohomological methods in profinite groups, and fixed points of automorphisms of free pro-p groups. The final part of the book is dedicated to applications of the profinite theory to abstract groups, with sections on finitely generated subgroups of free groups, separability conditions in free and amalgamated products, and algorithms in free groups and finite monoids. Profinite Graphs and Groups will appeal to students and researchers interested in profinite groups, geometric group theory, graphs and connections with the theory of formal languages. A complete reference on the subject, the book includes historical and bibliographical notes as well as a discussion of open quest...
Subdominant pseudoultrametric on graphs
Dovgoshei, A A; Petrov, E A [Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, Donetsk (Ukraine)
2013-08-31
Let (G,w) be a weighted graph. We find necessary and sufficient conditions under which the weight w:E(G)→R{sup +} can be extended to a pseudoultrametric on V(G), and establish a criterion for the uniqueness of such an extension. We demonstrate that (G,w) is a complete k-partite graph, for k≥2, if and only if for any weight that can be extended to a pseudoultrametric, among all such extensions one can find the least pseudoultrametric consistent with w. We give a structural characterization of graphs for which the subdominant pseudoultrametric is an ultrametric for any strictly positive weight that can be extended to a pseudoultrametric. Bibliography: 14 titles.
Human factors and fuzzy set theory for safety analysis
Nishiwaki, Y.
1987-01-01
Human reliability and performance is affected by many factors: medical, physiological and psychological, etc. The uncertainty involved in human factors may not necessarily be probabilistic, but fuzzy. Therefore, it is important to develop a theory by which both the non-probabilistic uncertainties, or fuzziness, of human factors and the probabilistic properties of machines can be treated consistently. In reality, randomness and fuzziness are sometimes mixed. From the mathematical point of view, probabilistic measures may be considered a special case of fuzzy measures. Therefore, fuzzy set theory seems to be an effective tool for analysing man-machine systems. The concept 'failure possibility' based on fuzzy sets is suggested as an approach to safety analysis and fault diagnosis of a large complex system. Fuzzy measures and fuzzy integrals are introduced and their possible applications are also discussed. (author)
Analysis of Doppler effect with JAERI-Fast set
Takano, Hideki; Matsui, Yasushi.
1977-07-01
Temperature dependence of group cross sections in the JAERI-Fast set versions I, IR, II and IIR has been tested from the analysis of Doppler experiments performed with two different methods. One is Doppler reactivity measurement for the whole core of SEFOR assembly, and the other sample Doppler reactivity measurement for natural UO 2 in FCA assemblies V-1, V-2, VI-1 and VI-2, ZPR-6-7, ZPR-3-47, and ZPPR-2 and 3. Doppler effects were calculated with one- and two-dimensional diffusion 1-st order perturbation code DOPP2D. The results calculated with the JAERI-Fast set versions II and IIR are in good agreement with the experimental ones. In these calculation, resonance heterogeneity effect, stainless-stell buffer effect and plate heterogeneity effect are considered, and these effects contribute significantly to Doppler effect. (auth.)
Quantitative graph theory mathematical foundations and applications
Dehmer, Matthias
2014-01-01
The first book devoted exclusively to quantitative graph theory, Quantitative Graph Theory: Mathematical Foundations and Applications presents and demonstrates existing and novel methods for analyzing graphs quantitatively. Incorporating interdisciplinary knowledge from graph theory, information theory, measurement theory, and statistical techniques, this book covers a wide range of quantitative-graph theoretical concepts and methods, including those pertaining to real and random graphs such as:Comparative approaches (graph similarity or distance)Graph measures to characterize graphs quantitat
Dayal, Amit; Brock, David
2018-01-01
Prashant Chandrasekar, a lead developer for the Social Interactome project, has tasked the team with creating a graph representation of the data collected from the social networks involved in that project. The data is currently stored in a MySQL database. The client requested that the graph database be Cayley, but after a literature review, Neo4j was chosen. The reasons for this shift will be explained in the design section. Secondarily, the team was tasked with coming up with three scena...
Stevanovic, Dragan
2015-01-01
Spectral Radius of Graphs provides a thorough overview of important results on the spectral radius of adjacency matrix of graphs that have appeared in the literature in the preceding ten years, most of them with proofs, and including some previously unpublished results of the author. The primer begins with a brief classical review, in order to provide the reader with a foundation for the subsequent chapters. Topics covered include spectral decomposition, the Perron-Frobenius theorem, the Rayleigh quotient, the Weyl inequalities, and the Interlacing theorem. From this introduction, the
An analysis of strategic price setting in retail gasoline markets
Jaureguiberry, Florencia
This dissertation studies price-setting behavior in the retail gasoline industry. The main questions addressed are: How important is a retail station's brand and proximity to competitors when retail stations set price? How do retailers adjust their pricing when they cater to consumers who are less aware of competing options or have less discretion over where they purchase gasoline? These questions are explored in two separate analyses using a unique datasets containing retail pricing behavior of stations in California and in 24 different metropolitan areas. The evidence suggests that brand and location generate local market power for gasoline stations. After controlling for market and station characteristics, the analysis finds a spread of 11 cents per gallon between the highest and the lowest priced retail gasoline brands. The analysis also indicates that when the nearest competitor is located over 2 miles away as opposed to next door, consumers will pay an additional 1 cent per gallon of gasoline. In order to quantify the significance of local market power, data for stations located near major airport rental car locations are utilized. The presumption here is that rental car users are less aware or less sensitive to fueling options near the rental car return location and are to some extent "captured consumers". Retailers located near rental car locations have incentives to adjust their pricing strategies to exploit this. The analysis of pricing near rental car locations indicates that retailers charge prices that are 4 cent per gallon higher than other stations in the same metropolitan area. This analysis is of interest to regulators who are concerned with issues of consolidation, market power, and pricing in the retail gasoline industry. This dissertation concludes with a discussion of the policy implications of the empirical analysis.
Dynamic Matchings in Convex Bipartite Graphs
Brodal, Gerth Stølting; Georgiadis, Loukas; Hansen, Kristoffer Arnsfelt
2007-01-01
We consider the problem of maintaining a maximum matching in a convex bipartite graph G = (V,E) under a set of update operations which includes insertions and deletions of vertices and edges. It is not hard to show that it is impossible to maintain an explicit representation of a maximum matching...
Handbook of graph grammars and computing by graph transformation
Engels, G; Kreowski, H J; Rozenberg, G
1999-01-01
Graph grammars originated in the late 60s, motivated by considerations about pattern recognition and compiler construction. Since then, the list of areas which have interacted with the development of graph grammars has grown quite impressively. Besides the aforementioned areas, it includes software specification and development, VLSI layout schemes, database design, modeling of concurrent systems, massively parallel computer architectures, logic programming, computer animation, developmental biology, music composition, visual languages, and many others.The area of graph grammars and graph tran
Topics in graph theory graphs and their Cartesian product
Imrich, Wilfried; Rall, Douglas F
2008-01-01
From specialists in the field, you will learn about interesting connections and recent developments in the field of graph theory by looking in particular at Cartesian products-arguably the most important of the four standard graph products. Many new results in this area appear for the first time in print in this book. Written in an accessible way, this book can be used for personal study in advanced applications of graph theory or for an advanced graph theory course.
Graph theory and the Virasoro master equation
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) diag , which is a set of unitary, generically irrational affine-Virasoro constructions on SO(n), and the unlabeled graphs of order n. On the one hand, the conformal constructions, are classified by the graphs, while, conversely, a group-theoretic and conformal field-theoretic identification is obtained for every graph of graph theory. He also defines a class of magic Lie group bases in which the Virasoro master equation admits a simple metric ansatz {g metric }, whose structure is visible in the high-level expansion. When a magic basis is real on compact g, the corresponding g metric is a large system of unitary, generically irrational conformal field theories. Examples in this class include the graph-theory ansatz SO(n) diag in the Cartesian basis of SO(n), and the ansatz SU(n) 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) 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 metric
Radiological error: analysis, standard setting, targeted instruction and teamworking
FitzGerald, Richard
2005-01-01
Diagnostic radiology does not have objective benchmarks for acceptable levels of missed diagnoses [1]. Until now, data collection of radiological discrepancies has been very time consuming. The culture within the specialty did not encourage it. However, public concern about patient safety is increasing. There have been recent innovations in compiling radiological interpretive discrepancy rates which may facilitate radiological standard setting. However standard setting alone will not optimise radiologists' performance or patient safety. We must use these new techniques in radiological discrepancy detection to stimulate greater knowledge sharing, targeted instruction and teamworking among radiologists. Not all radiological discrepancies are errors. Radiological discrepancy programmes must not be abused as an instrument for discrediting individual radiologists. Discrepancy rates must not be distorted as a weapon in turf battles. Radiological errors may be due to many causes and are often multifactorial. A systems approach to radiological error is required. Meaningful analysis of radiological discrepancies and errors is challenging. Valid standard setting will take time. Meanwhile, we need to develop top-up training, mentoring and rehabilitation programmes. (orig.)
Parallel Algorithm for Incremental Betweenness Centrality on Large Graphs
Jamour, Fuad Tarek
2017-10-17
Betweenness centrality quantifies the importance of nodes in a graph in many applications, including network analysis, community detection and identification of influential users. Typically, graphs in such applications evolve over time. Thus, the computation of betweenness centrality should be performed incrementally. This is challenging because updating even a single edge may trigger the computation of all-pairs shortest paths in the entire graph. Existing approaches cannot scale to large graphs: they either require excessive memory (i.e., quadratic to the size of the input graph) or perform unnecessary computations rendering them prohibitively slow. We propose iCentral; a novel incremental algorithm for computing betweenness centrality in evolving graphs. We decompose the graph into biconnected components and prove that processing can be localized within the affected components. iCentral is the first algorithm to support incremental betweeness centrality computation within a graph component. This is done efficiently, in linear space; consequently, iCentral scales to large graphs. We demonstrate with real datasets that the serial implementation of iCentral is up to 3.7 times faster than existing serial methods. Our parallel implementation that scales to large graphs, is an order of magnitude faster than the state-of-the-art parallel algorithm, while using an order of magnitude less computational resources.
Distributed graph coloring fundamentals and recent developments
Barenboim, Leonid
2013-01-01
The focus of this monograph is on symmetry breaking problems in the message-passing model of distributed computing. In this model a communication network is represented by a n-vertex graph G = (V,E), whose vertices host autonomous processors. The processors communicate over the edges of G in discrete rounds. The goal is to devise algorithms that use as few rounds as possible.A typical symmetry-breaking problem is the problem of graph coloring. Denote by ? the maximum degree of G. While coloring G with ? + 1 colors is trivial in the centralized setting, the problem becomes much more challenging
Test bank for precalculus functions & graphs
Kolman, Bernard; Levitan, Michael L
1984-01-01
Test Bank for Precalculus: Functions & Graphs is a supplementary material for the text, Precalculus: Functions & Graphs. The book is intended for use by mathematics teachers.The book contains standard tests for each chapter in the textbook. Each set of test focuses on gauging the level of knowledge the student has achieved during the course. The answers for each chapter test and the final exam are found at the end of the book.Mathematics teachers teaching calculus will find the book extremely useful.
A fuzzy set preference model for market share analysis
Turksen, I. B.; Willson, Ian A.
1992-01-01
Consumer preference models are widely used in new product design, marketing management, pricing, and market segmentation. The success of new products depends on accurate market share prediction and design decisions based on consumer preferences. The vague linguistic nature of consumer preferences and product attributes, combined with the substantial differences between individuals, creates a formidable challenge to marketing models. The most widely used methodology is conjoint analysis. Conjoint models, as currently implemented, represent linguistic preferences as ratio or interval-scaled numbers, use only numeric product attributes, and require aggregation of individuals for estimation purposes. It is not surprising that these models are costly to implement, are inflexible, and have a predictive validity that is not substantially better than chance. This affects the accuracy of market share estimates. A fuzzy set preference model can easily represent linguistic variables either in consumer preferences or product attributes with minimal measurement requirements (ordinal scales), while still estimating overall preferences suitable for market share prediction. This approach results in flexible individual-level conjoint models which can provide more accurate market share estimates from a smaller number of more meaningful consumer ratings. Fuzzy sets can be incorporated within existing preference model structures, such as a linear combination, using the techniques developed for conjoint analysis and market share estimation. The purpose of this article is to develop and fully test a fuzzy set preference model which can represent linguistic variables in individual-level models implemented in parallel with existing conjoint models. The potential improvements in market share prediction and predictive validity can substantially improve management decisions about what to make (product design), for whom to make it (market segmentation), and how much to make (market share
Bisseling, R.H.; Byrka, J.; Cerav-Erbas, S.; Gvozdenovic, N.; Lorenz, M.; Pendavingh, R.A.; Reeves, C.; Röger, M.; Verhoeven, A.; Berg, van den J.B.; Bhulai, S.; Hulshof, J.; Koole, G.; Quant, C.; Williams, J.F.
2006-01-01
Splitting a large software system into smaller and more manageable units has become an important problem for many organizations. The basic structure of a software system is given by a directed graph with vertices representing the programs of the system and arcs representing calls from one program to
Coloring geographical threshold graphs
Bradonjic, Milan [Los Alamos National Laboratory; Percus, Allon [Los Alamos National Laboratory; Muller, Tobias [EINDHOVEN UNIV. OF TECH
2008-01-01
We propose a coloring algorithm for sparse random graphs generated by the geographical threshold graph (GTG) model, a generalization of random geometric graphs (RGG). In a GTG, nodes are distributed in a Euclidean space, and edges are assigned according to a threshold function involving the distance between nodes as well as randomly chosen node weights. The motivation for analyzing this model is that many real networks (e.g., wireless networks, the Internet, etc.) need to be studied by using a 'richer' stochastic model (which in this case includes both a distance between nodes and weights on the nodes). Here, we analyze the GTG coloring algorithm together with the graph's clique number, showing formally that in spite of the differences in structure between GTG and RGG, the asymptotic behavior of the chromatic number is identical: {chi}1n 1n n / 1n n (1 + {omicron}(1)). Finally, we consider the leading corrections to this expression, again using the coloring algorithm and clique number to provide bounds on the chromatic number. We show that the gap between the lower and upper bound is within C 1n n / (1n 1n n){sup 2}, and specify the constant C.
Budhiraja, A.S.; Mukherjee, D.; Wu, R.
2017-01-01
We consider a variation of the supermarket model in which the servers can communicate with their neighbors and where the neighborhood relationships are described in terms of a suitable graph. Tasks with unit-exponential service time distributions arrive at each vertex as independent Poisson
Kucharik, Marcel; Hofacker, Ivo; Stadler, Peter
2014-01-01
of the folding free energy landscape, however, can provide the relevant information. Results We introduce the basin hopping graph (BHG) as a novel coarse-grained model of folding landscapes. Each vertex of the BHG is a local minimum, which represents the corresponding basin in the landscape. Its edges connect...
Percolator: Scalable Pattern Discovery in Dynamic Graphs
Choudhury, Sutanay; Purohit, Sumit; Lin, Peng; Wu, Yinghui; Holder, Lawrence B.; Agarwal, Khushbu
2018-02-06
We demonstrate Percolator, a distributed system for graph pattern discovery in dynamic graphs. In contrast to conventional mining systems, Percolator advocates efficient pattern mining schemes that (1) support pattern detection with keywords; (2) integrate incremental and parallel pattern mining; and (3) support analytical queries such as trend analysis. The core idea of Percolator is to dynamically decide and verify a small fraction of patterns and their in- stances that must be inspected in response to buffered updates in dynamic graphs, with a total mining cost independent of graph size. We demonstrate a) the feasibility of incremental pattern mining by walking through each component of Percolator, b) the efficiency and scalability of Percolator over the sheer size of real-world dynamic graphs, and c) how the user-friendly GUI of Percolator inter- acts with users to support keyword-based queries that detect, browse and inspect trending patterns. We also demonstrate two user cases of Percolator, in social media trend analysis and academic collaboration analysis, respectively.
The STAPL Parallel Graph Library
Harshvardhan,; Fidel, Adam; Amato, Nancy M.; Rauchwerger, Lawrence
2013-01-01
This paper describes the stapl Parallel Graph Library, a high-level framework that abstracts the user from data-distribution and parallelism details and allows them to concentrate on parallel graph algorithm development. It includes a customizable
A local search for a graph clustering problem
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.
Multiplicative Attribute Graph Model of Real-World Networks
Kim, Myunghwan [Stanford Univ., CA (United States); Leskovec, Jure [Stanford Univ., CA (United States)
2010-10-20
Large scale real-world network data, such as social networks, Internet andWeb graphs, is ubiquitous in a variety of scientific domains. The study of such social and information networks commonly finds patterns and explain their emergence through tractable models. In most networks, especially in social networks, nodes also have a rich set of attributes (e.g., age, gender) associatedwith them. However, most of the existing network models focus only on modeling the network structure while ignoring the features of nodes in the network. Here we present a class of network models that we refer to as the Multiplicative Attribute Graphs (MAG), which naturally captures the interactions between the network structure and node attributes. We consider a model where each node has a vector of categorical features associated with it. The probability of an edge between a pair of nodes then depends on the product of individual attributeattribute similarities. The model yields itself to mathematical analysis as well as fit to real data. We derive thresholds for the connectivity, the emergence of the giant connected component, and show that the model gives rise to graphs with a constant diameter. Moreover, we analyze the degree distribution to show that the model can produce networks with either lognormal or power-law degree distribution depending on certain conditions.
Evaluating de Bruijn graph assemblers on 454 transcriptomic data.
Xianwen Ren
Full Text Available Next generation sequencing (NGS technologies have greatly changed the landscape of transcriptomic studies of non-model organisms. Since there is no reference genome available, de novo assembly methods play key roles in the analysis of these data sets. Because of the huge amount of data generated by NGS technologies for each run, many assemblers, e.g., ABySS, Velvet and Trinity, are developed based on a de Bruijn graph due to its time- and space-efficiency. However, most of these assemblers were developed initially for the Illumina/Solexa platform. The performance of these assemblers on 454 transcriptomic data is unknown. In this study, we evaluated and compared the relative performance of these de Bruijn graph based assemblers on both simulated and real 454 transcriptomic data. The results suggest that Trinity, the Illumina/Solexa-specialized transcriptomic assembler, performs the best among the multiple de Bruijn graph assemblers, comparable to or even outperforming the standard 454 assembler Newbler which is based on the overlap-layout-consensus algorithm. Our evaluation is expected to provide helpful guidance for researchers to choose assemblers when analyzing 454 transcriptomic data.
Herdable Systems Over Signed, Directed Graphs
Ruf, Sebastian F.
2018-04-11
This paper considers the notion of herdability, a set-based reachability condition, which asks whether the state of a system can be controlled to be element-wise larger than a non-negative threshold. The basic theory of herdable systems is presented, including a necessary and sufficient condition for herdability. This paper then considers the impact of the underlying graph structure of a linear system on the herdability of the system, for the case where the graph is represented as signed and directed. By classifying nodes based on the length and sign of walks from an input, we find a class of completely herdable systems as well as provide a complete characterization of nodes that can be herded in systems with an underlying graph that is a directed out-branching rooted at a single input.
Herdable Systems Over Signed, Directed Graphs
Ruf, Sebastian F.; Egerstedt, Magnus; Shamma, Jeff S.
2018-01-01
This paper considers the notion of herdability, a set-based reachability condition, which asks whether the state of a system can be controlled to be element-wise larger than a non-negative threshold. The basic theory of herdable systems is presented, including a necessary and sufficient condition for herdability. This paper then considers the impact of the underlying graph structure of a linear system on the herdability of the system, for the case where the graph is represented as signed and directed. By classifying nodes based on the length and sign of walks from an input, we find a class of completely herdable systems as well as provide a complete characterization of nodes that can be herded in systems with an underlying graph that is a directed out-branching rooted at a single input.
A note on arbitrarily vertex decomposable graphs
Antoni Marczyk
2006-01-01
Full Text Available A graph \\(G\\ of order \\(n\\ is said to be arbitrarily vertex decomposable if for each sequence \\((n_{1},\\ldots,n_k\\ of positive integers such that \\(n_{1}+\\ldots+n_{k}=n\\ there exists a partition \\((V_{1},\\ldots,V_{k}\\ of the vertex set of \\(G\\ such that for each \\(i \\in \\{1,\\ldots,k\\}\\, \\(V_{i}\\ induces a connected subgraph of \\(G\\ on \\(n_i\\ vertices. In this paper we show that if \\(G\\ is a two-connected graph on \\(n\\ vertices with the independence number at most \\(\\lceil n/2\\rceil\\ and such that the degree sum of any pair of non-adjacent vertices is at least \\(n-3\\, then \\(G\\ is arbitrarily vertex decomposable. We present another result for connected graphs satisfying a similar condition, where the bound \\(n-3\\ is replaced by \\(n-2\\.
MOCUS, Minimal Cut Sets and Minimal Path Sets from Fault Tree Analysis
Fussell, J.B.; Henry, E.B.; Marshall, N.H.
1976-01-01
1 - Description of problem or function: From a description of the Boolean failure logic of a system, called a fault tree, and control parameters specifying the minimal cut set length to be obtained MOCUS determines the system failure modes, or minimal cut sets, and the system success modes, or minimal path sets. 2 - Method of solution: MOCUS uses direct resolution of the fault tree into the cut and path sets. The algorithm used starts with the main failure of interest, the top event, and proceeds to basic independent component failures, called primary events, to resolve the fault tree to obtain the minimal sets. A key point of the algorithm is that an and gate alone always increases the number of path sets; an or gate alone always increases the number of cut sets and increases the size of path sets. Other types of logic gates must be described in terms of and and or logic gates. 3 - Restrictions on the complexity of the problem: Output from MOCUS can include minimal cut and path sets for up to 20 gates
Groupies in multitype random graphs
Shang, Yilun
2016-01-01
A groupie in a graph is a vertex whose degree is not less than the average degree of its neighbors. Under some mild conditions, we show that the proportion of groupies is very close to 1/2 in multitype random graphs (such as stochastic block models), which include Erd?s-R?nyi random graphs, random bipartite, and multipartite graphs as special examples. Numerical examples are provided to illustrate the theoretical results.
Groupies in multitype random graphs.
Shang, Yilun
2016-01-01
A groupie in a graph is a vertex whose degree is not less than the average degree of its neighbors. Under some mild conditions, we show that the proportion of groupies is very close to 1/2 in multitype random graphs (such as stochastic block models), which include Erdős-Rényi random graphs, random bipartite, and multipartite graphs as special examples. Numerical examples are provided to illustrate the theoretical results.
Quantum walks on quotient graphs
Krovi, Hari; Brun, Todd A.
2007-01-01
A discrete-time quantum walk on a graph Γ is the repeated application of a unitary evolution operator to a Hilbert space corresponding to the graph. If this unitary evolution operator has an associated group of symmetries, then for certain initial states the walk will be confined to a subspace of the original Hilbert space. Symmetries of the original graph, given by its automorphism group, can be inherited by the evolution operator. We show that a quantum walk confined to the subspace corresponding to this symmetry group can be seen as a different quantum walk on a smaller quotient graph. We give an explicit construction of the quotient graph for any subgroup H of the automorphism group and illustrate it with examples. The automorphisms of the quotient graph which are inherited from the original graph are the original automorphism group modulo the subgroup H used to construct it. The quotient graph is constructed by removing the symmetries of the subgroup H from the original graph. We then analyze the behavior of hitting times on quotient graphs. Hitting time is the average time it takes a walk to reach a given final vertex from a given initial vertex. It has been shown in earlier work [Phys. Rev. A 74, 042334 (2006)] that the hitting time for certain initial states of a quantum walks can be infinite, in contrast to classical random walks. We give a condition which determines whether the quotient graph has infinite hitting times given that they exist in the original graph. We apply this condition for the examples discussed and determine which quotient graphs have infinite hitting times. All known examples of quantum walks with hitting times which are short compared to classical random walks correspond to systems with quotient graphs much smaller than the original graph; we conjecture that the existence of a small quotient graph with finite hitting times is necessary for a walk to exhibit a quantum speedup
Obtaining a minimal set of rewrite rules
Davel, M
2005-11-01
Full Text Available In this paper the authors describe a new approach to rewrite rule extraction and analysis, using Minimal Representation Graphs. This approach provides a mechanism for obtaining the smallest possible rule set – within a context-dependent rewrite rule...
Incremental Frequent Subgraph Mining on Large Evolving Graphs
Abdelhamid, Ehab
2017-08-22
Frequent subgraph mining is a core graph operation used in many domains, such as graph data management and knowledge exploration, bioinformatics and security. Most existing techniques target static graphs. However, modern applications, such as social networks, utilize large evolving graphs. Mining these graphs using existing techniques is infeasible, due to the high computational cost. In this paper, we propose IncGM+, a fast incremental approach for continuous frequent subgraph mining problem on a single large evolving graph. We adapt the notion of “fringe” to the graph context, that is the set of subgraphs on the border between frequent and infrequent subgraphs. IncGM+ maintains fringe subgraphs and exploits them to prune the search space. To boost the efficiency, we propose an efficient index structure to maintain selected embeddings with minimal memory overhead. These embeddings are utilized to avoid redundant expensive subgraph isomorphism operations. Moreover, the proposed system supports batch updates. Using large real-world graphs, we experimentally verify that IncGM+ outperforms existing methods by up to three orders of magnitude, scales to much larger graphs and consumes less memory.
Visualization of Morse connection graphs for topologically rich 2D vector fields.
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.
A graph-based approach to detect spatiotemporal dynamics in satellite image time series
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.
Transduction on Directed Graphs via Absorbing Random Walks.
De, Jaydeep; Zhang, Xiaowei; Lin, Feng; Cheng, Li
2017-08-11
In this paper we consider the problem of graph-based transductive classification, and we are particularly interested in the directed graph scenario which is a natural form for many real world applications.Different from existing research efforts that either only deal with undirected graphs or circumvent directionality by means of symmetrization, we propose a novel random walk approach on directed graphs using absorbing Markov chains, which can be regarded as maximizing the accumulated expected number of visits from the unlabeled transient states. Our algorithm is simple, easy to implement, and works with large-scale graphs on binary, multiclass, and multi-label prediction problems. Moreover, it is capable of preserving the graph structure even when the input graph is sparse and changes over time, as well as retaining weak signals presented in the directed edges. We present its intimate connections to a number of existing methods, including graph kernels, graph Laplacian based methods, and interestingly, spanning forest of graphs. Its computational complexity and the generalization error are also studied. Empirically our algorithm is systematically evaluated on a wide range of applications, where it has shown to perform competitively comparing to a suite of state-of-the-art methods. In particular, our algorithm is shown to work exceptionally well with large sparse directed graphs with e.g. millions of nodes and tens of millions of edges, where it significantly outperforms other state-of-the-art methods. In the dynamic graph setting involving insertion or deletion of nodes and edge-weight changes over time, it also allows efficient online updates that produce the same results as of the batch update counterparts.
Hierarchical graphs for rule-based modeling of biochemical systems
Hu Bin
2011-02-01
Full Text Available Abstract 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
The partition dimension of cycle books graph
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.
A generalization of total graphs
M Afkhami
2018-04-12
Apr 12, 2018 ... product of any lower triangular matrix with the transpose of any element of U belongs to U. The ... total graph of R, which is denoted by T( (R)), is a simple graph with all elements of R as vertices, and ...... [9] Badawi A, On dot-product graph of a commutative ring, Communications in Algebra 43 (2015). 43–50.
Graph transformation tool contest 2008
Rensink, Arend; van Gorp, Pieter
This special section is the outcome of the graph transformation tool contest organised during the Graph-Based Tools (GraBaTs) 2008 workshop, which took place as a satellite event of the International Conference on Graph Transformation (ICGT) 2008. The contest involved two parts: three “off-line case
On dominator colorings in graphs
colors required for a dominator coloring of G is called the dominator .... Theorem 1.3 shows that the complete graph Kn is the only connected graph of order n ... Conversely, if a graph G satisfies condition (i) or (ii), it is easy to see that χd(G) =.
Xuan, Junyu; Lu, Jie; Zhang, Guangquan; Luo, Xiangfeng
2015-12-01
Graph mining has been a popular research area because of its numerous application scenarios. Many unstructured and structured data can be represented as graphs, such as, documents, chemical molecular structures, and images. However, an issue in relation to current research on graphs is that they cannot adequately discover the topics hidden in graph-structured data which can be beneficial for both the unsupervised learning and supervised learning of the graphs. Although topic models have proved to be very successful in discovering latent topics, the standard topic models cannot be directly applied to graph-structured data due to the "bag-of-word" assumption. In this paper, an innovative graph topic model (GTM) is proposed to address this issue, which uses Bernoulli distributions to model the edges between nodes in a graph. It can, therefore, make the edges in a graph contribute to latent topic discovery and further improve the accuracy of the supervised and unsupervised learning of graphs. The experimental results on two different types of graph datasets show that the proposed GTM outperforms the latent Dirichlet allocation on classification by using the unveiled topics of these two models to represent graphs.
Distance 2-Domination in Prisms of Graphs
Hurtado Ferran
2017-05-01
Full Text Available A set of vertices D of a graph G is a distance 2-dominating set of G if the distance between each vertex u ∊ (V (G − D and D is at most two. Let γ2(G denote the size of a smallest distance 2-dominating set of G. For any permutation π of the vertex set of G, the prism of G with respect to π is the graph πG obtained from G and a copy G′ of G by joining u ∊ V(G with v′ ∊ V(G′ if and only if v′ = π(u. If γ2(πG = γ2(G for any permutation π of V(G, then G is called a universal γ2-fixer. In this work we characterize the cycles and paths that are universal γ2-fixers.
Clark, Neil R; Szymkiewicz, Maciej; Wang, Zichen; Monteiro, Caroline D; Jones, Matthew R; Ma'ayan, Avi
2015-11-01
Gene set analysis of differential expression, which identifies collectively differentially expressed gene sets, has become an important tool for biology. The power of this approach lies in its reduction of the dimensionality of the statistical problem and its incorporation of biological interpretation by construction. Many approaches to gene set analysis have been proposed, but benchmarking their performance in the setting of real biological data is difficult due to the lack of a gold standard. In a previously published work we proposed a geometrical approach to differential expression which performed highly in benchmarking tests and compared well to the most popular methods of differential gene expression. As reported, this approach has a natural extension to gene set analysis which we call Principal Angle Enrichment Analysis (PAEA). PAEA employs dimensionality reduction and a multivariate approach for gene set enrichment analysis. However, the performance of this method has not been assessed nor its implementation as a web-based tool. Here we describe new benchmarking protocols for gene set analysis methods and find that PAEA performs highly. The PAEA method is implemented as a user-friendly web-based tool, which contains 70 gene set libraries and is freely available to the community.
An internet graph model based on trade-off optimization
Alvarez-Hamelin, J. I.; Schabanel, N.
2004-03-01
This paper presents a new model for the Internet graph (AS graph) based on the concept of heuristic trade-off optimization, introduced by Fabrikant, Koutsoupias and Papadimitriou in[CITE] to grow a random tree with a heavily tailed degree distribution. We propose here a generalization of this approach to generate a general graph, as a candidate for modeling the Internet. We present the results of our simulations and an analysis of the standard parameters measured in our model, compared with measurements from the physical Internet graph.
Engineering design and analysis of Indian LLCB TBM set
Ranjithkumar, S., E-mail: ranjith@ipr.res.in [Institute for Plasma Research, Bhat, Gandhinagar 382428, Gujarat (India); Sharma, Deepak; Chaudhuri, Paritosh; Danani, Chandan; Kumar, E. Rajendra [Institute for Plasma Research, Bhat, Gandhinagar 382428, Gujarat (India); Khan, Istiyak; Bhattacharya, Sujay; Vyas, K.N. [Bhabha Atomic Research Centre, Trombay, Mumbai 400085 (India)
2016-11-01
India is developing Lead Lithium cooled Ceramic Breeder (LLCB) Test Blanket Module (TBM) for testing in ITER for the validation of fusion blanket design tools, tritium breeding performance and high grade heat extraction capability relevant to Indian DEMO. LLCB TBM is designed to withstand various ITER loads and its combinations, like thermal, mechanical including the high pressure coolant loads, electromagnetic loads during plasma disruption and seismic loading conditions. LLCB TBM system is designed in compliance with ITER Safety requirements and guidelines. A few challenging part in the design includes the design of helium cooled First Wall (FW) and back plates, the attachment system between TBM and the shield block to withstand loads for all the ITER operational modes, routing of high temperature process pipes between TBM and the shield block, interfaces between process pipes and the connecting flange, design of manifolds of different process fluids etc. Analysis has been performed on the LLCB TBM set using a Finite Element code, ANSYS. Relevant codes and standards, namely the French code RCC-MR, has been followed for the design analysis. The details of the analysis and further plans and proposals for improvement in design will be discussed in this paper.
Algorithms for Planar Graphs and Graphs in Metric Spaces
Wulff-Nilsen, Christian
structural properties that can be exploited. For instance, a road network or a wire layout on a microchip is typically (near-)planar and distances in the network are often defined w.r.t. the Euclidean or the rectilinear metric. Specialized algorithms that take advantage of such properties are often orders...... of magnitude faster than the corresponding algorithms for general graphs. The first and main part of this thesis focuses on the development of efficient planar graph algorithms. The most important contributions include a faster single-source shortest path algorithm, a distance oracle with subquadratic...... for geometric graphs and graphs embedded in metric spaces. Roughly speaking, the stretch factor is a real value expressing how well a (geo-)metric graph approximates the underlying complete graph w.r.t. distances. We give improved algorithms for computing the stretch factor of a given graph and for augmenting...
Analysis method set up to check against adulterated export honey
Lyon, G.L.
2001-01-01
Over the past few years, North America has experienced occasional problems with the adulteration of honey, mainly by additions of other, cheaper sugar to increase bulk and lower production costs. The main addition was usually high fructose corn syrup, which had a similar chemical composition to that of honey. As a consequence of this type of adulteration, a method for its detection was developed using isotope ratio mass spectroscopy (IRMS). This was later refined to be more sensitive and is now specified as an Official Test. The Institute of Geological and Nuclear Sciences has now set up the analysis method to the international criteria at the Rafter Stable Isotope Laboratory in Lower Hutt. 2 refs
Harary, Frank
2015-01-01
Presented in 1962-63 by experts at University College, London, these lectures offer a variety of perspectives on graph theory. Although the opening chapters form a coherent body of graph theoretic concepts, this volume is not a text on the subject but rather an introduction to the extensive literature of graph theory. The seminar's topics are geared toward advanced undergraduate students of mathematics.Lectures by this volume's editor, Frank Harary, include ""Some Theorems and Concepts of Graph Theory,"" ""Topological Concepts in Graph Theory,"" ""Graphical Reconstruction,"" and other introduc
Spectral fluctuations of quantum graphs
Pluhař, Z.; Weidenmüller, H. A.
2014-01-01
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
Dynamic Representations of Sparse Graphs
Brodal, Gerth Stølting; Fagerberg, Rolf
1999-01-01
We present a linear space data structure for maintaining graphs with bounded arboricity—a large class of sparse graphs containing e.g. planar graphs and graphs of bounded treewidth—under edge insertions, edge deletions, and adjacency queries. The data structure supports adjacency queries in worst...... case O(c) time, and edge insertions and edge deletions in amortized O(1) and O(c+log n) time, respectively, where n is the number of nodes in the graph, and c is the bound on the arboricity....
Graph Creation, Visualisation and Transformation
Maribel Fernández
2010-03-01
Full Text Available We describe a tool to create, edit, visualise and compute with interaction nets - a form of graph rewriting systems. The editor, called GraphPaper, allows users to create and edit graphs and their transformation rules using an intuitive user interface. The editor uses the functionalities of the TULIP system, which gives us access to a wealth of visualisation algorithms. Interaction nets are not only a formalism for the specification of graphs, but also a rewrite-based computation model. We discuss graph rewriting strategies and a language to express them in order to perform strategic interaction net rewriting.
Study of Chromatic parameters of Line, Total, Middle graphs and Graph operators of Bipartite graph
Nagarathinam, R.; Parvathi, N.
2018-04-01
Chromatic parameters have been explored on the basis of graph coloring process in which a couple of adjacent nodes receives different colors. But the Grundy and b-coloring executes maximum colors under certain restrictions. In this paper, Chromatic, b-chromatic and Grundy number of some graph operators of bipartite graph has been investigat