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

PubMed Central

Plaku, Erion; Kavraki, Lydia E.

2009-01-01

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

Graphs, matrices, and the GraphBLAS: Seven good reasons

DOE PAGES

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

2015-01-01

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

Phosphorylation of PPP(S/T)P motif of the free LRP6 intracellular domain is not required to activate the Wnt/beta-catenin pathway and attenuate GSK3beta activity.

PubMed

Beagle, Brandon; Mi, Kaihong; Johnson, Gail V W

2009-11-01

The canonical Wnt/beta-catenin signaling pathway plays a critical role in numerous physiological and pathological processes. LRP6 is an essential co-receptor for Wnt/beta-catenin signaling; as transduction of the Wnt signal is strongly dependent upon GSK3beta-mediated phosphorylation of multiple PPP(S/T)P motifs within the membrane-anchored LRP6 intracellular domain. Previously, we showed that the free LRP6 intracellular domain (LRP6-ICD) can activate the Wnt/beta-catenin pathway in a beta-catenin and TCF/LEF-1 dependent manner, as well as interact with and attenuate GSK3beta activity. However, it is unknown if the ability of LRP6-ICD to attenuate GSK3beta activity and modulate activation of the Wnt/beta-catenin pathway requires phosphorylation of the LRP6-ICD PPP(S/T)P motifs, in a manner similar to the membrane-anchored LRP6 intracellular domain. Here we provide evidence that the LRP6-ICD does not have to be phosphorylated at its PPP(S/T)P motif by GSK3beta to stabilize endogenous cytosolic beta-catenin resulting in activation of TCF/LEF-1 and the Wnt/beta-catenin pathway. LRP6-ICD and a mutant in which all 5 PPP(S/T)P motifs were changed to PPP(A)P motifs equivalently interacted with and attenuated GSK3beta activity in vitro, and both constructs inhibited the in situ GSK3beta-mediated phosphorylation of beta-catenin and tau to the same extent. These data indicate that the LRP6-ICD attenuates GSK3beta activity similar to other GSK3beta binding proteins, and is not a result of it being a GSK3beta substrate. Our findings suggest the functional and regulatory mechanisms governing the free LRP6-ICD may be distinct from membrane-anchored LRP6, and that release of the LRP6-ICD may provide a complimentary signaling cascade capable of modulating Wnt-dependent gene expression. (c) 2009 Wiley-Liss, Inc.

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

PubMed

Blin, Guillaume; Sikora, Florian; Vialette, Stéphane

2010-01-01

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

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

ERIC Educational Resources Information Center

Deskins, W. E.; And Others

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

CompariMotif: quick and easy comparisons of sequence motifs.

PubMed

Edwards, Richard J; Davey, Norman E; Shields, Denis C

2008-05-15

CompariMotif is a novel tool for making motif-motif comparisons, identifying and describing similarities between regular expression motifs. CompariMotif can identify a number of different relationships between motifs, including exact matches, variants of degenerate motifs and complex overlapping motifs. Motif relationships are scored using shared information content, allowing the best matches to be easily identified in large comparisons. Many input and search options are available, enabling a list of motifs to be compared to itself (to identify recurring motifs) or to datasets of known motifs. CompariMotif can be run online at http://bioware.ucd.ie/ and is freely available for academic use as a set of open source Python modules under a GNU General Public License from http://bioinformatics.ucd.ie/shields/software/comparimotif/

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

PubMed Central

Elmetwaly, Shereef; Schlick, Tamar

2014-01-01

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

Mapping the distribution of packing topologies within protein interiors shows predominant preference for specific packing motifs

PubMed Central

2011-01-01

Background Mapping protein primary sequences to their three dimensional folds referred to as the 'second genetic code' remains an unsolved scientific problem. A crucial part of the problem concerns the geometrical specificity in side chain association leading to densely packed protein cores, a hallmark of correctly folded native structures. Thus, any model of packing within proteins should constitute an indispensable component of protein folding and design. Results In this study an attempt has been made to find, characterize and classify recurring patterns in the packing of side chain atoms within a protein which sustains its native fold. The interaction of side chain atoms within the protein core has been represented as a contact network based on the surface complementarity and overlap between associating side chain surfaces. Some network topologies definitely appear to be preferred and they have been termed 'packing motifs', analogous to super secondary structures in proteins. Study of the distribution of these motifs reveals the ubiquitous presence of typical smaller graphs, which appear to get linked or coalesce to give larger graphs, reminiscent of the nucleation-condensation model in protein folding. One such frequently occurring motif, also envisaged as the unit of clustering, the three residue clique was invariably found in regions of dense packing. Finally, topological measures based on surface contact networks appeared to be effective in discriminating sequences native to a specific fold amongst a set of decoys. Conclusions Out of innumerable topological possibilities, only a finite number of specific packing motifs are actually realized in proteins. This small number of motifs could serve as a basis set in the construction of larger networks. Of these, the triplet clique exhibits distinct preference both in terms of composition and geometry. PMID:21605466

Modification of Prim’s algorithm on complete broadcasting graph

NASA Astrophysics Data System (ADS)

Dairina; Arif, Salmawaty; Munzir, Said; Halfiani, Vera; Ramli, Marwan

2017-09-01

Broadcasting is an information dissemination from one object to another object through communication between two objects in a network. Broadcasting for n objects can be solved by n - 1 communications and minimum time unit defined by ⌈2log n⌉ In this paper, weighted graph broadcasting is considered. The minimum weight of a complete broadcasting graph will be determined. Broadcasting graph is said to be complete if every vertex is connected. Thus to determine the minimum weight of complete broadcasting graph is equivalent to determine the minimum spanning tree of a complete graph. The Kruskal’s and Prim’s algorithm will be used to determine the minimum weight of a complete broadcasting graph regardless the minimum time unit ⌈2log n⌉ and modified Prim’s algorithm for the problems of the minimum time unit ⌈2log n⌉ is done. As an example case, here, the training of trainer problem is solved using these algorithms.

Well-Covered Graphs: A Survey

DTIC Science & Technology

1991-01-01

critical G’s/# G’s -) 0 as IV(G)I -- oo? References [B1] C. Berge, Regularizable graphs, Ann. Discrete Math ., 3, 1978, 11-19. [B2] _ _, Some common...Springer-Verlag, Berlin, 1980, 108-123. [B3] _ _, Some common properties for regularizable graphs, edge-critical graphs, and B-graphs, Ann. Discrete Math ., 12...graphs - an extension of the K6nig-Egervgiry theorem, Discrete Math ., 27, 1979, 23-33. [ER] M.N Ellingham and G.F. Royle, Well-covered cubic graphs

A proximity-based graph clustering method for the identification and application of transcription factor clusters.

PubMed

Spadafore, Maxwell; Najarian, Kayvan; Boyle, Alan P

2017-11-29

Transcription factors (TFs) form a complex regulatory network within the cell that is crucial to cell functioning and human health. While methods to establish where a TF binds to DNA are well established, these methods provide no information describing how TFs interact with one another when they do bind. TFs tend to bind the genome in clusters, and current methods to identify these clusters are either limited in scope, unable to detect relationships beyond motif similarity, or not applied to TF-TF interactions. Here, we present a proximity-based graph clustering approach to identify TF clusters using either ChIP-seq or motif search data. We use TF co-occurrence to construct a filtered, normalized adjacency matrix and use the Markov Clustering Algorithm to partition the graph while maintaining TF-cluster and cluster-cluster interactions. We then apply our graph structure beyond clustering, using it to increase the accuracy of motif-based TFBS searching for an example TF. We show that our method produces small, manageable clusters that encapsulate many known, experimentally validated transcription factor interactions and that our method is capable of capturing interactions that motif similarity methods might miss. Our graph structure is able to significantly increase the accuracy of motif TFBS searching, demonstrating that the TF-TF connections within the graph correlate with biological TF-TF interactions. The interactions identified by our method correspond to biological reality and allow for fast exploration of TF clustering and regulatory dynamics.

Distance Domination Number of Graphs Resulting from Edge Comb Product

NASA Astrophysics Data System (ADS)

Slamin; Dafik; Angger Waspodo, Gembong

2018-05-01

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

MOTIFSIM 2.1: An Enhanced Software Platform for Detecting Similarity in Multiple DNA Motif Data Sets

PubMed Central

Huang, Chun-Hsi

2017-01-01

Abstract Finding binding site motifs plays an important role in bioinformatics as it reveals the transcription factors that control the gene expression. The development for motif finders has flourished in the past years with many tools have been introduced to the research community. Although these tools possess exceptional features for detecting motifs, they report different results for an identical data set. Hence, using multiple tools is recommended because motifs reported by several tools are likely biologically significant. However, the results from multiple tools need to be compared for obtaining common significant motifs. MOTIFSIM web tool and command-line tool were developed for this purpose. In this work, we present several technical improvements as well as additional features to further support the motif analysis in our new release MOTIFSIM 2.1. PMID:28632401

The DRF motif of CXCR6 as chemokine receptor adaptation to adhesion.

PubMed

Koenen, Andrea; Babendreyer, Aaron; Schumacher, Julian; Pasqualon, Tobias; Schwarz, Nicole; Seifert, Anke; Deupi, Xavier; Ludwig, Andreas; Dreymueller, Daniela

2017-01-01

The CXC-chemokine receptor 6 (CXCR6) is a class A GTP-binding protein-coupled receptor (GPCRs) that mediates adhesion of leukocytes by interacting with the transmembrane cell surface-expressed chemokine ligand 16 (CXCL16), and also regulates leukocyte migration by interacting with the soluble shed variant of CXCL16. In contrast to virtually all other chemokine receptors with chemotactic activity, CXCR6 carries a DRF motif instead of the typical DRY motif as a key element in receptor activation and G protein coupling. In this work, modeling analyses revealed that the phenylalanine F3.51 in CXCR6 might have impact on intramolecular interactions including hydrogen bonds by this possibly changing receptor function. Initial investigations with embryonic kidney HEK293 cells and further studies with monocytic THP-1 cells showed that mutation of DRF into DRY does not influence ligand binding, receptor internalization, receptor recycling, and protein kinase B (AKT) signaling. Adhesion was slightly decreased in a time-dependent manner. However, CXCL16-induced calcium signaling and migration were increased. Vice versa, when the DRY motif of the related receptor CX3CR1 was mutated into DRF the migratory response towards CX3CL1 was diminished, indicating that the presence of a DRF motif generally impairs chemotaxis in chemokine receptors. Transmembrane and soluble CXCL16 play divergent roles in homeostasis, inflammation, and cancer, which can be beneficial or detrimental. Therefore, the DRF motif of CXCR6 may display a receptor adaptation allowing adhesion and cell retention by transmembrane CXCL16 but reducing the chemotactic response to soluble CXCL16. This adaptation may avoid permanent or uncontrolled recruitment of inflammatory cells as well as cancer metastasis.

Trend Motif: A Graph Mining Approach for Analysis of Dynamic Complex Networks

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

Jin, R; McCallen, S; Almaas, E

2007-05-28

Complex networks have been used successfully in scientific disciplines ranging from sociology to microbiology to describe systems of interacting units. Until recently, studies of complex networks have mainly focused on their network topology. However, in many real world applications, the edges and vertices have associated attributes that are frequently represented as vertex or edge weights. Furthermore, these weights are often not static, instead changing with time and forming a time series. Hence, to fully understand the dynamics of the complex network, we have to consider both network topology and related time series data. In this work, we propose a motifmore » mining approach to identify trend motifs for such purposes. Simply stated, a trend motif describes a recurring subgraph where each of its vertices or edges displays similar dynamics over a userdefined period. Given this, each trend motif occurrence can help reveal significant events in a complex system; frequent trend motifs may aid in uncovering dynamic rules of change for the system, and the distribution of trend motifs may characterize the global dynamics of the system. Here, we have developed efficient mining algorithms to extract trend motifs. Our experimental validation using three disparate empirical datasets, ranging from the stock market, world trade, to a protein interaction network, has demonstrated the efficiency and effectiveness of our approach.« less

A novel swarm intelligence algorithm for finding DNA motifs.

PubMed

Lei, Chengwei; Ruan, Jianhua

2009-01-01

Discovering DNA motifs from co-expressed or co-regulated genes is an important step towards deciphering complex gene regulatory networks and understanding gene functions. Despite significant improvement in the last decade, it still remains one of the most challenging problems in computational molecular biology. In this work, we propose a novel motif finding algorithm that finds consensus patterns using a population-based stochastic optimisation technique called Particle Swarm Optimisation (PSO), which has been shown to be effective in optimising difficult multidimensional problems in continuous domains. We propose to use a word dissimilarity graph to remap the neighborhood structure of the solution space of DNA motifs, and propose a modification of the naive PSO algorithm to accommodate discrete variables. In order to improve efficiency, we also propose several strategies for escaping from local optima and for automatically determining the termination criteria. Experimental results on simulated challenge problems show that our method is both more efficient and more accurate than several existing algorithms. Applications to several sets of real promoter sequences also show that our approach is able to detect known transcription factor binding sites, and outperforms two of the most popular existing algorithms.

The DRF motif of CXCR6 as chemokine receptor adaptation to adhesion

PubMed Central

Koenen, Andrea; Babendreyer, Aaron; Schumacher, Julian; Pasqualon, Tobias; Schwarz, Nicole; Seifert, Anke; Deupi, Xavier

2017-01-01

The CXC-chemokine receptor 6 (CXCR6) is a class A GTP-binding protein-coupled receptor (GPCRs) that mediates adhesion of leukocytes by interacting with the transmembrane cell surface-expressed chemokine ligand 16 (CXCL16), and also regulates leukocyte migration by interacting with the soluble shed variant of CXCL16. In contrast to virtually all other chemokine receptors with chemotactic activity, CXCR6 carries a DRF motif instead of the typical DRY motif as a key element in receptor activation and G protein coupling. In this work, modeling analyses revealed that the phenylalanine F3.51 in CXCR6 might have impact on intramolecular interactions including hydrogen bonds by this possibly changing receptor function. Initial investigations with embryonic kidney HEK293 cells and further studies with monocytic THP-1 cells showed that mutation of DRF into DRY does not influence ligand binding, receptor internalization, receptor recycling, and protein kinase B (AKT) signaling. Adhesion was slightly decreased in a time-dependent manner. However, CXCL16-induced calcium signaling and migration were increased. Vice versa, when the DRY motif of the related receptor CX3CR1 was mutated into DRF the migratory response towards CX3CL1 was diminished, indicating that the presence of a DRF motif generally impairs chemotaxis in chemokine receptors. Transmembrane and soluble CXCL16 play divergent roles in homeostasis, inflammation, and cancer, which can be beneficial or detrimental. Therefore, the DRF motif of CXCR6 may display a receptor adaptation allowing adhesion and cell retention by transmembrane CXCL16 but reducing the chemotactic response to soluble CXCL16. This adaptation may avoid permanent or uncontrolled recruitment of inflammatory cells as well as cancer metastasis. PMID:28267793

Probabilistic generation of random networks taking into account information on motifs occurrence.

PubMed

Bois, Frederic Y; Gayraud, Ghislaine

2015-01-01

Because of the huge number of graphs possible even with a small number of nodes, inference on network structure is known to be a challenging problem. Generating large random directed graphs with prescribed probabilities of occurrences of some meaningful patterns (motifs) is also difficult. We show how to generate such random graphs according to a formal probabilistic representation, using fast Markov chain Monte Carlo methods to sample them. As an illustration, we generate realistic graphs with several hundred nodes mimicking a gene transcription interaction network in Escherichia coli.

Probabilistic Generation of Random Networks Taking into Account Information on Motifs Occurrence

PubMed Central

Bois, Frederic Y.

2015-01-01

Abstract Because of the huge number of graphs possible even with a small number of nodes, inference on network structure is known to be a challenging problem. Generating large random directed graphs with prescribed probabilities of occurrences of some meaningful patterns (motifs) is also difficult. We show how to generate such random graphs according to a formal probabilistic representation, using fast Markov chain Monte Carlo methods to sample them. As an illustration, we generate realistic graphs with several hundred nodes mimicking a gene transcription interaction network in Escherichia coli. PMID:25493547

Unitary circular code motifs in genomes of eukaryotes.

PubMed

El Soufi, Karim; Michel, Christian J

A set X of 20 trinucleotides was identified in genes of bacteria, eukaryotes, plasmids and viruses, which has in average the highest occurrence in reading frame compared to its two shifted frames (Michel, 2015; Arquès and Michel, 1996). This set X has an interesting mathematical property as X is a circular code (Arquès and Michel, 1996). Thus, the motifs from this circular code X, called X motifs, have the property to always retrieve, synchronize and maintain the reading frame in genes. The origin of this circular code X in genes is an open problem since its discovery in 1996. Here, we first show that the unitary circular codes (UCC), i.e. sets of one word, allow to generate unitary circular code motifs (UCC motifs), i.e. a concatenation of the same motif (simple repeats) leading to low complexity DNA. Three classes of UCC motifs are studied here: repeated dinucleotides (D + motifs), repeated trinucleotides (T + motifs) and repeated tetranucleotides (T + motifs). Thus, the D + , T + and T + motifs allow to retrieve, synchronize and maintain a frame modulo 2, modulo 3 and modulo 4, respectively, and their shifted frames (1 modulo 2; 1 and 2 modulo 3; 1, 2 and 3 modulo 4 according to the C 2 , C 3 and C 4 properties, respectively) in the DNA sequences. The statistical distribution of the D + , T + and T + motifs is analyzed in the genomes of eukaryotes. A UCC motif and its comp lementary UCC motif have the same distribution in the eukaryotic genomes. Furthermore, a UCC motif and its complementary UCC motif have increasing occurrences contrary to their number of hydrogen bonds, very significant with the T + motifs. The longest D + , T + and T + motifs in the studied eukaryotic genomes are also given. Surprisingly, a scarcity of repeated trinucleotides (T + motifs) in the large eukaryotic genomes is observed compared to the D + and T + motifs. This result has been investigated and may be explained by two outcomes. Repeated trinucleotides (T + motifs) are identified

The partition dimension of cycle books graph

NASA Astrophysics Data System (ADS)

Santoso, Jaya; Darmaji

2018-03-01

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

Graph Mining Meets the Semantic Web

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

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

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

Motif enrichment tool.

PubMed

Blatti, Charles; Sinha, Saurabh

2014-07-01

The Motif Enrichment Tool (MET) provides an online interface that enables users to find major transcriptional regulators of their gene sets of interest. MET searches the appropriate regulatory region around each gene and identifies which transcription factor DNA-binding specificities (motifs) are statistically overrepresented. Motif enrichment analysis is currently available for many metazoan species including human, mouse, fruit fly, planaria and flowering plants. MET also leverages high-throughput experimental data such as ChIP-seq and DNase-seq from ENCODE and ModENCODE to identify the regulatory targets of a transcription factor with greater precision. The results from MET are produced in real time and are linked to a genome browser for easy follow-up analysis. Use of the web tool is free and open to all, and there is no login requirement. ADDRESS: http://veda.cs.uiuc.edu/MET/. © The Author(s) 2014. Published by Oxford University Press on behalf of Nucleic Acids Research.

Extracting Knowledge from Graph Data in Adversarial Settings

NASA Astrophysics Data System (ADS)

Skillicorn, David

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

n-Nucleotide circular codes in graph theory.

PubMed

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

2016-03-13

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

WebMOTIFS: automated discovery, filtering and scoring of DNA sequence motifs using multiple programs and Bayesian approaches

PubMed Central

Romer, Katherine A.; Kayombya, Guy-Richard; Fraenkel, Ernest

2007-01-01

WebMOTIFS provides a web interface that facilitates the discovery and analysis of DNA-sequence motifs. Several studies have shown that the accuracy of motif discovery can be significantly improved by using multiple de novo motif discovery programs and using randomized control calculations to identify the most significant motifs or by using Bayesian approaches. WebMOTIFS makes it easy to apply these strategies. Using a single submission form, users can run several motif discovery programs and score, cluster and visualize the results. In addition, the Bayesian motif discovery program THEME can be used to determine the class of transcription factors that is most likely to regulate a set of sequences. Input can be provided as a list of gene or probe identifiers. Used with the default settings, WebMOTIFS accurately identifies biologically relevant motifs from diverse data in several species. WebMOTIFS is freely available at http://fraenkel.mit.edu/webmotifs. PMID:17584794

A Monte Carlo-based framework enhances the discovery and interpretation of regulatory sequence motifs

PubMed Central

2012-01-01

Background Discovery of functionally significant short, statistically overrepresented subsequence patterns (motifs) in a set of sequences is a challenging problem in bioinformatics. Oftentimes, not all sequences in the set contain a motif. These non-motif-containing sequences complicate the algorithmic discovery of motifs. Filtering the non-motif-containing sequences from the larger set of sequences while simultaneously determining the identity of the motif is, therefore, desirable and a non-trivial problem in motif discovery research. Results We describe MotifCatcher, a framework that extends the sensitivity of existing motif-finding tools by employing random sampling to effectively remove non-motif-containing sequences from the motif search. We developed two implementations of our algorithm; each built around a commonly used motif-finding tool, and applied our algorithm to three diverse chromatin immunoprecipitation (ChIP) data sets. In each case, the motif finder with the MotifCatcher extension demonstrated improved sensitivity over the motif finder alone. Our approach organizes candidate functionally significant discovered motifs into a tree, which allowed us to make additional insights. In all cases, we were able to support our findings with experimental work from the literature. Conclusions Our framework demonstrates that additional processing at the sequence entry level can significantly improve the performance of existing motif-finding tools. For each biological data set tested, we were able to propose novel biological hypotheses supported by experimental work from the literature. Specifically, in Escherichia coli, we suggested binding site motifs for 6 non-traditional LexA protein binding sites; in Saccharomyces cerevisiae, we hypothesize 2 disparate mechanisms for novel binding sites of the Cse4p protein; and in Halobacterium sp. NRC-1, we discoverd subtle differences in a general transcription factor (GTF) binding site motif across several data sets. We

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

NASA Astrophysics Data System (ADS)

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

2010-11-01

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

Claw-Free Maximal Planar Graphs

DTIC Science & Technology

1989-01-01

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

Enrichment of Circular Code Motifs in the Genes of the Yeast Saccharomyces cerevisiae.

PubMed

Michel, Christian J; Ngoune, Viviane Nguefack; Poch, Olivier; Ripp, Raymond; Thompson, Julie D

2017-12-03

A set X of 20 trinucleotides has been found to have the highest average occurrence in the reading frame, compared to the two shifted frames, of genes of bacteria, archaea, eukaryotes, plasmids and viruses. This set X has an interesting mathematical property, since X is a maximal C3 self-complementary trinucleotide circular code. Furthermore, any motif obtained from this circular code X has the capacity to retrieve, maintain and synchronize the original (reading) frame. Since 1996, the theory of circular codes in genes has mainly been developed by analysing the properties of the 20 trinucleotides of X, using combinatorics and statistical approaches. For the first time, we test this theory by analysing the X motifs, i.e., motifs from the circular code X, in the complete genome of the yeast Saccharomyces cerevisiae . Several properties of X motifs are identified by basic statistics (at the frequency level), and evaluated by comparison to R motifs, i.e., random motifs generated from 30 different random codes R. We first show that the frequency of X motifs is significantly greater than that of R motifs in the genome of S. cerevisiae . We then verify that no significant difference is observed between the frequencies of X and R motifs in the non-coding regions of S. cerevisiae , but that the occurrence number of X motifs is significantly higher than R motifs in the genes (protein-coding regions). This property is true for all cardinalities of X motifs (from 4 to 20) and for all 16 chromosomes. We further investigate the distribution of X motifs in the three frames of S. cerevisiae genes and show that they occur more frequently in the reading frame, regardless of their cardinality or their length. Finally, the ratio of X genes, i.e., genes with at least one X motif, to non-X genes, in the set of verified genes is significantly different to that observed in the set of putative or dubious genes with no experimental evidence. These results, taken together, represent the first

DMINDA: an integrated web server for DNA motif identification and analyses.

PubMed

Ma, Qin; Zhang, Hanyuan; Mao, Xizeng; Zhou, Chuan; Liu, Bingqiang; Chen, Xin; Xu, Ying

2014-07-01

DMINDA (DNA motif identification and analyses) is an integrated web server for DNA motif identification and analyses, which is accessible at http://csbl.bmb.uga.edu/DMINDA/. This web site is freely available to all users and there is no login requirement. This server provides a suite of cis-regulatory motif analysis functions on DNA sequences, which are important to elucidation of the mechanisms of transcriptional regulation: (i) de novo motif finding for a given set of promoter sequences along with statistical scores for the predicted motifs derived based on information extracted from a control set, (ii) scanning motif instances of a query motif in provided genomic sequences, (iii) motif comparison and clustering of identified motifs, and (iv) co-occurrence analyses of query motifs in given promoter sequences. The server is powered by a backend computer cluster with over 150 computing nodes, and is particularly useful for motif prediction and analyses in prokaryotic genomes. We believe that DMINDA, as a new and comprehensive web server for cis-regulatory motif finding and analyses, will benefit the genomic research community in general and prokaryotic genome researchers in particular. © The Author(s) 2014. Published by Oxford University Press on behalf of Nucleic Acids Research.

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

DTIC Science & Technology

1989-10-15

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

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

ERIC Educational Resources Information Center

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

2017-01-01

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

Discriminative motif optimization based on perceptron training

PubMed Central

Patel, Ronak Y.; Stormo, Gary D.

2014-01-01

Motivation: Generating accurate transcription factor (TF) binding site motifs from data generated using the next-generation sequencing, especially ChIP-seq, is challenging. The challenge arises because a typical experiment reports a large number of sequences bound by a TF, and the length of each sequence is relatively long. Most traditional motif finders are slow in handling such enormous amount of data. To overcome this limitation, tools have been developed that compromise accuracy with speed by using heuristic discrete search strategies or limited optimization of identified seed motifs. However, such strategies may not fully use the information in input sequences to generate motifs. Such motifs often form good seeds and can be further improved with appropriate scoring functions and rapid optimization. Results: We report a tool named discriminative motif optimizer (DiMO). DiMO takes a seed motif along with a positive and a negative database and improves the motif based on a discriminative strategy. We use area under receiver-operating characteristic curve (AUC) as a measure of discriminating power of motifs and a strategy based on perceptron training that maximizes AUC rapidly in a discriminative manner. Using DiMO, on a large test set of 87 TFs from human, drosophila and yeast, we show that it is possible to significantly improve motifs identified by nine motif finders. The motifs are generated/optimized using training sets and evaluated on test sets. The AUC is improved for almost 90% of the TFs on test sets and the magnitude of increase is up to 39%. Availability and implementation: DiMO is available at http://stormo.wustl.edu/DiMO Contact: rpatel@genetics.wustl.edu, ronakypatel@gmail.com PMID:24369152

Local adjacency metric dimension of sun graph and stacked book graph

NASA Astrophysics Data System (ADS)

Yulisda Badri, Alifiah; Darmaji

2018-03-01

A graph is a mathematical system consisting of a non-empty set of nodes and a set of empty sides. One of the topics to be studied in graph theory is the metric dimension. Application in the metric dimension is the navigation robot system on a path. Robot moves from one vertex to another vertex in the field by minimizing the errors that occur in translating the instructions (code) obtained from the vertices of that location. To move the robot must give different instructions (code). In order for the robot to move efficiently, the robot must be fast to translate the code of the nodes of the location it passes. so that the location vertex has a minimum distance. However, if the robot must move with the vertex location on a very large field, so the robot can not detect because the distance is too far.[6] In this case, the robot can determine its position by utilizing location vertices based on adjacency. The problem is to find the minimum cardinality of the required location vertex, and where to put, so that the robot can determine its location. The solution to this problem is the dimension of adjacency metric and adjacency metric bases. Rodrguez-Velzquez and Fernau combine the adjacency metric dimensions with local metric dimensions, thus becoming the local adjacency metric dimension. In the local adjacency metric dimension each vertex in the graph may have the same adjacency representation as the terms of the vertices. To obtain the local metric dimension of values in the graph of the Sun and the stacked book graph is used the construction method by considering the representation of each adjacent vertex of the graph.

Motif-Synchronization: A new method for analysis of dynamic brain networks with EEG

NASA Astrophysics Data System (ADS)

Rosário, R. S.; Cardoso, P. T.; Muñoz, M. A.; Montoya, P.; Miranda, J. G. V.

2015-12-01

The major aim of this work was to propose a new association method known as Motif-Synchronization. This method was developed to provide information about the synchronization degree and direction between two nodes of a network by counting the number of occurrences of some patterns between any two time series. The second objective of this work was to present a new methodology for the analysis of dynamic brain networks, by combining the Time-Varying Graph (TVG) method with a directional association method. We further applied the new algorithms to a set of human electroencephalogram (EEG) signals to perform a dynamic analysis of the brain functional networks (BFN).

Identification of family-specific residue packing motifs and their use for structure-based protein function prediction: I. Method development.

PubMed

Bandyopadhyay, Deepak; Huan, Jun; Prins, Jan; Snoeyink, Jack; Wang, Wei; Tropsha, Alexander

2009-11-01

Protein function prediction is one of the central problems in computational biology. We present a novel automated protein structure-based function prediction method using libraries of local residue packing patterns that are common to most proteins in a known functional family. Critical to this approach is the representation of a protein structure as a graph where residue vertices (residue name used as a vertex label) are connected by geometrical proximity edges. The approach employs two steps. First, it uses a fast subgraph mining algorithm to find all occurrences of family-specific labeled subgraphs for all well characterized protein structural and functional families. Second, it queries a new structure for occurrences of a set of motifs characteristic of a known family, using a graph index to speed up Ullman's subgraph isomorphism algorithm. The confidence of function inference from structure depends on the number of family-specific motifs found in the query structure compared with their distribution in a large non-redundant database of proteins. This method can assign a new structure to a specific functional family in cases where sequence alignments, sequence patterns, structural superposition and active site templates fail to provide accurate annotation.

Efficient dynamic graph construction for inductive semi-supervised learning.

PubMed

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

2017-10-01

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

Discovery of phosphorylation motif mixtures in phosphoproteomics data

PubMed Central

Ritz, Anna; Shakhnarovich, Gregory; Salomon, Arthur R.; Raphael, Benjamin J.

2009-01-01

Motivation: Modification of proteins via phosphorylation is a primary mechanism for signal transduction in cells. Phosphorylation sites on proteins are determined in part through particular patterns, or motifs, present in the amino acid sequence. Results: We describe an algorithm that simultaneously discovers multiple motifs in a set of peptides that were phosphorylated by several different kinases. Such sets of peptides are routinely produced in proteomics experiments.Our motif-finding algorithm uses the principle of minimum description length to determine a mixture of sequence motifs that distinguish a foreground set of phosphopeptides from a background set of unphosphorylated peptides. We show that our algorithm outperforms existing motif-finding algorithms on synthetic datasets consisting of mixtures of known phosphorylation sites. We also derive a motif specificity score that quantifies whether or not the phosphoproteins containing an instance of a motif have a significant number of known interactions. Application of our motif-finding algorithm to recently published human and mouse proteomic studies recovers several known phosphorylation motifs and reveals a number of novel motifs that are enriched for interactions with a particular kinase or phosphatase. Our tools provide a new approach for uncovering the sequence specificities of uncharacterized kinases or phosphatases. Availability: Software is available at http:/cs.brown.edu/people/braphael/software.html. Contact: aritz@cs.brown.edu; braphael@cs.brown.edu Supplementary information: Supplementary data are available at Bioinformatics online. PMID:18996944

Supermanifolds from Feynman graphs

NASA Astrophysics Data System (ADS)

Marcolli, Matilde; Rej, Abhijnan

2008-08-01

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

Nested Tracking Graphs

DOE PAGES

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

2017-06-01

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

Integer Flows and Circuit Covers of Graphs and Signed Graphs

NASA Astrophysics Data System (ADS)

Cheng, Jian

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

Neural complexity: A graph theoretic interpretation

NASA Astrophysics Data System (ADS)

Barnett, L.; Buckley, C. L.; Bullock, S.

2011-04-01

One of the central challenges facing modern neuroscience is to explain the ability of the nervous system to coherently integrate information across distinct functional modules in the absence of a central executive. To this end, Tononi [Proc. Natl. Acad. Sci. USA.PNASA60027-842410.1073/pnas.91.11.5033 91, 5033 (1994)] proposed a measure of neural complexity that purports to capture this property based on mutual information between complementary subsets of a system. Neural complexity, so defined, is one of a family of information theoretic metrics developed to measure the balance between the segregation and integration of a system’s dynamics. One key question arising for such measures involves understanding how they are influenced by network topology. Sporns [Cereb. Cortex53OPAV1047-321110.1093/cercor/10.2.127 10, 127 (2000)] employed numerical models in order to determine the dependence of neural complexity on the topological features of a network. However, a complete picture has yet to be established. While De Lucia [Phys. Rev. EPLEEE81539-375510.1103/PhysRevE.71.016114 71, 016114 (2005)] made the first attempts at an analytical account of this relationship, their work utilized a formulation of neural complexity that, we argue, did not reflect the intuitions of the original work. In this paper we start by describing weighted connection matrices formed by applying a random continuous weight distribution to binary adjacency matrices. This allows us to derive an approximation for neural complexity in terms of the moments of the weight distribution and elementary graph motifs. In particular, we explicitly establish a dependency of neural complexity on cyclic graph motifs.

On a programming language for graph algorithms

NASA Technical Reports Server (NTRS)

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

1971-01-01

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

Network motif frequency vectors reveal evolving metabolic network organisation.

PubMed

Pearcy, Nicole; Crofts, Jonathan J; Chuzhanova, Nadia

2015-01-01

At the systems level many organisms of interest may be described by their patterns of interaction, and as such, are perhaps best characterised via network or graph models. Metabolic networks, in particular, are fundamental to the proper functioning of many important biological processes, and thus, have been widely studied over the past decade or so. Such investigations have revealed a number of shared topological features, such as a short characteristic path-length, large clustering coefficient and hierarchical modular structure. However, the extent to which evolutionary and functional properties of metabolism manifest via this underlying network architecture remains unclear. In this paper, we employ a novel graph embedding technique, based upon low-order network motifs, to compare metabolic network structure for 383 bacterial species categorised according to a number of biological features. In particular, we introduce a new global significance score which enables us to quantify important evolutionary relationships that exist between organisms and their physical environments. Using this new approach, we demonstrate a number of significant correlations between environmental factors, such as growth conditions and habitat variability, and network motif structure, providing evidence that organism adaptability leads to increased complexities in the resultant metabolic networks.

mpiGraph

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

Moody, Adam

2007-05-22

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

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

ERIC Educational Resources Information Center

Cosler, Norma, Ed.

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

Graph Theoretical Analysis Reveals: Women’s Brains Are Better Connected than Men’s

PubMed Central

Szalkai, Balázs; Varga, Bálint; Grolmusz, Vince

2015-01-01

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 in the brain graph

Hydrogen bonding motifs, spectral characterization, theoretical computations and anticancer studies on chloride salt of 6-mercaptopurine: An assembly of corrugated lamina shows enhanced solubility

NASA Astrophysics Data System (ADS)

Suresh Kumar, S.; Athimoolam, S.; Sridhar, B.

2015-10-01

6-Mercaptopurine (an anti cancer drug), is coming under the class II Biopharmaceutics Classification System (BCS). In order to enhance the solubility with retained physiochemical/pharmaceutical properties, the present work was attempted with its salt form. The single crystals of 6-mercaptopurinium chloride (6MPCl) were successfully grown by slow evaporation technique under ambient temperature. The X-ray diffraction study shows that the crystal packing is dominated by N-H⋯Cl classical hydrogen bonds leading to corrugated laminar network. The hydrogen bonds present in the lamina can be dismantled as three chain C21(6), C21(7) and C21(8) motifs running along ab-diagonal of the unit cell. These primary chain motifs are interlinked to each other forming ring R63(21) motifs. These chain and ring motifs are aggregated like a dendrimer structure leading to the above said corrugated lamina. This low dimensional molecular architecture differs from the ladder like arrays in pure drug though it possess lattice water molecule in lieu of the chloride anion in the present compound. Geometrical optimizations of 6MPCl were done by Density Functional Theory (DFT) using B3LYP function with two different basis sets. The optimized molecular geometries and computed vibrational spectra are compared with their experimental counterparts. The Natural Bond Orbital (NBO) analysis was carried out to interpret hyperconjugative interaction and Intramolecular Charge Transfer (ICT). The chemical hardness, electronegativity, chemical potential and electrophilicity index of 6MPCl were found along with the HOMO-LUMO plot. The lower band gap value obtained from the Frontier Molecular Orbital (FMO) analysis reiterates the pharmaceutical activity of the compound. The anticancer studies show that 6MPCl retains its activity against human cervical cancer cell line (HeLa). Hence, this anticancer efficacy and improved solubility demands 6MPCl towards the further pharmaceutical applications.

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

NASA Astrophysics Data System (ADS)

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

2016-05-01

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

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

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

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

2013-08-01

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

Event Networks and the Identification of Crime Pattern Motifs

PubMed Central

2015-01-01

In this paper we demonstrate the use of network analysis to characterise patterns of clustering in spatio-temporal events. Such clustering is of both theoretical and practical importance in the study of crime, and forms the basis for a number of preventative strategies. However, existing analytical methods show only that clustering is present in data, while offering little insight into the nature of the patterns present. Here, we show how the classification of pairs of events as close in space and time can be used to define a network, thereby generalising previous approaches. The application of graph-theoretic techniques to these networks can then offer significantly deeper insight into the structure of the data than previously possible. In particular, we focus on the identification of network motifs, which have clear interpretation in terms of spatio-temporal behaviour. Statistical analysis is complicated by the nature of the underlying data, and we provide a method by which appropriate randomised graphs can be generated. Two datasets are used as case studies: maritime piracy at the global scale, and residential burglary in an urban area. In both cases, the same significant 3-vertex motif is found; this result suggests that incidents tend to occur not just in pairs, but in fact in larger groups within a restricted spatio-temporal domain. In the 4-vertex case, different motifs are found to be significant in each case, suggesting that this technique is capable of discriminating between clustering patterns at a finer granularity than previously possible. PMID:26605544

Graph Theory Approach for Studying Food Webs

NASA Astrophysics Data System (ADS)

Longjas, A.; Tejedor, A.; Foufoula-Georgiou, E.

2017-12-01

Food webs are complex networks of feeding interactions among species in ecological communities. Metrics describing food web structure have been proposed to compare and classify food webs ranging from food chain length, connectance, degree distribution, centrality measures, to the presence of motifs (distinct compartments), among others. However, formal methodologies for studying both food web topology and the dynamic processes operating on them are still lacking. Here, we utilize a quantitative framework using graph theory within which a food web is represented by a directed graph, i.e., a collection of vertices (species or trophic species defined as sets of species sharing the same predators and prey) and directed edges (predation links). This framework allows us to identify apex (environmental "source" node) to outlet (top predators) subnetworks and compute the steady-state flux (e.g., carbon, nutrients, energy etc.) in the food web. We use this framework to (1) construct vulnerability maps that quantify the relative change of flux delivery to the top predators in response to perturbations in prey species (2) identify keystone species, whose loss would precipitate further species extinction, and (3) introduce a suite of graph-theoretic metrics to quantify the topologic (imposed by food web connectivity) and dynamic (dictated by the flux partitioning and distribution) components of a food web's complexity. By projecting food webs into a 2D Topodynamic Complexity Space whose coordinates are given by Number of alternative paths (topologic) and Leakage Index (dynamic), we show that this space provides a basis for food web comparison and provide physical insights into their dynamic behavior.

Motivated Proteins: A web application for studying small three-dimensional protein motifs

PubMed Central

Leader, David P; Milner-White, E James

2009-01-01

Background Small loop-shaped motifs are common constituents of the three-dimensional structure of proteins. Typically they comprise between three and seven amino acid residues, and are defined by a combination of dihedral angles and hydrogen bonding partners. The most abundant of these are αβ-motifs, asx-motifs, asx-turns, β-bulges, β-bulge loops, β-turns, nests, niches, Schellmann loops, ST-motifs, ST-staples and ST-turns. We have constructed a database of such motifs from a range of high-quality protein structures and built a web application as a visual interface to this. Description The web application, Motivated Proteins, provides access to these 12 motifs (with 48 sub-categories) in a database of over 400 representative proteins. Queries can be made for specific categories or sub-categories of motif, motifs in the vicinity of ligands, motifs which include part of an enzyme active site, overlapping motifs, or motifs which include a particular amino acid sequence. Individual proteins can be specified, or, where appropriate, motifs for all proteins listed. The results of queries are presented in textual form as an (X)HTML table, and may be saved as parsable plain text or XML. Motifs can be viewed and manipulated either individually or in the context of the protein in the Jmol applet structural viewer. Cartoons of the motifs imposed on a linear representation of protein secondary structure are also provided. Summary information for the motifs is available, as are histograms of amino acid distribution, and graphs of dihedral angles at individual positions in the motifs. Conclusion Motivated Proteins is a publicly and freely accessible web application that enables protein scientists to study small three-dimensional motifs without requiring knowledge of either Structured Query Language or the underlying database schema. PMID:19210785

The new protein topology graph library web server.

PubMed

Schäfer, Tim; Scheck, Andreas; Bruneß, Daniel; May, Patrick; Koch, Ina

2016-02-01

We present a new, extended version of the Protein Topology Graph Library web server. The Protein Topology Graph Library describes the protein topology on the super-secondary structure level. It allows to compute and visualize protein ligand graphs and search for protein structural motifs. The new server features additional information on ligand binding to secondary structure elements, increased usability and an application programming interface (API) to retrieve data, allowing for an automated analysis of protein topology. The Protein Topology Graph Library server is freely available on the web at http://ptgl.uni-frankfurt.de. The website is implemented in PHP, JavaScript, PostgreSQL and Apache. It is supported by all major browsers. The VPLG software that was used to compute the protein ligand graphs and all other data in the database is available under the GNU public license 2.0 from http://vplg.sourceforge.net. tim.schaefer@bioinformatik.uni-frankfurt.de; ina.koch@bioinformatik.uni-frankfurt.de Supplementary data are available at Bioinformatics online. © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

Metric learning with spectral graph convolutions on brain connectivity networks.

PubMed

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

2018-04-01

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

IndeCut evaluates performance of network motif discovery algorithms.

PubMed

Ansariola, Mitra; Megraw, Molly; Koslicki, David

2018-05-01

Genomic networks represent a complex map of molecular interactions which are descriptive of the biological processes occurring in living cells. Identifying the small over-represented circuitry patterns in these networks helps generate hypotheses about the functional basis of such complex processes. Network motif discovery is a systematic way of achieving this goal. However, a reliable network motif discovery outcome requires generating random background networks which are the result of a uniform and independent graph sampling method. To date, there has been no method to numerically evaluate whether any network motif discovery algorithm performs as intended on realistically sized datasets-thus it was not possible to assess the validity of resulting network motifs. In this work, we present IndeCut, the first method to date that characterizes network motif finding algorithm performance in terms of uniform sampling on realistically sized networks. We demonstrate that it is critical to use IndeCut prior to running any network motif finder for two reasons. First, IndeCut indicates the number of samples needed for a tool to produce an outcome that is both reproducible and accurate. Second, IndeCut allows users to choose the tool that generates samples in the most independent fashion for their network of interest among many available options. The open source software package is available at https://github.com/megrawlab/IndeCut. megrawm@science.oregonstate.edu or david.koslicki@math.oregonstate.edu. Supplementary data are available at Bioinformatics online.

Automated classification of RNA 3D motifs and the RNA 3D Motif Atlas

PubMed Central

Petrov, Anton I.; Zirbel, Craig L.; Leontis, Neocles B.

2013-01-01

The analysis of atomic-resolution RNA three-dimensional (3D) structures reveals that many internal and hairpin loops are modular, recurrent, and structured by conserved non-Watson–Crick base pairs. Structurally similar loops define RNA 3D motifs that are conserved in homologous RNA molecules, but can also occur at nonhomologous sites in diverse RNAs, and which often vary in sequence. To further our understanding of RNA motif structure and sequence variability and to provide a useful resource for structure modeling and prediction, we present a new method for automated classification of internal and hairpin loop RNA 3D motifs and a new online database called the RNA 3D Motif Atlas. To classify the motif instances, a representative set of internal and hairpin loops is automatically extracted from a nonredundant list of RNA-containing PDB files. Their structures are compared geometrically, all-against-all, using the FR3D program suite. The loops are clustered into motif groups, taking into account geometric similarity and structural annotations and making allowance for a variable number of bulged bases. The automated procedure that we have implemented identifies all hairpin and internal loop motifs previously described in the literature. All motif instances and motif groups are assigned unique and stable identifiers and are made available in the RNA 3D Motif Atlas (http://rna.bgsu.edu/motifs), which is automatically updated every four weeks. The RNA 3D Motif Atlas provides an interactive user interface for exploring motif diversity and tools for programmatic data access. PMID:23970545

Real World Graph Connectivity

ERIC Educational Resources Information Center

Lind, Joy; Narayan, Darren

2009-01-01

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

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

NASA Astrophysics Data System (ADS)

Kobylkin, Konstantin

2016-10-01

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

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

PubMed

Warnke-Sommer, Julia; Ali, Hesham

2016-05-06

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

Output-Sensitive Construction of Reeb Graphs.

PubMed

Doraiswamy, H; Natarajan, V

2012-01-01

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

Quantum walk on a chimera graph

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

CUDA Enabled Graph Subset Examiner

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

Johnston, Jeremy T.

2016-12-22

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

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

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

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

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

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

DOE PAGES

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

2016-01-01

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

QuateXelero: An Accelerated Exact Network Motif Detection Algorithm

PubMed Central

Khakabimamaghani, Sahand; Sharafuddin, Iman; Dichter, Norbert; Koch, Ina; Masoudi-Nejad, Ali

2013-01-01

Finding motifs in biological, social, technological, and other types of networks has become a widespread method to gain more knowledge about these networks’ structure and function. However, this task is very computationally demanding, because it is highly associated with the graph isomorphism which is an NP problem (not known to belong to P or NP-complete subsets yet). Accordingly, this research is endeavoring to decrease the need to call NAUTY isomorphism detection method, which is the most time-consuming step in many existing algorithms. The work provides an extremely fast motif detection algorithm called QuateXelero, which has a Quaternary Tree data structure in the heart. The proposed algorithm is based on the well-known ESU (FANMOD) motif detection algorithm. The results of experiments on some standard model networks approve the overal superiority of the proposed algorithm, namely QuateXelero, compared with two of the fastest existing algorithms, G-Tries and Kavosh. QuateXelero is especially fastest in constructing the central data structure of the algorithm from scratch based on the input network. PMID:23874498

Phospholipid composition and a polybasic motif determine D6 PROTEIN KINASE polar association with the plasma membrane and tropic responses.

PubMed

Barbosa, Inês C R; Shikata, Hiromasa; Zourelidou, Melina; Heilmann, Mareike; Heilmann, Ingo; Schwechheimer, Claus

2016-12-15

Polar transport of the phytohormone auxin through PIN-FORMED (PIN) auxin efflux carriers is essential for the spatiotemporal control of plant development. The Arabidopsis thaliana serine/threonine kinase D6 PROTEIN KINASE (D6PK) is polarly localized at the plasma membrane of many cells where it colocalizes with PINs and activates PIN-mediated auxin efflux. Here, we show that the association of D6PK with the basal plasma membrane and PINs is dependent on the phospholipid composition of the plasma membrane as well as on the phosphatidylinositol phosphate 5-kinases PIP5K1 and PIP5K2 in epidermis cells of the primary root. We further show that D6PK directly binds polyacidic phospholipids through a polybasic lysine-rich motif in the middle domain of the kinase. The lysine-rich motif is required for proper PIN3 phosphorylation and for auxin transport-dependent tropic growth. Polybasic motifs are also present at a conserved position in other D6PK-related kinases and required for membrane and phospholipid binding. Thus, phospholipid-dependent recruitment to membranes through polybasic motifs might not only be required for D6PK-mediated auxin transport but also other processes regulated by these, as yet, functionally uncharacterized kinases. © 2016. Published by The Company of Biologists Ltd.

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

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

Sengupta, Dipanjan; Song, Shuaiwen; Agarwal, Kapil

2015-11-15

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

Distribution of diameters for Erdős-Rényi random graphs.

PubMed

Hartmann, A K; Mézard, M

2018-03-01

We study the distribution of diameters d of Erdős-Rényi random graphs with average connectivity c. The diameter d is the maximum among all the shortest distances between pairs of nodes in a graph and an important quantity for all dynamic processes taking place on graphs. Here we study the distribution P(d) numerically for various values of c, in the nonpercolating and percolating regimes. Using large-deviation techniques, we are able to reach small probabilities like 10^{-100} which allow us to obtain the distribution over basically the full range of the support, for graphs up to N=1000 nodes. For values c<1, our results are in good agreement with analytical results, proving the reliability of our numerical approach. For c>1 the distribution is more complex and no complete analytical results are available. For this parameter range, P(d) exhibits an inflection point, which we found to be related to a structural change of the graphs. For all values of c, we determined the finite-size rate function Φ(d/N) and were able to extrapolate numerically to N→∞, indicating that the large-deviation principle holds.

Distribution of diameters for Erdős-Rényi random graphs

NASA Astrophysics Data System (ADS)

Hartmann, A. K.; Mézard, M.

2018-03-01

We study the distribution of diameters d of Erdős-Rényi random graphs with average connectivity c . The diameter d is the maximum among all the shortest distances between pairs of nodes in a graph and an important quantity for all dynamic processes taking place on graphs. Here we study the distribution P (d ) numerically for various values of c , in the nonpercolating and percolating regimes. Using large-deviation techniques, we are able to reach small probabilities like 10-100 which allow us to obtain the distribution over basically the full range of the support, for graphs up to N =1000 nodes. For values c <1 , our results are in good agreement with analytical results, proving the reliability of our numerical approach. For c >1 the distribution is more complex and no complete analytical results are available. For this parameter range, P (d ) exhibits an inflection point, which we found to be related to a structural change of the graphs. For all values of c , we determined the finite-size rate function Φ (d /N ) and were able to extrapolate numerically to N →∞ , indicating that the large-deviation principle holds.

Limitations and potentials of current motif discovery algorithms

PubMed Central

Hu, Jianjun; Li, Bin; Kihara, Daisuke

2005-01-01

Computational methods for de novo identification of gene regulation elements, such as transcription factor binding sites, have proved to be useful for deciphering genetic regulatory networks. However, despite the availability of a large number of algorithms, their strengths and weaknesses are not sufficiently understood. Here, we designed a comprehensive set of performance measures and benchmarked five modern sequence-based motif discovery algorithms using large datasets generated from Escherichia coli RegulonDB. Factors that affect the prediction accuracy, scalability and reliability are characterized. It is revealed that the nucleotide and the binding site level accuracy are very low, while the motif level accuracy is relatively high, which indicates that the algorithms can usually capture at least one correct motif in an input sequence. To exploit diverse predictions from multiple runs of one or more algorithms, a consensus ensemble algorithm has been developed, which achieved 6–45% improvement over the base algorithms by increasing both the sensitivity and specificity. Our study illustrates limitations and potentials of existing sequence-based motif discovery algorithms. Taking advantage of the revealed potentials, several promising directions for further improvements are discussed. Since the sequence-based algorithms are the baseline of most of the modern motif discovery algorithms, this paper suggests substantial improvements would be possible for them. PMID:16284194

Convex Graph Invariants

DTIC Science & Technology

2010-12-02

Motzkin, T. and Straus, E. (1965). Maxima for graphs and a new proof of a theorem of Turan . Canad. J. Math. 17 533–540. [33] Rendl, F. and Sotirov, R...Convex Graph Invariants Venkat Chandrasekaran, Pablo A . Parrilo, and Alan S. Willsky ∗ Laboratory for Information and Decision Systems Department of...this paper we study convex graph invariants, which are graph invariants that are convex functions of the adjacency matrix of a graph. Some examples

Enabling Graph Appliance for Genome Assembly

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

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

2015-01-01

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

Graphs and Tracks Revisited

NASA Astrophysics Data System (ADS)

Christian, Wolfgang; Belloni, Mario

2013-04-01

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

Graph-matching based CTA.

PubMed

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

2009-12-01

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

The Cytoplasmic Region of Inner Helix S6 Is an Important Determinant of Cardiac Ryanodine Receptor Channel Gating.

PubMed

Sun, Bo; Guo, Wenting; Tian, Xixi; Yao, Jinjing; Zhang, Lin; Wang, Ruiwu; Chen, S R Wayne

2016-12-09

The ryanodine receptor (RyR) channel pore is formed by four S6 inner helices, with its intracellular gate located at the S6 helix bundle crossing region. The cytoplasmic region of the extended S6 helix is held by the U motif of the central domain and is thought to control the opening and closing of the S6 helix bundle. However, the functional significance of the S6 cytoplasmic region in channel gating is unknown. Here we assessed the role of the S6 cytoplasmic region in the function of cardiac RyR (RyR2) via structure-guided site-directed mutagenesis. We mutated each residue in the S6 cytoplasmic region of the mouse RyR2 ( 4876 QQEQVKEDM 4884 ) and characterized their functional impact. We found that mutations Q4876A, V4880A, K4881A, and M4884A, located mainly on one side of the S6 helix that faces the U motif, enhanced basal channel activity and the sensitivity to Ca 2+ or caffeine activation, whereas mutations Q4877A, E4878A, Q4879A, and D4883A, located largely on the opposite side of S6, suppressed channel activity. Furthermore, V4880A, a cardiac arrhythmia-associated mutation, markedly enhanced the frequency of spontaneous openings and the sensitivity to cytosolic and luminal Ca 2+ activation of single RyR2 channels. V4880A also increased the propensity and reduced the threshold for arrhythmogenic spontaneous Ca 2+ release in HEK293 cells. Collectively, our data suggest that interactions between the cytoplasmic region of S6 and the U motif of RyR2 are important for stabilizing the closed state of the channel. Mutations in the S6/U motif domain interface likely destabilize the closed state of RyR2, resulting in enhanced basal channel activity and sensitivity to activation and increased propensity for spontaneous Ca 2+ release and cardiac arrhythmias. © 2016 by The American Society for Biochemistry and Molecular Biology, Inc.

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

PubMed

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

2016-01-01

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

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

DTIC Science & Technology

2013-05-01

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

2,6-Diiminopiperidin-1-ol: an overlooked motif relevant to uranyl and transition metal binding on poly(amidoxime) adsorbents

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

Kennedy, Zachary C.; Cardenas, Allan Jay P.; Corbey, Jordan F.

2016-01-01

Glutardiamidoxime, a structural motif on sorbents used in uranium extraction from seawater, was discovered to cyclize in situ at room temperature to 2,6-diimino-piperidin-1-ol in the presence of uranyl nitrate. The new diimino motif was also generated when exposed to competing transition metals Cu(II) and Ni(II). Multinuclear μ-O bridged U(VI), Cu(II), and Ni(II) complexes featuring bound diimino ligands were isolated. A Cu(II) complex with the historically relevant cyclic imide dioxime motif is also reported for structural comparison to the reported diimino complexes.

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

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

Sengupta, Dipanjan; Agarwal, Kapil; Song, Shuaiwen

2015-09-30

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

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

PubMed

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

2013-02-01

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

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

PubMed Central

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

2017-01-01

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

Movement Forms: A Graph-Dynamic Perspective

PubMed Central

Saltzman, Elliot; Holt, Ken

2014-01-01

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

GIV/Girdin activates Gαi and inhibits Gαs via the same motif

PubMed Central

Gupta, Vijay; Bhandari, Deepali; Leyme, Anthony; Aznar, Nicolas; Midde, Krishna K.; Lo, I-Chung; Ear, Jason; Niesman, Ingrid; López-Sánchez, Inmaculada; Blanco-Canosa, Juan Bautista; von Zastrow, Mark; Garcia-Marcos, Mikel; Farquhar, Marilyn G.; Ghosh, Pradipta

2016-01-01

We previously showed that guanine nucleotide-binding (G) protein α subunit (Gα)-interacting vesicle-associated protein (GIV), a guanine-nucleotide exchange factor (GEF), transactivates Gα activity-inhibiting polypeptide 1 (Gαi) proteins in response to growth factors, such as EGF, using a short C-terminal motif. Subsequent work demonstrated that GIV also binds Gαs and that inactive Gαs promotes maturation of endosomes and shuts down mitogenic MAPK–ERK1/2 signals from endosomes. However, the mechanism and consequences of dual coupling of GIV to two G proteins, Gαi and Gαs, remained unknown. Here we report that GIV is a bifunctional modulator of G proteins; it serves as a guanine nucleotide dissociation inhibitor (GDI) for Gαs using the same motif that allows it to serve as a GEF for Gαi. Upon EGF stimulation, GIV modulates Gαi and Gαs sequentially: first, a key phosphomodification favors the assembly of GIV–Gαi complexes and activates GIV’s GEF function; then a second phosphomodification terminates GIV’s GEF function, triggers the assembly of GIV–Gαs complexes, and activates GIV’s GDI function. By comparing WT and GIV mutants, we demonstrate that GIV inhibits Gαs activity in cells responding to EGF. Consequently, the cAMP→PKA→cAMP response element-binding protein signaling axis is inhibited, the transit time of EGF receptor through early endosomes are accelerated, mitogenic MAPK–ERK1/2 signals are rapidly terminated, and proliferation is suppressed. These insights define a paradigm in G-protein signaling in which a pleiotropically acting modulator uses the same motif both to activate and to inhibit G proteins. Our findings also illuminate how such modulation of two opposing Gα proteins integrates downstream signals and cellular responses. PMID:27621449

Prediction of virus-host protein-protein interactions mediated by short linear motifs.

PubMed

Becerra, Andrés; Bucheli, Victor A; Moreno, Pedro A

2017-03-09

Short linear motifs in host organisms proteins can be mimicked by viruses to create protein-protein interactions that disable or control metabolic pathways. Given that viral linear motif instances of host motif regular expressions can be found by chance, it is necessary to develop filtering methods of functional linear motifs. We conduct a systematic comparison of linear motifs filtering methods to develop a computational approach for predicting motif-mediated protein-protein interactions between human and the human immunodeficiency virus 1 (HIV-1). We implemented three filtering methods to obtain linear motif sets: 1) conserved in viral proteins (C), 2) located in disordered regions (D) and 3) rare or scarce in a set of randomized viral sequences (R). The sets C,D,R are united and intersected. The resulting sets are compared by the number of protein-protein interactions correctly inferred with them - with experimental validation. The comparison is done with HIV-1 sequences and interactions from the National Institute of Allergy and Infectious Diseases (NIAID). The number of correctly inferred interactions allows to rank the interactions by the sets used to deduce them: D∪R and C. The ordering of the sets is descending on the probability of capturing functional interactions. With respect to HIV-1, the sets C∪R, D∪R, C∪D∪R infer all known interactions between HIV1 and human proteins mediated by linear motifs. We found that the majority of conserved linear motifs in the virus are located in disordered regions. We have developed a method for predicting protein-protein interactions mediated by linear motifs between HIV-1 and human proteins. The method only use protein sequences as inputs. We can extend the software developed to any other eukaryotic virus and host in order to find and rank candidate interactions. In future works we will use it to explore possible viral attack mechanisms based on linear motif mimicry.

Graphing the order of the sexes: constructing, recalling, interpreting, and putting the self in gender difference graphs.

PubMed

Hegarty, Peter; Lemieux, Anthony F; McQueen, Grant

2010-03-01

Graphs seem to connote facts more than words or tables do. Consequently, they seem unlikely places to spot implicit sexism at work. Yet, in 6 studies (N = 741), women and men constructed (Study 1) and recalled (Study 2) gender difference graphs with men's data first, and graphed powerful groups (Study 3) and individuals (Study 4) ahead of weaker ones. Participants who interpreted graph order as evidence of author "bias" inferred that the author graphed his or her own gender group first (Study 5). Women's, but not men's, preferences to graph men first were mitigated when participants graphed a difference between themselves and an opposite-sex friend prior to graphing gender differences (Study 6). Graph production and comprehension are affected by beliefs and suppositions about the groups represented in graphs to a greater degree than cognitive models of graph comprehension or realist models of scientific thinking have yet acknowledged.

Visibility graphs and symbolic dynamics

NASA Astrophysics Data System (ADS)

Lacasa, Lucas; Just, Wolfram

2018-07-01

Visibility algorithms are a family of geometric and ordering criteria by which a real-valued time series of N data is mapped into a graph of N nodes. This graph has been shown to often inherit in its topology nontrivial properties of the series structure, and can thus be seen as a combinatorial representation of a dynamical system. Here we explore in some detail the relation between visibility graphs and symbolic dynamics. To do that, we consider the degree sequence of horizontal visibility graphs generated by the one-parameter logistic map, for a range of values of the parameter for which the map shows chaotic behaviour. Numerically, we observe that in the chaotic region the block entropies of these sequences systematically converge to the Lyapunov exponent of the time series. Hence, Pesin's identity suggests that these block entropies are converging to the Kolmogorov-Sinai entropy of the physical measure, which ultimately suggests that the algorithm is implicitly and adaptively constructing phase space partitions which might have the generating property. To give analytical insight, we explore the relation k(x) , x ∈ [ 0 , 1 ] that, for a given datum with value x, assigns in graph space a node with degree k. In the case of the out-degree sequence, such relation is indeed a piece-wise constant function. By making use of explicit methods and tools from symbolic dynamics we are able to analytically show that the algorithm indeed performs an effective partition of the phase space and that such partition is naturally expressed as a countable union of subintervals, where the endpoints of each subinterval are related to the fixed point structure of the iterates of the map and the subinterval enumeration is associated with particular ordering structures that we called motifs.

DMINDA: an integrated web server for DNA motif identification and analyses

PubMed Central

Ma, Qin; Zhang, Hanyuan; Mao, Xizeng; Zhou, Chuan; Liu, Bingqiang; Chen, Xin; Xu, Ying

2014-01-01

DMINDA (DNA motif identification and analyses) is an integrated web server for DNA motif identification and analyses, which is accessible at http://csbl.bmb.uga.edu/DMINDA/. This web site is freely available to all users and there is no login requirement. This server provides a suite of cis-regulatory motif analysis functions on DNA sequences, which are important to elucidation of the mechanisms of transcriptional regulation: (i) de novo motif finding for a given set of promoter sequences along with statistical scores for the predicted motifs derived based on information extracted from a control set, (ii) scanning motif instances of a query motif in provided genomic sequences, (iii) motif comparison and clustering of identified motifs, and (iv) co-occurrence analyses of query motifs in given promoter sequences. The server is powered by a backend computer cluster with over 150 computing nodes, and is particularly useful for motif prediction and analyses in prokaryotic genomes. We believe that DMINDA, as a new and comprehensive web server for cis-regulatory motif finding and analyses, will benefit the genomic research community in general and prokaryotic genome researchers in particular. PMID:24753419

The Quantity and Quality of Scientific Graphs in Pharmaceutical Advertisements

PubMed Central

Cooper, Richelle J; Schriger, David L; Wallace, Roger C; Mikulich, Vladislav J; Wilkes, Michael S

2003-01-01

We characterized the quantity and quality of graphs in all pharmaceutical advertisements, in the 10 U.S. medical journals. Four hundred eighty-four unique advertisements (of 3,185 total advertisements) contained 836 glossy and 455 small-print pages. Forty-nine percent of glossy page area was nonscientific figures/images, 0.4% tables, and 1.6% scientific graphs (74 graphs in 64 advertisements). All 74 graphs were univariate displays, 4% were distributions, and 4% contained confidence intervals for summary measures. Extraneous decoration (66%) and redundancy (46%) were common. Fifty-eight percent of graphs presented an outcome relevant to the drug's indication. Numeric distortion, specifically prohibited by FDA regulations, occurred in 36% of graphs. PMID:12709097

Results on Vertex Degree and K-Connectivity in Uniform S-Intersection Graphs

DTIC Science & Technology

2014-01-01

distribution. A uniform s-intersection graph models the topology of a secure wireless sensor network employing the widely used s-composite key predistribution scheme. Our theoretical findings is also confirmed by numerical results.

On face antimagic labeling of double duplication of graphs

NASA Astrophysics Data System (ADS)

Shobana, L.; Kuppan, R.

2018-04-01

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

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

PubMed Central

2014-01-01

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

Graphs and Matrices: Combinatorial Analysis, Competitions, Covers and Ranks

DTIC Science & Technology

1993-09-30

Math (J.R. Lundgren and S. Merz). 6. "Competition Graphs of Strongly Connected and Hamiltonian Digraphs," submitted to SIAM Journal of Discrete Math (K...34 Congressus Numerantium 91 (1992), 55-62 (J.R. Lundgren and J. Maybee with G. Bain). 14. "Interval Competition Graphs of Symmetric Digraphs," Discrete Math 119...1993), 113-122 (J.R. Lundgren and J. Maybee with C. Rasmussen). 15. "Two-Step Graphs of Trees," Discrete Math 119 (1993), 123-139 (J.R. Lundgren

SCOPE: a web server for practical de novo motif discovery.

PubMed

Carlson, Jonathan M; Chakravarty, Arijit; DeZiel, Charles E; Gross, Robert H

2007-07-01

SCOPE is a novel parameter-free method for the de novo identification of potential regulatory motifs in sets of coordinately regulated genes. The SCOPE algorithm combines the output of three component algorithms, each designed to identify a particular class of motifs. Using an ensemble learning approach, SCOPE identifies the best candidate motifs from its component algorithms. In tests on experimentally determined datasets, SCOPE identified motifs with a significantly higher level of accuracy than a number of other web-based motif finders run with their default parameters. Because SCOPE has no adjustable parameters, the web server has an intuitive interface, requiring only a set of gene names or FASTA sequences and a choice of species. The most significant motifs found by SCOPE are displayed graphically on the main results page with a table containing summary statistics for each motif. Detailed motif information, including the sequence logo, PWM, consensus sequence and specific matching sites can be viewed through a single click on a motif. SCOPE's efficient, parameter-free search strategy has enabled the development of a web server that is readily accessible to the practising biologist while providing results that compare favorably with those of other motif finders. The SCOPE web server is at .

Using SCOPE to identify potential regulatory motifs in coregulated genes.

PubMed

Martyanov, Viktor; Gross, Robert H

2011-05-31

SCOPE is an ensemble motif finder that uses three component algorithms in parallel to identify potential regulatory motifs by over-representation and motif position preference. Each component algorithm is optimized to find a different kind of motif. By taking the best of these three approaches, SCOPE performs better than any single algorithm, even in the presence of noisy data. In this article, we utilize a web version of SCOPE to examine genes that are involved in telomere maintenance. SCOPE has been incorporated into at least two other motif finding programs and has been used in other studies. The three algorithms that comprise SCOPE are BEAM, which finds non-degenerate motifs (ACCGGT), PRISM, which finds degenerate motifs (ASCGWT), and SPACER, which finds longer bipartite motifs (ACCnnnnnnnnGGT). These three algorithms have been optimized to find their corresponding type of motif. Together, they allow SCOPE to perform extremely well. Once a gene set has been analyzed and candidate motifs identified, SCOPE can look for other genes that contain the motif which, when added to the original set, will improve the motif score. This can occur through over-representation or motif position preference. Working with partial gene sets that have biologically verified transcription factor binding sites, SCOPE was able to identify most of the rest of the genes also regulated by the given transcription factor. Output from SCOPE shows candidate motifs, their significance, and other information both as a table and as a graphical motif map. FAQs and video tutorials are available at the SCOPE web site which also includes a "Sample Search" button that allows the user to perform a trial run. Scope has a very friendly user interface that enables novice users to access the algorithm's full power without having to become an expert in the bioinformatics of motif finding. As input, SCOPE can take a list of genes, or FASTA sequences. These can be entered in browser text fields, or read from

Classification of Domain Movements in Proteins Using Dynamic Contact Graphs

PubMed Central

Taylor, Daniel; Cawley, Gavin; Hayward, Steven

2013-01-01

A new method for the classification of domain movements in proteins is described and applied to 1822 pairs of structures from the Protein Data Bank that represent a domain movement in two-domain proteins. The method is based on changes in contacts between residues from the two domains in moving from one conformation to the other. We argue that there are five types of elemental contact changes and that these relate to five model domain movements called: “free”, “open-closed”, “anchored”, “sliding-twist”, and “see-saw.” A directed graph is introduced called the “Dynamic Contact Graph” which represents the contact changes in a domain movement. In many cases a graph, or part of a graph, provides a clear visual metaphor for the movement it represents and is a motif that can be easily recognised. The Dynamic Contact Graphs are often comprised of disconnected subgraphs indicating independent regions which may play different roles in the domain movement. The Dynamic Contact Graph for each domain movement is decomposed into elemental Dynamic Contact Graphs, those that represent elemental contact changes, allowing us to count the number of instances of each type of elemental contact change in the domain movement. This naturally leads to sixteen classes into which the 1822 domain movements are classified. PMID:24260562

Identifying novel sequence variants of RNA 3D motifs

PubMed Central

Zirbel, Craig L.; Roll, James; Sweeney, Blake A.; Petrov, Anton I.; Pirrung, Meg; Leontis, Neocles B.

2015-01-01

Predicting RNA 3D structure from sequence is a major challenge in biophysics. An important sub-goal is accurately identifying recurrent 3D motifs from RNA internal and hairpin loop sequences extracted from secondary structure (2D) diagrams. We have developed and validated new probabilistic models for 3D motif sequences based on hybrid Stochastic Context-Free Grammars and Markov Random Fields (SCFG/MRF). The SCFG/MRF models are constructed using atomic-resolution RNA 3D structures. To parameterize each model, we use all instances of each motif found in the RNA 3D Motif Atlas and annotations of pairwise nucleotide interactions generated by the FR3D software. Isostericity relations between non-Watson–Crick basepairs are used in scoring sequence variants. SCFG techniques model nested pairs and insertions, while MRF ideas handle crossing interactions and base triples. We use test sets of randomly-generated sequences to set acceptance and rejection thresholds for each motif group and thus control the false positive rate. Validation was carried out by comparing results for four motif groups to RMDetect. The software developed for sequence scoring (JAR3D) is structured to automatically incorporate new motifs as they accumulate in the RNA 3D Motif Atlas when new structures are solved and is available free for download. PMID:26130723

Occurrence probability of structured motifs in random sequences.

PubMed

Robin, S; Daudin, J-J; Richard, H; Sagot, M-F; Schbath, S

2002-01-01

The problem of extracting from a set of nucleic acid sequences motifs which may have biological function is more and more important. In this paper, we are interested in particular motifs that may be implicated in the transcription process. These motifs, called structured motifs, are composed of two ordered parts separated by a variable distance and allowing for substitutions. In order to assess their statistical significance, we propose approximations of the probability of occurrences of such a structured motif in a given sequence. An application of our method to evaluate candidate promoters in E. coli and B. subtilis is presented. Simulations show the goodness of the approximations.

meso-4,4′-Dimeth­oxy-2,2′-{[(3aR,7aS)-2,3,3a,4,5,6,7,7a-octa­hydro-1H-benz­imidazole-1,3-di­yl]bis­(methyl­ene)}diphenol

PubMed Central

Rivera, Augusto; Quiroga, Diego; Ríos-Motta, Jaime; Kučeraková, Monika; Dušek, Michal

2013-01-01

The title compound, C23H30N2O4, a di-Mannich base derived from 4-meth­oxy­phenol and cis-1,2-di­amine­cyclo­hexane, has a perhydro­benzimidazolidine nucleus, in which the cyclo­hexane ring adopts a chair conformation and the heterocyclic ring has a half-chair conformation with a C—N—C—C torsion angles of −48.14 (15) and −14.57 (16)°. The mean plane of the heterocycle makes dihedral angles of 86.29 (6) and 78.92 (6)° with the pendant benzene rings. The mol­ecular structure of the title compound shows the presence of two inter­actions between the N atoms of the imidazolidine ring and the hydroxyl groups through intra­molecular O—H⋯N hydrogen bonds with graph-set motif S(6). The unobserved lone pairs of the N atoms are presumed to be disposed in a syn conformation, being only the second example of an exception to the typical ‘rabbit-ears’ effect in 1,2-di­amines. PMID:24046631

On Edge Exchangeable Random Graphs

NASA Astrophysics Data System (ADS)

Janson, Svante

2017-06-01

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

Finding minimum-quotient cuts in planar graphs

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

Park, J.K.; Phillips, C.A.

Given a graph G = (V, E) where each vertex v {element_of} V is assigned a weight w(v) and each edge e {element_of} E is assigned a cost c(e), the quotient of a cut partitioning the vertices of V into sets S and {bar S} is c(S, {bar S})/min{l_brace}w(S), w(S){r_brace}, where c(S, {bar S}) is the sum of the costs of the edges crossing the cut and w(S) and w({bar S}) are the sum of the weights of the vertices in S and {bar S}, respectively. The problem of finding a cut whose quotient is minimum for a graph hasmore » in recent years attracted considerable attention, due in large part to the work of Rao and Leighton and Rao. They have shown that an algorithm (exact or approximation) for the minimum-quotient-cut problem can be used to obtain an approximation algorithm for the more famous minimumb-balanced-cut problem, which requires finding a cut (S,{bar S}) minimizing c(S,{bar S}) subject to the constraint bW {le} w(S) {le} (1 {minus} b)W, where W is the total vertex weight and b is some fixed balance in the range 0 < b {le} {1/2}. Unfortunately, the minimum-quotient-cut problem is strongly NP-hard for general graphs, and the best polynomial-time approximation algorithm known for the general problem guarantees only a cut whose quotient is at mostO(lg n) times optimal, where n is the size of the graph. However, for planar graphs, the minimum-quotient-cut problem appears more tractable, as Rao has developed several efficient approximation algorithms for the planar version of the problem capable of finding a cut whose quotient is at most some constant times optimal. In this paper, we improve Rao`s algorithms, both in terms of accuracy and speed. As our first result, we present two pseudopolynomial-time exact algorithms for the planar minimum-quotient-cut problem. As Rao`s most accurate approximation algorithm for the problem -- also a pseudopolynomial-time algorithm -- guarantees only a 1.5-times-optimal cut, our algorithms represent a significant advance.« less

Finding minimum-quotient cuts in planar graphs

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

Park, J.K.; Phillips, C.A.

Given a graph G = (V, E) where each vertex v [element of] V is assigned a weight w(v) and each edge e [element of] E is assigned a cost c(e), the quotient of a cut partitioning the vertices of V into sets S and [bar S] is c(S, [bar S])/min[l brace]w(S), w(S)[r brace], where c(S, [bar S]) is the sum of the costs of the edges crossing the cut and w(S) and w([bar S]) are the sum of the weights of the vertices in S and [bar S], respectively. The problem of finding a cut whose quotient is minimummore » for a graph has in recent years attracted considerable attention, due in large part to the work of Rao and Leighton and Rao. They have shown that an algorithm (exact or approximation) for the minimum-quotient-cut problem can be used to obtain an approximation algorithm for the more famous minimumb-balanced-cut problem, which requires finding a cut (S,[bar S]) minimizing c(S,[bar S]) subject to the constraint bW [le] w(S) [le] (1 [minus] b)W, where W is the total vertex weight and b is some fixed balance in the range 0 < b [le] [1/2]. Unfortunately, the minimum-quotient-cut problem is strongly NP-hard for general graphs, and the best polynomial-time approximation algorithm known for the general problem guarantees only a cut whose quotient is at mostO(lg n) times optimal, where n is the size of the graph. However, for planar graphs, the minimum-quotient-cut problem appears more tractable, as Rao has developed several efficient approximation algorithms for the planar version of the problem capable of finding a cut whose quotient is at most some constant times optimal. In this paper, we improve Rao's algorithms, both in terms of accuracy and speed. As our first result, we present two pseudopolynomial-time exact algorithms for the planar minimum-quotient-cut problem. As Rao's most accurate approximation algorithm for the problem -- also a pseudopolynomial-time algorithm -- guarantees only a 1.5-times-optimal cut, our algorithms represent a significant advance.« less

A graph theoretic approach to scene matching

NASA Technical Reports Server (NTRS)

Ranganath, Heggere S.; Chipman, Laure J.

1991-01-01

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

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

PubMed

Guturu, Parthasarathy; Dantu, Ram

2008-06-01

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

Return probabilities and hitting times of random walks on sparse Erdös-Rényi graphs.

PubMed

Martin, O C; Sulc, P

2010-03-01

We consider random walks on random graphs, focusing on return probabilities and hitting times for sparse Erdös-Rényi graphs. Using the tree approach, which is expected to be exact in the large graph limit, we show how to solve for the distribution of these quantities and we find that these distributions exhibit a form of self-similarity.

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

PubMed

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

2012-06-01

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

Synthetic approaches to peptides containing the L-Gln-L-Val-D(S)-Dmt motif.

PubMed

Suaifan, Ghadeer A R Y; Arafat, Tawfiq; Threadgill, Michael D

2007-05-15

The pseudoprolines S-Dmo (5,5-dimethyl-4-oxaproline) and R-Dmt (5,5-dimethyl-4-thiaproline) have been used to study the effects of forcing a fully cis conformation in peptides. Synthesis of peptides containing these (which have the same configuration as L-Pro) is straightforward. However, synthesis of peptides containing S-Dmt is difficult, owing to the rapid cyclisation of L-Aaa-S-Dmt amides and esters to form the corresponding diketopiperazines (DKP); thus the intermediacy of L-Aaa-S-Dmt amides and esters must be avoided in the synthetic sequence. Peptides containing the L-Gln-L-Val-D(S)-Dmt motif are particularly difficult, owing to the insolubility of coupling partners containing Gln. Introduction of Gln as N-Boc-pyroglutamate overcame the latter difficulty and the dipeptide active ester BocPygValOC(6)F(5) coupled in good yield with S-DmtOH. BocPygVal-S- DmtNH(CH(2))(2)C(6)H(4)NO(2) was converted quantitatively to BocGlnVal-S-DmtNH(CH(2))(2)C(6)H(4)NO(2) with ammonia, demonstrating the utility of this approach. Two peptide derivatives (CbzSerLysLeuGlnVal-S-DmtNH(CH(2))(2)C(6)H(4)NO(2) and CbzSerSerLysLeuGlnVal-S- DmtNH(CH(2))(2)C(6)H(4)NO(2)) were assembled, using these new methods of coupling a dipeptide acid active ester with S-DmtOH and introduction of Gln as Pyg, followed by conventional peptide couplings. The presence of the Val caused these peptides to be cleaved very slowly by prostate-specific antigen (PSA) at Leu Gln, rather than the expected Gln Val.

Genus Ranges of 4-Regular Rigid Vertex Graphs

PubMed Central

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

2016-01-01

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

Assessment of composite motif discovery methods.

PubMed

Klepper, Kjetil; Sandve, Geir K; Abul, Osman; Johansen, Jostein; Drablos, Finn

2008-02-26

Computational discovery of regulatory elements is an important area of bioinformatics research and more than a hundred motif discovery methods have been published. Traditionally, most of these methods have addressed the problem of single motif discovery - discovering binding motifs for individual transcription factors. In higher organisms, however, transcription factors usually act in combination with nearby bound factors to induce specific regulatory behaviours. Hence, recent focus has shifted from single motifs to the discovery of sets of motifs bound by multiple cooperating transcription factors, so called composite motifs or cis-regulatory modules. Given the large number and diversity of methods available, independent assessment of methods becomes important. Although there have been several benchmark studies of single motif discovery, no similar studies have previously been conducted concerning composite motif discovery. We have developed a benchmarking framework for composite motif discovery and used it to evaluate the performance of eight published module discovery tools. Benchmark datasets were constructed based on real genomic sequences containing experimentally verified regulatory modules, and the module discovery programs were asked to predict both the locations of these modules and to specify the single motifs involved. To aid the programs in their search, we provided position weight matrices corresponding to the binding motifs of the transcription factors involved. In addition, selections of decoy matrices were mixed with the genuine matrices on one dataset to test the response of programs to varying levels of noise. Although some of the methods tested tended to score somewhat better than others overall, there were still large variations between individual datasets and no single method performed consistently better than the rest in all situations. The variation in performance on individual datasets also shows that the new benchmark datasets represents a

Mathematical foundations of the GraphBLAS

DOE PAGES

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

2016-12-01

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

Hairpin structures with conserved sequence motifs determine the 3' ends of non-polyadenylated invertebrate iridovirus transcripts.

PubMed

İnce, İkbal Agah; Pijlman, Gorben P; Vlak, Just M; van Oers, Monique M

2017-11-01

Previously, we observed that the transcripts of Invertebrate iridescent virus 6 (IIV6) are not polyadenylated, in line with the absence of canonical poly(A) motifs (AATAAA) downstream of the open reading frames (ORFs) in the genome. Here, we determined the 3' ends of the transcripts of fifty-four IIV6 virion protein genes in infected Drosophila Schneider 2 (S2) cells. By using ligation-based amplification of cDNA ends (LACE) it was shown that the IIV6 mRNAs often ended with a CAUUA motif. In silico analysis showed that the 3'-untranslated regions of IIV6 genes have the ability to form hairpin structures (22-56 nt in length) and that for about half of all IIV6 genes these 3' sequences contained complementary TAATG and CATTA motifs. We also show that a hairpin in the 3' flanking region with conserved sequence motifs is a conserved feature in invertebrate-infecting iridoviruses (genus Iridovirus and Chloriridovirus). Copyright © 2017 Elsevier Inc. All rights reserved.

Graph Coloring Used to Model Traffic Lights.

ERIC Educational Resources Information Center

Williams, John

1992-01-01

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

Graphing Inequalities, Connecting Meaning

ERIC Educational Resources Information Center

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…

A PVS Graph Theory Library

NASA Technical Reports Server (NTRS)

Butler, Ricky W.; Sjogren, Jon A.

1998-01-01

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

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

PubMed

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

2008-01-01

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

Reflecting on Graphs: Attributes of Graph Choice and Construction Practices in Biology.

PubMed

Angra, Aakanksha; Gardner, Stephanie M

2017-01-01

Undergraduate biology education reform aims to engage students in scientific practices such as experimental design, experimentation, and data analysis and communication. Graphs are ubiquitous in the biological sciences, and creating effective graphical representations involves quantitative and disciplinary concepts and skills. Past studies document student difficulties with graphing within the contexts of classroom or national assessments without evaluating student reasoning. Operating under the metarepresentational competence framework, we conducted think-aloud interviews to reveal differences in reasoning and graph quality between undergraduate biology students, graduate students, and professors in a pen-and-paper graphing task. All professors planned and thought about data before graph construction. When reflecting on their graphs, professors and graduate students focused on the function of graphs and experimental design, while most undergraduate students relied on intuition and data provided in the task. Most undergraduate students meticulously plotted all data with scaled axes, while professors and some graduate students transformed the data, aligned the graph with the research question, and reflected on statistics and sample size. Differences in reasoning and approaches taken in graph choice and construction corroborate and extend previous findings and provide rich targets for undergraduate and graduate instruction. © 2017 A. Angra and S. M. Gardner. CBE—Life Sciences Education © 2017 The American Society for Cell Biology. This article is distributed by The American Society for Cell Biology under license from the author(s). It is available to the public under an Attribution–Noncommercial–Share Alike 3.0 Unported Creative Commons License (http://creativecommons.org/licenses/by-nc-sa/3.0).

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

PubMed

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

2017-07-01

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

MotifNet: a web-server for network motif analysis.

PubMed

Smoly, Ilan Y; Lerman, Eugene; Ziv-Ukelson, Michal; Yeger-Lotem, Esti

2017-06-15

Network motifs are small topological patterns that recur in a network significantly more often than expected by chance. Their identification emerged as a powerful approach for uncovering the design principles underlying complex networks. However, available tools for network motif analysis typically require download and execution of computationally intensive software on a local computer. We present MotifNet, the first open-access web-server for network motif analysis. MotifNet allows researchers to analyze integrated networks, where nodes and edges may be labeled, and to search for motifs of up to eight nodes. The output motifs are presented graphically and the user can interactively filter them by their significance, number of instances, node and edge labels, and node identities, and view their instances. MotifNet also allows the user to distinguish between motifs that are centered on specific nodes and motifs that recur in distinct parts of the network. MotifNet is freely available at http://netbio.bgu.ac.il/motifnet . The website was implemented using ReactJs and supports all major browsers. The server interface was implemented in Python with data stored on a MySQL database. estiyl@bgu.ac.il or michaluz@cs.bgu.ac.il. Supplementary data are available at Bioinformatics online. © The Author 2017. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com

DNA motif elucidation using belief propagation.

PubMed

Wong, Ka-Chun; Chan, Tak-Ming; Peng, Chengbin; Li, Yue; Zhang, Zhaolei

2013-09-01

Protein-binding microarray (PBM) is a high-throughout platform that can measure the DNA-binding preference of a protein in a comprehensive and unbiased manner. A typical PBM experiment can measure binding signal intensities of a protein to all the possible DNA k-mers (k=8∼10); such comprehensive binding affinity data usually need to be reduced and represented as motif models before they can be further analyzed and applied. Since proteins can often bind to DNA in multiple modes, one of the major challenges is to decompose the comprehensive affinity data into multimodal motif representations. Here, we describe a new algorithm that uses Hidden Markov Models (HMMs) and can derive precise and multimodal motifs using belief propagations. We describe an HMM-based approach using belief propagations (kmerHMM), which accepts and preprocesses PBM probe raw data into median-binding intensities of individual k-mers. The k-mers are ranked and aligned for training an HMM as the underlying motif representation. Multiple motifs are then extracted from the HMM using belief propagations. Comparisons of kmerHMM with other leading methods on several data sets demonstrated its effectiveness and uniqueness. Especially, it achieved the best performance on more than half of the data sets. In addition, the multiple binding modes derived by kmerHMM are biologically meaningful and will be useful in interpreting other genome-wide data such as those generated from ChIP-seq. The executables and source codes are available at the authors' websites: e.g. http://www.cs.toronto.edu/∼wkc/kmerHMM.

Retina verification system based on biometric graph matching.

PubMed

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

2013-09-01

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

Gibbs motif sampling: detection of bacterial outer membrane protein repeats.

PubMed Central

Neuwald, A. F.; Liu, J. S.; Lawrence, C. E.

1995-01-01

The detection and alignment of locally conserved regions (motifs) in multiple sequences can provide insight into protein structure, function, and evolution. A new Gibbs sampling algorithm is described that detects motif-encoding regions in sequences and optimally partitions them into distinct motif models; this is illustrated using a set of immunoglobulin fold proteins. When applied to sequences sharing a single motif, the sampler can be used to classify motif regions into related submodels, as is illustrated using helix-turn-helix DNA-binding proteins. Other statistically based procedures are described for searching a database for sequences matching motifs found by the sampler. When applied to a set of 32 very distantly related bacterial integral outer membrane proteins, the sampler revealed that they share a subtle, repetitive motif. Although BLAST (Altschul SF et al., 1990, J Mol Biol 215:403-410) fails to detect significant pairwise similarity between any of the sequences, the repeats present in these outer membrane proteins, taken as a whole, are highly significant (based on a generally applicable statistical test for motifs described here). Analysis of bacterial porins with known trimeric beta-barrel structure and related proteins reveals a similar repetitive motif corresponding to alternating membrane-spanning beta-strands. These beta-strands occur on the membrane interface (as opposed to the trimeric interface) of the beta-barrel. The broad conservation and structural location of these repeats suggests that they play important functional roles. PMID:8520488

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

PubMed Central

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

2008-01-01

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

A path following algorithm for the graph matching problem.

PubMed

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

2009-12-01

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

Graph determined symbolic dynamics and hybrid systems

NASA Astrophysics Data System (ADS)

Ayers, Kimberly Danielle

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

Adjusting protein graphs based on graph entropy.

PubMed

Peng, Sheng-Lung; Tsay, Yu-Wei

2014-01-01

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

Adjusting protein graphs based on graph entropy

PubMed Central

2014-01-01

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

Identification of structural domains in proteins by a graph heuristic.

PubMed

Wernisch, L; Hunting, M; Wodak, S J

1999-05-15

A novel automatic procedure for identifying domains from protein atomic coordinates is presented. The procedure, termed STRUDL (STRUctural Domain Limits), does not take into account information on secondary structures and handles any number of domains made up of contiguous or non-contiguous chain segments. The core algorithm uses the Kernighan-Lin graph heuristic to partition the protein into residue sets which display minimum interactions between them. These interactions are deduced from the weighted Voronoi diagram. The generated partitions are accepted or rejected on the basis of optimized criteria, representing basic expected physical properties of structural domains. The graph heuristic approach is shown to be very effective, it approximates closely the exact solution provided by a branch and bound algorithm for a number of test proteins. In addition, the overall performance of STRUDL is assessed on a set of 787 representative proteins from the Protein Data Bank by comparison to domain definitions in the CATH protein classification. The domains assigned by STRUDL agree with the CATH assignments in at least 81% of the tested proteins. This result is comparable to that obtained previously using PUU (Holm and Sander, Proteins 1994;9:256-268), the only other available algorithm designed to identify domains with any number of non-contiguous chain segments. A detailed discussion of the structures for which our assignments differ from those in CATH brings to light some clear inconsistencies between the concept of structural domains based on minimizing inter-domain interactions and that of delimiting structural motifs that represent acceptable folding topologies or architectures. Considering both concepts as complementary and combining them in a layered approach might be the way forward.

BayesMotif: de novo protein sorting motif discovery from impure datasets.

PubMed

Hu, Jianjun; Zhang, Fan

2010-01-18

Protein sorting is the process that newly synthesized proteins are transported to their target locations within or outside of the cell. This process is precisely regulated by protein sorting signals in different forms. A major category of sorting signals are amino acid sub-sequences usually located at the N-terminals or C-terminals of protein sequences. Genome-wide experimental identification of protein sorting signals is extremely time-consuming and costly. Effective computational algorithms for de novo discovery of protein sorting signals is needed to improve the understanding of protein sorting mechanisms. We formulated the protein sorting motif discovery problem as a classification problem and proposed a Bayesian classifier based algorithm (BayesMotif) for de novo identification of a common type of protein sorting motifs in which a highly conserved anchor is present along with a less conserved motif regions. A false positive removal procedure is developed to iteratively remove sequences that are unlikely to contain true motifs so that the algorithm can identify motifs from impure input sequences. Experiments on both implanted motif datasets and real-world datasets showed that the enhanced BayesMotif algorithm can identify anchored sorting motifs from pure or impure protein sequence dataset. It also shows that the false positive removal procedure can help to identify true motifs even when there is only 20% of the input sequences containing true motif instances. We proposed BayesMotif, a novel Bayesian classification based algorithm for de novo discovery of a special category of anchored protein sorting motifs from impure datasets. Compared to conventional motif discovery algorithms such as MEME, our algorithm can find less-conserved motifs with short highly conserved anchors. Our algorithm also has the advantage of easy incorporation of additional meta-sequence features such as hydrophobicity or charge of the motifs which may help to overcome the limitations of

Spreadsheet Works: Graphing Functions on a Spreadsheet.

ERIC Educational Resources Information Center

Ramamurthi, V. S.

1989-01-01

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

Locating domination number of m-shadowing of graphs

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

The BaMM web server for de-novo motif discovery and regulatory sequence analysis.

PubMed

Kiesel, Anja; Roth, Christian; Ge, Wanwan; Wess, Maximilian; Meier, Markus; Söding, Johannes

2018-05-28

The BaMM web server offers four tools: (i) de-novo discovery of enriched motifs in a set of nucleotide sequences, (ii) scanning a set of nucleotide sequences with motifs to find motif occurrences, (iii) searching with an input motif for similar motifs in our BaMM database with motifs for >1000 transcription factors, trained from the GTRD ChIP-seq database and (iv) browsing and keyword searching the motif database. In contrast to most other servers, we represent sequence motifs not by position weight matrices (PWMs) but by Bayesian Markov Models (BaMMs) of order 4, which we showed previously to perform substantially better in ROC analyses than PWMs or first order models. To address the inadequacy of P- and E-values as measures of motif quality, we introduce the AvRec score, the average recall over the TP-to-FP ratio between 1 and 100. The BaMM server is freely accessible without registration at https://bammmotif.mpibpc.mpg.de.

Characterizing Containment and Related Classes of Graphs,

DTIC Science & Technology

1985-01-01

Math . to appear. [G2] Golumbic,. Martin C., D. Rotem and J. Urrutia. "Comparability graphs and intersection graphs" Discrete Math . 43 (1983) 37-40. [G3...intersection classes of graphs" Discrete Math . to appear. [S2] Scheinerman, Edward R. Intersection Classes and Multiple Intersection Parameters of Graphs...graphs and of interval graphs" Canad. Jour. of blath. 16 (1964) 539-548. [G1] Golumbic, Martin C. "Containment graphs: and. intersection graphs" Discrete

Survey of Approaches to Generate Realistic Synthetic Graphs

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

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

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

RSAT matrix-clustering: dynamic exploration and redundancy reduction of transcription factor binding motif collections.

PubMed

Castro-Mondragon, Jaime Abraham; Jaeger, Sébastien; Thieffry, Denis; Thomas-Chollier, Morgane; van Helden, Jacques

2017-07-27

Transcription factor (TF) databases contain multitudes of binding motifs (TFBMs) from various sources, from which non-redundant collections are derived by manual curation. The advent of high-throughput methods stimulated the production of novel collections with increasing numbers of motifs. Meta-databases, built by merging these collections, contain redundant versions, because available tools are not suited to automatically identify and explore biologically relevant clusters among thousands of motifs. Motif discovery from genome-scale data sets (e.g. ChIP-seq) also produces redundant motifs, hampering the interpretation of results. We present matrix-clustering, a versatile tool that clusters similar TFBMs into multiple trees, and automatically creates non-redundant TFBM collections. A feature unique to matrix-clustering is its dynamic visualisation of aligned TFBMs, and its capability to simultaneously treat multiple collections from various sources. We demonstrate that matrix-clustering considerably simplifies the interpretation of combined results from multiple motif discovery tools, and highlights biologically relevant variations of similar motifs. We also ran a large-scale application to cluster ∼11 000 motifs from 24 entire databases, showing that matrix-clustering correctly groups motifs belonging to the same TF families, and drastically reduced motif redundancy. matrix-clustering is integrated within the RSAT suite (http://rsat.eu/), accessible through a user-friendly web interface or command-line for its integration in pipelines. © The Author(s) 2017. Published by Oxford University Press on behalf of Nucleic Acids Research.

Graph-Based Object Class Discovery

NASA Astrophysics Data System (ADS)

Xia, Shengping; Hancock, Edwin R.

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

Groupies in multitype random graphs.

PubMed

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.

Exploring and Making Sense of Large Graphs

DTIC Science & Technology

2015-08-01

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

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

DOE PAGES

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

2017-06-30

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

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

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

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

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

[Conserved motifs in voltage sensing proteins].

PubMed

Wang, Chang-He; Xie, Zhen-Li; Lv, Jian-Wei; Yu, Zhi-Dan; Shao, Shu-Li

2012-08-25

This paper was aimed to study conserved motifs of voltage sensing proteins (VSPs) and establish a voltage sensing model. All VSPs were collected from the Uniprot database using a comprehensive keyword search followed by manual curation, and the results indicated that there are only two types of known VSPs, voltage gated ion channels and voltage dependent phosphatases. All the VSPs have a common domain of four helical transmembrane segments (TMS, S1-S4), which constitute the voltage sensing module of the VSPs. The S1 segment was shown to be responsible for membrane targeting and insertion of these proteins, while S2-S4 segments, which can sense membrane potential, for protein properties. Conserved motifs/residues and their functional significance of each TMS were identified using profile-to-profile sequence alignments. Conserved motifs in these four segments are strikingly similar for all VSPs, especially, the conserved motif [RK]-X(2)-R-X(2)-R-X(2)-[RK] was presented in all the S4 segments, with positively charged arginine (R) alternating with two hydrophobic or uncharged residues. Movement of these arginines across the membrane electric field is the core mechanism by which the VSPs detect changes in membrane potential. The negatively charged aspartate (D) in the S3 segment is universally conserved in all the VSPs, suggesting that the aspartate residue may be involved in voltage sensing properties of VSPs as well as the electrostatic interactions with the positively charged residues in the S4 segment, which may enhance the thermodynamic stability of the S4 segments in plasma membrane.

Parasol: An Architecture for Cross-Cloud Federated Graph Querying

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

Lieberman, Michael; Choudhury, Sutanay; Hughes, Marisa

2014-06-22

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

DynaMIT: the dynamic motif integration toolkit

PubMed Central

Dassi, Erik; Quattrone, Alessandro

2016-01-01

De-novo motif search is a frequently applied bioinformatics procedure to identify and prioritize recurrent elements in sequences sets for biological investigation, such as the ones derived from high-throughput differential expression experiments. Several algorithms have been developed to perform motif search, employing widely different approaches and often giving divergent results. In order to maximize the power of these investigations and ultimately be able to draft solid biological hypotheses, there is the need for applying multiple tools on the same sequences and merge the obtained results. However, motif reporting formats and statistical evaluation methods currently make such an integration task difficult to perform and mostly restricted to specific scenarios. We thus introduce here the Dynamic Motif Integration Toolkit (DynaMIT), an extremely flexible platform allowing to identify motifs employing multiple algorithms, integrate them by means of a user-selected strategy and visualize results in several ways; furthermore, the platform is user-extendible in all its aspects. DynaMIT is freely available at http://cibioltg.bitbucket.org. PMID:26253738

A local search for a graph clustering problem

NASA Astrophysics Data System (ADS)

Navrotskaya, Anna; Il'ev, Victor

2016-10-01

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

Multi-scale modularity and motif distributional effect in metabolic networks.

PubMed

Gao, Shang; Chen, Alan; Rahmani, Ali; Zeng, Jia; Tan, Mehmet; Alhajj, Reda; Rokne, Jon; Demetrick, Douglas; Wei, Xiaohui

2016-01-01

Metabolism is a set of fundamental processes that play important roles in a plethora of biological and medical contexts. It is understood that the topological information of reconstructed metabolic networks, such as modular organization, has crucial implications on biological functions. Recent interpretations of modularity in network settings provide a view of multiple network partitions induced by different resolution parameters. Here we ask the question: How do multiple network partitions affect the organization of metabolic networks? Since network motifs are often interpreted as the super families of evolved units, we further investigate their impact under multiple network partitions and investigate how the distribution of network motifs influences the organization of metabolic networks. We studied Homo sapiens, Saccharomyces cerevisiae and Escherichia coli metabolic networks; we analyzed the relationship between different community structures and motif distribution patterns. Further, we quantified the degree to which motifs participate in the modular organization of metabolic networks.

Graph-state formalism for mutually unbiased bases

NASA Astrophysics Data System (ADS)

Spengler, Christoph; Kraus, Barbara

2013-11-01

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

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

NASA Astrophysics Data System (ADS)

Winarsih, Tri; Indriati, Diari

2018-04-01

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

Community structure and scale-free collections of Erdős-Rényi graphs.

PubMed

Seshadhri, C; Kolda, Tamara G; Pinar, Ali

2012-05-01

Community structure plays a significant role in the analysis of social networks and similar graphs, yet this structure is little understood and not well captured by most models. We formally define a community to be a subgraph that is internally highly connected and has no deeper substructure. We use tools of combinatorics to show that any such community must contain a dense Erdős-Rényi (ER) subgraph. Based on mathematical arguments, we hypothesize that any graph with a heavy-tailed degree distribution and community structure must contain a scale-free collection of dense ER subgraphs. These theoretical observations corroborate well with empirical evidence. From this, we propose the Block Two-Level Erdős-Rényi (BTER) model, and demonstrate that it accurately captures the observable properties of many real-world social networks.

Ca2+-binding Motif of βγ-Crystallins*

PubMed Central

Srivastava, Shanti Swaroop; Mishra, Amita; Krishnan, Bal; Sharma, Yogendra

2014-01-01

βγ-Crystallin-type double clamp (N/D)(N/D)XX(S/T)S motif is an established but sparsely investigated motif for Ca2+ binding. A βγ-crystallin domain is formed of two Greek key motifs, accommodating two Ca2+-binding sites. βγ-Crystallins make a separate class of Ca2+-binding proteins (CaBP), apparently a major group of CaBP in bacteria. Paralleling the diversity in βγ-crystallin domains, these motifs also show great diversity, both in structure and in function. Although the expression of some of them has been associated with stress, virulence, and adhesion, the functional implications of Ca2+ binding to βγ-crystallins in mediating biological processes are yet to be elucidated. PMID:24567326

Gambler's ruin problem on Erdős-Rényi graphs

NASA Astrophysics Data System (ADS)

Néda, Zoltán; Davidova, Larissa; Újvári, Szeréna; Istrate, Gabriel

2017-02-01

A multiagent ruin-game is studied on Erdős-Rényi type graphs. Initially the players have the same wealth. At each time step a monopolist game is played on all active links (links that connect nodes with nonzero wealth). In such a game each player puts a unit wealth in the pot and the pot is won with equal probability by one of the players. The game ends when there are no connected players such that both of them have non-zero wealth. In order to characterize the final state for dense graphs a compact formula is given for the expected number of the remaining players with non-zero wealth and the wealth distribution among these players. Theoretical predictions are given for the expected duration of the ruin game. The dynamics of the number of active players is also investigated. Validity of the theoretical predictions is investigated by Monte Carlo experiments.

Graph drawing using tabu search coupled with path relinking

PubMed Central

Rodgers, Peter

2018-01-01

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

Identity and functions of CxxC-derived motifs.

PubMed

Fomenko, Dmitri E; Gladyshev, Vadim N

2003-09-30

Two cysteines separated by two other residues (the CxxC motif) are employed by many redox proteins for formation, isomerization, and reduction of disulfide bonds and for other redox functions. The place of the C-terminal cysteine in this motif may be occupied by serine (the CxxS motif), modifying the functional repertoire of redox proteins. Here we found that the CxxC motif may also give rise to a motif, in which the C-terminal cysteine is replaced with threonine (the CxxT motif). Moreover, in contrast to a view that the N-terminal cysteine in the CxxC motif always serves as a nucleophilic attacking group, this residue could also be replaced with threonine (the TxxC motif), serine (the SxxC motif), or other residues. In each of these CxxC-derived motifs, the presence of a downstream alpha-helix was strongly favored. A search for conserved CxxC-derived motif/helix patterns in four complete genomes representing bacteria, archaea, and eukaryotes identified known redox proteins and suggested possible redox functions for several additional proteins. Catalytic sites in peroxiredoxins were major representatives of the TxxC motif, whereas those in glutathione peroxidases represented the CxxT motif. Structural assessments indicated that threonines in these enzymes could stabilize catalytic thiolates, suggesting revisions to previously proposed catalytic triads. Each of the CxxC-derived motifs was also observed in natural selenium-containing proteins, in which selenocysteine was present in place of a catalytic cysteine.

A model of language inflection graphs

NASA Astrophysics Data System (ADS)

Fukś, Henryk; Farzad, Babak; Cao, Yi

2014-01-01

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

Graph processing platforms at scale: practices and experiences

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

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

2015-01-01

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

A simple method for finding the scattering coefficients of quantum graphs

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

Cottrell, Seth S.

2015-09-15

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

Efficient enumeration of monocyclic chemical graphs with given path frequencies

PubMed Central

2014-01-01

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

Student Reasoning about Graphs in Different Contexts

ERIC Educational Resources Information Center

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

2016-01-01

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

GrouseFlocks: steerable exploration of graph hierarchy space.

PubMed

Archambault, Daniel; Munzner, Tamara; Auber, David

2008-01-01

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

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

NASA Astrophysics Data System (ADS)

Darmaji, Alfarisi, Ridho

2017-08-01

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

DLocalMotif: a discriminative approach for discovering local motifs in protein sequences.

PubMed

Mehdi, Ahmed M; Sehgal, Muhammad Shoaib B; Kobe, Bostjan; Bailey, Timothy L; Bodén, Mikael

2013-01-01

Local motifs are patterns of DNA or protein sequences that occur within a sequence interval relative to a biologically defined anchor or landmark. Current protein motif discovery methods do not adequately consider such constraints to identify biologically significant motifs that are only weakly over-represented but spatially confined. Using negatives, i.e. sequences known to not contain a local motif, can further increase the specificity of their discovery. This article introduces the method DLocalMotif that makes use of positional information and negative data for local motif discovery in protein sequences. DLocalMotif combines three scoring functions, measuring degrees of motif over-representation, entropy and spatial confinement, specifically designed to discriminatively exploit the availability of negative data. The method is shown to outperform current methods that use only a subset of these motif characteristics. We apply the method to several biological datasets. The analysis of peroxisomal targeting signals uncovers several novel motifs that occur immediately upstream of the dominant peroxisomal targeting signal-1 signal. The analysis of proline-tyrosine nuclear localization signals uncovers multiple novel motifs that overlap with C2H2 zinc finger domains. We also evaluate the method on classical nuclear localization signals and endoplasmic reticulum retention signals and find that DLocalMotif successfully recovers biologically relevant sequence properties. http://bioinf.scmb.uq.edu.au/dlocalmotif/

A Graph-Based Recovery and Decomposition of Swanson’s Hypothesis using Semantic Predications

PubMed Central

Cameron, Delroy; Bodenreider, Olivier; Yalamanchili, Hima; Danh, Tu; Vallabhaneni, Sreeram; Thirunarayan, Krishnaprasad; Sheth, Amit P.; Rindflesch, Thomas C.

2014-01-01

Objectives This paper presents a methodology for recovering and decomposing Swanson’s Raynaud Syndrome–Fish Oil Hypothesis semi-automatically. The methodology leverages the semantics of assertions extracted from biomedical literature (called semantic predications) along with structured background knowledge and graph-based algorithms to semi-automatically capture the informative associations originally discovered manually by Swanson. Demonstrating that Swanson’s manually intensive techniques can be undertaken semi-automatically, paves the way for fully automatic semantics-based hypothesis generation from scientific literature. Methods Semantic predications obtained from biomedical literature allow the construction of labeled directed graphs which contain various associations among concepts from the literature. By aggregating such associations into informative subgraphs, some of the relevant details originally articulated by Swanson has been uncovered. However, by leveraging background knowledge to bridge important knowledge gaps in the literature, a methodology for semi-automatically capturing the detailed associations originally explicated in natural language by Swanson has been developed. Results Our methodology not only recovered the 3 associations commonly recognized as Swanson’s Hypothesis, but also decomposed them into an additional 16 detailed associations, formulated as chains of semantic predications. Altogether, 14 out of the 19 associations that can be attributed to Swanson were retrieved using our approach. To the best of our knowledge, such an in-depth recovery and decomposition of Swanson’s Hypothesis has never been attempted. Conclusion In this work therefore, we presented a methodology for semi- automatically recovering and decomposing Swanson’s RS-DFO Hypothesis using semantic representations and graph algorithms. Our methodology provides new insights into potential prerequisites for semantics-driven Literature-Based Discovery (LBD

SING: Subgraph search In Non-homogeneous Graphs

PubMed Central

2010-01-01

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

A set of tetra-nucleotide core motif SSR markers for efficient identification of potato (Solanum tuberosum) cultivars.

PubMed

Kishine, Masahiro; Tsutsumi, Katsuji; Kitta, Kazumi

2017-12-01

Simple sequence repeat (SSR) is a popular tool for individual fingerprinting. The long-core motif (e.g. tetra-, penta-, and hexa-nucleotide) simple sequence repeats (SSRs) are preferred because they make it easier to separate and distinguish neighbor alleles. In the present study, a new set of 8 tetra-nucleotide SSRs in potato ( Solanum tuberosum ) is reported. By using these 8 markers, 72 out of 76 cultivars obtained from Japan and the United States were clearly discriminated, while two pairs, both of which arose from natural variation, showed identical profiles. The combined probability of identity between two random cultivars for the set of 8 SSR markers was estimated to be 1.10 × 10 -8 , confirming the usefulness of the proposed SSR markers for fingerprinting analyses of potato.

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

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

2015-01-16

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

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

PubMed

Lyman, R Lee

2009-02-01

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

Distance Magic-Type and Distance Antimagic-Type Labelings of Graphs

NASA Astrophysics Data System (ADS)

Freyberg, Bryan J.

Generally speaking, a distance magic-type labeling of a graph G of order n is a bijection l from the vertex set of the graph to the first n natural numbers or to the elements of a group of order n, with the property that the weight of each vertex is the same. The weight of a vertex x is defined as the sum (or appropriate group operation) of all the labels of vertices adjacent to x. If instead we require that all weights differ, then we refer to the labeling as a distance antimagic-type labeling. This idea can be generalized for directed graphs; the weight will take into consideration the direction of the arcs. In this manuscript, we provide new results for d-handicap labeling, a distance antimagic-type labeling, and introduce a new distance magic-type labeling called orientable Gamma-distance magic labeling. A d-handicap distance antimagic labeling (or just d-handicap labeling for short) of a graph G = ( V,E) of order n is a bijection l from V to the set {1,2,...,n} with induced weight function [special characters omitted]. such that l(xi) = i and the sequence of weights w(x 1),w(x2),...,w (xn) forms an arithmetic sequence with constant difference d at least 1. If a graph G admits a d-handicap labeling, we say G is a d-handicap graph. A d-handicap incomplete tournament, H(n,k,d ) is an incomplete tournament of n teams ranked with the first n natural numbers such that each team plays exactly k games and the strength of schedule of the ith ranked team is d more than the i + 1st ranked team. That is, strength of schedule increases arithmetically with strength of team. Constructing an H(n,k,d) is equivalent to finding a d-handicap labeling of a k-regular graph of order n.. In Chapter 2 we provide general constructions for every d for large classes of both n and k, providing breadfth and depth to the catalog of known H(n,k,d)'s. In Chapters 3 - 6, we introduce a new type of labeling called orientable Gamma-distance magic labeling. Let Gamma be an abelian group of order

SALAD database: a motif-based database of protein annotations for plant comparative genomics

PubMed Central

Mihara, Motohiro; Itoh, Takeshi; Izawa, Takeshi

2010-01-01

Proteins often have several motifs with distinct evolutionary histories. Proteins with similar motifs have similar biochemical properties and thus related biological functions. We constructed a unique comparative genomics database termed the SALAD database (http://salad.dna.affrc.go.jp/salad/) from plant-genome-based proteome data sets. We extracted evolutionarily conserved motifs by MEME software from 209 529 protein-sequence annotation groups selected by BLASTP from the proteome data sets of 10 species: rice, sorghum, Arabidopsis thaliana, grape, a lycophyte, a moss, 3 algae, and yeast. Similarity clustering of each protein group was performed by pairwise scoring of the motif patterns of the sequences. The SALAD database provides a user-friendly graphical viewer that displays a motif pattern diagram linked to the resulting bootstrapped dendrogram for each protein group. Amino-acid-sequence-based and nucleotide-sequence-based phylogenetic trees for motif combination alignment, a logo comparison diagram for each clade in the tree, and a Pfam-domain pattern diagram are also available. We also developed a viewer named ‘SALAD on ARRAYs’ to view arbitrary microarray data sets of paralogous genes linked to the same dendrogram in a window. The SALAD database is a powerful tool for comparing protein sequences and can provide valuable hints for biological analysis. PMID:19854933

SALAD database: a motif-based database of protein annotations for plant comparative genomics.

PubMed

Mihara, Motohiro; Itoh, Takeshi; Izawa, Takeshi

2010-01-01

Proteins often have several motifs with distinct evolutionary histories. Proteins with similar motifs have similar biochemical properties and thus related biological functions. We constructed a unique comparative genomics database termed the SALAD database (http://salad.dna.affrc.go.jp/salad/) from plant-genome-based proteome data sets. We extracted evolutionarily conserved motifs by MEME software from 209,529 protein-sequence annotation groups selected by BLASTP from the proteome data sets of 10 species: rice, sorghum, Arabidopsis thaliana, grape, a lycophyte, a moss, 3 algae, and yeast. Similarity clustering of each protein group was performed by pairwise scoring of the motif patterns of the sequences. The SALAD database provides a user-friendly graphical viewer that displays a motif pattern diagram linked to the resulting bootstrapped dendrogram for each protein group. Amino-acid-sequence-based and nucleotide-sequence-based phylogenetic trees for motif combination alignment, a logo comparison diagram for each clade in the tree, and a Pfam-domain pattern diagram are also available. We also developed a viewer named 'SALAD on ARRAYs' to view arbitrary microarray data sets of paralogous genes linked to the same dendrogram in a window. The SALAD database is a powerful tool for comparing protein sequences and can provide valuable hints for biological analysis.

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

PubMed

Gnutzmann, Sven; Waltner, Daniel

2016-12-01

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

Upper bound for the span of pencil graph

NASA Astrophysics Data System (ADS)

Parvathi, N.; Vimala Rani, A.

2018-04-01

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

Comparison of University Students' Understanding of Graphs in Different Contexts

ERIC Educational Resources Information Center

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

2013-01-01

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

ATtRACT-a database of RNA-binding proteins and associated motifs.

PubMed

Giudice, Girolamo; Sánchez-Cabo, Fátima; Torroja, Carlos; Lara-Pezzi, Enrique

2016-01-01

RNA-binding proteins (RBPs) play a crucial role in key cellular processes, including RNA transport, splicing, polyadenylation and stability. Understanding the interaction between RBPs and RNA is key to improve our knowledge of RNA processing, localization and regulation in a global manner. Despite advances in recent years, a unified non-redundant resource that includes information on experimentally validated motifs, RBPs and integrated tools to exploit this information is lacking. Here, we developed a database named ATtRACT (available athttp://attract.cnic.es) that compiles information on 370 RBPs and 1583 RBP consensus binding motifs, 192 of which are not present in any other database. To populate ATtRACT we (i) extracted and hand-curated experimentally validated data from CISBP-RNA, SpliceAid-F, RBPDB databases, (ii) integrated and updated the unavailable ASD database and (iii) extracted information from Protein-RNA complexes present in Protein Data Bank database through computational analyses. ATtRACT provides also efficient algorithms to search a specific motif and scan one or more RNA sequences at a time. It also allows discoveringde novomotifs enriched in a set of related sequences and compare them with the motifs included in the database.Database URL:http:// attract. cnic. es. © The Author(s) 2016. Published by Oxford University Press.

Analyzing and synthesizing phylogenies using tree alignment graphs.

PubMed

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

2013-01-01

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

Analyzing and Synthesizing Phylogenies Using Tree Alignment Graphs

PubMed Central

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

2013-01-01

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

On the 2-Extendability of Planar Graphs

DTIC Science & Technology

1989-01-01

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

A fast algorithm for vertex-frequency representations of signals on graphs

PubMed Central

Jestrović, Iva; Coyle, James L.; Sejdić, Ervin

2016-01-01

The windowed Fourier transform (short time Fourier transform) and the S-transform are widely used signal processing tools for extracting frequency information from non-stationary signals. Previously, the windowed Fourier transform had been adopted for signals on graphs and has been shown to be very useful for extracting vertex-frequency information from graphs. However, high computational complexity makes these algorithms impractical. We sought to develop a fast windowed graph Fourier transform and a fast graph S-transform requiring significantly shorter computation time. The proposed schemes have been tested with synthetic test graph signals and real graph signals derived from electroencephalography recordings made during swallowing. The results showed that the proposed schemes provide significantly lower computation time in comparison with the standard windowed graph Fourier transform and the fast graph S-transform. Also, the results showed that noise has no effect on the results of the algorithm for the fast windowed graph Fourier transform or on the graph S-transform. Finally, we showed that graphs can be reconstructed from the vertex-frequency representations obtained with the proposed algorithms. PMID:28479645

Discriminative graph embedding for label propagation.

PubMed

Nguyen, Canh Hao; Mamitsuka, Hiroshi

2011-09-01

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

Student reasoning about graphs in different contexts

NASA Astrophysics Data System (ADS)

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

2016-06-01

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

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

PubMed Central

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

2017-01-01

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

Scaling Up Graph-Based Semisupervised Learning via Prototype Vector Machines

PubMed Central

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

2014-01-01

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

An analysis of the positional distribution of DNA motifs in promoter regions and its biological relevance.

PubMed

Casimiro, Ana C; Vinga, Susana; Freitas, Ana T; Oliveira, Arlindo L

2008-02-07

Motif finding algorithms have developed in their ability to use computationally efficient methods to detect patterns in biological sequences. However the posterior classification of the output still suffers from some limitations, which makes it difficult to assess the biological significance of the motifs found. Previous work has highlighted the existence of positional bias of motifs in the DNA sequences, which might indicate not only that the pattern is important, but also provide hints of the positions where these patterns occur preferentially. We propose to integrate position uniformity tests and over-representation tests to improve the accuracy of the classification of motifs. Using artificial data, we have compared three different statistical tests (Chi-Square, Kolmogorov-Smirnov and a Chi-Square bootstrap) to assess whether a given motif occurs uniformly in the promoter region of a gene. Using the test that performed better in this dataset, we proceeded to study the positional distribution of several well known cis-regulatory elements, in the promoter sequences of different organisms (S. cerevisiae, H. sapiens, D. melanogaster, E. coli and several Dicotyledons plants). The results show that position conservation is relevant for the transcriptional machinery. We conclude that many biologically relevant motifs appear heterogeneously distributed in the promoter region of genes, and therefore, that non-uniformity is a good indicator of biological relevance and can be used to complement over-representation tests commonly used. In this article we present the results obtained for the S. cerevisiae data sets.

Discovery of T Cell Receptor β Motifs Specific to HLA-B27-Positive Ankylosing Spondylitis by Deep Repertoire Sequence Analysis.

PubMed

Faham, Malek; Carlton, Victoria; Moorhead, Martin; Zheng, Jianbiao; Klinger, Mark; Pepin, Francois; Asbury, Thomas; Vignali, Marissa; Emerson, Ryan O; Robins, Harlan S; Ireland, James; Baechler-Gillespie, Emily; Inman, Robert D

2017-04-01

Ankylosing spondylitis (AS), a chronic inflammatory disorder, has a notable association with HLA-B27. One hypothesis suggests that a common antigen that binds to HLA-B27 is important for AS disease pathogenesis. This study was undertaken to determine sequences and motifs that are shared among HLA-B27-positive AS patients, using T cell repertoire next-generation sequencing. To identify motifs enriched among B27-positive AS patients, we performed T cell receptor β (TCRβ) repertoire sequencing on samples from 191 B27-positive AS patients, 43 B27-negative AS patients, and 227 controls, and we obtained >77 million TCRβ clonotype sequences. First, we assessed whether any of 50 previously published sequences were enriched in B27-positive AS patients. We then used training and test cohorts to identify discovered motifs that were enriched in B27-positive AS patients versus controls. Six previously published and 11 discovered motifs were enriched in the B27-positive AS samples as compared to controls. After combining motifs related by sequence, we identified a total of 15 independent motifs. Both the full set of 15 motifs and a set of 6 published motifs were enriched in the B27-positive AS patients as compared to B27-positive healthy individuals (P = 0.049 and P = 0.001, respectively). Using an independent cohort, we validated that at least some of these motifs were associated with AS, and not simply with B27-positive status. We identified TCRβ motifs that are enriched in B27-positive AS patients as compared to B27-positive healthy controls. This suggests that a common antigen, presented by HLA-B27 and detected by CD8+ T cells, may be associated with AS disease pathogenesis. © 2016, American College of Rheumatology.

On cordial labeling of double duplication for some families of graph

NASA Astrophysics Data System (ADS)

Shobana, L.; Remigius Perpetua Mary, F.

2018-04-01

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

A Critical Review of Line Graphs in Behavior Analytic Journals

ERIC Educational Resources Information Center

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

2017-01-01

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

Integer sequence discovery from small graphs

PubMed Central

Hoppe, Travis; Petrone, Anna

2015-01-01

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

Graph wavelet alignment kernels for drug virtual screening.

PubMed

Smalter, Aaron; Huan, Jun; Lushington, Gerald

2009-06-01

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

Multiclass Data Segmentation using Diffuse Interface Methods on Graphs

DTIC Science & Technology

2014-01-01

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

Motif discovery and motif finding from genome-mapped DNase footprint data.

PubMed

Kulakovskiy, Ivan V; Favorov, Alexander V; Makeev, Vsevolod J

2009-09-15

Footprint data is an important source of information on transcription factor recognition motifs. However, a footprinting fragment can contain no sequences similar to known protein recognition sites. Inspection of genome fragments nearby can help to identify missing site positions. Genome fragments containing footprints were supplied to a pipeline that constructed a position weight matrix (PWM) for different motif lengths and selected the optimal PWM. Fragments were aligned with the SeSiMCMC sampler and a new heuristic algorithm, Bigfoot. Footprints with missing hits were found for approximately 50% of factors. Adding only 2 bp on both sides of a footprinting fragment recovered most hits. We automatically constructed motifs for 41 Drosophila factors. New motifs can recognize footprints with a greater sensitivity at the same false positive rate than existing models. Also we discuss possible overfitting of constructed motifs. Software and the collection of regulatory motifs are freely available at http://line.imb.ac.ru/DMMPMM.

Fully Automated Segmentation of Fluid/Cyst Regions in Optical Coherence Tomography Images With Diabetic Macular Edema Using Neutrosophic Sets and Graph Algorithms.

PubMed

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.

Genome alignment with graph data structures: a comparison

PubMed Central

2014-01-01

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

Assessment of tautomer distribution using the condensed reaction graph approach

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

The Role of BRCA1 Domains and Motifs in Tumor Suppression

DTIC Science & Technology

2010-08-01

contained in this report are those of the author( s ) and should not be construed as an official Department of the Army position, policy or decision...and Motifs in Tumor Suppression 5a. CONTRACT NUMBER 5b. GRANT NUMBER W81XWH-08-1-0509 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR( S ) Aneliya...Velkova 5d. PROJECT NUMBER Email: aneliya.velkova@moffitt.org 5e. TASK NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME( S

Electronic and geometric structures of Au30 clusters: a network of 2e-superatom Au cores protected by tridentate protecting motifs with u3-S

NASA Astrophysics Data System (ADS)

Tian, Zhimei; Cheng, Longjiu

2015-12-01

Density functional theory calculations have been performed to study the experimentally synthesized Au30S(SR)18 and two related Au30(SR)18 and Au30S2(SR)18 clusters. The patterns of thiolate ligands on the gold cores for the three thiolate-protected Au30 nanoclusters are on the basis of the ``divide and protect'' concept. A novel extended protecting motif with u3-S, S(Au2(SR)2)2AuSR, is discovered, which is termed the tridentate protecting motif. The Au cores of Au30S(SR)18, Au30(SR)18 and Au30S2(SR)18 clusters are Au17, Au20 and Au14, respectively. The superatom-network (SAN) model and the superatom complex (SAC) model are used to explain the chemical bonding patterns, which are verified by chemical bonding analysis based on the adaptive natural density partitioning (AdNDP) method and aromatic analysis on the basis of the nucleus-independent chemical shift (NICS) method. The Au17 core of the Au30S(SR)18 cluster can be viewed as a SAN of one Au6 superatom and four Au4 superatoms. The shape of the Au6 core is identical to that revealed in the recently synthesized Au18(SR)14 cluster. The Au20 core of the Au30(SR)18 cluster can be viewed as a SAN of two Au6 superatoms and four Au4 superatoms. The Au14 core of Au30S2(SR)18 can be regarded as a SAN of two pairs of two vertex-sharing Au4 superatoms. Meanwhile, the Au14 core is an 8e-superatom with 1S21P6 configuration. Our work may aid understanding and give new insights into the chemical synthesis of thiolate-protected Au clusters.Density functional theory calculations have been performed to study the experimentally synthesized Au30S(SR)18 and two related Au30(SR)18 and Au30S2(SR)18 clusters. The patterns of thiolate ligands on the gold cores for the three thiolate-protected Au30 nanoclusters are on the basis of the ``divide and protect'' concept. A novel extended protecting motif with u3-S, S(Au2(SR)2)2AuSR, is discovered, which is termed the tridentate protecting motif. The Au cores of Au30S(SR)18, Au30(SR)18 and Au30S

Identification of sequence motifs significantly associated with antisense activity.

PubMed

McQuisten, Kyle A; Peek, Andrew S

2007-06-07

Predicting the suppression activity of antisense oligonucleotide sequences is the main goal of the rational design of nucleic acids. To create an effective predictive model, it is important to know what properties of an oligonucleotide sequence associate significantly with antisense activity. Also, for the model to be efficient we must know what properties do not associate significantly and can be omitted from the model. This paper will discuss the results of a randomization procedure to find motifs that associate significantly with either high or low antisense suppression activity, analysis of their properties, as well as the results of support vector machine modelling using these significant motifs as features. We discovered 155 motifs that associate significantly with high antisense suppression activity and 202 motifs that associate significantly with low suppression activity. The motifs range in length from 2 to 5 bases, contain several motifs that have been previously discovered as associating highly with antisense activity, and have thermodynamic properties consistent with previous work associating thermodynamic properties of sequences with their antisense activity. Statistical analysis revealed no correlation between a motif's position within an antisense sequence and that sequences antisense activity. Also, many significant motifs existed as subwords of other significant motifs. Support vector regression experiments indicated that the feature set of significant motifs increased correlation compared to all possible motifs as well as several subsets of the significant motifs. The thermodynamic properties of the significantly associated motifs support existing data correlating the thermodynamic properties of the antisense oligonucleotide with antisense efficiency, reinforcing our hypothesis that antisense suppression is strongly associated with probe/target thermodynamics, as there are no enzymatic mediators to speed the process along like the RNA Induced

GraphBench

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

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

2016-06-01

GraphBench is a benchmark suite for graph pattern mining and graph analysis systems. The benchmark suite is a significant addition to conducting apples-apples comparison of graph analysis software (databases, in-memory tools, triple stores, etc.)

The nodal count {0,1,2,3,…} implies the graph is a tree

PubMed Central

Band, Ram

2014-01-01

Sturm's oscillation theorem states that the nth eigenfunction of a Sturm–Liouville operator on the interval has n−1 zeros (nodes) (Sturm 1836 J. Math. Pures Appl. 1, 106–186; 373–444). This result was generalized for all metric tree graphs (Pokornyĭ et al. 1996 Mat. Zametki 60, 468–470 (doi:10.1007/BF02320380); Schapotschnikow 2006 Waves Random Complex Media 16, 167–178 (doi:10.1080/1745530600702535)) and an analogous theorem was proved for discrete tree graphs (Berkolaiko 2007 Commun. Math. Phys. 278, 803–819 (doi:10.1007/S00220-007-0391-3); Dhar & Ramaswamy 1985 Phys. Rev. Lett. 54, 1346–1349 (doi:10.1103/PhysRevLett.54.1346); Fiedler 1975 Czechoslovak Math. J. 25, 607–618). We prove the converse theorems for both discrete and metric graphs. Namely if for all n, the nth eigenfunction of the graph has n−1 zeros, then the graph is a tree. Our proofs use a recently obtained connection between the graph's nodal count and the magnetic stability of its eigenvalues (Berkolaiko 2013 Anal. PDE 6, 1213–1233 (doi:10.2140/apde.2013.6.1213); Berkolaiko & Weyand 2014 Phil. Trans. R. Soc. A 372, 20120522 (doi:10.1098/rsta.2012.0522); Colin de Verdière 2013 Anal. PDE 6, 1235–1242 (doi:10.2140/apde.2013.6.1235)). In the course of the proof, we show that it is not possible for all (or even almost all, in the metric case) the eigenvalues to exhibit a diamagnetic behaviour. In addition, we develop a notion of ‘discretized’ versions of a metric graph and prove that their nodal counts are related to those of the metric graph. PMID:24344337

Nicotine induced CpG methylation of Pax6 binding motif in StAR promoter reduces the gene expression and cortisol production

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

Wang, Tingting; Department of Pharmacology, Uniformed Services University of the Health Sciences, Bethesda, Maryland; Chen, Man

Steroidogenic acute regulatory protein (StAR) mediates the rate-limiting step in the synthesis of steroid hormones, essential to fetal development. We have reported that the StAR expression in fetal adrenal is inhibited in a rat model of nicotine-induced intrauterine growth retardation (IUGR). Here using primary human fetal adrenal cortex (pHFAC) cells and a human fetal adrenal cell line NCI-H295A, we show that nicotine inhibits StAR expression and cortisol production in a dose- and time-dependent manner, and prolongs the inhibitory effect on cells proliferating over 5 passages after termination of nicotine treatment. Methylation detection within the StAR promoter region uncovers a singlemore » site CpG methylation at nt -377 that is sensitive to nicotine treatment. Nicotine-induced alterations in frequency of this point methylation correlates well with the levels of StAR expression, suggesting an important role of the single site in regulating StAR expression. Further studies using bioinformatics analysis and siRNA approach reveal that the single CpG site is part of the Pax6 binding motif (CGCCTGA) in the StAR promoter. The luciferase activity assays validate that Pax6 increases StAR gene expression by binding to the glucagon G3-like motif (CGCCTGA) and methylation of this site blocks Pax6 binding and thus suppresses StAR expression. These data identify a nicotine-sensitive CpG site at the Pax6 binding motif in the StAR promoter that may play a central role in regulating StAR expression. The results suggest an epigenetic mechanism that may explain how nicotine contributes to onset of adult diseases or disorders such as metabolic syndrome via fetal programming. -- Highlights: Black-Right-Pointing-Pointer Nicotine-induced StAR inhibition in two human adrenal cell models. Black-Right-Pointing-Pointer Nicotine-induced single CpG site methylation in StAR promoter. Black-Right-Pointing-Pointer Persistent StAR inhibition and single CpG methylation after nicotine

Evolution of tag-based cooperation on Erdős-Rényi random graphs

NASA Astrophysics Data System (ADS)

Lima, F. W. S.; Hadzibeganovic, Tarik; Stauffer, Dietrich

2014-12-01

Here, we study an agent-based model of the evolution of tag-mediated cooperation on Erdős-Rényi random graphs. In our model, agents with heritable phenotypic traits play pairwise Prisoner's Dilemma-like games and follow one of the four possible strategies: Ethnocentric, altruistic, egoistic and cosmopolitan. Ethnocentric and cosmopolitan strategies are conditional, i.e. their selection depends upon the shared phenotypic similarity among interacting agents. The remaining two strategies are always unconditional, meaning that egoists always defect while altruists always cooperate. Our simulations revealed that ethnocentrism can win in both early and later evolutionary stages on directed random graphs when reproduction of artificial agents was asexual; however, under the sexual mode of reproduction on a directed random graph, we found that altruists dominate initially for a rather short period of time, whereas ethnocentrics and egoists suppress other strategists and compete for dominance in the intermediate and later evolutionary stages. Among our results, we also find surprisingly regular oscillations which are not damped in the course of time even after half a million Monte Carlo steps. Unlike most previous studies, our findings highlight conditions under which ethnocentrism is less stable or suppressed by other competing strategies.

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

PubMed

Navigli, Roberto; Lapata, Mirella

2010-04-01

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

Differentials on graph complexes II: hairy graphs

NASA Astrophysics Data System (ADS)

Khoroshkin, Anton; Willwacher, Thomas; Živković, Marko

2017-10-01

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

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

NASA Astrophysics Data System (ADS)

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

2016-03-01

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

Argo_CUDA: Exhaustive GPU based approach for motif discovery in large DNA datasets.

PubMed

Vishnevsky, Oleg V; Bocharnikov, Andrey V; Kolchanov, Nikolay A

2018-02-01

The development of chromatin immunoprecipitation sequencing (ChIP-seq) technology has revolutionized the genetic analysis of the basic mechanisms underlying transcription regulation and led to accumulation of information about a huge amount of DNA sequences. There are a lot of web services which are currently available for de novo motif discovery in datasets containing information about DNA/protein binding. An enormous motif diversity makes their finding challenging. In order to avoid the difficulties, researchers use different stochastic approaches. Unfortunately, the efficiency of the motif discovery programs dramatically declines with the query set size increase. This leads to the fact that only a fraction of top "peak" ChIP-Seq segments can be analyzed or the area of analysis should be narrowed. Thus, the motif discovery in massive datasets remains a challenging issue. Argo_Compute Unified Device Architecture (CUDA) web service is designed to process the massive DNA data. It is a program for the detection of degenerate oligonucleotide motifs of fixed length written in 15-letter IUPAC code. Argo_CUDA is a full-exhaustive approach based on the high-performance GPU technologies. Compared with the existing motif discovery web services, Argo_CUDA shows good prediction quality on simulated sets. The analysis of ChIP-Seq sequences revealed the motifs which correspond to known transcription factor binding sites.

Extending Matchings in Graphs: A Survey

DTIC Science & Technology

1990-01-01

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

Evolutionary Games of Multiplayer Cooperation on Graphs

PubMed Central

Arranz, Jordi; Traulsen, Arne

2016-01-01

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

Function plot response: A scalable system for teaching kinematics graphs

NASA Astrophysics Data System (ADS)

Laverty, James; Kortemeyer, Gerd

2012-08-01

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

Sequence information gain based motif analysis.

PubMed

Maynou, Joan; Pairó, Erola; Marco, Santiago; Perera, Alexandre

2015-11-09

The detection of regulatory regions in candidate sequences is essential for the understanding of the regulation of a particular gene and the mechanisms involved. This paper proposes a novel methodology based on information theoretic metrics for finding regulatory sequences in promoter regions. This methodology (SIGMA) has been tested on genomic sequence data for Homo sapiens and Mus musculus. SIGMA has been compared with different publicly available alternatives for motif detection, such as MEME/MAST, Biostrings (Bioconductor package), MotifRegressor, and previous work such Qresiduals projections or information theoretic based detectors. Comparative results, in the form of Receiver Operating Characteristic curves, show how, in 70% of the studied Transcription Factor Binding Sites, the SIGMA detector has a better performance and behaves more robustly than the methods compared, while having a similar computational time. The performance of SIGMA can be explained by its parametric simplicity in the modelling of the non-linear co-variability in the binding motif positions. Sequence Information Gain based Motif Analysis is a generalisation of a non-linear model of the cis-regulatory sequences detection based on Information Theory. This generalisation allows us to detect transcription factor binding sites with maximum performance disregarding the covariability observed in the positions of the training set of sequences. SIGMA is freely available to the public at http://b2slab.upc.edu.

PTAP motif duplication in the p6 Gag protein confers a replication advantage on HIV-1 subtype C.

PubMed

Sharma, Shilpee; Arunachalam, Prabhu S; Menon, Malini; Ragupathy, Viswanath; Satya, Ravi Vijaya; Jebaraj, Joshua; Ganeshappa Aralaguppe, Shambhu; Rao, Chaitra; Pal, Sreshtha; Saravanan, Shanmugam; Murugavel, Kailapuri G; Balakrishnan, Pachamuthu; Solomon, Suniti; Hewlett, Indira; Ranga, Udaykumar

2018-05-17

HIV-1 subtype C (HIV-1C) may duplicate longer amino acid stretches in the p6 Gag protein, leading to the creation of an additional Pro-Thr/Ser-Ala-Pro (PTAP) motif necessary for viral packaging. However, the biological significance of a duplication of the PTAP motif for HIV-1 replication and pathogenesis has not been experimentally validated. In a longitudinal study of two different clinical cohorts of select HIV-1 seropositive, drug-naive individuals from India, we found that 8 of 50 of these individuals harbored a mixed infection of viral strains discordant for the PTAP duplication. Conventional and next-generation sequencing of six primary viral quasispecies at multiple time points disclosed that in a mixed infection, the viral strains containing the PTAP duplication dominated the infection. The dominance of the double-PTAP viral strains over a genetically similar single-PTAP viral clone was confirmed in viral proliferation and pairwise competition assays. Of note, in the proximity ligation assay, double-PTAP Gag proteins exhibited a significantly enhanced interaction with the host protein tumor susceptibility gene 101 (Tsg101). Moreover, Tsg101 overexpression resulted in a biphasic effect on HIV-1C proliferation - an enhanced effect at low concentration and an inhibitory effect only at higher concentrations - unlike a uniformly inhibitory effect on subtype B strains. In summary, our results indicate that the duplication of the PTAP motif in the p6 Gag protein enhances the replication fitness of HIV-1C by engaging the Tsg101 host protein with a higher affinity. Our results have implications for HIV-1 pathogenesis, especially of HIV-1C. Copyright © 2018, The American Society for Biochemistry and Molecular Biology.

Seed storage protein gene promoters contain conserved DNA motifs in Brassicaceae, Fabaceae and Poaceae

PubMed Central

Fauteux, François; Strömvik, Martina V

2009-01-01

Background Accurate computational identification of cis-regulatory motifs is difficult, particularly in eukaryotic promoters, which typically contain multiple short and degenerate DNA sequences bound by several interacting factors. Enrichment in combinations of rare motifs in the promoter sequence of functionally or evolutionarily related genes among several species is an indicator of conserved transcriptional regulatory mechanisms. This provides a basis for the computational identification of cis-regulatory motifs. Results We have used a discriminative seeding DNA motif discovery algorithm for an in-depth analysis of 54 seed storage protein (SSP) gene promoters from three plant families, namely Brassicaceae (mustards), Fabaceae (legumes) and Poaceae (grasses) using backgrounds based on complete sets of promoters from a representative species in each family, namely Arabidopsis (Arabidopsis thaliana (L.) Heynh.), soybean (Glycine max (L.) Merr.) and rice (Oryza sativa L.) respectively. We have identified three conserved motifs (two RY-like and one ACGT-like) in Brassicaceae and Fabaceae SSP gene promoters that are similar to experimentally characterized seed-specific cis-regulatory elements. Fabaceae SSP gene promoter sequences are also enriched in a novel, seed-specific E2Fb-like motif. Conserved motifs identified in Poaceae SSP gene promoters include a GCN4-like motif, two prolamin-box-like motifs and an Skn-1-like motif. Evidence of the presence of a variant of the TATA-box is found in the SSP gene promoters from the three plant families. Motifs discovered in SSP gene promoters were used to score whole-genome sets of promoters from Arabidopsis, soybean and rice. The highest-scoring promoters are associated with genes coding for different subunits or precursors of seed storage proteins. Conclusion Seed storage protein gene promoter motifs are conserved in diverse species, and different plant families are characterized by a distinct combination of conserved motifs

Cluster Tails for Critical Power-Law Inhomogeneous Random Graphs

NASA Astrophysics Data System (ADS)

van der Hofstad, Remco; Kliem, Sandra; van Leeuwaarden, Johan S. H.

2018-04-01

Recently, the scaling limit of cluster sizes for critical inhomogeneous random graphs of rank-1 type having finite variance but infinite third moment degrees was obtained in Bhamidi et al. (Ann Probab 40:2299-2361, 2012). It was proved that when the degrees obey a power law with exponent τ \\in (3,4), the sequence of clusters ordered in decreasing size and multiplied through by n^{-(τ -2)/(τ -1)} converges as n→ ∞ to a sequence of decreasing non-degenerate random variables. Here, we study the tails of the limit of the rescaled largest cluster, i.e., the probability that the scaling limit of the largest cluster takes a large value u, as a function of u. This extends a related result of Pittel (J Combin Theory Ser B 82(2):237-269, 2001) for the Erdős-Rényi random graph to the setting of rank-1 inhomogeneous random graphs with infinite third moment degrees. We make use of delicate large deviations and weak convergence arguments.

Identifying the scale-dependent motifs in atmospheric surface layer by ordinal pattern analysis

NASA Astrophysics Data System (ADS)

Li, Qinglei; Fu, Zuntao

2018-07-01

Ramp-like structures in various atmospheric surface layer time series have been long studied, but the presence of motifs with the finer scale embedded within larger scale ramp-like structures has largely been overlooked in the reported literature. Here a novel, objective and well-adapted methodology, the ordinal pattern analysis, is adopted to study the finer-scaled motifs in atmospheric boundary-layer (ABL) time series. The studies show that the motifs represented by different ordinal patterns take clustering properties and 6 dominated motifs out of the whole 24 motifs account for about 45% of the time series under particular scales, which indicates the higher contribution of motifs with the finer scale to the series. Further studies indicate that motif statistics are similar for both stable conditions and unstable conditions at larger scales, but large discrepancies are found at smaller scales, and the frequencies of motifs "1234" and/or "4321" are a bit higher under stable conditions than unstable conditions. Under stable conditions, there are great changes for the occurrence frequencies of motifs "1234" and "4321", where the occurrence frequencies of motif "1234" decrease from nearly 24% to 4.5% with the scale factor increasing, and the occurrence frequencies of motif "4321" change nonlinearly with the scale increasing. These great differences of dominated motifs change with scale can be taken as an indicator to quantify the flow structure changes under different stability conditions, and motif entropy can be defined just by only 6 dominated motifs to quantify this time-scale independent property of the motifs. All these results suggest that the defined scale of motifs with the finer scale should be carefully taken into consideration in the interpretation of turbulence coherent structures.

Movement Forms: A Graph-Dynamic Perspective.

PubMed

Saltzman, Elliot; Holt, Ken

2014-01-01

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

VISAGE: Interactive Visual Graph Querying

PubMed Central

Pienta, Robert; Navathe, Shamkant; Tamersoy, Acar; Tong, Hanghang; Endert, Alex; Chau, Duen Horng

2017-01-01

Extracting useful patterns from large network datasets has become a fundamental challenge in many domains. We present VISAGE, an interactive visual graph querying approach that empowers users to construct expressive queries, without writing complex code (e.g., finding money laundering rings of bankers and business owners). Our contributions are as follows: (1) we introduce graph autocomplete, an interactive approach that guides users to construct and refine queries, preventing over-specification; (2) VISAGE guides the construction of graph queries using a data-driven approach, enabling users to specify queries with varying levels of specificity, from concrete and detailed (e.g., query by example), to abstract (e.g., with “wildcard” nodes of any types), to purely structural matching; (3) a twelve-participant, within-subject user study demonstrates VISAGE’s ease of use and the ability to construct graph queries significantly faster than using a conventional query language; (4) VISAGE works on real graphs with over 468K edges, achieving sub-second response times for common queries. PMID:28553670

On the Total Edge Irregularity Strength of Generalized Butterfly Graph

NASA Astrophysics Data System (ADS)

Dwi Wahyuna, Hafidhyah; Indriati, Diari

2018-04-01

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

Discovering Motifs in Biological Sequences Using the Micron Automata Processor.

PubMed

Roy, Indranil; Aluru, Srinivas

2016-01-01

Finding approximately conserved sequences, called motifs, across multiple DNA or protein sequences is an important problem in computational biology. In this paper, we consider the (l, d) motif search problem of identifying one or more motifs of length l present in at least q of the n given sequences, with each occurrence differing from the motif in at most d substitutions. The problem is known to be NP-complete, and the largest solved instance reported to date is (26,11). We propose a novel algorithm for the (l,d) motif search problem using streaming execution over a large set of non-deterministic finite automata (NFA). This solution is designed to take advantage of the micron automata processor, a new technology close to deployment that can simultaneously execute multiple NFA in parallel. We demonstrate the capability for solving much larger instances of the (l, d) motif search problem using the resources available within a single automata processor board, by estimating run-times for problem instances (39,18) and (40,17). The paper serves as a useful guide to solving problems using this new accelerator technology.

Search for global-minimum geometries of medium-sized germanium clusters. II. Motif-based low-lying clusters Ge21-Ge29

NASA Astrophysics Data System (ADS)

Yoo, S.; Zeng, X. C.

2006-05-01

We performed a constrained search for the geometries of low-lying neutral germanium clusters GeN in the size range of 21⩽N⩽29. The basin-hopping global optimization method is employed for the search. The potential-energy surface is computed based on the plane-wave pseudopotential density functional theory. A new series of low-lying clusters is found on the basis of several generic structural motifs identified previously for silicon clusters [S. Yoo and X. C. Zeng, J. Chem. Phys. 124, 054304 (2006)] as well as for smaller-sized germanium clusters [S. Bulusu et al., J. Chem. Phys. 122, 164305 (2005)]. Among the generic motifs examined, we found that two motifs stand out in producing most low-lying clusters, namely, the six/nine motif, a puckered-hexagonal-ring Ge6 unit attached to a tricapped trigonal prism Ge9, and the six/ten motif, a puckered-hexagonal-ring Ge6 unit attached to a bicapped antiprism Ge10. The low-lying clusters obtained are all prolate in shape and their energies are appreciably lower than the near-spherical low-energy clusters. This result is consistent with the ion-mobility measurement in that medium-sized germanium clusters detected are all prolate in shape until the size N ˜65.

Learning locality preserving graph from data.

PubMed

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

2014-11-01

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

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

PubMed

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

2014-07-01

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

A survey of motif finding Web tools for detecting binding site motifs in ChIP-Seq data

PubMed Central

2014-01-01

Abstract ChIP-Seq (chromatin immunoprecipitation sequencing) has provided the advantage for finding motifs as ChIP-Seq experiments narrow down the motif finding to binding site locations. Recent motif finding tools facilitate the motif detection by providing user-friendly Web interface. In this work, we reviewed nine motif finding Web tools that are capable for detecting binding site motifs in ChIP-Seq data. We showed each motif finding Web tool has its own advantages for detecting motifs that other tools may not discover. We recommended the users to use multiple motif finding Web tools that implement different algorithms for obtaining significant motifs, overlapping resemble motifs, and non-overlapping motifs. Finally, we provided our suggestions for future development of motif finding Web tool that better assists researchers for finding motifs in ChIP-Seq data. Reviewers This article was reviewed by Prof. Sandor Pongor, Dr. Yuriy Gusev, and Dr. Shyam Prabhakar (nominated by Prof. Limsoon Wong). PMID:24555784

DELTACON: A Principled Massive-Graph Similarity Function with Attribution

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

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

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

DELTACON: A Principled Massive-Graph Similarity Function with Attribution

DOE PAGES

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

2014-05-22

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

Combinatorial Histone Acetylation Patterns Are Generated by Motif-Specific Reactions.

PubMed

Blasi, Thomas; Feller, Christian; Feigelman, Justin; Hasenauer, Jan; Imhof, Axel; Theis, Fabian J; Becker, Peter B; Marr, Carsten

2016-01-27

Post-translational modifications (PTMs) are pivotal to cellular information processing, but how combinatorial PTM patterns ("motifs") are set remains elusive. We develop a computational framework, which we provide as open source code, to investigate the design principles generating the combinatorial acetylation patterns on histone H4 in Drosophila melanogaster. We find that models assuming purely unspecific or lysine site-specific acetylation rates were insufficient to explain the experimentally determined motif abundances. Rather, these abundances were best described by an ensemble of models with acetylation rates that were specific to motifs. The model ensemble converged upon four acetylation pathways; we validated three of these using independent data from a systematic enzyme depletion study. Our findings suggest that histone acetylation patterns originate through specific pathways involving motif-specific acetylation activity. Copyright © 2016 Elsevier Inc. All rights reserved.

Compound analysis via graph kernels incorporating chirality.

PubMed

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

2010-12-01

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

Composite Structural Motifs of Binding Sites for Delineating Biological Functions of Proteins

PubMed Central

Kinjo, Akira R.; Nakamura, Haruki

2012-01-01

Most biological processes are described as a series of interactions between proteins and other molecules, and interactions are in turn described in terms of atomic structures. To annotate protein functions as sets of interaction states at atomic resolution, and thereby to better understand the relation between protein interactions and biological functions, we conducted exhaustive all-against-all atomic structure comparisons of all known binding sites for ligands including small molecules, proteins and nucleic acids, and identified recurring elementary motifs. By integrating the elementary motifs associated with each subunit, we defined composite motifs that represent context-dependent combinations of elementary motifs. It is demonstrated that function similarity can be better inferred from composite motif similarity compared to the similarity of protein sequences or of individual binding sites. By integrating the composite motifs associated with each protein function, we define meta-composite motifs each of which is regarded as a time-independent diagrammatic representation of a biological process. It is shown that meta-composite motifs provide richer annotations of biological processes than sequence clusters. The present results serve as a basis for bridging atomic structures to higher-order biological phenomena by classification and integration of binding site structures. PMID:22347478

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

PubMed

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

2009-01-01

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

Inferring ontology graph structures using OWL reasoning.

PubMed

Rodríguez-García, Miguel Ángel; Hoehndorf, Robert

2018-01-05

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

[Prediction of Promoter Motifs in Virophages].

PubMed

Gong, Chaowen; Zhou, Xuewen; Pan, Yingjie; Wang, Yongjie

2015-07-01

Virophages have crucial roles in ecosystems and are the transport vectors of genetic materials. To shed light on regulation and control mechanisms in virophage--host systems as well as evolution between virophages and their hosts, the promoter motifs of virophages were predicted on the upstream regions of start codons using an analytical tool for prediction of promoter motifs: Multiple EM for Motif Elicitation. Seventeen potential promoter motifs were identified based on the E-value, location, number and length of promoters in genomes. Sputnik and zamilon motif 2 with AT-rich regions were distributed widely on genomes, suggesting that these motifs may be associated with regulation of the expression of various genes. Motifs containing the TCTA box were predicted to be late promoter motif in mavirus; motifs containing the ATCT box were the potential late promoter motif in the Ace Lake mavirus . AT-rich regions were identified on motif 2 in the Organic Lake virophage, motif 3 in Yellowstone Lake virophage (YSLV)1 and 2, motif 1 in YSLV3, and motif 1 and 2 in YSLV4, respectively. AT-rich regions were distributed widely on the genomes of virophages. All of these motifs may be promoter motifs of virophages. Our results provide insights into further exploration of temporal expression of genes in virophages as well as associations between virophages and giant viruses.

Resistance Distances and Kirchhoff Index in Generalised Join Graphs

NASA Astrophysics Data System (ADS)

Chen, Haiyan

2017-03-01

The resistance distance between any two vertices of a connected graph is defined as the effective resistance between them in the electrical network constructed from the graph by replacing each edge with a unit resistor. The Kirchhoff index of a graph is defined as the sum of all the resistance distances between any pair of vertices of the graph. Let G=H[G1, G2, …, Gk ] be the generalised join graph of G1, G2, …, Gk determined by H. In this paper, we first give formulae for resistance distances and Kirchhoff index of G in terms of parameters of {G'_i}s and H. Then, we show that computing resistance distances and Kirchhoff index of G can be decomposed into simpler ones. Finally, we obtain explicit formulae for resistance distances and Kirchhoff index of G when {G'_i}s and H take some special graphs, such as the complete graph, the path, and the cycle.

Horizontal visibility graphs generated by type-I intermittency

NASA Astrophysics Data System (ADS)

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

2013-05-01

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

SVM2Motif—Reconstructing Overlapping DNA Sequence Motifs by Mimicking an SVM Predictor

PubMed Central

Vidovic, Marina M. -C.; Görnitz, Nico; Müller, Klaus-Robert; Rätsch, Gunnar; Kloft, Marius

2015-01-01

Identifying discriminative motifs underlying the functionality and evolution of organisms is a major challenge in computational biology. Machine learning approaches such as support vector machines (SVMs) achieve state-of-the-art performances in genomic discrimination tasks, but—due to its black-box character—motifs underlying its decision function are largely unknown. As a remedy, positional oligomer importance matrices (POIMs) allow us to visualize the significance of position-specific subsequences. Although being a major step towards the explanation of trained SVM models, they suffer from the fact that their size grows exponentially in the length of the motif, which renders their manual inspection feasible only for comparably small motif sizes, typically k ≤ 5. In this work, we extend the work on positional oligomer importance matrices, by presenting a new machine-learning methodology, entitled motifPOIM, to extract the truly relevant motifs—regardless of their length and complexity—underlying the predictions of a trained SVM model. Our framework thereby considers the motifs as free parameters in a probabilistic model, a task which can be phrased as a non-convex optimization problem. The exponential dependence of the POIM size on the oligomer length poses a major numerical challenge, which we address by an efficient optimization framework that allows us to find possibly overlapping motifs consisting of up to hundreds of nucleotides. We demonstrate the efficacy of our approach on a synthetic data set as well as a real-world human splice site data set. PMID:26690911

Native characterization of nucleic acid motif thermodynamics via non-covalent catalysis

PubMed Central

Wang, Chunyan; Bae, Jin H.; Zhang, David Yu

2016-01-01

DNA hybridization thermodynamics is critical for accurate design of oligonucleotides for biotechnology and nanotechnology applications, but parameters currently in use are inaccurately extrapolated based on limited quantitative understanding of thermal behaviours. Here, we present a method to measure the ΔG° of DNA motifs at temperatures and buffer conditions of interest, with significantly better accuracy (6- to 14-fold lower s.e.) than prior methods. The equilibrium constant of a reaction with thermodynamics closely approximating that of a desired motif is numerically calculated from directly observed reactant and product equilibrium concentrations; a DNA catalyst is designed to accelerate equilibration. We measured the ΔG° of terminal fluorophores, single-nucleotide dangles and multinucleotide dangles, in temperatures ranging from 10 to 45 °C. PMID:26782977

Knowledge Representation Issues in Semantic Graphs for Relationship Detection

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

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

2005-02-02

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

The Pt site reactivity of the molecular graphs of Au6Pt isomers

NASA Astrophysics Data System (ADS)

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

2013-12-01

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

Mining for class-specific motifs in protein sequence classification

PubMed Central

2013-01-01

Background In protein sequence classification, identification of the sequence motifs or n-grams that can precisely discriminate between classes is a more interesting scientific question than the classification itself. A number of classification methods aim at accurate classification but fail to explain which sequence features indeed contribute to the accuracy. We hypothesize that sequences in lower denominations (n-grams) can be used to explore the sequence landscape and to identify class-specific motifs that discriminate between classes during classification. Discriminative n-grams are short peptide sequences that are highly frequent in one class but are either minimally present or absent in other classes. In this study, we present a new substitution-based scoring function for identifying discriminative n-grams that are highly specific to a class. Results We present a scoring function based on discriminative n-grams that can effectively discriminate between classes. The scoring function, initially, harvests the entire set of 4- to 8-grams from the protein sequences of different classes in the dataset. Similar n-grams of the same size are combined to form new n-grams, where the similarity is defined by positive amino acid substitution scores in the BLOSUM62 matrix. Substitution has resulted in a large increase in the number of discriminatory n-grams harvested. Due to the unbalanced nature of the dataset, the frequencies of the n-grams are normalized using a dampening factor, which gives more weightage to the n-grams that appear in fewer classes and vice-versa. After the n-grams are normalized, the scoring function identifies discriminative 4- to 8-grams for each class that are frequent enough to be above a selection threshold. By mapping these discriminative n-grams back to the protein sequences, we obtained contiguous n-grams that represent short class-specific motifs in protein sequences. Our method fared well compared to an existing motif finding method known as

Multigraph: Reusable Interactive Data Graphs

NASA Astrophysics Data System (ADS)

Phillips, M. B.

2010-12-01

There are surprisingly few good software tools available for presenting time series data on the internet. The most common practice is to use a desktop program such as Excel or Matlab to save a graph as an image which can be included in a web page like any other image. This disconnects the graph from the data in a way that makes updating a graph with new data a cumbersome manual process, and it limits the user to one particular view of the data. The Multigraph project defines an XML format for describing interactive data graphs, and software tools for creating and rendering those graphs in web pages and other internet connected applications. Viewing a Multigraph graph is extremely simple and intuitive, and requires no instructions; the user can pan and zoom by clicking and dragging, in a familiar "Google Maps" kind of way. Creating a new graph for inclusion in a web page involves writing a simple XML configuration file. Multigraph can read data in a variety of formats, and can display data from a web service, allowing users to "surf" through large data sets, downloading only those the parts of the data that are needed for display. The Multigraph XML format, or "MUGL" for short, provides a concise description of the visual properties of a graph, such as axes, plot styles, data sources, labels, etc, as well as interactivity properties such as how and whether the user can pan or zoom along each axis. Multigraph reads a file in this format, draws the described graph, and allows the user to interact with it. Multigraph software currently includes a Flash application for embedding graphs in web pages, a Flex component for embedding graphs in larger Flex/Flash applications, and a plugin for creating graphs in the WordPress content management system. Plans for the future include a Java version for desktop viewing and editing, a command line version for batch and server side rendering, and possibly Android and iPhone versions. Multigraph is currently in use on several web

Acceleration of Binding Site Comparisons by Graph Partitioning.

PubMed

Krotzky, Timo; Klebe, Gerhard

2015-08-01

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

An integrative and applicable phylogenetic footprinting framework for cis-regulatory motifs identification in prokaryotic genomes.

PubMed

Liu, Bingqiang; Zhang, Hanyuan; Zhou, Chuan; Li, Guojun; Fennell, Anne; Wang, Guanghui; Kang, Yu; Liu, Qi; Ma, Qin

2016-08-09

Phylogenetic footprinting is an important computational technique for identifying cis-regulatory motifs in orthologous regulatory regions from multiple genomes, as motifs tend to evolve slower than their surrounding non-functional sequences. Its application, however, has several difficulties for optimizing the selection of orthologous data and reducing the false positives in motif prediction. Here we present an integrative phylogenetic footprinting framework for accurate motif predictions in prokaryotic genomes (MP(3)). The framework includes a new orthologous data preparation procedure, an additional promoter scoring and pruning method and an integration of six existing motif finding algorithms as basic motif search engines. Specifically, we collected orthologous genes from available prokaryotic genomes and built the orthologous regulatory regions based on sequence similarity of promoter regions. This procedure made full use of the large-scale genomic data and taxonomy information and filtered out the promoters with limited contribution to produce a high quality orthologous promoter set. The promoter scoring and pruning is implemented through motif voting by a set of complementary predicting tools that mine as many motif candidates as possible and simultaneously eliminate the effect of random noise. We have applied the framework to Escherichia coli k12 genome and evaluated the prediction performance through comparison with seven existing programs. This evaluation was systematically carried out at the nucleotide and binding site level, and the results showed that MP(3) consistently outperformed other popular motif finding tools. We have integrated MP(3) into our motif identification and analysis server DMINDA, allowing users to efficiently identify and analyze motifs in 2,072 completely sequenced prokaryotic genomes. The performance evaluation indicated that MP(3) is effective for predicting regulatory motifs in prokaryotic genomes. Its application may enhance

graphkernels: R and Python packages for graph comparison.

PubMed

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

2018-02-01

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

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

PubMed Central

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

2015-01-01

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

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

PubMed

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

2017-10-01

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

Mechanisms of Zero-Lag Synchronization in Cortical Motifs

PubMed Central

Gollo, Leonardo L.; Mirasso, Claudio; Sporns, Olaf; Breakspear, Michael

2014-01-01

Zero-lag synchronization between distant cortical areas has been observed in a diversity of experimental data sets and between many different regions of the brain. Several computational mechanisms have been proposed to account for such isochronous synchronization in the presence of long conduction delays: Of these, the phenomenon of “dynamical relaying” – a mechanism that relies on a specific network motif – has proven to be the most robust with respect to parameter mismatch and system noise. Surprisingly, despite a contrary belief in the community, the common driving motif is an unreliable means of establishing zero-lag synchrony. Although dynamical relaying has been validated in empirical and computational studies, the deeper dynamical mechanisms and comparison to dynamics on other motifs is lacking. By systematically comparing synchronization on a variety of small motifs, we establish that the presence of a single reciprocally connected pair – a “resonance pair” – plays a crucial role in disambiguating those motifs that foster zero-lag synchrony in the presence of conduction delays (such as dynamical relaying) from those that do not (such as the common driving triad). Remarkably, minor structural changes to the common driving motif that incorporate a reciprocal pair recover robust zero-lag synchrony. The findings are observed in computational models of spiking neurons, populations of spiking neurons and neural mass models, and arise whether the oscillatory systems are periodic, chaotic, noise-free or driven by stochastic inputs. The influence of the resonance pair is also robust to parameter mismatch and asymmetrical time delays amongst the elements of the motif. We call this manner of facilitating zero-lag synchrony resonance-induced synchronization, outline the conditions for its occurrence, and propose that it may be a general mechanism to promote zero-lag synchrony in the brain. PMID:24763382

Efficient sequential and parallel algorithms for finding edit distance based motifs.

PubMed

Pal, Soumitra; Xiao, Peng; Rajasekaran, Sanguthevar

2016-08-18

Motif search is an important step in extracting meaningful patterns from biological data. The general problem of motif search is intractable and there is a pressing need to develop efficient, exact and approximation algorithms to solve this problem. In this paper, we present several novel, exact, sequential and parallel algorithms for solving the (l,d) Edit-distance-based Motif Search (EMS) problem: given two integers l,d and n biological strings, find all strings of length l that appear in each input string with atmost d errors of types substitution, insertion and deletion. One popular technique to solve the problem is to explore for each input string the set of all possible l-mers that belong to the d-neighborhood of any substring of the input string and output those which are common for all input strings. We introduce a novel and provably efficient neighborhood exploration technique. We show that it is enough to consider the candidates in neighborhood which are at a distance exactly d. We compactly represent these candidate motifs using wildcard characters and efficiently explore them with very few repetitions. Our sequential algorithm uses a trie based data structure to efficiently store and sort the candidate motifs. Our parallel algorithm in a multi-core shared memory setting uses arrays for storing and a novel modification of radix-sort for sorting the candidate motifs. The algorithms for EMS are customarily evaluated on several challenging instances such as (8,1), (12,2), (16,3), (20,4), and so on. The best previously known algorithm, EMS1, is sequential and in estimated 3 days solves up to instance (16,3). Our sequential algorithms are more than 20 times faster on (16,3). On other hard instances such as (9,2), (11,3), (13,4), our algorithms are much faster. Our parallel algorithm has more than 600 % scaling performance while using 16 threads. Our algorithms have pushed up the state-of-the-art of EMS solvers and we believe that the techniques introduced in

Super (a*, d*)-ℋ-antimagic total covering of second order of shackle graphs

NASA Astrophysics Data System (ADS)

Hesti Agustin, Ika; Dafik; Nisviasari, Rosanita; Prihandini, R. M.

2017-12-01

Let H be a simple and connected graph. A shackle of graph H, denoted by G = shack(H, v, n), is a graph G constructed by non-trivial graphs H 1, H 2, …, H n such that, for every 1 ≤ s, t ≤ n, H s and Ht have no a common vertex with |s - t| ≥ 2 and for every 1 ≤ i ≤ n - 1, Hi and H i+1 share exactly one common vertex v, called connecting vertex, and those k - 1 connecting vertices are all distinct. The graph G is said to be an (a*, d*)-H-antimagic total graph of second order if there exist a bijective function f : V(G) ∪ E(G) → {1, 2, …, |V(G)| + |E(G)|} such that for all subgraphs isomorphic to H, the total H-weights W(H)=\\displaystyle {\\sum }v\\in V(H)f(v)+\\displaystyle {\\sum }e\\in E(H)f(e) form an arithmetic sequence of second order of \\{a* ,a* +d* ,a* +3d* ,a* +6d* ,\\ldots ,a* +(\\frac{{n}2-n}{2})d* \\}, where a* and d* are positive integers and n is the number of all subgraphs isomorphic to H. An (a*, d*)-H-antimagic total labeling of second order f is called super if the smallest labels appear in the vertices. In this paper, we study a super (a*, d*)-H antimagic total labeling of second order of G = shack(H, v, n) by using a partition technique of second order.

Graph Structured Program Evolution: Evolution of Loop Structures

NASA Astrophysics Data System (ADS)

Shirakawa, Shinichi; Nagao, Tomoharu

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

Several classes of graphs and their r-dynamic chromatic numbers

NASA Astrophysics Data System (ADS)

Dafik; Meganingtyas, D. E. W.; Dwidja Purnomo, K.; Dicky Tarmidzi, M.; Hesti Agustin, Ika

2017-06-01

Let G be a simple, connected and undirected graph. Let r, k be natural numbers. By a proper k-coloring of a graph G, we mean a map c : V (G) → S, where |S| = k, such that any two adjacent vertices receive different colors. An r-dynamic k-coloring is a proper k-coloring c of G such that |c(N(v))| ≥ min{r, d(v)} for each vertex v in V (G), where N(v) is the neighborhood of v and c(S) = {c(v) : v ∈ S} for a vertex subset S. The r-dynamic chromatic number, written as χ r (G), is the minimum k such that G has an r-dynamic k-coloring. By simple observation it is easy to see that χ r (G) ≤ χ r+1(G), however χ r+1(G) - χ r (G) does not always show a small difference for any r. Thus, finding an exact value of χ r (G) is significantly useful. In this paper, we will study some of them especially when G are prism graph, three-cyclical ladder graph, joint graph and circulant graph.

Simple scale interpolator facilitates reading of graphs

NASA Technical Reports Server (NTRS)

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

1966-01-01

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

Affinity learning with diffusion on tensor product graph.

PubMed

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

2013-01-01

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

Space-related pharma-motifs for fast search of protein binding motifs and polypharmacological targets

PubMed Central

2012-01-01

Background To discover a compound inhibiting multiple proteins (i.e. polypharmacological targets) is a new paradigm for the complex diseases (e.g. cancers and diabetes). In general, the polypharmacological proteins often share similar local binding environments and motifs. As the exponential growth of the number of protein structures, to find the similar structural binding motifs (pharma-motifs) is an emergency task for drug discovery (e.g. side effects and new uses for old drugs) and protein functions. Results We have developed a Space-Related Pharmamotifs (called SRPmotif) method to recognize the binding motifs by searching against protein structure database. SRPmotif is able to recognize conserved binding environments containing spatially discontinuous pharma-motifs which are often short conserved peptides with specific physico-chemical properties for protein functions. Among 356 pharma-motifs, 56.5% interacting residues are highly conserved. Experimental results indicate that 81.1% and 92.7% polypharmacological targets of each protein-ligand complex are annotated with same biological process (BP) and molecular function (MF) terms, respectively, based on Gene Ontology (GO). Our experimental results show that the identified pharma-motifs often consist of key residues in functional (active) sites and play the key roles for protein functions. The SRPmotif is available at http://gemdock.life.nctu.edu.tw/SRP/. Conclusions SRPmotif is able to identify similar pharma-interfaces and pharma-motifs sharing similar binding environments for polypharmacological targets by rapidly searching against the protein structure database. Pharma-motifs describe the conservations of binding environments for drug discovery and protein functions. Additionally, these pharma-motifs provide the clues for discovering new sequence-based motifs to predict protein functions from protein sequence databases. We believe that SRPmotif is useful for elucidating protein functions and drug discovery

Space-related pharma-motifs for fast search of protein binding motifs and polypharmacological targets.

PubMed

Chiu, Yi-Yuan; Lin, Chun-Yu; Lin, Chih-Ta; Hsu, Kai-Cheng; Chang, Li-Zen; Yang, Jinn-Moon

2012-01-01

To discover a compound inhibiting multiple proteins (i.e. polypharmacological targets) is a new paradigm for the complex diseases (e.g. cancers and diabetes). In general, the polypharmacological proteins often share similar local binding environments and motifs. As the exponential growth of the number of protein structures, to find the similar structural binding motifs (pharma-motifs) is an emergency task for drug discovery (e.g. side effects and new uses for old drugs) and protein functions. We have developed a Space-Related Pharmamotifs (called SRPmotif) method to recognize the binding motifs by searching against protein structure database. SRPmotif is able to recognize conserved binding environments containing spatially discontinuous pharma-motifs which are often short conserved peptides with specific physico-chemical properties for protein functions. Among 356 pharma-motifs, 56.5% interacting residues are highly conserved. Experimental results indicate that 81.1% and 92.7% polypharmacological targets of each protein-ligand complex are annotated with same biological process (BP) and molecular function (MF) terms, respectively, based on Gene Ontology (GO). Our experimental results show that the identified pharma-motifs often consist of key residues in functional (active) sites and play the key roles for protein functions. The SRPmotif is available at http://gemdock.life.nctu.edu.tw/SRP/. SRPmotif is able to identify similar pharma-interfaces and pharma-motifs sharing similar binding environments for polypharmacological targets by rapidly searching against the protein structure database. Pharma-motifs describe the conservations of binding environments for drug discovery and protein functions. Additionally, these pharma-motifs provide the clues for discovering new sequence-based motifs to predict protein functions from protein sequence databases. We believe that SRPmotif is useful for elucidating protein functions and drug discovery.

Nicotine Induced CpG methylation of Pax6 binding motif in StAR promoter reduces the gene expression and cortisol production

PubMed Central

Wang, Tingting; Chen, Man; Liu, Lian; Cheng, Huaiyan; Yan, You-E; Feng, Ying-Hong; Wang, Hui

2011-01-01

Steroidogenic acute regulatory protein (StAR) mediates the rate-limiting step in the synthesis of steroid hormones, essential to fetal development. We have reported that the StAR expression in fetal adrenal is inhibited in a rat model of nicotine-induced intrauterine growth retardation (IUGR). Here using primary human fetal adrenal cortex (pHFAC) cells and a human fetal adrenal cell line NCI-H295A, we show that nicotine inhibits StAR expression and cortisol production in a dose- and time-dependent manner, and prolongs the inhibitory effect on cells proliferating over 5 passages after termination of nicotine treatment. Methylation detection within the StAR promoter region uncovers a single site CpG methylation at nt −377 that is sensitive to nicotine treatment. Nicotine-induced alterations in frequency of this point methylation correlates well with the levels of StAR expression, suggesting an important role of the single site in regulating StAR expression. Further studies using bioinformatics analysis and siRNA approach reveal that the single CpG site is part of the Pax6 binding motif (CGCCTGA) in the StAR promoter. The luciferase activity assays validate that Pax6 increases StAR gene expression by binding to the glucagon G3-like motif (CGCCTGA) and methylation of this site blocks Pax6 binding and thus suppresses StAR expression. These data identify a nicotine-sensitive CpG site at the Pax6 binding motif in the StAR promoter that may play a central role in regulating StAR expression. The results suggest an epigenetic mechanism that may explain how nicotine contributes to onset of adult diseases or disorders such as metabolic syndrome via fetal programming. PMID:21971485

The Replicator Equation on Graphs

PubMed Central

Ohtsuki, Hisashi; Nowak, Martin A.

2008-01-01

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

Edge compression techniques for visualization of dense directed graphs.

PubMed

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

2013-12-01

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

A Graph Summarization Algorithm Based on RFID Logistics

NASA Astrophysics Data System (ADS)

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

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

Proline Scan of the hERG Channel S6 Helix Reveals the Location of the Intracellular Pore Gate

PubMed Central

Thouta, Samrat; Sokolov, Stanislav; Abe, Yuki; Clark, Sheldon J.; Cheng, Yen M.; Claydon, Tom W.

2014-01-01

In Shaker-like channels, the activation gate is formed at the bundle crossing by the convergence of the inner S6 helices near a conserved proline-valine-proline motif, which introduces a kink that allows for electromechanical coupling with voltage sensor motions via the S4-S5 linker. Human ether-a-go-go-related gene (hERG) channels lack the proline-valine-proline motif and the location of the intracellular pore gate and how it is coupled to S4 movement is less clear. Here, we show that proline substitutions within the S6 of hERG perturbed pore gate closure, trapping channels in the open state. Performing a proline scan of the inner S6 helix, from Ile655 to Tyr667 revealed that gate perturbation occurred with proximal (I655P-Q664P), but not distal (R665P-Y667P) substitutions, suggesting that Gln664 marks the position of the intracellular gate in hERG channels. Using voltage-clamp fluorimetry and gating current analysis, we demonstrate that proline substitutions trap the activation gate open by disrupting the coupling between the voltage-sensing unit and the pore of the channel. We characterize voltage sensor movement in one such trapped-open mutant channel and demonstrate the kinetics of what we interpret to be intrinsic hERG voltage sensor movement. PMID:24606930

A motif detection and classification method for peptide sequences using genetic programming.

PubMed

Tomita, Yasuyuki; Kato, Ryuji; Okochi, Mina; Honda, Hiroyuki

2008-08-01

An exploration of common rules (property motifs) in amino acid sequences has been required for the design of novel sequences and elucidation of the interactions between molecules controlled by the structural or physical environment. In the present study, we developed a new method to search property motifs that are common in peptide sequence data. Our method comprises the following two characteristics: (i) the automatic determination of the position and length of common property motifs by calculating the physicochemical similarity of amino acids, and (ii) the quick and effective exploration of motif candidates that discriminates the positives and negatives by the introduction of genetic programming (GP). Our method was evaluated by two types of model data sets. First, the intentionally buried property motifs were searched in the artificially derived peptide data containing intentionally buried property motifs. As a result, the expected property motifs were correctly extracted by our algorithm. Second, the peptide data that interact with MHC class II molecules were analyzed as one of the models of biologically active peptides with buried motifs in various lengths. Twofold MHC class II binding peptides were identified with the rule using our method, compared to the existing scoring matrix method. In conclusion, our GP based motif searching approach enabled to obtain knowledge of functional aspects of the peptides without any prior knowledge.

Molecular Interaction Between Smurfl WW2 Domain and PPXY Motifs of Smadl, Smad5, and Smad6-Modeling and Analysis.

PubMed

Sangadala, Sreedhara; Rao Metpally, Raghu Prasad; B Reddy, Boojala Vijay

2007-08-01

Abstract The ubiquitin-proteasome proteolytic pathway is essential for various important biological processes including cell cycle progression, gene transcription, and signal transduction. One of the important regulatory mechanisms by which the bone-inducing activity of the bone morphogenetic protein (BMP) signaling is modulated involves ubiquitin-mediated proteasomal degradation. The BMP induced receptor signal is transmitted intracellularly by phosphorylation of Smad proteins by the activated receptor I. The phosphorylated Smads 1, 5, and 8 (R-Smads) oligomerize with the co-Smad (Smad4). The complex, thus, formed translocates to the nucleus and interacts with other cofactors to regulate the expression of downstream target genes. R-Smads contain PPXY motif in the linker region that interacts with Smad ubiquitin regulatory factor 1 (Smurf1), an E3 ubiquitin ligase that catalyzes ubiquitination of target proteins for proteasomal degradation. Smurf1 contains a HECT domain, a C2 domain, and 2 WW domains (WW1, WW2). The PPXY motif in target proteins and its interaction with Smurf1 may form the basis for regulation of steady-state levels of Smads in controlling BMP-responsiveness of cells. Here, we present a homology-based model of the Smurf1 WW2 domain and the target octa-peptides containing PPXY motif of Smurf1- interacting Smads. We carried out docking of Smurf1 WW2 domain with the PPXY motifs of Smadl, Smad5, and Smad6 and identified the key amino acid residues involved in interaction. Furthermore, we present experimental evidence that WW2 domain of Smurf1 does indeed interact with the Smad proteins and that the deletion of WW2 domain of Smurf1 results in loss of its binding to Smads using the purified recombinant proteins. Finally, we also present data confirming that the deletion of WW2 domain in Smurf1 abolishes its ubiquitination activity on Smad1 in an in vitro ubiquitination assay. It shows that the interaction between the WW domain and Smad PPXY motif is a

Biological network motif detection and evaluation

PubMed Central

2011-01-01

Background Molecular level of biological data can be constructed into system level of data as biological networks. Network motifs are defined as over-represented small connected subgraphs in networks and they have been used for many biological applications. Since network motif discovery involves computationally challenging processes, previous algorithms have focused on computational efficiency. However, we believe that the biological quality of network motifs is also very important. Results We define biological network motifs as biologically significant subgraphs and traditional network motifs are differentiated as structural network motifs in this paper. We develop five algorithms, namely, EDGEGO-BNM, EDGEBETWEENNESS-BNM, NMF-BNM, NMFGO-BNM and VOLTAGE-BNM, for efficient detection of biological network motifs, and introduce several evaluation measures including motifs included in complex, motifs included in functional module and GO term clustering score in this paper. Experimental results show that EDGEGO-BNM and EDGEBETWEENNESS-BNM perform better than existing algorithms and all of our algorithms are applicable to find structural network motifs as well. Conclusion We provide new approaches to finding network motifs in biological networks. Our algorithms efficiently detect biological network motifs and further improve existing algorithms to find high quality structural network motifs, which would be impossible using existing algorithms. The performances of the algorithms are compared based on our new evaluation measures in biological contexts. We believe that our work gives some guidelines of network motifs research for the biological networks. PMID:22784624

Multiple Illuminant Colour Estimation via Statistical Inference on Factor Graphs.

PubMed

Mutimbu, Lawrence; Robles-Kelly, Antonio

2016-08-31

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

A characterization of horizontal visibility graphs and combinatorics on words

NASA Astrophysics Data System (ADS)

Gutin, Gregory; Mansour, Toufik; Severini, Simone

2011-06-01

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

A dinucleotide motif in oligonucleotides shows potent immunomodulatory activity and overrides species-specific recognition observed with CpG motif.

PubMed

Kandimalla, Ekambar R; Bhagat, Lakshmi; Zhu, Fu-Gang; Yu, Dong; Cong, Yan-Ping; Wang, Daqing; Tang, Jimmy X; Tang, Jin-Yan; Knetter, Cathrine F; Lien, Egil; Agrawal, Sudhir

2003-11-25

Bacterial and synthetic DNAs containing CpG dinucleotides in specific sequence contexts activate the vertebrate immune system through Toll-like receptor 9 (TLR9). In the present study, we used a synthetic nucleoside with a bicyclic heterobase [1-(2'-deoxy-beta-d-ribofuranosyl)-2-oxo-7-deaza-8-methyl-purine; R] to replace the C in CpG, resulting in an RpG dinucleotide. The RpG dinucleotide was incorporated in mouse- and human-specific motifs in oligodeoxynucleotides (oligos) and 3'-3-linked oligos, referred to as immunomers. Oligos containing the RpG motif induced cytokine secretion in mouse spleen-cell cultures. Immunomers containing RpG dinucleotides showed activity in transfected-HEK293 cells stably expressing mouse TLR9, suggesting direct involvement of TLR9 in the recognition of RpG motif. In J774 macrophages, RpG motifs activated NF-kappa B and mitogen-activated protein kinase pathways. Immunomers containing the RpG dinucleotide induced high levels of IL-12 and IFN-gamma, but lower IL-6 in time- and concentration-dependent fashion in mouse spleen-cell cultures costimulated with IL-2. Importantly, immunomers containing GTRGTT and GARGTT motifs were recognized to a similar extent by both mouse and human immune systems. Additionally, both mouse- and human-specific RpG immunomers potently stimulated proliferation of peripheral blood mononuclear cells obtained from diverse vertebrate species, including monkey, pig, horse, sheep, goat, rat, and chicken. An immunomer containing GTRGTT motif prevented conalbumin-induced and ragweed allergen-induced allergic inflammation in mice. We show that a synthetic bicyclic nucleotide is recognized in the C position of a CpG dinucleotide by immune cells from diverse vertebrate species without bias for flanking sequences, suggesting a divergent nucleotide motif recognition pattern of TLR9.

Empirical Determination of Pattern Match Confidence in Labeled Graphs

DTIC Science & Technology

2014-02-07

were explored; Erdős–Rényi [6] random graphs, Barabási–Albert preferential attachment graphs [2], and Watts– Strogatz [18] small world graphs. The ER...B. Erdos - Renyi Barabasi - Albert Gr ap h Ty pe Strogatz - Watts Direct Within 2 nodes Within 4 nodes Search Limit 1 10 100 1000 10000 100000 100...Barabási–Albert (BA, crosses) and Watts– Strogatz (WS, trian- gles) graphs were generated with sizes ranging from 50 to 2500 nodes, and labeled

Asymptote Misconception on Graphing Functions: Does Graphing Software Resolve It?

ERIC Educational Resources Information Center

Öçal, Mehmet Fatih

2017-01-01

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…

D-MATRIX: A web tool for constructing weight matrix of conserved DNA motifs

PubMed Central

Sen, Naresh; Mishra, Manoj; Khan, Feroz; Meena, Abha; Sharma, Ashok

2009-01-01

Despite considerable efforts to date, DNA motif prediction in whole genome remains a challenge for researchers. Currently the genome wide motif prediction tools required either direct pattern sequence (for single motif) or weight matrix (for multiple motifs). Although there are known motif pattern databases and tools for genome level prediction but no tool for weight matrix construction. Considering this, we developed a D-MATRIX tool which predicts the different types of weight matrix based on user defined aligned motif sequence set and motif width. For retrieval of known motif sequences user can access the commonly used databases such as TFD, RegulonDB, DBTBS, Transfac. D­MATRIX program uses a simple statistical approach for weight matrix construction, which can be converted into different file formats according to user requirement. It provides the possibility to identify the conserved motifs in the co­regulated genes or whole genome. As example, we successfully constructed the weight matrix of LexA transcription factor binding site with the help of known sos­box cis­regulatory elements in Deinococcus radiodurans genome. The algorithm is implemented in C-Sharp and wrapped in ASP.Net to maintain a user friendly web interface. D­MATRIX tool is accessible through the CIMAP domain network. Availability http://203.190.147.116/dmatrix/ PMID:19759861

D-MATRIX: a web tool for constructing weight matrix of conserved DNA motifs.

PubMed

Sen, Naresh; Mishra, Manoj; Khan, Feroz; Meena, Abha; Sharma, Ashok

2009-07-27

Despite considerable efforts to date, DNA motif prediction in whole genome remains a challenge for researchers. Currently the genome wide motif prediction tools required either direct pattern sequence (for single motif) or weight matrix (for multiple motifs). Although there are known motif pattern databases and tools for genome level prediction but no tool for weight matrix construction. Considering this, we developed a D-MATRIX tool which predicts the different types of weight matrix based on user defined aligned motif sequence set and motif width. For retrieval of known motif sequences user can access the commonly used databases such as TFD, RegulonDB, DBTBS, Transfac. D-MATRIX program uses a simple statistical approach for weight matrix construction, which can be converted into different file formats according to user requirement. It provides the possibility to identify the conserved motifs in the co-regulated genes or whole genome. As example, we successfully constructed the weight matrix of LexA transcription factor binding site with the help of known sos-box cis-regulatory elements in Deinococcus radiodurans genome. The algorithm is implemented in C-Sharp and wrapped in ASP.Net to maintain a user friendly web interface. D-MATRIX tool is accessible through the CIMAP domain network. http://203.190.147.116/dmatrix/

A Gibbs sampler for motif detection in phylogenetically close sequences

NASA Astrophysics Data System (ADS)

Siddharthan, Rahul; van Nimwegen, Erik; Siggia, Eric

2004-03-01

Genes are regulated by transcription factors that bind to DNA upstream of genes and recognize short conserved ``motifs'' in a random intergenic ``background''. Motif-finders such as the Gibbs sampler compare the probability of these short sequences being represented by ``weight matrices'' to the probability of their arising from the background ``null model'', and explore this space (analogous to a free-energy landscape). But closely related species may show conservation not because of functional sites but simply because they have not had sufficient time to diverge, so conventional methods will fail. We introduce a new Gibbs sampler algorithm that accounts for common ancestry when searching for motifs, while requiring minimal ``prior'' assumptions on the number and types of motifs, assessing the significance of detected motifs by ``tracking'' clusters that stay together. We apply this scheme to motif detection in sporulation-cycle genes in the yeast S. cerevisiae, using recent sequences of other closely-related Saccharomyces species.

Evaluation of Graph Pattern Matching Workloads in Graph Analysis Systems

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

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

2016-01-01

Graph analysis has emerged as a powerful method for data scientists to represent, integrate, query, and explore heterogeneous data sources. As a result, graph data management and mining became a popular area of research, and led to the development of plethora of systems in recent years. Unfortunately, the number of emerging graph analysis systems and the wide range of applications, coupled with a lack of apples-to-apples comparisons, make it difficult to understand the trade-offs between different systems and the graph operations for which they are designed. A fair comparison of these systems is a challenging task for the following reasons:more » multiple data models, non-standardized serialization formats, various query interfaces to users, and diverse environments they operate in. To address these key challenges, in this paper we present a new benchmark suite by extending the Lehigh University Benchmark (LUBM) to cover the most common capabilities of various graph analysis systems. We provide the design process of the benchmark, which generalizes the workflow for data scientists to conduct the desired graph analysis on different graph analysis systems. Equipped with this extended benchmark suite, we present performance comparison for nine subgraph pattern retrieval operations over six graph analysis systems, namely NetworkX, Neo4j, Jena, Titan, GraphX, and uRiKA. Through the proposed benchmark suite, this study reveals both quantitative and qualitative findings in (1) implications in loading data into each system; (2) challenges in describing graph patterns for each query interface; and (3) different sensitivity of each system to query selectivity. We envision that this study will pave the road for: (i) data scientists to select the suitable graph analysis systems, and (ii) data management system designers to advance graph analysis systems.« less

Large-scale Graph Computation on Just a PC

DTIC Science & Technology

2014-05-01

edges for several vertices simultaneously). We compared the performance of GraphChi-DB to Neo4j using their Java API (we discuss MySQL comparison in the...75 4.7.6 Comparison to RDBMS ( MySQL ) . . . . . . . . . . . . . . . . . . . . . 75 4.7.7 Summary of the...Windows method, GraphChi. The C++ implementation has circa 8,000 lines of code. We have also de- veloped a Java -version of GraphChi, but it does not

Classification of user interfaces for graph-based online analytical processing

NASA Astrophysics Data System (ADS)

Michaelis, James R.

2016-05-01

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

An enhanced digital line graph design

USGS Publications Warehouse

Guptill, Stephen C.

1990-01-01

In response to increasing information demands on its digital cartographic data, the U.S. Geological Survey has designed an enhanced version of the Digital Line Graph, termed Digital Line Graph - Enhanced (DLG-E). In the DLG-E model, the phenomena represented by geographic and cartographic data are termed entities. Entities represent individual phenomena in the real world. A feature is an abstraction of a set of entities, with the feature description encompassing only selected properties of the entities (typically the properties that have been portrayed cartographically on a map). Buildings, bridges, roads, streams, grasslands, and counties are examples of features. A feature instance, that is, one occurrence of a feature, is described in the digital environment by feature objects and spatial objects. A feature object identifies a feature instance and its nonlocational attributes. Nontopological relationships are associated with feature objects. The locational aspects of the feature instance are represented by spatial objects. Four spatial objects (points, nodes, chains, and polygons) and their topological relationships are defined. To link the locational and nonlocational aspects of the feature instance, a given feature object is associated with (or is composed of) a set of spatial objects. These objects, attributes, and relationships are the components of the DLG-E data model. To establish a domain of features for DLG-E, an approach using a set of classes, or views, of spatial entities was adopted. The five views that were developed are cover, division, ecosystem, geoposition, and morphology. The views are exclusive; each view is a self-contained analytical approach to the entire range of world features. Because each view is independent of the others, a single point on the surface of the Earth can be represented under multiple views. Under the five views, over 200 features were identified and defined. This set constitutes an initial domain of DLG-E features.

Comparison of university students' understanding of graphs in different contexts

NASA Astrophysics Data System (ADS)

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

2013-12-01

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

CircularLogo: A lightweight web application to visualize intra-motif dependencies.

PubMed

Ye, Zhenqing; Ma, Tao; Kalmbach, Michael T; Dasari, Surendra; Kocher, Jean-Pierre A; Wang, Liguo

2017-05-22

The sequence logo has been widely used to represent DNA or RNA motifs for more than three decades. Despite its intelligibility and intuitiveness, the traditional sequence logo is unable to display the intra-motif dependencies and therefore is insufficient to fully characterize nucleotide motifs. Many methods have been developed to quantify the intra-motif dependencies, but fewer tools are available for visualization. We developed CircularLogo, a web-based interactive application, which is able to not only visualize the position-specific nucleotide consensus and diversity but also display the intra-motif dependencies. Applying CircularLogo to HNF6 binding sites and tRNA sequences demonstrated its ability to show intra-motif dependencies and intuitively reveal biomolecular structure. CircularLogo is implemented in JavaScript and Python based on the Django web framework. The program's source code and user's manual are freely available at http://circularlogo.sourceforge.net . CircularLogo web server can be accessed from http://bioinformaticstools.mayo.edu/circularlogo/index.html . CircularLogo is an innovative web application that is specifically designed to visualize and interactively explore intra-motif dependencies.

Study of Chromatic parameters of Line, Total, Middle graphs and Graph operators of Bipartite graph

NASA Astrophysics Data System (ADS)

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

On the star partition dimension of comb product of cycle and complete graph

NASA Astrophysics Data System (ADS)

Alfarisi, Ridho; Darmaji; Dafik

2017-06-01

Let G = (V, E) be a connected graphs with vertex set V (G), edge set E(G) and S ⊆ V (G). For an ordered partition Π = {S 1, S 2, S 3, …, Sk } of V (G), the representation of a vertex v ∈ V (G) with respect to Π is the k-vectors r(v|Π) = (d(v, S 1), d(v, S 2), …, d(v, Sk )), where d(v, Sk ) represents the distance between the vertex v and the set Sk , defined by d(v, Sk ) = min{d(v, x)|x ∈ Sk}. The partition Π of V (G) is a resolving partition if the k-vektors r(v|Π), v ∈ V (G) are distinct. The minimum resolving partition Π is a partition dimension of G, denoted by pd(G). The resolving partition Π = {S 1, S 2, S 3, …, Sk} is called a star resolving partition for G if it is a resolving partition and each subgraph induced by Si , 1 ≤ i ≤ k, is a star. The minimum k for which there exists a star resolving partition of V (G) is the star partition dimension of G, denoted by spd(G). Finding a star partition dimension of G is classified to be a NP-Hard problem. Furthermore, the comb product between G and H, denoted by G ⊲ H, is a graph obtained by taking one copy of G and |V (G)| copies of H and grafting the i-th copy of H at the vertex o to the i-th vertex of G. By definition of comb product, we can say that V (G ⊲ H) = {(a, u)|a ∈ V (G), u ∈ V (H)} and (a, u)(b, v) ∈ E(G ⊲ H) whenever a = b and uv ∈ E(H), or ab ∈ E(G) and u = v = o. In this paper, we will study the star partition dimension of comb product of cycle and complete graph, namely Cn ⊲ Km and Km ⊲ Cn for n ≥ 3 and m ≥ 3.

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

NASA Astrophysics Data System (ADS)

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

2017-09-01

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

Systematic comparison of the response properties of protein and RNA mediated gene regulatory motifs.

PubMed

Iyengar, Bharat Ravi; Pillai, Beena; Venkatesh, K V; Gadgil, Chetan J

2017-05-30

We present a framework enabling the dissection of the effects of motif structure (feedback or feedforward), the nature of the controller (RNA or protein), and the regulation mode (transcriptional, post-transcriptional or translational) on the response to a step change in the input. We have used a common model framework for gene expression where both motif structures have an activating input and repressing regulator, with the same set of parameters, to enable a comparison of the responses. We studied the global sensitivity of the system properties, such as steady-state gain, overshoot, peak time, and peak duration, to parameters. We find that, in all motifs, overshoot correlated negatively whereas peak duration varied concavely with peak time. Differences in the other system properties were found to be mainly dependent on the nature of the controller rather than the motif structure. Protein mediated motifs showed a higher degree of adaptation i.e. a tendency to return to baseline levels; in particular, feedforward motifs exhibited perfect adaptation. RNA mediated motifs had a mild regulatory effect; they also exhibited a lower peaking tendency and mean overshoot. Protein mediated feedforward motifs showed higher overshoot and lower peak time compared to the corresponding feedback motifs.

Searching RNA motifs and their intermolecular contacts with constraint networks.

PubMed

Thébault, P; de Givry, S; Schiex, T; Gaspin, C

2006-09-01

Searching RNA gene occurrences in genomic sequences is a task whose importance has been renewed by the recent discovery of numerous functional RNA, often interacting with other ligands. Even if several programs exist for RNA motif search, none exists that can represent and solve the problem of searching for occurrences of RNA motifs in interaction with other molecules. We present a constraint network formulation of this problem. RNA are represented as structured motifs that can occur on more than one sequence and which are related together by possible hybridization. The implemented tool MilPat is used to search for several sRNA families in genomic sequences. Results show that MilPat allows to efficiently search for interacting motifs in large genomic sequences and offers a simple and extensible framework to solve such problems. New and known sRNA are identified as H/ACA candidates in Methanocaldococcus jannaschii. http://carlit.toulouse.inra.fr/MilPaT/MilPat.pl.

Statistics of Gaussian packets on metric and decorated graphs.

PubMed

Chernyshev, V L; Shafarevich, A I

2014-01-28

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

Plane representations of graphs and visibility between parallel segments

NASA Astrophysics Data System (ADS)

Tamassia, R.; Tollis, I. G.

1985-04-01

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

Label Information Guided Graph Construction for Semi-Supervised Learning.

PubMed

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

2017-09-01

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

Efficient Graph Based Assembly of Short-Read Sequences on Hybrid Core Architecture

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

Sczyrba, Alex; Pratap, Abhishek; Canon, Shane

2011-03-22

Advanced architectures can deliver dramatically increased throughput for genomics and proteomics applications, reducing time-to-completion in some cases from days to minutes. One such architecture, hybrid-core computing, marries a traditional x86 environment with a reconfigurable coprocessor, based on field programmable gate array (FPGA) technology. In addition to higher throughput, increased performance can fundamentally improve research quality by allowing more accurate, previously impractical approaches. We will discuss the approach used by Convey?s de Bruijn graph constructor for short-read, de-novo assembly. Bioinformatics applications that have random access patterns to large memory spaces, such as graph-based algorithms, experience memory performance limitations on cache-based x86more » servers. Convey?s highly parallel memory subsystem allows application-specific logic to simultaneously access 8192 individual words in memory, significantly increasing effective memory bandwidth over cache-based memory systems. Many algorithms, such as Velvet and other de Bruijn graph based, short-read, de-novo assemblers, can greatly benefit from this type of memory architecture. Furthermore, small data type operations (four nucleotides can be represented in two bits) make more efficient use of logic gates than the data types dictated by conventional programming models.JGI is comparing the performance of Convey?s graph constructor and Velvet on both synthetic and real data. We will present preliminary results on memory usage and run time metrics for various data sets with different sizes, from small microbial and fungal genomes to very large cow rumen metagenome. For genomes with references we will also present assembly quality comparisons between the two assemblers.« less

Graphing Polar Curves

ERIC Educational Resources Information Center

Lawes, Jonathan F.

2013-01-01

Graphing polar curves typically involves a combination of three traditional techniques, all of which can be time-consuming and tedious. However, an alternative method--graphing the polar function on a rectangular plane--simplifies graphing, increases student understanding of the polar coordinate system, and reinforces graphing techniques learned…

Spectral statistics of random geometric graphs

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

Graph Coarsening for Path Finding in Cybersecurity Graphs

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

Hogan, Emilie A.; Johnson, John R.; Halappanavar, Mahantesh

2013-01-01

n the pass-the-hash attack, hackers repeatedly steal password hashes and move through a computer network with the goal of reaching a computer with high level administrative privileges. In this paper we apply graph coarsening in network graphs for the purpose of detecting hackers using this attack or assessing the risk level of the network's current state. We repeatedly take graph minors, which preserve the existence of paths in the graph, and take powers of the adjacency matrix to count the paths. This allows us to detect the existence of paths as well as find paths that have high risk ofmore » being used by adversaries.« less

Efficient exact motif discovery.

PubMed

Marschall, Tobias; Rahmann, Sven

2009-06-15

The motif discovery problem consists of finding over-represented patterns in a collection of biosequences. It is one of the classical sequence analysis problems, but still has not been satisfactorily solved in an exact and efficient manner. This is partly due to the large number of possibilities of defining the motif search space and the notion of over-representation. Even for well-defined formalizations, the problem is frequently solved in an ad hoc manner with heuristics that do not guarantee to find the best motif. We show how to solve the motif discovery problem (almost) exactly on a practically relevant space of IUPAC generalized string patterns, using the p-value with respect to an i.i.d. model or a Markov model as the measure of over-representation. In particular, (i) we use a highly accurate compound Poisson approximation for the null distribution of the number of motif occurrences. We show how to compute the exact clump size distribution using a recently introduced device called probabilistic arithmetic automaton (PAA). (ii) We define two p-value scores for over-representation, the first one based on the total number of motif occurrences, the second one based on the number of sequences in a collection with at least one occurrence. (iii) We describe an algorithm to discover the optimal pattern with respect to either of the scores. The method exploits monotonicity properties of the compound Poisson approximation and is by orders of magnitude faster than exhaustive enumeration of IUPAC strings (11.8 h compared with an extrapolated runtime of 4.8 years). (iv) We justify the use of the proposed scores for motif discovery by showing our method to outperform other motif discovery algorithms (e.g. MEME, Weeder) on benchmark datasets. We also propose new motifs on Mycobacterium tuberculosis. The method has been implemented in Java. It can be obtained from http://ls11-www.cs.tu-dortmund.de/people/marschal/paa_md/.

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

PubMed

Grady, Leo; Jolly, Marie-Pierre

2008-01-01

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

Strong parameterization and coordination encirclements of graph of Penrose tiling vertices

NASA Astrophysics Data System (ADS)

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

2017-07-01

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

Antiferromagnetic Potts Model on the Erdős-Rényi Random Graph

NASA Astrophysics Data System (ADS)

Contucci, Pierluigi; Dommers, Sander; Giardinà, Cristian; Starr, Shannon

2013-10-01

We study the antiferromagnetic Potts model on the Poissonian Erdős-Rényi random graph. By identifying a suitable interpolation structure and an extended variational principle, together with a positive temperature second-moment analysis we prove the existence of a phase transition at a positive critical temperature. Upper and lower bounds on the temperature critical value are obtained from the stability analysis of the replica symmetric solution (recovered in the framework of Derrida-Ruelle probability cascades) and from an entropy positivity argument.

Counting motifs in dynamic networks.

PubMed

Mukherjee, Kingshuk; Hasan, Md Mahmudul; Boucher, Christina; Kahveci, Tamer

2018-04-11

A network motif is a sub-network that occurs frequently in a given network. Detection of such motifs is important since they uncover functions and local properties of the given biological network. Finding motifs is however a computationally challenging task as it requires solving the costly subgraph isomorphism problem. Moreover, the topology of biological networks change over time. These changing networks are called dynamic biological networks. As the network evolves, frequency of each motif in the network also changes. Computing the frequency of a given motif from scratch in a dynamic network as the network topology evolves is infeasible, particularly for large and fast evolving networks. In this article, we design and develop a scalable method for counting the number of motifs in a dynamic biological network. Our method incrementally updates the frequency of each motif as the underlying network's topology evolves. Our experiments demonstrate that our method can update the frequency of each motif in orders of magnitude faster than counting the motif embeddings every time the network changes. If the network evolves more frequently, the margin with which our method outperforms the existing static methods, increases. We evaluated our method extensively using synthetic and real datasets, and show that our method is highly accurate(≥ 96%) and that it can be scaled to large dense networks. The results on real data demonstrate the utility of our method in revealing interesting insights on the evolution of biological processes.

Interval Graph Limits

PubMed Central

Diaconis, Persi; Holmes, Susan; Janson, Svante

2015-01-01

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

Introducing the slime mold graph repository

NASA Astrophysics Data System (ADS)

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

2017-07-01

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

Graphing with "LogoWriter."

ERIC Educational Resources Information Center

Yoder, Sharon K.

This book discusses four kinds of graphs that are taught in mathematics at the middle school level: pictographs, bar graphs, line graphs, and circle graphs. The chapters on each of these types of graphs contain information such as starting, scaling, drawing, labeling, and finishing the graphs using "LogoWriter." The final chapter of the…

Labeled Graph Kernel for Behavior Analysis.

PubMed

Zhao, Ruiqi; Martinez, Aleix M

2016-08-01

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

Building dynamic population graph for accurate correspondence detection.

PubMed

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

2015-12-01

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

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

PubMed

Zhang, Qin

2015-07-01

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

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

PubMed

Jain, Swati; Schlick, Tamar

2017-11-24

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

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

DTIC Science & Technology

2012-06-01

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

Applying Graph Theory to Problems in Air Traffic Management

NASA Technical Reports Server (NTRS)

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

2017-01-01

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

Applying Graph Theory to Problems in Air Traffic Management

NASA Technical Reports Server (NTRS)

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

2017-01-01

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

RSAT matrix-clustering: dynamic exploration and redundancy reduction of transcription factor binding motif collections

PubMed Central

Jaeger, Sébastien; Thieffry, Denis

2017-01-01

Abstract Transcription factor (TF) databases contain multitudes of binding motifs (TFBMs) from various sources, from which non-redundant collections are derived by manual curation. The advent of high-throughput methods stimulated the production of novel collections with increasing numbers of motifs. Meta-databases, built by merging these collections, contain redundant versions, because available tools are not suited to automatically identify and explore biologically relevant clusters among thousands of motifs. Motif discovery from genome-scale data sets (e.g. ChIP-seq) also produces redundant motifs, hampering the interpretation of results. We present matrix-clustering, a versatile tool that clusters similar TFBMs into multiple trees, and automatically creates non-redundant TFBM collections. A feature unique to matrix-clustering is its dynamic visualisation of aligned TFBMs, and its capability to simultaneously treat multiple collections from various sources. We demonstrate that matrix-clustering considerably simplifies the interpretation of combined results from multiple motif discovery tools, and highlights biologically relevant variations of similar motifs. We also ran a large-scale application to cluster ∼11 000 motifs from 24 entire databases, showing that matrix-clustering correctly groups motifs belonging to the same TF families, and drastically reduced motif redundancy. matrix-clustering is integrated within the RSAT suite (http://rsat.eu/), accessible through a user-friendly web interface or command-line for its integration in pipelines. PMID:28591841

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

PubMed

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

2013-01-01

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

An Efficient Scheme for Crystal Structure Prediction Based on Structural Motifs

DOE PAGES

Zhu, Zizhong; Wu, Ping; Wu, Shunqing; ...

2017-05-15

An efficient scheme based on structural motifs is proposed for the crystal structure prediction of materials. The key advantage of the present method comes in two fold: first, the degrees of freedom of the system are greatly reduced, since each structural motif, regardless of its size, can always be described by a set of parameters (R, θ, φ) with five degrees of freedom; second, the motifs could always appear in the predicted structures when the energies of the structures are relatively low. Both features make the present scheme a very efficient method for predicting desired materials. The method has beenmore » applied to the case of LiFePO 4, an important cathode material for lithium-ion batteries. Numerous new structures of LiFePO 4 have been found, compared to those currently available, available, demonstrating the reliability of the present methodology and illustrating the promise of the concept of structural motifs.« less

An Efficient Scheme for Crystal Structure Prediction Based on Structural Motifs

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

Zhu, Zizhong; Wu, Ping; Wu, Shunqing

An efficient scheme based on structural motifs is proposed for the crystal structure prediction of materials. The key advantage of the present method comes in two fold: first, the degrees of freedom of the system are greatly reduced, since each structural motif, regardless of its size, can always be described by a set of parameters (R, θ, φ) with five degrees of freedom; second, the motifs could always appear in the predicted structures when the energies of the structures are relatively low. Both features make the present scheme a very efficient method for predicting desired materials. The method has beenmore » applied to the case of LiFePO 4, an important cathode material for lithium-ion batteries. Numerous new structures of LiFePO 4 have been found, compared to those currently available, available, demonstrating the reliability of the present methodology and illustrating the promise of the concept of structural motifs.« less

De Novo Regulatory Motif Discovery Identifies Significant Motifs in Promoters of Five Classes of Plant Dehydrin Genes.

PubMed

Zolotarov, Yevgen; Strömvik, Martina

2015-01-01

Plants accumulate dehydrins in response to osmotic stresses. Dehydrins are divided into five different classes, which are thought to be regulated in different manners. To better understand differences in transcriptional regulation of the five dehydrin classes, de novo motif discovery was performed on 350 dehydrin promoter sequences from a total of 51 plant genomes. Overrepresented motifs were identified in the promoters of five dehydrin classes. The Kn dehydrin promoters contain motifs linked with meristem specific expression, as well as motifs linked with cold/dehydration and abscisic acid response. KS dehydrin promoters contain a motif with a GATA core. SKn and YnSKn dehydrin promoters contain motifs that match elements connected with cold/dehydration, abscisic acid and light response. YnKn dehydrin promoters contain motifs that match abscisic acid and light response elements, but not cold/dehydration response elements. Conserved promoter motifs are present in the dehydrin classes and across different plant lineages, indicating that dehydrin gene regulation is likely also conserved.

The Hexahistidine Motif of Host-Defense Protein Human Calprotectin Contributes to Zinc Withholding and Its Functional Versatility.

PubMed

Nakashige, Toshiki G; Stephan, Jules R; Cunden, Lisa S; Brophy, Megan Brunjes; Wommack, Andrew J; Keegan, Brenna C; Shearer, Jason M; Nolan, Elizabeth M

2016-09-21

Human calprotectin (CP, S100A8/S100A9 oligomer, MRP-8/MRP-14 oligomer) is an abundant host-defense protein that is involved in the metal-withholding innate immune response. CP coordinates a variety of divalent first-row transition metal ions, which is implicated in its antimicrobial function, and its ability to sequester nutrient Zn(II) ions from microbial pathogens has been recognized for over two decades. CP has two distinct transition-metal-binding sites formed at the S100A8/S100A9 dimer interface, including a histidine-rich site composed of S100A8 residues His17 and His27 and S100A9 residues His91 and His95. In this study, we report that CP binds Zn(II) at this site using a hexahistidine motif, completed by His103 and His105 of the S100A9 C-terminal tail and previously identified as the high-affinity Mn(II) and Fe(II) coordination site. Zn(II) binding at this unique site shields the S100A9 C-terminal tail from proteolytic degradation by proteinase K. X-ray absorption spectroscopy and Zn(II) competition titrations support the formation of a Zn(II)-His6 motif. Microbial growth studies indicate that the hexahistidine motif is important for preventing microbial Zn(II) acquisition from CP by the probiotic Lactobacillus plantarum and the opportunistic human pathogen Candida albicans. The Zn(II)-His6 site of CP expands the known biological coordination chemistry of Zn(II) and provides new insight into how the human innate immune system starves microbes of essential metal nutrients.

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

PubMed

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

2012-01-01

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

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

PubMed

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

2016-09-01

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

Extending Matchings in Planar Graphs 4

DTIC Science & Technology

1989-01-01

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

X-Graphs: Language and Algorithms for Heterogeneous Graph Streams

DTIC Science & Technology

2017-09-01

INTRODUCTION 1 3 METHODS , ASUMPTIONS, AND PROCEDURES 2 Software Abstractions for Graph Analytic Applications 2 High performance Platforms for Graph Processing...data is stored in a distributed file system. 3 METHODS , ASUMPTIONS, AND PROCEDURES Software Abstractions for Graph Analytic Applications To...implementations of novel methods for networks analysis: several methods for detection of overlapping communities, personalized PageRank, node embeddings into a d

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

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

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

1996-12-31

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

Graph theory and the Virasoro master equation

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

Obers, N.A.J.

1991-04-01

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

Mixotrophy and intraguild predation - dynamic consequences of shifts between food web motifs

NASA Astrophysics Data System (ADS)

Karnatak, Rajat; Wollrab, Sabine

2017-06-01

Mixotrophy is ubiquitous in microbial communities of aquatic systems with many flagellates being able to use autotroph as well as heterotroph pathways for energy acquisition. The usage of one over the other pathway is associated with resource availability and the coupling of alternative pathways has strong implications for system stability. We investigated the impact of dominance of different energy pathways related to relative resource availability on system dynamics in the setting of a tritrophic food web motif. This motif consists of a mixotroph feeding on a purely autotroph species while competing for a shared resource. In addition, the autotroph can use an additional exclusive food source. By changing the relative abundance of shared vs. exclusive food source, we shift the food web motif from an intraguild predation motif to a food chain motif. We analyzed the dependence of system dynamics on absolute and relative resource availability. In general, the system exhibits a transition from stable to oscillatory dynamics with increasing nutrient availability. However, this transition occurs at a much lower nutrient level for the food chain in comparison to the intraguild predation motif. A similar transition is also observed with variations in the relative abundance of food sources for a range of nutrient levels. We expect this shift in food web motifs to occur frequently in microbial communities and therefore the results from our study are highly relevant for natural systems.

Quantization of gauge fields, graph polynomials and graph homology

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

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

2013-09-15

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

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

PubMed

He, Tiantian; Chan, Keith C C

2018-05-01

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

Graphing trillions of triangles

PubMed Central

Burkhardt, Paul

2016-01-01

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. PMID:28690426

Graphing trillions of triangles.

PubMed

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.

A Benes-like theorem for the shuffle-exchange graph

NASA Technical Reports Server (NTRS)

Schwabe, Eric J.

1992-01-01

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

A global/local affinity graph for image segmentation.

PubMed

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

2015-04-01

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

Learning graph matching.

PubMed

Caetano, Tibério S; McAuley, Julian J; Cheng, Li; Le, Quoc V; Smola, Alex J

2009-06-01

As a fundamental problem in pattern recognition, graph matching has applications in a variety of fields, from computer vision to computational biology. In graph matching, patterns are modeled as graphs and pattern recognition amounts to finding a correspondence between the nodes of different graphs. Many formulations of this problem can be cast in general as a quadratic assignment problem, where a linear term in the objective function encodes node compatibility and a quadratic term encodes edge compatibility. The main research focus in this theme is about designing efficient algorithms for approximately solving the quadratic assignment problem, since it is NP-hard. In this paper we turn our attention to a different question: how to estimate compatibility functions such that the solution of the resulting graph matching problem best matches the expected solution that a human would manually provide. We present a method for learning graph matching: the training examples are pairs of graphs and the 'labels' are matches between them. Our experimental results reveal that learning can substantially improve the performance of standard graph matching algorithms. In particular, we find that simple linear assignment with such a learning scheme outperforms Graduated Assignment with bistochastic normalisation, a state-of-the-art quadratic assignment relaxation algorithm.

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

ERIC Educational Resources Information Center

Thelwall, Mike; Wilkinson, David

2003-01-01

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

EvoGraph: On-The-Fly Efficient Mining of Evolving Graphs on GPU

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

Sengupta, Dipanjan; Song, Shuaiwen

With the prevalence of the World Wide Web and social networks, there has been a growing interest in high performance analytics for constantly-evolving dynamic graphs. Modern GPUs provide massive AQ1 amount of parallelism for efficient graph processing, but the challenges remain due to their lack of support for the near real-time streaming nature of dynamic graphs. Specifically, due to the current high volume and velocity of graph data combined with the complexity of user queries, traditional processing methods by first storing the updates and then repeatedly running static graph analytics on a sequence of versions or snapshots are deemed undesirablemore » and computational infeasible on GPU. We present EvoGraph, a highly efficient and scalable GPU- based dynamic graph analytics framework.« less

Reflecting on Graphs: Attributes of Graph Choice and Construction Practices in Biology

PubMed Central

Angra, Aakanksha; Gardner, Stephanie M.

2017-01-01

Undergraduate biology education reform aims to engage students in scientific practices such as experimental design, experimentation, and data analysis and communication. Graphs are ubiquitous in the biological sciences, and creating effective graphical representations involves quantitative and disciplinary concepts and skills. Past studies document student difficulties with graphing within the contexts of classroom or national assessments without evaluating student reasoning. Operating under the metarepresentational competence framework, we conducted think-aloud interviews to reveal differences in reasoning and graph quality between undergraduate biology students, graduate students, and professors in a pen-and-paper graphing task. All professors planned and thought about data before graph construction. When reflecting on their graphs, professors and graduate students focused on the function of graphs and experimental design, while most undergraduate students relied on intuition and data provided in the task. Most undergraduate students meticulously plotted all data with scaled axes, while professors and some graduate students transformed the data, aligned the graph with the research question, and reflected on statistics and sample size. Differences in reasoning and approaches taken in graph choice and construction corroborate and extend previous findings and provide rich targets for undergraduate and graduate instruction. PMID:28821538

Detecting Statistically Significant Communities of Triangle Motifs in Undirected Networks

DTIC Science & Technology

2016-04-26

REPORT TYPE Final 3. DATES COVERED (From - To) 15 Oct 2014 to 14 Jan 2015 4. TITLE AND SUBTITLE Detecting statistically significant clusters of...extend the work of Perry et al. [6] by developing a statistical framework that supports the detection of triangle motif-based clusters in complex...priori, the need for triangle motif-based clustering . 2. Developed an algorithm for clustering undirected networks, where the triangle con guration was

Multi-Level Anomaly Detection on Time-Varying Graph Data

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

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

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

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

PubMed

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

2016-01-15

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

Molecular interaction between Smurf1 WW2 domain and PPXY motifs of Smad1, Smad5, and Smad6--modeling and analysis.

PubMed

Sangadala, Sreedhara; Metpally, Raghu Prasad Rao; Reddy, Boojala Vijay B

2007-08-01

The ubiquitin-proteasome proteolytic pathway is essential for various important biological processes including cell cycle progression, gene transcription, and signal transduction. One of the important regulatory mechanisms by which the bone-inducing activity of the bone morphogenetic protein (BMP) signaling is modulated involves ubiquitin-mediated proteasomal degradation. The BMP induced receptor signal is transmitted intracellularly by phosphorylation of Smad proteins by the activated receptor I. The phosphorylated Smads 1, 5, and 8 (R-Smads) oligomerize with the co-Smad (Smad4). The complex, thus, formed translocates to the nucleus and interacts with other cofactors to regulate the expression of downstream target genes. R-Smads contain PPXY motif in the linker region that interacts with Smad ubiquitin regulatory factor 1 (Smurf1), an E3 ubiquitin ligase that catalyzes ubiquitination of target proteins for proteasomal degradation. Smurf1 contains a HECT domain, a C2 domain, and 2 WW domains (WW1, WW2). The PPXY motif in target proteins and its interaction with Smurf1 may form the basis for regulation of steady-state levels of Smads in controlling BMP-responsiveness of cells. Here, we present a homology-based model of the Smurf1 WW2 domain and the target octa-peptides containing PPXY motif of Smurf1-interacting Smads. We carried out docking of Smurf1 WW2 domain with the PPXY motifs of Smad1, Smad5, and Smad6 and identified the key amino acid residues involved in interaction. Furthermore, we present experimental evidence that WW2 domain of Smurf1 does indeed interact with the Smad proteins and that the deletion of WW2 domain of Smurf1 results in loss of its binding to Smads using the purified recombinant proteins. Finally, we also present data confirming that the deletion of WW2 domain in Smurf1 abolishes its ubiquitination activity on Smad1 in an in vitro ubiquitination assay. It shows that the interaction between the WW domain and Smad PPXY motif is a key step in

Graphing Calculator Mini Course

NASA Technical Reports Server (NTRS)

Karnawat, Sunil R.

1996-01-01

The "Graphing Calculator Mini Course" project provided a mathematically-intensive technologically-based summer enrichment workshop for teachers of American Indian students on the Turtle Mountain Indian Reservation. Eleven such teachers participated in the six-day workshop in summer of 1996 and three Sunday workshops in the academic year. The project aimed to improve science and mathematics education on the reservation by showing teachers effective ways to use high-end graphing calculators as teaching and learning tools in science and mathematics courses at all levels. In particular, the workshop concentrated on applying TI-82's user-friendly features to understand the various mathematical and scientific concepts.

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

NASA Astrophysics Data System (ADS)

Jiang, Minghui

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

Evaluating structural pattern recognition for handwritten math via primitive label graphs

NASA Astrophysics Data System (ADS)

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

2013-01-01

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

SA-Mot: a web server for the identification of motifs of interest extracted from protein loops

PubMed Central

Regad, Leslie; Saladin, Adrien; Maupetit, Julien; Geneix, Colette; Camproux, Anne-Claude

2011-01-01

The detection of functional motifs is an important step for the determination of protein functions. We present here a new web server SA-Mot (Structural Alphabet Motif) for the extraction and location of structural motifs of interest from protein loops. Contrary to other methods, SA-Mot does not focus only on functional motifs, but it extracts recurrent and conserved structural motifs involved in structural redundancy of loops. SA-Mot uses the structural word notion to extract all structural motifs from uni-dimensional sequences corresponding to loop structures. Then, SA-Mot provides a description of these structural motifs using statistics computed in the loop data set and in SCOP superfamily, sequence and structural parameters. SA-Mot results correspond to an interactive table listing all structural motifs extracted from a target structure and their associated descriptors. Using this information, the users can easily locate loop regions that are important for the protein folding and function. The SA-Mot web server is available at http://sa-mot.mti.univ-paris-diderot.fr. PMID:21665924

SA-Mot: a web server for the identification of motifs of interest extracted from protein loops.

PubMed

Regad, Leslie; Saladin, Adrien; Maupetit, Julien; Geneix, Colette; Camproux, Anne-Claude

2011-07-01

The detection of functional motifs is an important step for the determination of protein functions. We present here a new web server SA-Mot (Structural Alphabet Motif) for the extraction and location of structural motifs of interest from protein loops. Contrary to other methods, SA-Mot does not focus only on functional motifs, but it extracts recurrent and conserved structural motifs involved in structural redundancy of loops. SA-Mot uses the structural word notion to extract all structural motifs from uni-dimensional sequences corresponding to loop structures. Then, SA-Mot provides a description of these structural motifs using statistics computed in the loop data set and in SCOP superfamily, sequence and structural parameters. SA-Mot results correspond to an interactive table listing all structural motifs extracted from a target structure and their associated descriptors. Using this information, the users can easily locate loop regions that are important for the protein folding and function. The SA-Mot web server is available at http://sa-mot.mti.univ-paris-diderot.fr.

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

DTIC Science & Technology

2014-01-01

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

Hierarchical graphs for rule-based modeling of biochemical systems

PubMed Central

2011-01-01

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

Graph theory and the Virasoro master equation

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

Obers, N.A.J.

1991-01-01

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

A Wave Chaotic Study of Quantum Graphs with Microwave Networks

NASA Astrophysics Data System (ADS)

Fu, Ziyuan

Quantum graphs provide a setting to test the hypothesis that all ray-chaotic systems show universal wave chaotic properties. I study the quantum graphs with a wave chaotic approach. Here, an experimental setup consisting of a microwave coaxial cable network is used to simulate quantum graphs. Some basic features and the distributions of impedance statistics are analyzed from experimental data on an ensemble of tetrahedral networks. The random coupling model (RCM) is applied in an attempt to uncover the universal statistical properties of the system. Deviations from RCM predictions have been observed in that the statistics of diagonal and off-diagonal impedance elements are different. Waves trapped due to multiple reflections on bonds between nodes in the graph most likely cause the deviations from universal behavior in the finite-size realization of a quantum graph. In addition, I have done some investigations on the Random Coupling Model, which are useful for further research.

Fast Solitons on Star Graphs

NASA Astrophysics Data System (ADS)

Adami, Riccardo; Cacciapuoti, Claudio; Finco, Domenico; Noja, Diego

We define the Schrödinger equation with focusing, cubic nonlinearity on one-vertex graphs. We prove global well-posedness in the energy domain and conservation laws for some self-adjoint boundary conditions at the vertex, i.e. Kirchhoff boundary condition and the so-called δ and δ‧ boundary conditions. Moreover, in the same setting, we study the collision of a fast solitary wave with the vertex and we show that it splits in reflected and transmitted components. The outgoing waves preserve a soliton character over a time which depends on the logarithm of the velocity of the ingoing solitary wave. Over the same timescale, the reflection and transmission coefficients of the outgoing waves coincide with the corresponding coefficients of the linear problem. In the analysis of the problem, we follow ideas borrowed from the seminal paper [17] about scattering of fast solitons by a delta interaction on the line, by Holmer, Marzuola and Zworski. The present paper represents an extension of their work to the case of graphs and, as a byproduct, it shows how to extend the analysis of soliton scattering by other point interactions on the line, interpreted as a degenerate graph.

Model of twelve properties of a set of organic solvents with graph-theoretical and/or experimental parameters.

PubMed

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.

Graph drawing using tabu search coupled with path relinking.

PubMed

Dib, Fadi K; Rodgers, Peter

2018-01-01

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

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

ERIC Educational Resources Information Center

Tatsuoka, Maurice M.

1986-01-01

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

A study on the application of topic models to motif finding algorithms.

PubMed

Basha Gutierrez, Josep; Nakai, Kenta

2016-12-22

Topic models are statistical algorithms which try to discover the structure of a set of documents according to the abstract topics contained in them. Here we try to apply this approach to the discovery of the structure of the transcription factor binding sites (TFBS) contained in a set of biological sequences, which is a fundamental problem in molecular biology research for the understanding of transcriptional regulation. Here we present two methods that make use of topic models for motif finding. First, we developed an algorithm in which first a set of biological sequences are treated as text documents, and the k-mers contained in them as words, to then build a correlated topic model (CTM) and iteratively reduce its perplexity. We also used the perplexity measurement of CTMs to improve our previous algorithm based on a genetic algorithm and several statistical coefficients. The algorithms were tested with 56 data sets from four different species and compared to 14 other methods by the use of several coefficients both at nucleotide and site level. The results of our first approach showed a performance comparable to the other methods studied, especially at site level and in sensitivity scores, in which it scored better than any of the 14 existing tools. In the case of our previous algorithm, the new approach with the addition of the perplexity measurement clearly outperformed all of the other methods in sensitivity, both at nucleotide and site level, and in overall performance at site level. The statistics obtained show that the performance of a motif finding method based on the use of a CTM is satisfying enough to conclude that the application of topic models is a valid method for developing motif finding algorithms. Moreover, the addition of topic models to a previously developed method dramatically increased its performance, suggesting that this combined algorithm can be a useful tool to successfully predict motifs in different kinds of sets of DNA sequences.

An MBO Scheme for Minimizing the Graph Ohta-Kawasaki Functional

NASA Astrophysics Data System (ADS)

van Gennip, Yves

2018-06-01

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

Minimum nonuniform graph partitioning with unrelated weights

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Graph theoretical model of a sensorimotor connectome in zebrafish.

PubMed

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

2012-01-01

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

Knowledge boosting: a graph-based integration approach with multi-omics data and genomic knowledge for cancer clinical outcome prediction

PubMed Central

Kim, Dokyoon; Joung, Je-Gun; Sohn, Kyung-Ah; Shin, Hyunjung; Park, Yu Rang; Ritchie, Marylyn D; Kim, Ju Han

2015-01-01

Objective Cancer can involve gene dysregulation via multiple mechanisms, so no single level of genomic data fully elucidates tumor behavior due to the presence of numerous genomic variations within or between levels in a biological system. We have previously proposed a graph-based integration approach that combines multi-omics data including copy number alteration, methylation, miRNA, and gene expression data for predicting clinical outcome in cancer. However, genomic features likely interact with other genomic features in complex signaling or regulatory networks, since cancer is caused by alterations in pathways or complete processes. Methods Here we propose a new graph-based framework for integrating multi-omics data and genomic knowledge to improve power in predicting clinical outcomes and elucidate interplay between different levels. To highlight the validity of our proposed framework, we used an ovarian cancer dataset from The Cancer Genome Atlas for predicting stage, grade, and survival outcomes. Results Integrating multi-omics data with genomic knowledge to construct pre-defined features resulted in higher performance in clinical outcome prediction and higher stability. For the grade outcome, the model with gene expression data produced an area under the receiver operating characteristic curve (AUC) of 0.7866. However, models of the integration with pathway, Gene Ontology, chromosomal gene set, and motif gene set consistently outperformed the model with genomic data only, attaining AUCs of 0.7873, 0.8433, 0.8254, and 0.8179, respectively. Conclusions Integrating multi-omics data and genomic knowledge to improve understanding of molecular pathogenesis and underlying biology in cancer should improve diagnostic and prognostic indicators and the effectiveness of therapies. PMID:25002459

Knowledge boosting: a graph-based integration approach with multi-omics data and genomic knowledge for cancer clinical outcome prediction.

PubMed

Kim, Dokyoon; Joung, Je-Gun; Sohn, Kyung-Ah; Shin, Hyunjung; Park, Yu Rang; Ritchie, Marylyn D; Kim, Ju Han

2015-01-01

Cancer can involve gene dysregulation via multiple mechanisms, so no single level of genomic data fully elucidates tumor behavior due to the presence of numerous genomic variations within or between levels in a biological system. We have previously proposed a graph-based integration approach that combines multi-omics data including copy number alteration, methylation, miRNA, and gene expression data for predicting clinical outcome in cancer. However, genomic features likely interact with other genomic features in complex signaling or regulatory networks, since cancer is caused by alterations in pathways or complete processes. Here we propose a new graph-based framework for integrating multi-omics data and genomic knowledge to improve power in predicting clinical outcomes and elucidate interplay between different levels. To highlight the validity of our proposed framework, we used an ovarian cancer dataset from The Cancer Genome Atlas for predicting stage, grade, and survival outcomes. Integrating multi-omics data with genomic knowledge to construct pre-defined features resulted in higher performance in clinical outcome prediction and higher stability. For the grade outcome, the model with gene expression data produced an area under the receiver operating characteristic curve (AUC) of 0.7866. However, models of the integration with pathway, Gene Ontology, chromosomal gene set, and motif gene set consistently outperformed the model with genomic data only, attaining AUCs of 0.7873, 0.8433, 0.8254, and 0.8179, respectively. Integrating multi-omics data and genomic knowledge to improve understanding of molecular pathogenesis and underlying biology in cancer should improve diagnostic and prognostic indicators and the effectiveness of therapies. © The Author 2014. Published by Oxford University Press on behalf of the American Medical Informatics Association.

GraphMeta: Managing HPC Rich Metadata in Graphs

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

Dai, Dong; Chen, Yong; Carns, Philip

High-performance computing (HPC) systems face increasingly critical metadata management challenges, especially in the approaching exascale era. These challenges arise not only from exploding metadata volumes, but also from increasingly diverse metadata, which contains data provenance and arbitrary user-defined attributes in addition to traditional POSIX metadata. This ‘rich’ metadata is becoming critical to supporting advanced data management functionality such as data auditing and validation. In our prior work, we identified a graph-based model as a promising solution to uniformly manage HPC rich metadata due to its flexibility and generality. However, at the same time, graph-based HPC rich metadata anagement also introducesmore » significant challenges to the underlying infrastructure. In this study, we first identify the challenges on the underlying infrastructure to support scalable, high-performance rich metadata management. Based on that, we introduce GraphMeta, a graphbased engine designed for this use case. It achieves performance scalability by introducing a new graph partitioning algorithm and a write-optimal storage engine. We evaluate GraphMeta under both synthetic and real HPC metadata workloads, compare it with other approaches, and demonstrate its advantages in terms of efficiency and usability for rich metadata management in HPC systems.« less

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

NASA Technical Reports Server (NTRS)

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

1989-01-01

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

Motif finding in DNA sequences based on skipping nonconserved positions in background Markov chains.

PubMed

Zhao, Xiaoyan; Sze, Sing-Hoi

2011-05-01

One strategy to identify transcription factor binding sites is through motif finding in upstream DNA sequences of potentially co-regulated genes. Despite extensive efforts, none of the existing algorithms perform very well. We consider a string representation that allows arbitrary ignored positions within the nonconserved portion of single motifs, and use O(2(l)) Markov chains to model the background distributions of motifs of length l while skipping these positions within each Markov chain. By focusing initially on positions that have fixed nucleotides to define core occurrences, we develop an algorithm to identify motifs of moderate lengths. We compare the performance of our algorithm to other motif finding algorithms on a few benchmark data sets, and show that significant improvement in accuracy can be obtained when the sites are sufficiently conserved within a given sample, while comparable performance is obtained when the site conservation rate is low. A software program (PosMotif ) and detailed results are available online at http://faculty.cse.tamu.edu/shsze/posmotif.

A Cyclic Nucleotide-Gated Channel Mutation Associated with Canine Daylight Blindness Provides Insight into a Role for the S2 Segment Tri-Asp motif in Channel Biogenesis

PubMed Central

Tanaka, Naoto; Delemotte, Lucie; Klein, Michael L.; Komáromy, András M.; Tanaka, Jacqueline C.

2014-01-01

Cone cyclic nucleotide-gated channels are tetramers formed by CNGA3 and CNGB3 subunits; CNGA3 subunits function as homotetrameric channels but CNGB3 exhibits channel function only when co-expressed with CNGA3. An aspartatic acid (Asp) to asparagine (Asn) missense mutation at position 262 in the canine CNGB3 (D262N) subunit results in loss of cone function (daylight blindness), suggesting an important role for this aspartic acid residue in channel biogenesis and/or function. Asp 262 is located in a conserved region of the second transmembrane segment containing three Asp residues designated the Tri-Asp motif. This motif is conserved in all CNG channels. Here we examine mutations in canine CNGA3 homomeric channels using a combination of experimental and computational approaches. Mutations of these conserved Asp residues result in the absence of nucleotide-activated currents in heterologous expression. A fluorescent tag on CNGA3 shows mislocalization of mutant channels. Co-expressing CNGB3 Tri-Asp mutants with wild type CNGA3 results in some functional channels, however, their electrophysiological characterization matches the properties of homomeric CNGA3 channels. This failure to record heteromeric currents suggests that Asp/Asn mutations affect heteromeric subunit assembly. A homology model of S1–S6 of the CNGA3 channel was generated and relaxed in a membrane using molecular dynamics simulations. The model predicts that the Tri-Asp motif is involved in non-specific salt bridge pairings with positive residues of S3/S4. We propose that the D262N mutation in dogs with CNGB3-day blindness results in the loss of these inter-helical interactions altering the electrostatic equilibrium within in the S1–S4 bundle. Because residues analogous to Tri-Asp in the voltage-gated Shaker potassium channel family were implicated in monomer folding, we hypothesize that destabilizing these electrostatic interactions impairs the monomer folding state in D262N mutant CNG channels

Statistical tests to compare motif count exceptionalities

PubMed Central

Robin, Stéphane; Schbath, Sophie; Vandewalle, Vincent

2007-01-01

Background Finding over- or under-represented motifs in biological sequences is now a common task in genomics. Thanks to p-value calculation for motif counts, exceptional motifs are identified and represent candidate functional motifs. The present work addresses the related question of comparing the exceptionality of one motif in two different sequences. Just comparing the motif count p-values in each sequence is indeed not sufficient to decide if this motif is significantly more exceptional in one sequence compared to the other one. A statistical test is required. Results We develop and analyze two statistical tests, an exact binomial one and an asymptotic likelihood ratio test, to decide whether the exceptionality of a given motif is equivalent or significantly different in two sequences of interest. For that purpose, motif occurrences are modeled by Poisson processes, with a special care for overlapping motifs. Both tests can take the sequence compositions into account. As an illustration, we compare the octamer exceptionalities in the Escherichia coli K-12 backbone versus variable strain-specific loops. Conclusion The exact binomial test is particularly adapted for small counts. For large counts, we advise to use the likelihood ratio test which is asymptotic but strongly correlated with the exact binomial test and very simple to use. PMID:17346349

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

PubMed

Jing, X; Cimino, J J

2014-01-01

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

Experimental Study of Quantum Graphs with Microwave Networks

NASA Astrophysics Data System (ADS)

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

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

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

Graphing Important People

ERIC Educational Resources Information Center

Reading Teacher, 2012

2012-01-01

The "Toolbox" column features content adapted from ReadWriteThink.org lesson plans and provides practical tools for classroom teachers. This issue's column features a lesson plan adapted from "Graphing Plot and Character in a Novel" by Lisa Storm Fink and "Bio-graph: Graphing Life Events" by Susan Spangler. Students retell biographic events…

Finding specific RNA motifs: Function in a zeptomole world?

PubMed Central

KNIGHT, ROB; YARUS, MICHAEL

2003-01-01

We have developed a new method for estimating the abundance of any modular (piecewise) RNA motif within a longer random region. We have used this method to estimate the size of the active motifs available to modern SELEX experiments (picomoles of unique sequences) and to a plausible RNA World (zeptomoles of unique sequences: 1 zmole = 602 sequences). Unexpectedly, activities such as specific isoleucine binding are almost certainly present in zeptomoles of molecules, and even ribozymes such as self-cleavage motifs may appear (depending on assumptions about the minimal structures). The number of specified nucleotides is not the only important determinant of a motif’s rarity: The number of modules into which it is divided, and the details of this division, are also crucial. We propose three maxims for easily isolated motifs: the Maxim of Minimization, the Maxim of Multiplicity, and the Maxim of the Median. These maxims together state that selected motifs should be small and composed of as many separate, equally sized modules as possible. For evenly divided motifs with four modules, the largest accessible activity in picomole scale (1–1000 pmole) pools of length 100 is about 34 nucleotides; while for zeptomole scale (1–1000 zmole) pools it is about 20 specific nucleotides (50% probability of occurrence). This latter figure includes some ribozymes and aptamers. Consequently, an RNA metabolism apparently could have begun with only zeptomoles of RNA molecules. PMID:12554865

Resistance Distances and Kirchhoff Index in Generalised Join Graphs

NASA Astrophysics Data System (ADS)

Chen, Haiyan

2017-03-01

The resistance distance between any two vertices of a connected graph is defined as the effective resistance between them in the electrical network constructed from the graph by replacing each edge with a unit resistor. The Kirchhoff index of a graph is defined as the sum of all the resistance distances between any pair of vertices of the graph. Let G=H[G1, G2, …, Gk ] be the generalised join graph of G1, G2, …, Gk determined by H. In this paper, we first give formulae for resistance distances and Kirchhoff index of G in terms of parameters of G'is {G'_i}s and H. Then, we show that computing resistance distances and Kirchhoff index of G can be decomposed into simpler ones. Finally, we obtain explicit formulae for resistance distances and Kirchhoff index of G when G'is {G'_i}s and H take some special graphs, such as the complete graph, the path, and the cycle.

Primitive graphs with small exponent and small scrambling index

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

Competition between drum and quasi-planar structures in RhB18-: motifs for metallo-boronanotubes and metallo-borophenes.

PubMed

Jian, Tian; Li, Wan-Lu; Chen, Xin; Chen, Teng-Teng; Lopez, Gary V; Li, Jun; Wang, Lai-Sheng

2016-12-01

Metal-doped boron clusters provide new opportunities to design nanoclusters with interesting structures and bonding. A cobalt-doped boron cluster, CoB 18 - , has been observed recently to be planar and can be viewed as a motif for metallo-borophenes, whereas the D 9d drum isomer as a motif for metallo-boronanotubes is found to be much higher in energy. Hence, whether larger doped boron drums are possible is still an open question. Here we report that for RhB 18 - the drum and quasi-planar structures become much closer in energy and co-exist experimentally, revealing a competition between the metallo-boronanotube and metallo-borophene structures. Photoelectron spectroscopy of RhB 18 - shows a complicated spectral pattern, suggesting the presence of two isomers. Quantum chemistry studies indicate that the D 9d drum isomer and a quasi-planar isomer ( C s ) compete for the global minimum. The enhanced stability of the drum isomer in RhB 18 - is due to the less contracted Rh 4d orbitals, which can have favorable interactions with the B 18 drum motif. Chemical bonding analyses show that the quasi-planar isomer of RhB 18 - is aromatic with 10 π electrons, whereas the observed RhB 18 - drum cluster sets a new record for coordination number of eighteen among metal complexes. The current finding shows that the size of the boron drum can be tuned by appropriate metal dopants, suggesting that even larger boron drums with 5d, 6d transition metal, lanthanide or actinide metal atoms are possible.

Topic Model for Graph Mining.

PubMed

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.

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

ERIC Educational Resources Information Center

Carr, Linda

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

Evolutionary dynamics on graphs

NASA Astrophysics Data System (ADS)

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

2005-01-01

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

Interplay between Graph Topology and Correlations of Third Order in Spiking Neuronal Networks.

PubMed

Jovanović, Stojan; Rotter, Stefan

2016-06-01

The study of processes evolving on networks has recently become a very popular research field, not only because of the rich mathematical theory that underpins it, but also because of its many possible applications, a number of them in the field of biology. Indeed, molecular signaling pathways, gene regulation, predator-prey interactions and the communication between neurons in the brain can be seen as examples of networks with complex dynamics. The properties of such dynamics depend largely on the topology of the underlying network graph. In this work, we want to answer the following question: Knowing network connectivity, what can be said about the level of third-order correlations that will characterize the network dynamics? We consider a linear point process as a model for pulse-coded, or spiking activity in a neuronal network. Using recent results from theory of such processes, we study third-order correlations between spike trains in such a system and explain which features of the network graph (i.e. which topological motifs) are responsible for their emergence. Comparing two different models of network topology-random networks of Erdős-Rényi type and networks with highly interconnected hubs-we find that, in random networks, the average measure of third-order correlations does not depend on the local connectivity properties, but rather on global parameters, such as the connection probability. This, however, ceases to be the case in networks with a geometric out-degree distribution, where topological specificities have a strong impact on average correlations.

A graph edit dictionary for correcting errors in roof topology graphs reconstructed from point clouds

NASA Astrophysics Data System (ADS)

Xiong, B.; Oude Elberink, S.; Vosselman, G.

2014-07-01

In the task of 3D building model reconstruction from point clouds we face the problem of recovering a roof topology graph in the presence of noise, small roof faces and low point densities. Errors in roof topology graphs will seriously affect the final modelling results. The aim of this research is to automatically correct these errors. We define the graph correction as a graph-to-graph problem, similar to the spelling correction problem (also called the string-to-string problem). The graph correction is more complex than string correction, as the graphs are 2D while strings are only 1D. We design a strategy based on a dictionary of graph edit operations to automatically identify and correct the errors in the input graph. For each type of error the graph edit dictionary stores a representative erroneous subgraph as well as the corrected version. As an erroneous roof topology graph may contain several errors, a heuristic search is applied to find the optimum sequence of graph edits to correct the errors one by one. The graph edit dictionary can be expanded to include entries needed to cope with errors that were previously not encountered. Experiments show that the dictionary with only fifteen entries already properly corrects one quarter of erroneous graphs in about 4500 buildings, and even half of the erroneous graphs in one test area, achieving as high as a 95% acceptance rate of the reconstructed models.

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

PubMed

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

2015-02-01

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

On Super Edge-magic Total Labeling of Modified Watermill Graph