An improved spectral graph partitioning algorithm for mapping parallel computations
Hendrickson, B.; Leland, R.
1992-09-01
Efficient use of a distributed memory parallel computer requires that the computational load be balanced across processors in a way that minimizes interprocessor communication. We present a new domain mapping algorithm that extends recent work in which ideas from spectral graph theory have been applied to this problem. Our generalization of spectral graph bisection involves a novel use of multiple eigenvectors to allow for division of a computation into four or eight parts at each stage of a recursive decomposition. The resulting method is suitable for scientific computations like irregular finite elements or differences performed on hypercube or mesh architecture machines. Experimental results confirm that the new method provides better decompositions arrived at more economically and robustly than with previous spectral methods. We have also improved upon the known spectral lower bound for graph bisection.
Graph Partitioning Models for Parallel Computing
Hendrickson, B.; Kolda, T.G.
1999-03-02
Calculations can naturally be described as graphs in which vertices represent computation and edges reflect data dependencies. By partitioning the vertices of a graph, the calculation can be divided among processors of a parallel computer. However, the standard methodology for graph partitioning minimizes the wrong metric and lacks expressibility. We survey several recently proposed alternatives and discuss their relative merits.
Efficient multiple-way graph partitioning algorithms
Dasdan, A.; Aykanat, C.
1995-12-01
Graph partitioning deals with evenly dividing a graph into two or more parts such that the total weight of edges interconnecting these parts, i.e., cutsize, is minimized. Graph partitioning has important applications in VLSI layout, mapping, and sparse Gaussian elimination. Since graph partitioning problem is NP-hard, we should resort to polynomial-time algorithms to obtain a good solution, or hopefully a near-optimal solution. Kernighan-Lin (KL) propsoed a 2-way partitioning algorithms. Fiduccia-Mattheyses (FM) introduced a faster version of KL algorithm. Sanchis (FMS) generalized FM algorithm to a multiple-way partitioning algorithm. Simulated Annealing (SA) is one of the most successful approaches that are not KL-based.
Bipartite graph partitioning and data clustering
Zha, Hongyuan; He, Xiaofeng; Ding, Chris; Gu, Ming; Simon, Horst D.
2001-05-07
Many data types arising from data mining applications can be modeled as bipartite graphs, examples include terms and documents in a text corpus, customers and purchasing items in market basket analysis and reviewers and movies in a movie recommender system. In this paper, the authors propose a new data clustering method based on partitioning the underlying biopartite graph. The partition is constructed by minimizing a normalized sum of edge weights between unmatched pairs of vertices of the bipartite graph. They show that an approximate solution to the minimization problem can be obtained by computing a partial singular value decomposition (SVD) of the associated edge weight matrix of the bipartite graph. They point out the connection of their clustering algorithm to correspondence analysis used in multivariate analysis. They also briefly discuss the issue of assigning data objects to multiple clusters. In the experimental results, they apply their clustering algorithm to the problem of document clustering to illustrate its effectiveness and efficiency.
Linear Time Vertex Partitioning on Massive Graphs.
Mell, Peter; Harang, Richard; Gueye, Assane
The problem of optimally removing a set of vertices from a graph to minimize the size of the largest resultant component is known to be NP-complete. Prior work has provided near optimal heuristics with a high time complexity that function on up to hundreds of nodes and less optimal but faster techniques that function on up to thousands of nodes. In this work, we analyze how to perform vertex partitioning on massive graphs of tens of millions of nodes. We use a previously known and very simple heuristic technique: iteratively removing the node of largest degree and all of its edges. This approach has an apparent quadratic complexity since, upon removal of a node and adjoining set of edges, the node degree calculations must be updated prior to choosing the next node. However, we describe a linear time complexity solution using an array whose indices map to node degree and whose values are hash tables indicating the presence or absence of a node at that degree value. This approach also has a linear growth with respect to memory usage which is surprising since we lowered the time complexity from quadratic to linear. We empirically demonstrate linear scalability and linear memory usage on random graphs of up to 15000 nodes. We then demonstrate tractability on massive graphs through execution on a graph with 34 million nodes representing Internet wide router connectivity.
Linear Time Vertex Partitioning on Massive Graphs
Mell, Peter; Harang, Richard; Gueye, Assane
2016-01-01
The problem of optimally removing a set of vertices from a graph to minimize the size of the largest resultant component is known to be NP-complete. Prior work has provided near optimal heuristics with a high time complexity that function on up to hundreds of nodes and less optimal but faster techniques that function on up to thousands of nodes. In this work, we analyze how to perform vertex partitioning on massive graphs of tens of millions of nodes. We use a previously known and very simple heuristic technique: iteratively removing the node of largest degree and all of its edges. This approach has an apparent quadratic complexity since, upon removal of a node and adjoining set of edges, the node degree calculations must be updated prior to choosing the next node. However, we describe a linear time complexity solution using an array whose indices map to node degree and whose values are hash tables indicating the presence or absence of a node at that degree value. This approach also has a linear growth with respect to memory usage which is surprising since we lowered the time complexity from quadratic to linear. We empirically demonstrate linear scalability and linear memory usage on random graphs of up to 15000 nodes. We then demonstrate tractability on massive graphs through execution on a graph with 34 million nodes representing Internet wide router connectivity. PMID:27336059
Kim, Namhee; Zheng, Zhe; 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
Partitioning and modularity of graphs with arbitrary degree distribution
NASA Astrophysics Data System (ADS)
Reichardt, Jörg; Bornholdt, Stefan
2007-07-01
We solve the graph bipartitioning problem in dense graphs with arbitrary degree distribution using the replica method. We find the cut size to scale universally with ⟨k⟩ . In contrast, earlier results studying the problem in graphs with a Poissonian degree distribution had found a scaling with ⟨k⟩ [Fu and Anderson, J. Phys. A 19, 1605 (1986)]. Our results also generalize to the problem of q partitioning. They can be used to find the expected modularity Q [Newman and Girvan, Phys. Rev. E 69, 026113 (2004)] of random graphs and allow for the assessment of the statistical significance of the output of community detection algorithms.
Partitioning sparse matrices with eigenvectors of graphs
NASA Technical Reports Server (NTRS)
Pothen, Alex; Simon, Horst D.; Liou, Kang-Pu
1990-01-01
The problem of computing a small vertex separator in a graph arises in the context of computing a good ordering for the parallel factorization of sparse, symmetric matrices. An algebraic approach for computing vertex separators is considered in this paper. It is shown that lower bounds on separator sizes can be obtained in terms of the eigenvalues of the Laplacian matrix associated with a graph. The Laplacian eigenvectors of grid graphs can be computed from Kronecker products involving the eigenvectors of path graphs, and these eigenvectors can be used to compute good separators in grid graphs. A heuristic algorithm is designed to compute a vertex separator in a general graph by first computing an edge separator in the graph from an eigenvector of the Laplacian matrix, and then using a maximum matching in a subgraph to compute the vertex separator. Results on the quality of the separators computed by the spectral algorithm are presented, and these are compared with separators obtained from other algorithms for computing separators. Finally, the time required to compute the Laplacian eigenvector is reported, and the accuracy with which the eigenvector must be computed to obtain good separators is considered. The spectral algorithm has the advantage that it can be implemented on a medium-size multiprocessor in a straightforward manner.
Continuous Graph Partitioning for Camera Network Surveillance
2012-07-23
Symmetric Gossip partitioning algorithm The distributed algorithm presented in this section assumes a symmetric gossip -type communication protocol . In... gossip communication. We prove convergence of all these algorithms, and we analyze their performance in a simulation study. 2 Continuous Partitions of...section assumes an asymmetric broadcast communication protocol . In particular, at each iteration only one camera updates its state by using local
Graph Partitioning for Parallel Applications in Heterogeneous Grid Environments
NASA Technical Reports Server (NTRS)
Bisws, Rupak; Kumar, Shailendra; Das, Sajal K.; Biegel, Bryan (Technical Monitor)
2002-01-01
The problem of partitioning irregular graphs and meshes for parallel computations on homogeneous systems has been extensively studied. However, these partitioning schemes fail when the target system architecture exhibits heterogeneity in resource characteristics. With the emergence of technologies such as the Grid, it is imperative to study the partitioning problem taking into consideration the differing capabilities of such distributed heterogeneous systems. In our model, the heterogeneous system consists of processors with varying processing power and an underlying non-uniform communication network. We present in this paper a novel multilevel partitioning scheme for irregular graphs and meshes, that takes into account issues pertinent to Grid computing environments. Our partitioning algorithm, called MiniMax, generates and maps partitions onto a heterogeneous system with the objective of minimizing the maximum execution time of the parallel distributed application. For experimental performance study, we have considered both a realistic mesh problem from NASA as well as synthetic workloads. Simulation results demonstrate that MiniMax generates high quality partitions for various classes of applications targeted for parallel execution in a distributed heterogeneous environment.
Interactive image segmentation by constrained spectral graph partitioning
NASA Astrophysics Data System (ADS)
Zhang, Hao; He, Jin; Zhang, Hong; Huang, Zhanhua
2010-11-01
This paper proposed an interactive image segmentation algorithm that can tolerate slightly incorrect user constraints. Interactive image segmentation was formulated as a constrained spectral graph partitioning problem. Furthermore, it was proven to equal to a supervised classification problem, where the feature space was formed by rows of the eigenvector matrix that was computed by spectral graph analysis. ν-SVM (support vector machine) was preferred as the classifier. Some incorrect labels in user constraints were tolerated by being identified as margin errors in ν-SVM. Comparison with other algorithms on real color images was reported.
Graph partitions and cluster synchronization in networks of oscillators
Schaub, Michael T.; O’Clery, Neave; Billeh, Yazan N.; Delvenne, Jean-Charles; Lambiotte, Renaud; Barahona, Mauricio
2017-01-01
Synchronization over networks depends strongly on the structure of the coupling between the oscillators. When the coupling presents certain regularities, the dynamics can be coarse-grained into clusters by means of External Equitable Partitions of the network graph and their associated quotient graphs. We exploit this graph-theoretical concept to study the phenomenon of cluster synchronization, in which different groups of nodes converge to distinct behaviors. We derive conditions and properties of networks in which such clustered behavior emerges, and show that the ensuing dynamics is the result of the localization of the eigenvectors of the associated graph Laplacians linked to the existence of invariant subspaces. The framework is applied to both linear and non-linear models, first for the standard case of networks with positive edges, before being generalized to the case of signed networks with both positive and negative interactions. We illustrate our results with examples of both signed and unsigned graphs for consensus dynamics and for partial synchronization of oscillator networks under the master stability function as well as Kuramoto oscillators. PMID:27781454
Extracting building patterns with multilevel graph partition and building grouping
NASA Astrophysics Data System (ADS)
Du, Shihong; Luo, Liqun; Cao, Kai; Shu, Mi
2016-12-01
Building patterns are crucial for urban landscape evaluation, social analyses and multiscale spatial data automatic production. Although many studies have been conducted, there is still lack of satisfying results due to the incomplete typology of building patterns and the ineffective extraction methods. This study aims at providing a typology with four types of building patterns (e.g., collinear patterns, curvilinear patterns, parallel and perpendicular groups, and grid patterns) and presenting four integrated strategies for extracting these patterns effectively and efficiently. First, the multilevel graph partition method is utilized to generate globally optimal building clusters considering area, shape and visual distance similarities. In this step, the weights of similarity measurements are automatically estimated using Relief-F algorithm instead of manual selection, thus building clusters with high quality can be obtained. Second, based on the clusters produced in the first step, the extraction strategies group the buildings from each cluster into patterns according to the criteria of proximity, continuity and directionality. The proposed methods are tested using three datasets. The experimental results indicate that the proposed methods can produce satisfying results, and demonstrate that the F-Histogram model is better than the two widely used models (i.e., centroid model and the Voronoi graph) to represent relative directions for building patterns extraction.
A Weakly Robust PTAS for Minimum Clique Partition in Unit Disk Graphs
NASA Astrophysics Data System (ADS)
Pirwani, Imran A.; Salavatipour, Mohammad R.
We consider the problem of partitioning the set of vertices of a given unit disk graph (UDG) into a minimum number of cliques. The problem is NP-hard and various constant factor approximations are known, with the best known ratio of 3. Our main result is a weakly robust polynomial time approximation scheme (PTAS) for UDGs expressed with edge-lengths and ɛ> 0 that either (i) computes a clique partition, or (ii) produces a certificate proving that the graph is not a UDG; if the graph is a UDG, then our partition is guaranteed to be within (1 + ɛ) ratio of the optimum; however, if the graph is not a UDG, it either computes a clique partition, or detects that the graph is not a UDG. Noting that recognition of UDG's is NP-hard even with edge lengths, this is a significant weakening of the input model.
Semiclassical limits of quantum partition functions on infinite graphs
Güneysu, Batu
2015-02-15
We prove that if H denotes the operator corresponding to the canonical Dirichlet form on a possibly locally infinite weighted graph (X, b, m), and if v : X → ℝ is such that H + v/ħ is well-defined as a form sum for all ħ > 0, then the quantum partition function tr(e{sup −βħ(H+v/ħ)}) converges to ∑{sub x∈X}e{sup −βv(x)} as ħ → 0 +, for all β > 0, regardless of the fact whether e{sup −βv} is a priori summable or not. This fact can be interpreted as a semiclassical limit, and it allows geometric Weyl-type convergence results. We also prove natural generalizations of this semiclassical limit to a large class of covariant Schrödinger operators that act on sections in Hermitian vector bundle over (X, m, b), a result that particularly applies to magnetic Schrödinger operators that are defined on (X, m, b)
A Graph Partitioning Approach to Simultaneous Angular Reconstitution
Pragier, Gabi; Greenberg, Ido; Cheng, Xiuyuan; Shkolnisky, Yoel
2016-01-01
One of the primary challenges in single particle reconstruction with cryo-electron microscopy is to find a three-dimensional model of a molecule using its noisy two-dimensional projection-images. As the imaging orientations of the projection-images are unknown, we suggest a common-lines-based method to simultaneously estimate the imaging orientations of all images that is independent of the distribution of the orientations. Since the relative orientation of each pair of images may only be estimated up to a two-way handedness ambiguity, we suggest an efficient procedure to consistently assign the same handedness to all relative orientations. This is achieved by casting the handedness assignment problem as a graph-partitioning problem. Once a consistent handedness of all relative orientations is determined, the orientations corresponding to all projection-images are determined simultaneously, thus rendering the method robust to noise. Our proposed method has also the advantage of allowing one to incorporate confidence information regarding the trustworthiness of each relative orientation in a natural manner. We demonstrate the efficacy of our approach using simulated clean and noisy data. PMID:28217720
De novo analysis of peptide tandem mass spectra by spectral graph partitioning.
Bern, Marshall; Goldberg, David
2006-03-01
We report on a new de novo peptide sequencing algorithm that uses spectral graph partitioning. In this approach, relationships between m/z peaks are represented by attractive and repulsive springs, and the vibrational modes of the spring system are used to infer information about the peaks (such as "likely b-ion" or "likely y-ion"). We demonstrate the effectiveness of this approach by comparison with other de novo sequencers on test sets of ion-trap and QTOF spectra, including spectra of mixtures of peptides. On all datasets, we outperform the other sequencers. Along with spectral graph theory techniques, the new de novo sequencer EigenMS incorporates another improvement of independent interest: robust statistical methods for recalibration of time-of-flight mass measurements. Robust recalibration greatly outperforms simple least-squares recalibration, achieving about three times the accuracy for one QTOF dataset.
SpecP: A tool for spectral partitioning of protein contact graph.
Namboodiri, Saritha; K, Kripadas
2013-01-01
SpecP is an open-source Python module that performs Spectral Partitioning on Protein Contact Graphs. Protein Contact Graphs are graph theory based representation of the protein structure, where each amino acid forms a 'vertex' and spatial contact of any two amino acids is an 'edge' between them. Spectral partitioning is carried out in SpecP based on the second smallest spectral value (eigen value) of the Protein Contact Graph. The eigen vector corresponding to the second smallest spectral value are partitioned into two clusters based on the sign of the corresponding vector entry. Spectral Partitioning algorithm is repeatedly carried out until the desired numbers of partitions are obtained. SpecP visualizes the spectrally partitioned clusters of protein structure along with the Protein Contact Map and Protein Contact Graph which can be saved for later use. It also possesses an interactive mode whereby the user has the ability to zoom, pan, resize and save these raster images in various image formats (.eps, .jpg, .png) manually. SpecP is a stand-alone extensible tool useful for structural analysis of proteins.
Kawamoto, Tatsuro; Kabashima, Yoshiyuki
2015-06-01
Investigating the performance of different methods is a fundamental problem in graph partitioning. In this paper, we estimate the so-called detectability threshold for the spectral method with both un-normalized and normalized Laplacians in sparse graphs. The detectability threshold is the critical point at which the result of the spectral method is completely uncorrelated to the planted partition. We also analyze whether the localization of eigenvectors affects the partitioning performance in the detectable region. We use the replica method, which is often used in the field of spin-glass theory, and focus on the case of bisection. We show that the gap between the estimated threshold for the spectral method and the threshold obtained from Bayesian inference is considerable in sparse graphs, even without eigenvector localization. This gap closes in a dense limit.
NASA Astrophysics Data System (ADS)
Kawamoto, Tatsuro; Kabashima, Yoshiyuki
2015-06-01
Investigating the performance of different methods is a fundamental problem in graph partitioning. In this paper, we estimate the so-called detectability threshold for the spectral method with both un-normalized and normalized Laplacians in sparse graphs. The detectability threshold is the critical point at which the result of the spectral method is completely uncorrelated to the planted partition. We also analyze whether the localization of eigenvectors affects the partitioning performance in the detectable region. We use the replica method, which is often used in the field of spin-glass theory, and focus on the case of bisection. We show that the gap between the estimated threshold for the spectral method and the threshold obtained from Bayesian inference is considerable in sparse graphs, even without eigenvector localization. This gap closes in a dense limit.
Integrating graph partitioning and matching for trajectory analysis in video surveillance.
Lin, Liang; Lu, Yongyi; Pan, Yan; Chen, Xiaowu
2012-12-01
In order to track moving objects in long range against occlusion, interruption, and background clutter, this paper proposes a unified approach for global trajectory analysis. Instead of the traditional frame-by-frame tracking, our method recovers target trajectories based on a short sequence of video frames, e.g., 15 frames. We initially calculate a foreground map at each frame obtained from a state-of-the-art background model. An attribute graph is then extracted from the foreground map, where the graph vertices are image primitives represented by the composite features. With this graph representation, we pose trajectory analysis as a joint task of spatial graph partitioning and temporal graph matching. The task can be formulated by maximizing a posteriori under the Bayesian framework, in which we integrate the spatio-temporal contexts and the appearance models. The probabilistic inference is achieved by a data-driven Markov chain Monte Carlo algorithm. Given a period of observed frames, the algorithm simulates an ergodic and aperiodic Markov chain, and it visits a sequence of solution states in the joint space of spatial graph partitioning and temporal graph matching. In the experiments, our method is tested on several challenging videos from the public datasets of visual surveillance, and it outperforms the state-of-the-art methods.
A novel graph-based partitioning algorithm for large-scale dynamical systems
NASA Astrophysics Data System (ADS)
Kamelian, Saeed; Salahshoor, Karim
2015-01-01
In this paper, a novel graph-based system partitioning approach is proposed to facilitate the design of distributed or decentralised control in large-scale dynamical systems. In large-scale dynamical systems, a decomposition method is required to determine a suitable set of distributed subsystems and their relevant variables. In the proposed approach, a decomposition algorithm starts to generate an overall graph representation of the system model in the form of a new weighted digraph on the basis of a sensitivity analysis concept to quantify the coupling strengths among the system variables in terms of graph edge weights. The produced weighted digraph and its structural information are then used to partition the system model. All the potential system control inputs are first characterised as the main graph vertices, representing fixed subsystems centres. Then, the remaining vertices, representing system states or outputs, are assigned to the created subgraphs. Once the initial grouping is accordingly formed, a merging routine is automatically conducted to merge the small subgraphs in other subgraphs in an iterative searching way to find the smaller cut sizes. Each time a merging occurs, the total cost of the merged configuration, being defined in terms of an averaged linear quadratic regulator (LQR) metric, is used as a novel dynamic performance metric versus total group number reduction to terminate the algorithm for the best grouping result. A chemical industrial process plant is used as a benchmark to assess performance of the proposed methodology to fulfil the system partitioning objective. The output result of the algorithm is then comparatively used for a decentralised non-linear model-based predictive control methodology to demonstrate its ultimate merits.
Partitioning a chordal graph into transitive subgraphs for parallel sparse triangular solution
Peyton, B.W.; Pothen, A.; Yuan, Xiaoqing
1992-12-01
A recent approach for solving sparse triangular systems of equations on massively parallel computers employs a factorization of the triangular coefficient matrix to obtain a representation of its inverse in product form. The number of general communication steps required by this approach is proportional to the number of factors in the factorization. The triangular matrix can be symmetrically permuted to minimize the number of factors over suitable classes of permutations, and thereby the complexity of the parallel algorithm can be minimized. Algorithms for minimizing the number of factors over several classes of permutations have been considered in earlier work. Let F = L+L{sup T} denote the symmetric filled matrix corresponding to a Cholesky factor L, and let G{sub F} denote the adjacency graph of F. In this paper we consider the problem of minirriizing the number of factors over all permutations which preserve the structure of G{sub F}. The graph model of this problem is to partition the vertices G{sub F} into the fewest transitively closed subgraphs over all perfect elimination orderings while satisfying a certain precedence relationship. The solution to this chordal graph partitioning problem can be described by a greedy scheme which eliminates a largest permissible subgraph at each step. Further, the subgraph eliminated at each step can be characterized in terms of lengths of chordless paths in the current elimination graph. This solution relies on several results concerning transitive perfect elimination orderings introduced in this paper. We describe a partitioning algorithm with {Omicron}({vert_bar}V{vert_bar} + {vert_bar}E{vert_bar}) time and space complexity.
Partitioning a chordal graph into transitive subgraphs for parallel sparse triangular solution
Peyton, B.W. ); Pothen, A. . Dept. of Computer Science); Yuan, Xiaoqing )
1992-12-01
A recent approach for solving sparse triangular systems of equations on massively parallel computers employs a factorization of the triangular coefficient matrix to obtain a representation of its inverse in product form. The number of general communication steps required by this approach is proportional to the number of factors in the factorization. The triangular matrix can be symmetrically permuted to minimize the number of factors over suitable classes of permutations, and thereby the complexity of the parallel algorithm can be minimized. Algorithms for minimizing the number of factors over several classes of permutations have been considered in earlier work. Let F = L+L[sup T] denote the symmetric filled matrix corresponding to a Cholesky factor L, and let G[sub F] denote the adjacency graph of F. In this paper we consider the problem of minirriizing the number of factors over all permutations which preserve the structure of G[sub F]. The graph model of this problem is to partition the vertices G[sub F] into the fewest transitively closed subgraphs over all perfect elimination orderings while satisfying a certain precedence relationship. The solution to this chordal graph partitioning problem can be described by a greedy scheme which eliminates a largest permissible subgraph at each step. Further, the subgraph eliminated at each step can be characterized in terms of lengths of chordless paths in the current elimination graph. This solution relies on several results concerning transitive perfect elimination orderings introduced in this paper. We describe a partitioning algorithm with [Omicron]([vert bar]V[vert bar] + [vert bar]E[vert bar]) time and space complexity.
Protein and gene model inference based on statistical modeling in k-partite graphs.
Gerster, Sarah; Qeli, Ermir; Ahrens, Christian H; Bühlmann, Peter
2010-07-06
One of the major goals of proteomics is the comprehensive and accurate description of a proteome. Shotgun proteomics, the method of choice for the analysis of complex protein mixtures, requires that experimentally observed peptides are mapped back to the proteins they were derived from. This process is also known as protein inference. We present Markovian Inference of Proteins and Gene Models (MIPGEM), a statistical model based on clearly stated assumptions to address the problem of protein and gene model inference for shotgun proteomics data. In particular, we are dealing with dependencies among peptides and proteins using a Markovian assumption on k-partite graphs. We are also addressing the problems of shared peptides and ambiguous proteins by scoring the encoding gene models. Empirical results on two control datasets with synthetic mixtures of proteins and on complex protein samples of Saccharomyces cerevisiae, Drosophila melanogaster, and Arabidopsis thaliana suggest that the results with MIPGEM are competitive with existing tools for protein inference.
Kuhlemann, Verena; Vassilevski, Panayot S.
2013-10-28
Matrix-vector multiplication is the key operation in any Krylov-subspace iteration method. We are interested in Krylov methods applied to problems associated with the graph Laplacian arising from large scale-free graphs. Furthermore, computations with graphs of this type on parallel distributed-memory computers are challenging. This is due to the fact that scale-free graphs have a degree distribution that follows a power law, and currently available graph partitioners are not efficient for such an irregular degree distribution. The lack of a good partitioning leads to excessive interprocessor communication requirements during every matrix-vector product. Here, we present an approach to alleviate this problem based on embedding the original irregular graph into a more regular one by disaggregating (splitting up) vertices in the original graph. The matrix-vector operations for the original graph are performed via a factored triple matrix-vector product involving the embedding graph. And even though the latter graph is larger, we are able to decrease the communication requirements considerably and improve the performance of the matrix-vector product.
Improving Attack Graph Visualization through Data Reduction and Attack Grouping
John Homer; Ashok Varikuti; Xinming Ou; Miles A. McQueen
2008-09-01
Various tools exist to analyze enterprise network systems and to produce attack graphs detailing how attackers might penetrate into the system. These attack graphs, however, are often complex and difficult to comprehend fully, and a human user may find it problematic to reach appropriate configuration decisions. This paper presents methodologies that can 1) automatically identify portions of an attack graph that do not help a user to understand the core security problems and so can be trimmed, and 2) automatically group similar attack steps as virtual nodes in a model of the network topology, to immediately increase the understandability of the data. We believe both methods are important steps toward improving visualization of attack graphs to make them more useful in configuration management for large enterprise networks. We implemented our methods using one of the existing attack-graph toolkits. Initial experimentation shows that the proposed approaches can 1) significantly reduce the complexity of attack graphs by trimming a large portion of the graph that is not needed for a user to understand the security problem, and 2) significantly increase the accessibility and understandability of the data presented in the attack graph by clearly showing, within a generated visualization of the network topology, the number and type of potential attacks to which each host is exposed.
Spatial partitioning improves the reliability of biochemical signaling
Mugler, Andrew; Tostevin, Filipe; ten Wolde, Pieter Rein
2013-01-01
Spatial heterogeneity is a hallmark of living systems, even at the molecular scale in individual cells. A key example is the partitioning of membrane-bound proteins via lipid domain formation or cytoskeleton-induced corralling. However, the impact of this spatial heterogeneity on biochemical signaling processes is poorly understood. Here, we demonstrate that partitioning improves the reliability of biochemical signaling. We exactly solve a stochastic model describing a ubiquitous motif in membrane signaling. The solution reveals that partitioning improves signaling reliability via two effects: it moderates the nonlinearity of the switching response, and it reduces noise in the response by suppressing correlations between molecules. An optimal partition size arises from a trade-off between minimizing the number of proteins per partition to improve signaling reliability and ensuring sufficient proteins per partition to maintain signal propagation. The predicted optimal partition size agrees quantitatively with experimentally observed systems. These results persist in spatial simulations with explicit diffusion barriers. Our findings suggest that molecular partitioning is not merely a consequence of the complexity of cellular substructures, but also plays an important functional role in cell signaling. PMID:23530194
Co-Clustering by Bipartite Spectral Graph Partitioning for Out-of-Tutor Prediction
ERIC Educational Resources Information Center
Trivedi, Shubhendu; Pardos, Zachary A.; Sarkozy, Gabor N.; Heffernan, Neil T.
2012-01-01
Learning a more distributed representation of the input feature space is a powerful method to boost the performance of a given predictor. Often this is accomplished by partitioning the data into homogeneous groups by clustering so that separate models could be trained on each cluster. Intuitively each such predictor is a better representative of…
Improving Neural-Network Classifiers Using Nearest Neighbor Partitioning.
Wang, Lin; Yang, Bo; Chen, Yuehui; Zhang, Xiaoqian; Orchard, Jeff
2016-06-30
This paper presents a nearest neighbor partitioning method designed to improve the performance of a neural-network classifier. For neural-network classifiers, usually the number, positions, and labels of centroids are fixed in partition space before training. However, that approach limits the search for potential neural networks during optimization; the quality of a neural network classifier is based on how clear the decision boundaries are between classes. Although attempts have been made to generate floating centroids automatically, these methods still tend to generate sphere-like partitions and cannot produce flexible decision boundaries. We propose the use of nearest neighbor classification in conjunction with a neural-network classifier. Instead of being bound by sphere-like boundaries (such as the case with centroid-based methods), the flexibility of nearest neighbors increases the chance of finding potential neural networks that have arbitrarily shaped boundaries in partition space. Experimental results demonstrate that the proposed method exhibits superior performance on accuracy and average f-measure.
Cascading failures in bi-partite graphs: model for systemic risk propagation.
Huang, Xuqing; Vodenska, Irena; Havlin, Shlomo; Stanley, H Eugene
2013-01-01
As economic entities become increasingly interconnected, a shock in a financial network can provoke significant cascading failures throughout the system. To study the systemic risk of financial systems, we create a bi-partite banking network model composed of banks and bank assets and propose a cascading failure model to describe the risk propagation process during crises. We empirically test the model with 2007 US commercial banks balance sheet data and compare the model prediction of the failed banks with the real failed banks after 2007. We find that our model efficiently identifies a significant portion of the actual failed banks reported by Federal Deposit Insurance Corporation. The results suggest that this model could be useful for systemic risk stress testing for financial systems. The model also identifies that commercial rather than residential real estate assets are major culprits for the failure of over 350 US commercial banks during 2008-2011.
Cascading Failures in Bi-partite Graphs: Model for Systemic Risk Propagation
Huang, Xuqing; Vodenska, Irena; Havlin, Shlomo; Stanley, H. Eugene
2013-01-01
As economic entities become increasingly interconnected, a shock in a financial network can provoke significant cascading failures throughout the system. To study the systemic risk of financial systems, we create a bi-partite banking network model composed of banks and bank assets and propose a cascading failure model to describe the risk propagation process during crises. We empirically test the model with 2007 US commercial banks balance sheet data and compare the model prediction of the failed banks with the real failed banks after 2007. We find that our model efficiently identifies a significant portion of the actual failed banks reported by Federal Deposit Insurance Corporation. The results suggest that this model could be useful for systemic risk stress testing for financial systems. The model also identifies that commercial rather than residential real estate assets are major culprits for the failure of over 350 US commercial banks during 2008–2011. PMID:23386974
Improving Student Knowledge of the Graphing Calculator's Capabilities.
ERIC Educational Resources Information Center
Hubbard, Donna
This paper describes an intervention in two Algebra II classes in which the graphing calculator was incorporated into the curriculum as often as possible. The targeted population consisted of high school students in a growing middle to upper class community located in a suburb of a large city. The problem of a lack of understanding of the…
Spectral Graph Theory Analysis of Software-Defined Networks to Improve Performance and Security
2015-09-01
networks for transmission operations in smart grids,” in the Proc. IEEE PES Innovative Smart Grid Technologies (ISGT), Washington, DC, 2013. [34] D...GRAPH THEORY ANALYSIS OF SOFTWARE-DEFINED NETWORKS TO IMPROVE PERFORMANCE AND SECURITY by Thomas C. Parker September 2015 Dissertation Co...September 2015 3. REPORT TYPE AND DATES COVERED Dissertation 4. TITLE AND SUBTITLE SPECTRAL GRAPH THEORY ANALYSIS OF SOFTWARE-DEFINED NETWORKS
On Improved Exact Algorithms for L(2,1)-Labeling of Graphs
NASA Astrophysics Data System (ADS)
Junosza-Szaniawski, Konstanty; Rzążewski, Paweł
L(2,1)-labeling is graph labeling model where adjacent vertices get labels that differ by at least 2 and vertices in distance 2 get different labels. In this paper we present an algorithm for finding an optimal L(2,1)-labeling (i.e. an L(2,1)-labeling in which largest label is the least possible) of a graph with time complexity O * ( 3.5616 n ), which improves a previous best result: O * ( 3.8739 n ).
Bayesian Estimation of Conditional Independence Graphs Improves Functional Connectivity Estimates
Hinne, Max; Janssen, Ronald J.; Heskes, Tom; van Gerven, Marcel A.J.
2015-01-01
Functional connectivity concerns the correlated activity between neuronal populations in spatially segregated regions of the brain, which may be studied using functional magnetic resonance imaging (fMRI). This coupled activity is conveniently expressed using covariance, but this measure fails to distinguish between direct and indirect effects. A popular alternative that addresses this issue is partial correlation, which regresses out the signal of potentially confounding variables, resulting in a measure that reveals only direct connections. Importantly, provided the data are normally distributed, if two variables are conditionally independent given all other variables, their respective partial correlation is zero. In this paper, we propose a probabilistic generative model that allows us to estimate functional connectivity in terms of both partial correlations and a graph representing conditional independencies. Simulation results show that this methodology is able to outperform the graphical LASSO, which is the de facto standard for estimating partial correlations. Furthermore, we apply the model to estimate functional connectivity for twenty subjects using resting-state fMRI data. Results show that our model provides a richer representation of functional connectivity as compared to considering partial correlations alone. Finally, we demonstrate how our approach can be extended in several ways, for instance to achieve data fusion by informing the conditional independence graph with data from probabilistic tractography. As our Bayesian formulation of functional connectivity provides access to the posterior distribution instead of only to point estimates, we are able to quantify the uncertainty associated with our results. This reveals that while we are able to infer a clear backbone of connectivity in our empirical results, the data are not accurately described by simply looking at the mode of the distribution over connectivity. The implication of this is that
Improved visibility graph fractality with application for the diagnosis of Autism Spectrum Disorder
NASA Astrophysics Data System (ADS)
Ahmadlou, Mehran; Adeli, Hojjat; Adeli, Amir
2012-10-01
Recently, the visibility graph (VG) algorithm was proposed for mapping a time series to a graph to study complexity and fractality of the time series through investigation of the complexity of its graph. The visibility graph algorithm converts a fractal time series to a scale-free graph. VG has been used for the investigation of fractality in the dynamic behavior of both artificial and natural complex systems. However, robustness and performance of the power of scale-freeness of VG (PSVG) as an effective method for measuring fractality has not been investigated. Since noise is unavoidable in real life time series, the robustness of a fractality measure is of paramount importance. To improve the accuracy and robustness of PSVG to noise for measurement of fractality of time series in biological time-series, an improved PSVG is presented in this paper. The proposed method is evaluated using two examples: a synthetic benchmark time series and a complicated real life Electroencephalograms (EEG)-based diagnostic problem, that is distinguishing autistic children from non-autistic children. It is shown that the proposed improved PSVG is less sensitive to noise and therefore more robust compared with PSVG. Further, it is shown that using improved PSVG in the wavelet-chaos neural network model of Adeli and c-workers in place of the Katz fractality dimension results in a more accurate diagnosis of autism, a complicated neurological and psychiatric disorder.
ERIC Educational Resources Information Center
Araujo, Ives Solano; Veit, Eliane Angela; Moreira, Marco Antonio
2008-01-01
The purpose of this study was to investigate undergraduate students' performance while exposed to complementary computational modelling activities to improve physics learning, using the software "Modellus." Interpretation of kinematics graphs was the physics topic chosen for investigation. The theoretical framework adopted was based on Halloun's…
Xu, Xiayu; Reinhardt, Joseph M; Hu, Qiao; Bakall, Benjamin; Tlucek, Paul S; Bertelsen, Geir; Abràmoff, Michael D
2012-01-01
The retinal vessel width relationship at vessel branch points in fundus images is an important biomarker of retinal and systemic disease. We propose a fully automatic method to measure the vessel widths at branch points in fundus images. The method is a graph-based method, in which a graph construction method based on electric field theory is applied which specifically deals with complex branching patterns. The vessel centerline image is used as the initial segmentation of the graph. Branching points are detected on the vessel centerline image using a set of detection kernels. Crossing points are distinguished from branch points and excluded. The electric field based graph method is applied to construct the graph. This method is inspired by the non-intersecting force lines in an electric field. At last, the method is further improved to give a consistent vessel width measurement for the whole vessel tree. The algorithm was validated on 100 artery branchings and 100 vein branchings selected from 50 fundus images by comparing with vessel width measurements from two human experts.
A graph-based method for improving GSAT
Kask, K.; Dechter, R.
1996-12-31
GSAT is a randomized greedy local repair procedure that was introduced for solving propositional satisfiability and constraint satisfaction problems. We present an improvement to GSAT that is sensitive to the problem`s structure. When the problem has a tree structure the algorithm is guaranteed to find a solution in linear time. For non-tree networks, the algorithm designates a subset of nodes, called cutset, and executes a regular GSAT algorithm on this set of variables. On all the rest of the variables it executes a specialized local search algorithm for trees. This algorithm finds an assignment that, like GSAT, locally minimizes the sum of unsatisfied constraints and also globally minimizes the number of conflicts in every tree-like sub-network. We will present results of experiments showing that this new algorithm outperforms regular GSAT on sparse networks whose cycle-cutset size is bounded by 30% of the nodes.
Yang, Jing; Li, Yuan-Yuan; Li, Yi-Xue; Ye, Zhi-Qiang
2012-03-02
Highlights: Black-Right-Pointing-Pointer Proper dataset partition can improve the prediction of deleterious nsSNPs. Black-Right-Pointing-Pointer Partition according to original residue type at nsSNP is a good criterion. Black-Right-Pointing-Pointer Similar strategy is supposed promising in other machine learning problems. -- Abstract: Many non-synonymous SNPs (nsSNPs) are associated with diseases, and numerous machine learning methods have been applied to train classifiers for sorting disease-associated nsSNPs from neutral ones. The continuously accumulated nsSNP data allows us to further explore better prediction approaches. In this work, we partitioned the training data into 20 subsets according to either original or substituted amino acid type at the nsSNP site. Using support vector machine (SVM), training classification models on each subset resulted in an overall accuracy of 76.3% or 74.9% depending on the two different partition criteria, while training on the whole dataset obtained an accuracy of only 72.6%. Moreover, the dataset was also randomly divided into 20 subsets, but the corresponding accuracy was only 73.2%. Our results demonstrated that partitioning the whole training dataset into subsets properly, i.e., according to the residue type at the nsSNP site, will improve the performance of the trained classifiers significantly, which should be valuable in developing better tools for predicting the disease-association of nsSNPs.
High dimensional data clustering by partitioning the hypergraphs using dense subgraph partition
NASA Astrophysics Data System (ADS)
Sun, Xili; Tian, Shoucai; Lu, Yonggang
2015-12-01
Due to the curse of dimensionality, traditional clustering methods usually fail to produce meaningful results for the high dimensional data. Hypergraph partition is believed to be a promising method for dealing with this challenge. In this paper, we first construct a graph G from the data by defining an adjacency relationship between the data points using Shared Reverse k Nearest Neighbors (SRNN). Then a hypergraph is created from the graph G by defining the hyperedges to be all the maximal cliques in the graph G. After the hypergraph is produced, a powerful hypergraph partitioning method called dense subgraph partition (DSP) combined with the k-medoids method is used to produce the final clustering results. The proposed method is evaluated on several real high-dimensional datasets, and the experimental results show that the proposed method can improve the clustering results of the high dimensional data compared with applying k-medoids method directly on the original data.
Clique graphs and overlapping communities
NASA Astrophysics Data System (ADS)
Evans, T. S.
2010-12-01
It is shown how to construct a clique graph in which properties of cliques of a fixed order in a given graph are represented by vertices in a weighted graph. Various definitions and motivations for these weights are given. The detection of communities or clusters is used to illustrate how a clique graph may be exploited. In particular a benchmark network is shown where clique graphs find the overlapping communities accurately while vertex partition methods fail.
Improved genome inference in the MHC using a population reference graph.
Dilthey, Alexander; Cox, Charles; Iqbal, Zamin; Nelson, Matthew R; McVean, Gil
2015-06-01
Although much is known about human genetic variation, such information is typically ignored in assembling new genomes. Instead, reads are mapped to a single reference, which can lead to poor characterization of regions of high sequence or structural diversity. We introduce a population reference graph, which combines multiple reference sequences and catalogs of variation. The genomes of new samples are reconstructed as paths through the graph using an efficient hidden Markov model, allowing for recombination between different haplotypes and additional variants. By applying the method to the 4.5-Mb extended MHC region on human chromosome 6, combining 8 assembled haplotypes, the sequences of known classical HLA alleles and 87,640 SNP variants from the 1000 Genomes Project, we demonstrate using simulations, SNP genotyping, and short-read and long-read data how the method improves the accuracy of genome inference and identified regions where the current set of reference sequences is substantially incomplete.
An Improved Multi-Sensor Fusion Navigation Algorithm Based on the Factor Graph
Zeng, Qinghua; Chen, Weina; Liu, Jianye; Wang, Huizhe
2017-01-01
An integrated navigation system coupled with additional sensors can be used in the Micro Unmanned Aerial Vehicle (MUAV) applications because the multi-sensor information is redundant and complementary, which can markedly improve the system accuracy. How to deal with the information gathered from different sensors efficiently is an important problem. The fact that different sensors provide measurements asynchronously may complicate the processing of these measurements. In addition, the output signals of some sensors appear to have a non-linear character. In order to incorporate these measurements and calculate a navigation solution in real time, the multi-sensor fusion algorithm based on factor graph is proposed. The global optimum solution is factorized according to the chain structure of the factor graph, which allows for a more general form of the conditional probability density. It can convert the fusion matter into connecting factors defined by these measurements to the graph without considering the relationship between the sensor update frequency and the fusion period. An experimental MUAV system has been built and some experiments have been performed to prove the effectiveness of the proposed method. PMID:28335570
An Improved Multi-Sensor Fusion Navigation Algorithm Based on the Factor Graph.
Zeng, Qinghua; Chen, Weina; Liu, Jianye; Wang, Huizhe
2017-03-21
An integrated navigation system coupled with additional sensors can be used in the Micro Unmanned Aerial Vehicle (MUAV) applications because the multi-sensor information is redundant and complementary, which can markedly improve the system accuracy. How to deal with the information gathered from different sensors efficiently is an important problem. The fact that different sensors provide measurements asynchronously may complicate the processing of these measurements. In addition, the output signals of some sensors appear to have a non-linear character. In order to incorporate these measurements and calculate a navigation solution in real time, the multi-sensor fusion algorithm based on factor graph is proposed. The global optimum solution is factorized according to the chain structure of the factor graph, which allows for a more general form of the conditional probability density. It can convert the fusion matter into connecting factors defined by these measurements to the graph without considering the relationship between the sensor update frequency and the fusion period. An experimental MUAV system has been built and some experiments have been performed to prove the effectiveness of the proposed method.
An improved bi-level algorithm for partitioning dynamic grid hierarchies.
Deiterding, Ralf (California Institute of Technology, Pasadena, CA); Johansson, Henrik (Uppsala University, Uppsala, Sweden); Steensland, Johan; Ray, Jaideep
2006-05-01
Structured adaptive mesh refinement methods are being widely used for computer simulations of various physical phenomena. Parallel implementations potentially offer realistic simulations of complex three-dimensional applications. But achieving good scalability for large-scale applications is non-trivial. Performance is limited by the partitioner's ability to efficiently use the underlying parallel computer's resources. Designed on sound SAMR principles, Nature+Fable is a hybrid, dedicated SAMR partitioning tool that brings together the advantages of both domain-based and patch-based techniques while avoiding their drawbacks. But the original bi-level partitioning approach in Nature+Fable is insufficient as it for realistic applications regards frequently occurring bi-levels as ''impossible'' and fails. This document describes an improved bi-level partitioning algorithm that successfully copes with all possible bi-levels. The improved algorithm uses the original approach side-by-side with a new, complementing approach. By using a new, customized classification method, the improved algorithm switches automatically between the two approaches. This document describes the algorithms, discusses implementation issues, and presents experimental results. The improved version of Nature+Fable was found to be able to handle realistic applications and also to generate less imbalances, similar box count, but more communication as compared to the native, domain-based partitioner in the SAMR framework AMROC.
Ginsberg, M.L.
1996-12-31
We introduce a new form of game search called partition search that incorporates dependency analysis, allowing substantial reductions in the portion of the tree that needs to be expanded. Both theoretical results and experimental data are presented. For the game of bridge, partition search provides approximately as much of an improvement over existing methods as {alpha}-{beta} pruning provides over minimax.
An improved image compression algorithm using binary space partition scheme and geometric wavelets.
Chopra, Garima; Pal, A K
2011-01-01
Geometric wavelet is a recent development in the field of multivariate nonlinear piecewise polynomials approximation. The present study improves the geometric wavelet (GW) image coding method by using the slope intercept representation of the straight line in the binary space partition scheme. The performance of the proposed algorithm is compared with the wavelet transform-based compression methods such as the embedded zerotree wavelet (EZW), the set partitioning in hierarchical trees (SPIHT) and the embedded block coding with optimized truncation (EBCOT), and other recently developed "sparse geometric representation" based compression algorithms. The proposed image compression algorithm outperforms the EZW, the Bandelets and the GW algorithm. The presented algorithm reports a gain of 0.22 dB over the GW method at the compression ratio of 64 for the Cameraman test image.
NASA Astrophysics Data System (ADS)
Popovas, A.; Jørgensen, U. G.
2016-11-01
Context. Hydrogen is the most abundant molecule in the Universe. Its thermodynamic quantities dominate the physical conditions in molecular clouds, protoplanetary disks, etc. It is also of high interest in plasma physics. Therefore thermodynamic data for molecular hydrogen have to be as accurate as possible in a wide temperature range. Aims: We here rigorously show the shortcomings of various simplifications that are used to calculate the total internal partition function. These shortcomings can lead to errors of up to 40 percent or more in the estimated partition function. These errors carry on to calculations of thermodynamic quantities. Therefore a more complicated approach has to be taken. Methods: Seven possible simplifications of various complexity are described, together with advantages and disadvantages of direct summation of experimental values. These were compared to what we consider the most accurate and most complete treatment (case 8). Dunham coefficients were determined from experimental and theoretical energy levels of a number of electronically excited states of H2. Both equilibrium and normal hydrogen was taken into consideration. Results: Various shortcomings in existing calculations are demonstrated, and the reasons for them are explained. New partition functions for equilibrium, normal, and ortho and para hydrogen are calculated and thermodynamic quantities are reported for the temperature range 1-20 000 K. Our results are compared to previous estimates in the literature. The calculations are not limited to the ground electronic state, but include all bound and quasi-bound levels of excited electronic states. Dunham coefficients of these states of H2 are also reported. Conclusions: For most of the relevant astrophysical cases it is strongly advised to avoid using simplifications, such as a harmonic oscillator and rigid rotor or ad hoc summation limits of the eigenstates to estimate accurate partition functions and to be particularly careful when
Improving Students' Understanding of Waves by Plotting a Displacement-Time Graph in Class
NASA Astrophysics Data System (ADS)
Wei, Yajun
2012-04-01
The topic of waves is one that many high school physics students find difficult to understand. This is especially true when using some A-level textbooks1,2used in the U.K., where the concept of waves is introduced prior to the concept of simple harmonic oscillations. One of the challenges my students encounter is understanding the difference between displacement-time graphs and displacement-position graphs. Many students wonder why these two graphs have the same sinusoidal shape. Having the students use multimedia simulations allows them to see, in a hands-on fashion, the relationship between the two graphs.
Improved microarray-based decision support with graph encoded interactome data.
Daemen, Anneleen; Signoretto, Marco; Gevaert, Olivier; Suykens, Johan A K; De Moor, Bart
2010-04-19
In the past, microarray studies have been criticized due to noise and the limited overlap between gene signatures. Prior biological knowledge should therefore be incorporated as side information in models based on gene expression data to improve the accuracy of diagnosis and prognosis in cancer. As prior knowledge, we investigated interaction and pathway information from the human interactome on different aspects of biological systems. By exploiting the properties of kernel methods, relations between genes with similar functions but active in alternative pathways could be incorporated in a support vector machine classifier based on spectral graph theory. Using 10 microarray data sets, we first reduced the number of data sources relevant for multiple cancer types and outcomes. Three sources on metabolic pathway information (KEGG), protein-protein interactions (OPHID) and miRNA-gene targeting (microRNA.org) outperformed the other sources with regard to the considered class of models. Both fixed and adaptive approaches were subsequently considered to combine the three corresponding classifiers. Averaging the predictions of these classifiers performed best and was significantly better than the model based on microarray data only. These results were confirmed on 6 validation microarray sets, with a significantly improved performance in 4 of them. Integrating interactome data thus improves classification of cancer outcome for the investigated microarray technologies and cancer types. Moreover, this strategy can be incorporated in any kernel method or non-linear version of a non-kernel method.
Clustering gene expression data using graph separators.
Kaba, Bangaly; Pinet, Nicolas; Lelandais, Gaëlle; Sigayret, Alain; Berry, Anne
2007-01-01
Recent work has used graphs to modelize expression data from microarray experiments, in view of partitioning the genes into clusters. In this paper, we introduce the use of a decomposition by clique separators. Our aim is to improve the classical clustering methods in two ways: first we want to allow an overlap between clusters, as this seems biologically sound, and second we want to be guided by the structure of the graph to define the number of clusters. We test this approach with a well-known yeast database (Saccharomyces cerevisiae). Our results are good, as the expression profiles of the clusters we find are very coherent. Moreover, we are able to organize into another graph the clusters we find, and order them in a fashion which turns out to respect the chronological order defined by the the sporulation process.
Using cascading Bloom filters to improve the memory usage for de Brujin graphs
2014-01-01
Background De Brujin graphs are widely used in bioinformatics for processing next-generation sequencing data. Due to a very large size of NGS datasets, it is essential to represent de Bruijn graphs compactly, and several approaches to this problem have been proposed recently. Results In this work, we show how to reduce the memory required by the data structure of Chikhi and Rizk (WABI’12) that represents de Brujin graphs using Bloom filters. Our method requires 30% to 40% less memory with respect to their method, with insignificant impact on construction time. At the same time, our experiments showed a better query time compared to the method of Chikhi and Rizk. Conclusion The proposed data structure constitutes, to our knowledge, currently the most efficient practical representation of de Bruijn graphs. PMID:24565280
Multibody graph transformations and analysis
2013-01-01
This two-part paper uses graph transformation methods to develop methods for partitioning, aggregating, and constraint embedding for multibody systems. This first part focuses on tree-topology systems and reviews the key notion of spatial kernel operator (SKO) models for such systems. It develops systematic and rigorous techniques for partitioning SKO models in terms of the SKO models of the component subsystems based on the path-induced property of the component subgraphs. It shows that the sparsity structure of key matrix operators and the mass matrix for the multibody system can be described using partitioning transformations. Subsequently, the notions of node contractions and subgraph aggregation and their role in coarsening graphs are discussed. It is shown that the tree property of a graph is preserved after subgraph aggregation if and only if the subgraph satisfies an aggregation condition. These graph theory ideas are used to develop SKO models for the aggregated tree multibody systems. PMID:24288438
On some trees having partition dimension four
NASA Astrophysics Data System (ADS)
Ida Bagus Kade Puja Arimbawa, K.; Baskoro, Edy Tri
2016-02-01
In 1998, G. Chartrand, E. Salehi and P. Zhang introduced the notion of partition dimension of a graph. Since then, the study of this graph parameter has received much attention. A number of results have been obtained to know the values of partition dimensions of various classes of graphs. However, for some particular classes of graphs, finding of their partition dimensions is still not completely solved, for instances a class of general tree. In this paper, we study the properties of trees having partition dimension 4. In particular, we show that, for olive trees O(n), its partition dimension is equal to 4 if and only if 8 ≤ n ≤ 17. We also characterize all centipede trees having partition dimension 4.
Graph-based sampling for approximating global helical topologies of RNA.
Kim, Namhee; Laing, Christian; Elmetwaly, Shereef; Jung, Segun; Curuksu, Jeremy; Schlick, Tamar
2014-03-18
A current challenge in RNA structure prediction is the description of global helical arrangements compatible with a given secondary structure. Here we address this problem by developing a hierarchical graph sampling/data mining approach to reduce conformational space and accelerate global sampling of candidate topologies. Starting from a 2D structure, we construct an initial graph from size measures deduced from solved RNAs and junction topologies predicted by our data-mining algorithm RNAJAG trained on known RNAs. We sample these graphs in 3D space guided by knowledge-based statistical potentials derived from bending and torsion measures of internal loops as well as radii of gyration for known RNAs. Graph sampling results for 30 representative RNAs are analyzed and compared with reference graphs from both solved structures and predicted structures by available programs. This comparison indicates promise for our graph-based sampling approach for characterizing global helical arrangements in large RNAs: graph rmsds range from 2.52 to 28.24 Å for RNAs of size 25-158 nucleotides, and more than half of our graph predictions improve upon other programs. The efficiency in graph sampling, however, implies an additional step of translating candidate graphs into atomic models. Such models can be built with the same idea of graph partitioning and build-up procedures we used for RNA design.
Graph ensemble boosting for imbalanced noisy graph stream classification.
Pan, Shirui; Wu, Jia; Zhu, Xingquan; Zhang, Chengqi
2015-05-01
Many applications involve stream data with structural dependency, graph representations, and continuously increasing volumes. For these applications, it is very common that their class distributions are imbalanced with minority (or positive) samples being only a small portion of the population, which imposes significant challenges for learning models to accurately identify minority samples. This problem is further complicated with the presence of noise, because they are similar to minority samples and any treatment for the class imbalance may falsely focus on the noise and result in deterioration of accuracy. In this paper, we propose a classification model to tackle imbalanced graph streams with noise. Our method, graph ensemble boosting, employs an ensemble-based framework to partition graph stream into chunks each containing a number of noisy graphs with imbalanced class distributions. For each individual chunk, we propose a boosting algorithm to combine discriminative subgraph pattern selection and model learning as a unified framework for graph classification. To tackle concept drifting in graph streams, an instance level weighting mechanism is used to dynamically adjust the instance weight, through which the boosting framework can emphasize on difficult graph samples. The classifiers built from different graph chunks form an ensemble for graph stream classification. Experiments on real-life imbalanced graph streams demonstrate clear benefits of our boosting design for handling imbalanced noisy graph stream.
Xia, Zhining; Jiang, Xuemei; Mu, Xiaojing; Chen, Hua
2008-02-01
Microemulsion electrokinetic chromatography (MEEKC) has been used to indirectly measure octanol-water partition coefficients (log P(ow)) of compounds. In order to obtain an accurate log P(ow) value, the electrophoretic mobilities of the microemulsion phase (mu(me)) and the analyte (mu(eff)) in MEEKC must be accurately required. However, in conventional MEEKC, the shortage of obtaining mu(me) with a tracing method was discovered, and the influences of concentration, injection volume of analyte, and high electric field on measuring mu(eff) were also found. In this paper, a novel method called improved MEEKC (I-MEEKC) was developed to avoid the problems mentioned above. In I-MEEKC, a nonlinearity fitting program was used to obtain mu(me) to avoid the error from tracing mu(me); the extrapolating method was used to eliminate the effects of concentrations and injection volumes of analytes on mu(eff) measurement, and an enough stable microemulsion was selected to eliminate the effect of high electric field on mu(eff )measurement. Then the novel method was applied to estimate log P(ow) of uncharged compounds and charged pharmaceuticals compared to the conventional MEEKC. The log P(ow) of all analytes obtained by I-MEEKC agreed with those obtained by classical shake flask or literature values, the errors between them were within 0.1 logarithm units, better than the ones by conventional MEEKC.
Improved initialisation of model-based clustering using Gaussian hierarchical partitions
Scrucca, Luca; Raftery, Adrian E.
2015-01-01
Initialisation of the EM algorithm in model-based clustering is often crucial. Various starting points in the parameter space often lead to different local maxima of the likelihood function and, so to different clustering partitions. Among the several approaches available in the literature, model-based agglomerative hierarchical clustering is used to provide initial partitions in the popular mclust R package. This choice is computationally convenient and often yields good clustering partitions. However, in certain circumstances, poor initial partitions may cause the EM algorithm to converge to a local maximum of the likelihood function. We propose several simple and fast refinements based on data transformations and illustrate them through data examples. PMID:26949421
Anatomically-adapted graph wavelets for improved group-level fMRI activation mapping.
Behjat, Hamid; Leonardi, Nora; Sörnmo, Leif; Van De Ville, Dimitri
2015-12-01
A graph based framework for fMRI brain activation mapping is presented. The approach exploits the spectral graph wavelet transform (SGWT) for the purpose of defining an advanced multi-resolutional spatial transformation for fMRI data. The framework extends wavelet based SPM (WSPM), which is an alternative to the conventional approach of statistical parametric mapping (SPM), and is developed specifically for group-level analysis. We present a novel procedure for constructing brain graphs, with subgraphs that separately encode the structural connectivity of the cerebral and cerebellar gray matter (GM), and address the inter-subject GM variability by the use of template GM representations. Graph wavelets tailored to the convoluted boundaries of GM are then constructed as a means to implement a GM-based spatial transformation on fMRI data. The proposed approach is evaluated using real as well as semi-synthetic multi-subject data. Compared to SPM and WSPM using classical wavelets, the proposed approach shows superior type-I error control. The results on real data suggest a higher detection sensitivity as well as the capability to capture subtle, connected patterns of brain activity.
Duan, Wuhua; Chen, Jing; Wang, Jianchen; Wang, Shuwei; Feng, Xiaogui; Wang, Xinghai; Li, Shaowei; Xu, Chao
2014-08-15
High level liquid waste (HLLW) produced from the reprocessing of the spent nuclear fuel still contains moderate amounts of uranium, transuranium (TRU) actinides, (90)Sr, (137)Cs, etc., and thus constitutes a permanent hazard to the environment. The partitioning and transmutation (P&T) strategy has increasingly attracted interest for the safe treatment and disposal of HLLW, in which the partitioning of HLLW is one of the critical technical issues. An improved total partitioning process, including a TRPO (tri-alkylphosphine oxide) process for the removal of actinides, a CESE (crown ether strontium extraction) process for the removal of Sr, and a CECE (calixcrown ether cesium extraction) process for the removal of Cs, has been developed to treat Chinese HLLW. A 160-hour hot test of the improved total partitioning process was carried out using 72-stage 10-mm-dia annular centrifugal contactors (ACCs) and genuine HLLW. The hot test results showed that the average DFs of total α activity, Sr and Cs were 3.57 × 10(3), 2.25 × 10(4) and 1.68 × 10(4) after the hot test reached equilibrium, respectively. During the hot test, 72-stage 10-mm-dia ACCs worked stable, continuously with no stage failing or interruption of the operation.
Meylan, W.M.; Howard, P.H.; Aronson, D.; Printup, H.; Gouchie, S.; Boethling, R.S.
1999-04-01
A compound`s bioconcentration factor (BDF) is the most commonly used indicator of its tendency to accumulate in aquatic organisms from the surrounding medium. Because it is expensive to measure, the BCF is generally estimated from the octanol/water partition coefficient (K{sub ow}), but currently used regression equations were developed from small data sets that do not adequately represent the wide range of chemical substances now subject to review. To develop and improved method, the authors collected BCF data in a file that contained information on measured BCFs and other key experimental details for 694 chemicals. Log BCF was then regressed against log K{sub ow} and chemicals with significant deviations from the line of best fit were analyzed by chemical structure. The resulting algorithm classifies a substance as either nonionic or ionic, the latter group including carboxylic acids, sulfonic acids and their salts, and quaternary N compounds. Log BCF for nonionics is estimated from log K{sub ow} and a series of correction factors if applicable; different equations apply for log K{sub ow} 1.0 to 7.0 and >7.0. For ionics, chemicals are categorized by log K{sub ow} and a log BCF in the range 0.5 to 1.75 is assigned. Organometallics, nonionics with long alkyl chains, and aromatic azo compounds receive special treatment. The correlation coefficient and mean error for log BCF indicate that the new method is a significantly better fit to existing data than other methods.
Schulz, Martin; Arnold, Dorian
2007-06-12
GraphLib is a support library used by other tools to create, manipulate, store, and export graphs. It provides a simple interface to specifS arbitrary directed and undirected graphs by adding nodes and edges. Each node and edge can be associated with a set of attributes describing size, color, and shape. Once created, graphs can be manipulated using a set of graph analysis algorithms, including merge, prune, and path coloring operations. GraphLib also has the ability to export graphs into various open formats such as DOT and GML.
Partitioning technique for discrete quantum systems
Jin, L.; Song, Z.
2011-06-15
We develop the partitioning technique for quantum discrete systems. The graph consists of several subgraphs: a central graph and several branch graphs, with each branch graph being rooted by an individual node on the central one. We show that the effective Hamiltonian on the central graph can be constructed by adding additional potentials on the branch-root nodes, which generates the same result as does the the original Hamiltonian on the entire graph. Exactly solvable models are presented to demonstrate the main points of this paper.
Some trees with partition dimension three
NASA Astrophysics Data System (ADS)
Fredlina, Ketut Queena; Baskoro, Edy Tri
2016-02-01
The concept of partition dimension of a graph was introduced by Chartrand, E. Salehi and P. Zhang (1998) [2]. Let G(V, E) be a connected graph. For S ⊆ V (G) and v ∈ V (G), define the distance d(v, S) from v to S is min{d(v, x)|x ∈ S}. Let Π be an ordered partition of V (G) and Π = {S1, S2, ..., Sk }. The representation r(v|Π) of vertex v with respect to Π is (d(v, S1), d(v, S2), ..., d(v, Sk)). If the representations of all vertices are distinct, then the partition Π is called a resolving partition of G. The partition dimension of G is the minimum k such that G has a resolving partition with k partition classes. In this paper, we characterize some classes of trees with partition dimension three, namely olive trees, weeds, and centipedes.
Partitioning Breaks Communities
NASA Astrophysics Data System (ADS)
Reid, Fergal; McDaid, Aaron; Hurley, Neil
Considering a clique as a conservative definition of community structure, we examine how graph partitioning algorithms interact with cliques. Many popular community-finding algorithms partition the entire graph into non-overlapping communities. We show that on a wide range of empirical networks, from different domains, significant numbers of cliques are split across the separate partitions produced by these algorithms. We then examine the largest connected component of the subgraph formed by retaining only edges in cliques, and apply partitioning strategies that explicitly minimise the number of cliques split. We further examine several modern overlapping community finding algorithms, in terms of the interaction between cliques and the communities they find, and in terms of the global overlap of the sets of communities they find. We conclude that, due to the connectedness of many networks, any community finding algorithm that produces partitions must fail to find at least some significant structures. Moreover, contrary to traditional intuition, in some empirical networks, strong ties and cliques frequently do cross community boundaries; much community structure is fundamentally overlapping and unpartitionable in nature.
Subdominant pseudoultrametric on graphs
Dovgoshei, A A; Petrov, E A
2013-08-31
Let (G,w) be a weighted graph. We find necessary and sufficient conditions under which the weight w:E(G)→R{sup +} can be extended to a pseudoultrametric on V(G), and establish a criterion for the uniqueness of such an extension. We demonstrate that (G,w) is a complete k-partite graph, for k≥2, if and only if for any weight that can be extended to a pseudoultrametric, among all such extensions one can find the least pseudoultrametric consistent with w. We give a structural characterization of graphs for which the subdominant pseudoultrametric is an ultrametric for any strictly positive weight that can be extended to a pseudoultrametric. Bibliography: 14 titles.
Higher-order graph wavelets and sparsity on circulant graphs
NASA Astrophysics Data System (ADS)
Kotzagiannidis, Madeleine S.; Dragotti, Pier Luigi
2015-08-01
The notion of a graph wavelet gives rise to more advanced processing of data on graphs due to its ability to operate in a localized manner, across newly arising data-dependency structures, with respect to the graph signal and underlying graph structure, thereby taking into consideration the inherent geometry of the data. In this work, we tackle the problem of creating graph wavelet filterbanks on circulant graphs for a sparse representation of certain classes of graph signals. The underlying graph can hereby be data-driven as well as fixed, for applications including image processing and social network theory, whereby clusters can be modelled as circulant graphs, respectively. We present a set of novel graph wavelet filter-bank constructions, which annihilate higher-order polynomial graph signals (up to a border effect) defined on the vertices of undirected, circulant graphs, and are localised in the vertex domain. We give preliminary results on their performance for non-linear graph signal approximation and denoising. Furthermore, we provide extensions to our previously developed segmentation-inspired graph wavelet framework for non-linear image approximation, by incorporating notions of smoothness and vanishing moments, which further improve performance compared to traditional methods.
Automatic analysis of D-partition
NASA Astrophysics Data System (ADS)
Bogaevskaya, V. G.
2017-01-01
The paper is dedicated to automatization of D-partition analysis. D-partition is one of the most common methods for determination of solution stability in systems with time-delayed feedback control and its dependency on values of control parameters. A transition from analytical form of D-partition to plain graph has been investigated. An algorithm of graph faces determination and calculation of count of characteristic equation roots with positive real part for appropriate area of D-partition has been developed. The algorithm keeps an information about analytical formulas for edges of faces. It allows to make further analytical research based on the results of computer analysis.
Light Competition and Carbon Partitioning-Allocation in an improved Forest Ecosystem Model
NASA Astrophysics Data System (ADS)
Collalti, Alessio; Santini, Monia; Valentini Valentini, Riccardo
2010-05-01
In Italy about 100.000 km2 are covered by forests. This surface is the 30% of the whole national land and this shows how the forests are important both for socio-economic and for environmental aspects. Forests changes affect a delicate balance that involve not only vegetation components but also bio-geochemical cycles and global climate. The knowledge of the amount of Carbon sequestered by forests represents a precious information for their sustainable management in the framework of climate changes. Primary studies in terms of model about this important issue, has been done through Forest Ecosystem Model (FEM), well known and validated as 3PG (Landsberg et Waring, 1997; Sands 2004). It is based on light use efficiency approach at the canopy level. The present study started from the original model 3PG, producing an improved version that uses many of explicit formulations of all relevant ecophysiological processes but makes it able to be applied for natural forests. The mutual interaction of forest growth and light conditions causes vertical and horizontal differentiation in the natural forest mosaic. Only ecophysiological parameters which can be either directly measured or estimates with reasonable certainty are used. The model has been written in C language and has been created considering a tri-dimensional cell structure with different vertical layers depending on the forest type that has to be simulated. This 3PG 'improved' version enable to work on multi-layer and multi-species forests type with cell resolution of one hectare for the typical Italian forest species. The multi-layer version is the result of the implementation and development of Lambert-Beer law for the estimation of intercepted, absorbed and transmitted light through different storeys of the forest. It is possible estimates, for each storey, a Par value (Photosynthetic Active Radiation) through Leaf Area Index (LAI), Light Extinction Coefficient and cell Canopy Cover using a "Big Leaf" approach
Ahrens, Lutz; Harner, Tom; Shoeib, Mahiba; Lane, Douglas A; Murphy, Jennifer G
2012-07-03
Gas-phase perfluoroalkyl carboxylic acids (PFCAs) sorb strongly on filter material (i.e., GFF, QFF) used in conventional high volume air samplers, which results in an overestimation of the particle-phase concentration. In this study, we investigated an improved technique for measuring the gas-particle partitioning of per- and polyfluoroalkyl substances (PFASs) using an annular diffusion denuder sampler. Samples were analyzed for 7 PFAS classes [i.e., PFCAs, perfluoroalkane sulfonic acids (PFSAs), fluorotelomer alcohols (FTOHs), fluorotelomer methacrylates (FTMACs), fluorotelomer acrylates (FTACs), perfluorooctane sulfonamides (FOSAs), and perfluorooctane sulfonamidoethanols (FOSEs)]. The measured particulate associated fraction (Φ') using the diffusion denuder sampler generally followed the trend FTACs (0%) < FTOHs (~8%) < FOSAs (~21%) < PFSAs (~29%) < FOSEs (~66%), whereas the Φ' of the C(8)-C(18) PFCAs increased with carbon chain length, and ranged from 6% to 100%. The ionizability of some PFASs, when associated with particles, is an important consideration when calculating the gas-particle partitioning coefficient as both ionic and neutral forms can be present in the particles. Here we differentiate between a gas-particle partitioning coefficient for neutral species, K(p), and one that accounts for both ionic and neutral species of a compound, K(p)'. The measured K(p)' for PFSAs and PFCAs was 4-5 log units higher compared to the interpolated K(p) for the neutral form only. The measured K(p)' can be corrected (to apply to the neutral form only) with knowledge of the pK(a) of the chemical and the pH of the condensed medium ("wet" particle or aqueous aerosol). The denuder-based sampling of PFASs has yielded a robust data set that demonstrates the importance of atmospheric pH and chemical pK(a) values in determining gas-particle partitioning of PFASs.
PIGS: improved estimates of identity-by-descent probabilities by probabilistic IBD graph sampling
2015-01-01
Identifying segments in the genome of different individuals that are identical-by-descent (IBD) is a fundamental element of genetics. IBD data is used for numerous applications including demographic inference, heritability estimation, and mapping disease loci. Simultaneous detection of IBD over multiple haplotypes has proven to be computationally difficult. To overcome this, many state of the art methods estimate the probability of IBD between each pair of haplotypes separately. While computationally efficient, these methods fail to leverage the clique structure of IBD resulting in less powerful IBD identification, especially for small IBD segments. We develop a hybrid approach (PIGS), which combines the computational efficiency of pairwise methods with the power of multiway methods. It leverages the IBD graph structure to compute the probability of IBD conditional on all pairwise estimates simultaneously. We show via extensive simulations and analysis of real data that our method produces a substantial increase in the number of identified small IBD segments. PMID:25860540
Graph cut and image intensity-based splitting improves nuclei segmentation in high-content screening
NASA Astrophysics Data System (ADS)
Farhan, Muhammad; Ruusuvuori, Pekka; Emmenlauer, Mario; Rämö, Pauli; Yli-Harja, Olli; Dehio, Christoph
2013-02-01
Quantification of phenotypes in high-content screening experiments depends on the accuracy of single cell analysis. In such analysis workflows, cell nuclei segmentation is typically the first step and is followed by cell body segmentation, feature extraction, and subsequent data analysis workflows. Therefore, it is of utmost importance that the first steps of high-content analysis are done accurately in order to guarantee correctness of the final analysis results. In this paper, we present a novel cell nuclei image segmentation framework which exploits robustness of graph cut to obtain initial segmentation for image intensity-based clump splitting method to deliver the accurate overall segmentation. By using quantitative benchmarks and qualitative comparison with real images from high-content screening experiments with complicated multinucleate cells, we show that our method outperforms other state-of-the-art nuclei segmentation methods. Moreover, we provide a modular and easy-to-use implementation of the method for a widely used platform.
Path similarity skeleton graph matching.
Bai, Xiang; Latecki, Longin Jan
2008-07-01
This paper presents a novel framework to for shape recognition based on object silhouettes. The main idea is to match skeleton graphs by comparing the shortest paths between skeleton endpoints. In contrast to typical tree or graph matching methods, we completely ignore the topological graph structure. Our approach is motivated by the fact that visually similar skeleton graphs may have completely different topological structures. The proposed comparison of shortest paths between endpoints of skeleton graphs yields correct matching results in such cases. The skeletons are pruned by contour partitioning with Discrete Curve Evolution, which implies that the endpoints of skeleton branches correspond to visual parts of the objects. The experimental results demonstrate that our method is able to produce correct results in the presence of articulations, stretching, and occlusion.
The peculiar phase structure of random graph bisection
Percus, Allon G; Istrate, Gabriel; Goncalves, Bruno T; Sumi, Robert Z
2008-01-01
The mincut graph bisection problem involves partitioning the n vertices of a graph into disjoint subsets, each containing exactly n/2 vertices, while minimizing the number of 'cut' edges with an endpoint in each subset. When considered over sparse random graphs, the phase structure of the graph bisection problem displays certain familiar properties, but also some surprises. It is known that when the mean degree is below the critical value of 2 log 2, the cutsize is zero with high probability. We study how the minimum cutsize increases with mean degree above this critical threshold, finding a new analytical upper bound that improves considerably upon previous bounds. Combined with recent results on expander graphs, our bound suggests the unusual scenario that random graph bisection is replica symmetric up to and beyond the critical threshold, with a replica symmetry breaking transition possibly taking place above the threshold. An intriguing algorithmic consequence is that although the problem is NP-hard, we can find near-optimal cutsizes (whose ratio to the optimal value approaches 1 asymptotically) in polynomial time for typical instances near the phase transition.
Kim, Z-Hun; Park, Hanwool; Hong, Seong-Joo; Lim, Sang-Min; Lee, Choul-Gyun
2016-05-01
Culturing microalgae in the ocean has potentials that may reduce the production cost and provide an option for an economic biofuel production from microalgae. The ocean holds great potentials for mass microalgal cultivation with its high specific heat, mixing energy from waves, and large cultivable area. Suitable photobioreactors (PBRs) that are capable of integrating marine energy into the culture systems need to be developed for the successful ocean cultivation. In this study, prototype floating PBRs were designed and constructed using transparent low-density polyethylene film for microalgal culture in the ocean. To improve the mixing efficiency, various types of internal partitions were introduced within PBRs. Three different types of internal partitions were evaluated for their effects on the mixing efficiency in terms of mass transfer (k(L)a) and mixing time in the PBRs. The partition type with the best mixing efficiency was selected, and the number of partitions was varied from one to three for investigation of its effect on mixing efficiency. When the number of partitions is increased, mass transfer increased in proportion to the number of partitions. However, mixing time was not directly related to the number of partitions. When a green microalga, Tetraselmis sp. was cultivated using PBRs with the selected partition under semi-continuous mode in the ocean, biomass and fatty acid productivities in the PBRs were increased by up to 50 % and 44% at high initial cell density, respectively, compared to non-partitioned ones. The results of internally partitioned PBRs demonstrated potentials for culturing microalgae by efficiently utilizing ocean wave energy into culture mixing in the ocean.
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.
Banerjee, S.; Howard, P.H.
1988-07-01
Octanol-water partition coefficients (K/sub ow/) of 75 compounds ranging over 9 orders of magnitude are correlated by log K/sub ow/ = -0.40 + 0.73 log (..gamma../sub W/)/sub U/ -0.39 log (..gamma../sub 0/)/sub U/ (r = 0.98), where (..gamma..//sub W/)/sub U/ and (..gamma../sub 0/)/sub U/ are UNIFAC-derived activity coefficients in water and octanol, respectively. The constants 0.73 and -0.39 are obtained empirically and are intended to compensate for group nonadditivity. Correction factors of similar magnitude are obtained in independent correlations of water solubility with (..gamma../sub W/)/sub U/ and of octanol solubility with (..gamma../sub 0/)/sub U/, thereby confirming the validity of the approach.
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.
On bottleneck partitioning k-ary n-cubes
NASA Technical Reports Server (NTRS)
Nicol, David M.; Mao, Weizhen
1994-01-01
Graph partitioning is a topic of extensive interest, with applications to parallel processing. In this context graph nodes typically represent computation, and edges represent communication. One seeks to distribute the workload by partitioning the graph so that every processor has approximately the same workload, and the communication cost (measured as a function of edges exposed by the partition) is minimized. Measures of partition quality vary; in this paper we consider a processor's cost to be the sum of its computation and communication costs, and consider the cost of a partition to be the bottleneck, or maximal processor cost induced by the partition. For a general graph the problem of finding an optimal partitioning is intractable. In this paper we restrict our attention to the class of k-art n-cube graphs with uniformly weighted nodes. Given mild restrictions on the node weight and number of processors, we identify partitions yielding the smallest bottleneck. We also demonstrate by example that some restrictions are necessary for the partitions we identify to be optimal. In particular, there exist cases where partitions that evenly partition nodes need not be optimal.
Improved method for estimating water solubility from octanol/water partition coefficient
Meylan, W.; Howard, P.; Boethling, R.
1994-12-31
Water solubility (wsol) is a critical property in risk assessments for chemicals. It is often necessary to estimate wsol because measured values are unavailable. However, the most widely used estimation methods predict wsol from the logarithm of the octanol/water partition coefficient (log K{sub ow}), via regression equations based on approximately 200 (or fewer) measured values of log K{sub ow}. The overall accuracy of these correlations is only about {+-} one order of magnitude. To update and enhance existing wsol estimation methods, the authors first collected 3,000+ measured values from a variety of sources. The range of chemical structures represented by this data set is much greater than for the older regressions. They then investigated the accuracy of wsol/log K{sub ow} correlations for the entire data set and for various chemical classes, as well as the importance of melting point (mp) to the estimate. The results of this investigation include a new regression equation for estimating wsol. This method has been encoded in a computer program that is compatible with other programs in the Estimation Programs Interface (EPI), a program used by OPPT to estimate key properties and fate parameters for existing and Premanufacture Notice (PMN) chemicals. To estimate wsol the user can enter a measured value of log K{sub ow}, or allow the program to estimate log K{sub ow} from the chemical`s SMILES notation.
ERIC Educational Resources Information Center
Connery, Keely Flynn
2007-01-01
Graphing predictions is especially important in classes where relationships between variables need to be explored and derived. In this article, the author describes how his students sketch the graphs of their predictions before they begin their investigations on two laboratory activities: Distance Versus Time Cart Race Lab and Resistance; and…
Yadav, Umesh P.; Ayre, Brian G.; Bush, Daniel R.
2015-04-22
The principal components of plant productivity and nutritional value, from the standpoint of modern agriculture, are the acquisition and partitioning of organic carbon (C) and nitrogen (N) compounds among the various organs of the plant. The flow of essential organic nutrients among the plant organ systems is mediated by its complex vascular system, and is driven by a series of transport steps including export from sites of primary assimilation, transport into and out of the phloem and xylem, and transport into the various import-dependent organs. Manipulating C and N partitioning to enhance yield of harvested organs is evident in the earliest crop domestication events and continues to be a goal for modern plant biology. Research on the biochemistry, molecular and cellular biology, and physiology of C and N partitioning has now matured to an extent that strategic manipulation of these transport systems through biotechnology are being attempted to improve movement from source to sink tissues in general, but also to target partitioning to specific organs. These nascent efforts are demonstrating the potential of applied biomass targeting but are also identifying interactions between essential nutrients that require further basic research. In this review, we summarize the key transport steps involved in C and N partitioning, and discuss various transgenic approaches for directly manipulating key C and N transporters involved. In addition, we propose several experiments that could enhance biomass accumulation in targeted organs while simultaneously testing current partitioning models.
Yadav, Umesh P.; Ayre, Brian G.; Bush, Daniel R.
2015-04-22
The principal components of plant productivity and nutritional value, from the standpoint of modern agriculture, are the acquisition and partitioning of organic carbon (C) and nitrogen (N) compounds among the various organs of the plant. The flow of essential organic nutrients among the plant organ systems is mediated by its complex vascular system, and is driven by a series of transport steps including export from sites of primary assimilation, transport into and out of the phloem and xylem, and transport into the various import-dependent organs. Manipulating C and N partitioning to enhance yield of harvested organs is evident in themore » earliest crop domestication events and continues to be a goal for modern plant biology. Research on the biochemistry, molecular and cellular biology, and physiology of C and N partitioning has now matured to an extent that strategic manipulation of these transport systems through biotechnology are being attempted to improve movement from source to sink tissues in general, but also to target partitioning to specific organs. These nascent efforts are demonstrating the potential of applied biomass targeting but are also identifying interactions between essential nutrients that require further basic research. In this review, we summarize the key transport steps involved in C and N partitioning, and discuss various transgenic approaches for directly manipulating key C and N transporters involved. In addition, we propose several experiments that could enhance biomass accumulation in targeted organs while simultaneously testing current partitioning models.« less
Yadav, Umesh P.; Ayre, Brian G.; Bush, Daniel R.
2015-01-01
The principal components of plant productivity and nutritional value, from the standpoint of modern agriculture, are the acquisition and partitioning of organic carbon (C) and nitrogen (N) compounds among the various organs of the plant. The flow of essential organic nutrients among the plant organ systems is mediated by its complex vascular system, and is driven by a series of transport steps including export from sites of primary assimilation, transport into and out of the phloem and xylem, and transport into the various import-dependent organs. Manipulating C and N partitioning to enhance yield of harvested organs is evident in the earliest crop domestication events and continues to be a goal for modern plant biology. Research on the biochemistry, molecular and cellular biology, and physiology of C and N partitioning has now matured to an extent that strategic manipulation of these transport systems through biotechnology are being attempted to improve movement from source to sink tissues in general, but also to target partitioning to specific organs. These nascent efforts are demonstrating the potential of applied biomass targeting but are also identifying interactions between essential nutrients that require further basic research. In this review, we summarize the key transport steps involved in C and N partitioning, and discuss various transgenic approaches for directly manipulating key C and N transporters involved. In addition, we propose several experiments that could enhance biomass accumulation in targeted organs while simultaneously testing current partitioning models. PMID:25954297
Scenario Graphs and Attack Graphs
2004-04-14
46 6.1 Vulnerability Analysis of a Network . . . . . . . . . . . . . . . . . . . . . . . . . 53 6.2 Sandia Red Team Attack Graph...asymptotic bound. The test machine was a 1Ghz Pentium III with 1GB of RAM, running Red Hat Linux 7.3. Figure 4.1(a) plots running time of the implemen...host scanning tools network information vulnerability Attack Graph network Red
Sanfilippo, Antonio P.
2005-12-27
Graph theory is a branch of discrete combinatorial mathematics that studies the properties of graphs. The theory was pioneered by the Swiss mathematician Leonhard Euler in the 18th century, commenced its formal development during the second half of the 19th century, and has witnessed substantial growth during the last seventy years, with applications in areas as diverse as engineering, computer science, physics, sociology, chemistry and biology. Graph theory has also had a strong impact in computational linguistics by providing the foundations for the theory of features structures that has emerged as one of the most widely used frameworks for the representation of grammar formalisms.
Warren, Jeffrey; Garten Jr, Charles T; Iversen, Colleen M; Norby, Richard J; Thornton, Peter E; Weston, David; Gu, Lianhong; Brice, Deanne Jane; Childs, Joanne; Evans, R
2012-01-01
Summary The dynamics of rapid changes in carbon (C) partitioning within forest ecosystems are not well understood, which limits improvement of mechanistic models of C cycling. Our objective was to inform model processes by describing relationships between C partitioning and accessible environmental or physiological measurements, with a special emphasis on belowground C flux. We exposed eight 7-year-old loblolly pine trees to air enriched with 13CO2 and then implemented adjacent light shade (LS) and heavy shade (HS) treatments in order to manipulate C uptake and flux. A soil pit was dug adjacent to the trees to provide greater access belowground. The impacts of shading on photosynthesis, plant water potential, sap flow, basal area growth, root growth, and soil C exchange rate (CER) were assessed for each tree over a three-week period. The progression of the 13C label was concurrently tracked from the atmosphere through foliage, phloem, roots, and soil CO2 efflux. The HS treatment significantly reduced C uptake, sap flow, stem growth and root standing crop, and resulted in greater residual soil water content to 1 m depth. Sap flow was strongly correlated with CER on the previous day, but not the current day, with no apparent treatment effect on the relationship. The 13C label was immediately detected in foliage on label day (half-life = 0.5 d), progressed through phloem by day 2 (half-life = 4.7 d), roots by day 2-4, and subsequently was evident as respiratory release from soil which peaked between days 3-6. The 13C of soil CO2 efflux was strongly correlated with phloem 13C on the previous day, or two days earlier. These data detail the timing and relative magnitude of C flux through a young pine stand in relation to environmental conditions. Refinement of belowground sampling will be necessary to adequately separate and quantify the flux of recently fixed C into roots, and fate of that new C as respiratory, mycorrhizal or exudative release, storage or partitioning
Unsupervised spectral mesh segmentation driven by heterogeneous graphs.
Theologou, Panagiotis; Pratikakis, Ioannis; Theoharis, Theoharis
2016-03-21
A fully automatic mesh segmentation scheme using heterogeneous graphs is presented. We introduce a spectral framework where local geometry affinities are coupled with surface patch affinities. A heterogeneous graph is constructed combining two distinct graphs: a weighted graph based on adjacency of patches of an initial over-segmentation, and the weighted dual mesh graph. The partitioning relies on processing each eigenvector of the heterogeneous graph Laplacian individually, taking into account the nodal set and nodal domain theory. Experiments on standard datasets show that the proposed unsupervised approach outperforms the state-of-the-art unsupervised methodologies and is comparable to the best supervised approaches.
Unsupervised Spectral Mesh Segmentation Driven by Heterogeneous Graphs.
Theologou, Panagiotis; Pratikakis, Ioannis; Theoharis, Theoharis
2017-02-01
A fully automatic mesh segmentation scheme using heterogeneous graphs is presented. We introduce a spectral framework where local geometry affinities are coupled with surface patch affinities. A heterogeneous graph is constructed combining two distinct graphs: a weighted graph based on adjacency of patches of an initial over-segmentation, and the weighted dual mesh graph. The partitioning relies on processing each eigenvector of the heterogeneous graph Laplacian individually, taking into account the nodal set and nodal domain theory. Experiments on standard datasets show that the proposed unsupervised approach outperforms the state-of-the-art unsupervised methodologies and is comparable to the best supervised approaches.
Effects of Constituent Properties on Performance Improvement of a Quenching and Partitioning Steel
Choi, Kyoo Sil; Hu, Xiaohua; Sun, Xin; Taylor, Mark D.; De Moor, Emmanuel; Speer, John; Matlock, David K.
2014-04-01
In this paper, a two-dimensional microstructure-based finite element modeling method is adopted to investigate the effects of material parameters of the constituent phases on the macroscopic tensile behavior of Q&P steel and then to do a computational materials design approach for its performance improvement. For this purpose, a model Q&P steel is first produced and various experiments are then performed to characterize the steel. Actual microstructure-based model is generated based on the information from EBSD, SEM and nano-indentation test, and the material properties for the constituent phases are determined based on the initial constituents’ properties from HEXRD test and the subsequent calibration of model prediction to tensile test results. Influence of various material parameters of the constituents on the macroscopic behaviors is then investigated by separately adjusting them by small amount. Based on the observation on the respective influence of constituents’ material parameters, a new set of material parameters are devised, which results in better performance in ductility. The results indicate that various material parameters may need to be concurrently adjusted in a cohesive way in order to improve the performance of Q&P steel. In summary, higher austenite stability, less strength difference between the phases, higher hardening exponents of the phases are generally beneficial for the performance improvement. The information from this study can be used to devise new Q&P heat-treating parameters to produce the Q&P steels with better performance.
Lung segmentation with graph cuts: Graph size versus performance
NASA Astrophysics Data System (ADS)
Pazokifard, Banafsheh; Sowmya, Arcot
2013-10-01
The effect of graph size on segmentation performance and speed is investigated, where segmentation is based on the graph cuts algorithm. The study is performed on lung extraction in 50 complete multi detector computed tomography (MDCT) datasets, and a fully automatic procedure. The experiments were performed on different graph sizes for both 2-D (4 and 8 neighbours) and 3-D (6 and 26 neighbours) graphs. Five slices from each segmented dataset were compared to the reference delineation provided by a radiologist. Our evaluations highlight the fact that when medical image segmentation is performed using graph cuts, increasing graph and neighbourhood connection size does not necessarily improve the segmentation performance, but also increase the running time dramatically.
GRACE-assisted Budyko Hypothesis for Improved Estimates of Long-term Water Partitioning
NASA Astrophysics Data System (ADS)
Fang, K.; Shen, C.; Fisher, J. B.; Niu, J.
2015-12-01
The Budyko hypothesis provides a reference condition of water balance and describes an empirical relationship between precipitation (P), evapotranspiration (E) and potential evapotranspiration (Ep). However, real-world catchments often deviate significantly from the theoretical Budyko curve. Recent advances of understanding in the impacts of seasonal water balances on long-term averaged water balance showed that phase difference between P and Ep is a major cause of downward departure from the Budyko curve. The phase difference and its processing by the catchments are in fact recorded over the globe in the form of Gravity Recovery and Climate Experiment satellite (GRACE) terrestrial water storage anomalies (TWSA). Here we present a GRACE-assisted Budyko-type formula that has improved predictive accuracy for long term E/P using the aridity index and storage patterns. We established an error model for the residual between Turk-Pike form of the Budyko curve and the observed E, based on a seamless United States basin water balance dataset. We found that the error model could improve the prediction efficiency by more than 60% comparing to Budyko model. The form of the error model was supported by Monte Carlo analysis. We compared the results with NLDAS predict E and found that the GRACE-corrected formula are in closer agreement with NLDAS than that without GRACE correction. In addition, we apply this error model to the whole world and global E was predicted. By comparing with other E products we found this error model can correct Budyko curve effectively.
Adjusting protein graphs based on graph entropy.
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.
2013-01-01
optimization problem (2)–(3) is convex and can 1We adopt the convention that yii = 1 for any node i that belongs to a cluster. 2We assume aii = 1 for all i. 3The...relaxations: The formulation (2)–(3) is not the only way to relax the non - convex ML estimator. Instead of the nuclear norm regularizer, a hard constraint ...presented a convex optimization formulation, essentially a convexification of the maximum likelihood estimator. Our theoretic analysis shows that this
Test of Graphing and Graph Interpretation Skills.
ERIC Educational Resources Information Center
Hermann, J.
This monograph is a test of graphing and graph interpretation skills which assesses performance on all the skills of graphing which are contained in the AAAS program, Science - A Process Approach. The testing includes construction of bar graphs, interpreting information on graphs, the use of the Cartesian coordinate system, making predictions from…
Jarvis, Nicholas
2016-01-01
Models used to assess leaching of pesticides to groundwater still rely on the sorption koc value, even though its limitations have been known for several decades, especially for soils of low organic carbon content (i.e. subsoils). This is mainly because the general applicability of any improved model approach that is also simple enough to use for regulatory purposes has not been demonstrated. The objective of this study was to test and compare alternative models of sorption that could be useful in pesticide risk assessment and management. To this end, a database containing the results of batch sorption experiments for pesticides was compiled from published studies in the literature, which placed at least as much emphasis on measurements in subsoil horizons as in topsoil. The database includes 785 data entries from 34 different published studies and for 21 different active substances. Overall, the apparent koc value, koc(app), roughly doubled as the soil organic carbon content decreased by a factor of ten. Nevertheless, in nearly half of the individual datasets, a constant koc value proved to be an adequate model. Further analysis showed that significant increases in koc(app) in subsoil were found primarily for the more weakly adsorbing compounds (koc values
Accelerating semantic graph databases on commodity clusters
Morari, Alessandro; Castellana, Vito G.; Haglin, David J.; Feo, John T.; Weaver, Jesse R.; Tumeo, Antonino; Villa, Oreste
2013-10-06
We are developing a full software system for accelerating semantic graph databases on commodity cluster that scales to hundreds of nodes while maintaining constant query throughput. Our framework comprises a SPARQL to C++ compiler, a library of parallel graph methods and a custom multithreaded runtime layer, which provides a Partitioned Global Address Space (PGAS) programming model with fork/join parallelism and automatic load balancing over a commodity clusters. We present preliminary results for the compiler and for the runtime.
Capacitated max -Batching with Interval Graph Compatibilities
NASA Astrophysics Data System (ADS)
Nonner, Tim
We consider the problem of partitioning interval graphs into cliques of bounded size. Each interval has a weight, and the weight of a clique is the maximum weight of any interval in the clique. This natural graph problem can be interpreted as a batch scheduling problem. Solving a long-standing open problem, we show NP-hardness, even if the bound on the clique sizes is constant. Moreover, we give a PTAS based on a novel dynamic programming technique for this case.
NASA Astrophysics Data System (ADS)
Beeken, Paul
2014-11-01
Graphing is an essential skill that forms the foundation of any physical science.1 Understanding the relationships between measurements ultimately determines which modeling equations are successful in predicting observations.2 Over the years, science and math teachers have approached teaching this skill with a variety of techniques. For secondary school instruction, the job of graphing skills falls heavily on physics teachers. By virtue of the nature of the topics we cover, it is our mission to develop this skill to the fine art that it is.
Threshold Graph Limits and Random Threshold Graphs
Diaconis, Persi; Holmes, Susan; Janson, Svante
2010-01-01
We study the limit theory of large threshold graphs and apply this to a variety of models for random threshold graphs. The results give a nice set of examples for the emerging theory of graph limits. PMID:20811581
ERIC Educational Resources Information Center
Beeken, Paul
2014-01-01
Graphing is an essential skill that forms the foundation of any physical science. Understanding the relationships between measurements ultimately determines which modeling equations are successful in predicting observations. Over the years, science and math teachers have approached teaching this skill with a variety of techniques. For secondary…
Sukumar, Sreenivas R.; Hong, Seokyong; Lee, Sangkeun; Lim, Seung-Hwan
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.)
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.
GraphMeta: Managing HPC Rich Metadata in Graphs
Dai, Dong; Chen, Yong; Carns, Philip; Jenkins, John; Zhang, Wei; Ross, Robert
2016-01-01
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 introduces 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.
NASA Astrophysics Data System (ADS)
Warchalowski, Wiktor; Krawczyk, Malgorzata J.
2017-03-01
We found the Lindenmayer systems for line graphs built on selected fractals. We show that the fractal dimension of such obtained graphs in all analysed cases is the same as for their original graphs. Both for the original graphs and for their line graphs we identified classes of nodes which reflect symmetry of the graph.
Teaching and Assessing Graphing Using Active Learning
ERIC Educational Resources Information Center
McFarland, Jenny
2010-01-01
As a college biology instructor, I often see graphs in lab reports that do not meet my expectations. I also observe that many college students do not always adequately differentiate between good and poor (or misleading) graphs. The activity described in this paper is the result of my work with students to improve their graphing literacy. The…
NASA Astrophysics Data System (ADS)
Fang, Kuai; Shen, Chaopeng; Fisher, Joshua B.; Niu, Jie
2016-07-01
The Budyko hypothesis provides a first-order estimate of water partitioning into runoff (Q) and evapotranspiration (E). Observations, however, often show significant departures from the Budyko curve; moreover, past improvements to Budyko curve tend to lose predictive power when migrated between regions or to small scales. Here to estimate departures from the Budyko curve, we use hydrologic signatures extracted from Gravity Recovery And Climate Experiment (GRACE) terrestrial water storage anomalies. The signatures include GRACE amplitude as a fraction of precipitation (A/P), interannual variability, and 1-month lag autocorrelation. We created a group of linear models embodying two alternate hypotheses that departures can be predicted by (a) Taylor series expansion based on the deviation of physical characteristics (seasonality, snow fraction, and vegetation index) from reference conditions and (b) surrogate indicators covarying with E, e.g., A/P. These models are fitted using a mesoscale USA data set (HUC4) and then evaluated using world data sets and USA basins <1 × 105 km2. The model with A/P could reduce error by 50% compared to Budyko itself. We found that seasonality and fraction of precipitation as snow account for a major portion of the predictive power of A/P, while the remainder is attributed to unexplained basin characteristics. When migrated to a global data set, type b models performed better than type a. This contrast in transferability is argued to be due to data set limitations and catchment coevolution. The GRACE-based correction performs well for USA basins >1000 km2 and, according to comparison with other global data sets, is suitable for data fusion purposes, with GRACE error as estimates of uncertainty.
Optimal Clustering in Graphs with Weighted Edges: A Unified Approach to the Threshold Problem.
ERIC Educational Resources Information Center
Goetschel, Roy; Voxman, William
1987-01-01
Relations on a finite set V are viewed as weighted graphs. Using the language of graph theory, two methods of partitioning V are examined: selecting threshold values and applying them to a maximal weighted spanning forest, and using a parametric linear program to obtain a most adhesive partition. (Author/EM)
NASA Astrophysics Data System (ADS)
Feldman, Michal; Tennenholtz, Moshe
We introduce partition equilibrium and study its existence in resource selection games (RSG). In partition equilibrium the agents are partitioned into coalitions, and only deviations by the prescribed coalitions are considered. This is in difference to the classical concept of strong equilibrium according to which any subset of the agents may deviate. In resource selection games, each agent selects a resource from a set of resources, and its payoff is an increasing (or non-decreasing) function of the number of agents selecting its resource. While it has been shown that strong equilibrium exists in resource selection games, these games do not possess super-strong equilibrium, in which a fruitful deviation benefits at least one deviator without hurting any other deviator, even in the case of two identical resources with increasing cost functions. Similarly, strong equilibrium does not exist for that restricted two identical resources setting when the game is played repeatedly. We prove that for any given partition there exists a super-strong equilibrium for resource selection games of identical resources with increasing cost functions; we also show similar existence results for a variety of other classes of resource selection games. For the case of repeated games we identify partitions that guarantee the existence of strong equilibrium. Together, our work introduces a natural concept, which turns out to lead to positive and applicable results in one of the basic domains studied in the literature.
Martínez-García, E; Dadi, T; Rubio, E; García-Morote, F A; Andrés-Abellán, M; López-Serrano, F R
2017-02-15
Total wood CO2 efflux (Rw) varies vertically within individual trees, and leaves experience large variations in foliar respiration (Rf) rates over their life spans and during daily periods. Therefore, accurate sampling approaches are required to improve aboveground autotrophic respiration (RAa) estimations in stand-scale carbon cycling studies. We scaled-up Rw (comprising stem and branch CO2 efflux; ES and EB, respectively) and Rf from biometric and flux-chamber measurements taken between 2011 and 2013 in a Spanish black pine (Pinus nigra Arn. ssp. salzmannii) forest at an unburnt (UB) site and a low burn-severity (LS) site. We measured seasonal ES at breast height (1.30m) on 9 trees at each site, which was also vertically examined on 5 of those trees. We also measured seasonal Rf in current- and previous-year needles on 3 trees at each site, and quantified Rf variations in darkness and light. Finally, we compared complex and simple scale-up methods which did or did not account for the vertical variation in Rw and the effects of leaf ageing and light inhibition on Rf, respectively. The simple methods underestimated the annual stand-level stem, branch, and total wood respiration ≈35%, 55%, and 41%, respectively, and overestimated annual stand-level whole-canopy foliage respiration ≈43% at both sites. Both methods provided similar annual stand-level RAa estimates, although the complex methods improved estimations of the relative contribution of RAa components. Thus, based on the complex methods the mean annual RAa at the stand-level was 4.53±0.25 and 4.45±0.12MgCha(-1)year(-1) at the UB and LS sites, respectively. Our data also confirmed that the low-severity fire did not alter the RAa rates. Collectively, this study reveals that complex approaches, applicable in other forest ecosystems, enhance the accuracy of partitioning RAa sources by reducing the error in scaling-up in chamber-based measurements.
Network reconstruction via graph blending
NASA Astrophysics Data System (ADS)
Estrada, Rolando
2016-05-01
Graphs estimated from empirical data are often noisy and incomplete due to the difficulty of faithfully observing all the components (nodes and edges) of the true graph. This problem is particularly acute for large networks where the number of components may far exceed available surveillance capabilities. Errors in the observed graph can render subsequent analyses invalid, so it is vital to develop robust methods that can minimize these observational errors. Errors in the observed graph may include missing and spurious components, as well fused (multiple nodes are merged into one) and split (a single node is misinterpreted as many) nodes. Traditional graph reconstruction methods are only able to identify missing or spurious components (primarily edges, and to a lesser degree nodes), so we developed a novel graph blending framework that allows us to cast the full estimation problem as a simple edge addition/deletion problem. Armed with this framework, we systematically investigate the viability of various topological graph features, such as the degree distribution or the clustering coefficients, and existing graph reconstruction methods for tackling the full estimation problem. Our experimental results suggest that incorporating any topological feature as a source of information actually hinders reconstruction accuracy. We provide a theoretical analysis of this phenomenon and suggest several avenues for improving this estimation problem.
Zhang, Feng; Liao, Xiangke; Peng, Shaoliang; Cui, Yingbo; Wang, Bingqiang; Zhu, Xiaoqian; Liu, Jie
2016-06-01
' The de novo assembly of DNA sequences is increasingly important for biological researches in the genomic era. After more than one decade since the Human Genome Project, some challenges still exist and new solutions are being explored to improve de novo assembly of genomes. String graph assembler (SGA), based on the string graph theory, is a new method/tool developed to address the challenges. In this paper, based on an in-depth analysis of SGA we prove that the SGA-based sequence de novo assembly is an NP-complete problem. According to our analysis, SGA outperforms other similar methods/tools in memory consumption, but costs much more time, of which 60-70 % is spent on the index construction. Upon this analysis, we introduce a hybrid parallel optimization algorithm and implement this algorithm in the TianHe-2's parallel framework. Simulations are performed with different datasets. For data of small size the optimized solution is 3.06 times faster than before, and for data of middle size it's 1.60 times. The results demonstrate an evident performance improvement, with the linear scalability for parallel FM-index construction. This results thus contribute significantly to improving the efficiency of de novo assembly of DNA sequences.
Bipartite Graphs for Visualization Analysis of Microbiome Data
Sedlar, Karel; Videnska, Petra; Skutkova, Helena; Rychlik, Ivan; Provaznik, Ivo
2016-01-01
Visualization analysis plays an important role in metagenomics research. Proper and clear visualization can help researchers get their first insights into data and by selecting different features, also revealing and highlighting hidden relationships and drawing conclusions. To prevent the resulting presentations from becoming chaotic, visualization techniques have to properly tackle the high dimensionality of microbiome data. Although a number of different methods based on dimensionality reduction, correlations, Venn diagrams, and network representations have already been published, there is still room for further improvement, especially in the techniques that allow visual comparison of several environments or developmental stages in one environment. In this article, we represent microbiome data by bipartite graphs, where one partition stands for taxa and the other stands for samples. We demonstrated that community detection is independent of taxonomical level. Moreover, focusing on higher taxonomical levels and the appropriate merging of samples greatly helps improving graph organization and makes our presentations clearer than other graph and network visualizations. Capturing labels in the vertices also brings the possibility of clearly comparing two or more microbial communities by showing their common and unique parts. PMID:27279729
A Partition Formula for Fibonacci Numbers
NASA Astrophysics Data System (ADS)
Fahr, Philipp; Ringerl, Claus Michael
2008-02-01
We present a partition formula for the even index Fibonacci numbers. The formula is motivated by the appearance of these Fibonacci numbers in the representation theory of the socalled 3-Kronecker quiver, i.e., the oriented graph with two vertices and three arrows in the same direction.
Chiou, C.T.; Schmedding, D.W.; Manes, M.
2005-01-01
A volume-fraction-based solvent-water partition model for dilute solutes, in which the partition coefficient shows a dependence on solute molar volume (V??), is adapted to predict the octanol-water partition coefficient (K ow) from the liquid or supercooled-liquid solute water solubility (Sw), or vice versa. The established correlation is tested for a wide range of industrial compounds and pesticides (e.g., halogenated aliphatic hydrocarbons, alkylbenzenes, halogenated benzenes, ethers, esters, PAHs, PCBs, organochlorines, organophosphates, carbamates, and amidesureas-triazines), which comprise a total of 215 test compounds spanning about 10 orders of magnitude in Sw and 8.5 orders of magnitude in Kow. Except for phenols and alcohols, which require special considerations of the Kow data, the correlation predicts the Kow within 0.1 log units for most compounds, much independent of the compound type or the magnitude in K ow. With reliable Sw and V data for compounds of interest, the correlation provides an effective means for either predicting the unavailable log Kow values or verifying the reliability of the reported log Kow data. ?? 2005 American Chemical Society.
Parallel hypergraph partitioning for scientific computing.
Heaphy, Robert; Devine, Karen Dragon; Catalyurek, Umit; Bisseling, Robert; Hendrickson, Bruce Alan; Boman, Erik Gunnar
2005-07-01
Graph partitioning is often used for load balancing in parallel computing, but it is known that hypergraph partitioning has several advantages. First, hypergraphs more accurately model communication volume, and second, they are more expressive and can better represent nonsymmetric problems. Hypergraph partitioning is particularly suited to parallel sparse matrix-vector multiplication, a common kernel in scientific computing. We present a parallel software package for hypergraph (and sparse matrix) partitioning developed at Sandia National Labs. The algorithm is a variation on multilevel partitioning. Our parallel implementation is novel in that it uses a two-dimensional data distribution among processors. We present empirical results that show our parallel implementation achieves good speedup on several large problems (up to 33 million nonzeros) with up to 64 processors on a Linux cluster.
Mielke, Steven L. E-mail: truhlar@umn.edu; Truhlar, Donald G. E-mail: truhlar@umn.edu
2015-01-28
We present an improved version of our “path-by-path” enhanced same path extrapolation scheme for Feynman path integral (FPI) calculations that permits rapid convergence with discretization errors ranging from O(P{sup −6}) to O(P{sup −12}), where P is the number of path discretization points. We also present two extensions of our importance sampling and stratified sampling schemes for calculating vibrational–rotational partition functions by the FPI method. The first is the use of importance functions for dihedral angles between sets of generalized Jacobi coordinate vectors. The second is an extension of our stratification scheme to allow some strata to be defined based only on coordinate information while other strata are defined based on both the geometry and the energy of the centroid of the Feynman path. These enhanced methods are applied to calculate converged partition functions by FPI methods, and these results are compared to ones obtained earlier by vibrational configuration interaction (VCI) calculations, both calculations being for the Jordan–Gilbert potential energy surface. The earlier VCI calculations are found to agree well (within ∼1.5%) with the new benchmarks. The FPI partition functions presented here are estimated to be converged to within a 2σ statistical uncertainty of between 0.04% and 0.07% for the given potential energy surface for temperatures in the range 300–3000 K and are the most accurately converged partition functions for a given potential energy surface for any molecule with five or more atoms. We also tabulate free energies, enthalpies, entropies, and heat capacities.
Mielke, Steven L; Truhlar, Donald G
2015-01-28
We present an improved version of our "path-by-path" enhanced same path extrapolation scheme for Feynman path integral (FPI) calculations that permits rapid convergence with discretization errors ranging from O(P(-6)) to O(P(-12)), where P is the number of path discretization points. We also present two extensions of our importance sampling and stratified sampling schemes for calculating vibrational-rotational partition functions by the FPI method. The first is the use of importance functions for dihedral angles between sets of generalized Jacobi coordinate vectors. The second is an extension of our stratification scheme to allow some strata to be defined based only on coordinate information while other strata are defined based on both the geometry and the energy of the centroid of the Feynman path. These enhanced methods are applied to calculate converged partition functions by FPI methods, and these results are compared to ones obtained earlier by vibrational configuration interaction (VCI) calculations, both calculations being for the Jordan-Gilbert potential energy surface. The earlier VCI calculations are found to agree well (within ∼1.5%) with the new benchmarks. The FPI partition functions presented here are estimated to be converged to within a 2σ statistical uncertainty of between 0.04% and 0.07% for the given potential energy surface for temperatures in the range 300-3000 K and are the most accurately converged partition functions for a given potential energy surface for any molecule with five or more atoms. We also tabulate free energies, enthalpies, entropies, and heat capacities.
Molecular graph convolutions: moving beyond fingerprints.
Kearnes, Steven; McCloskey, Kevin; Berndl, Marc; Pande, Vijay; Riley, Patrick
2016-08-01
Molecular "fingerprints" encoding structural information are the workhorse of cheminformatics and machine learning in drug discovery applications. However, fingerprint representations necessarily emphasize particular aspects of the molecular structure while ignoring others, rather than allowing the model to make data-driven decisions. We describe molecular graph convolutions, a machine learning architecture for learning from undirected graphs, specifically small molecules. Graph convolutions use a simple encoding of the molecular graph-atoms, bonds, distances, etc.-which allows the model to take greater advantage of information in the graph structure. Although graph convolutions do not outperform all fingerprint-based methods, they (along with other graph-based methods) represent a new paradigm in ligand-based virtual screening with exciting opportunities for future improvement.
NASA Technical Reports Server (NTRS)
Gray, Vernon H.
1950-01-01
The effect of modifying the gas passage of hollow metal airfoils by the additIon of internal fins and partitions was experimentally investigated and comparisons were made among a basic unfinned airfoil section and two airfoil designs having metal fins attached at the leading edge of the internal gas passage. An analysis considering the effects of heat conduction in the airfoil metal was made to determine the internal modification effectiveness that may be obtained in gas-heated components, such as turbojet-inlet guide vanes, support struts, hollow propeller blades, arid. thin wings. Over a wide range of heated-gas flow and tunnel-air velocity, the increase In surface-heating rates with internal finning was marked (up to 3.5 times), with the greatest increase occurring at the leading edge where anti-icing heat requirements are most critical. Variations in the amount and the location of internal finning and. partitioning provided. control over the local rates of surface heat transfer and permitted efficient anti-icing utilization of the gas-stream heat content.
Polania, Jose A; Poschenrieder, Charlotte; Beebe, Stephen; Rao, Idupulapati M
2016-01-01
Common bean (Phaseolus vulgaris L.) is the most important food legume in the diet of poor people in the tropics. Drought causes severe yield loss in this crop. Identification of traits associated with drought resistance contributes to improving the process of generating bean genotypes adapted to these conditions. Field studies were conducted at the International Center for Tropical Agriculture (CIAT), Palmira, Colombia, to determine the relationship between grain yield and different parameters such as effective use of water (EUW), canopy biomass, and dry partitioning indices (pod partitioning index, harvest index, and pod harvest index) in elite lines selected for drought resistance over the past decade. Carbon isotope discrimination (CID) was used for estimation of water use efficiency (WUE). The main objectives were: (i) to identify specific morpho-physiological traits that contribute to improved resistance to drought in lines developed over several cycles of breeding and that could be useful as selection criteria in breeding; and (ii) to identify genotypes with desirable traits that could serve as parents in the corresponding breeding programs. A set of 36 bean genotypes belonging to the Middle American gene pool were evaluated under field conditions with two levels of water supply (irrigated and drought) over two seasons. Eight bean lines (NCB 280, NCB 226, SEN 56, SCR 2, SCR 16, SMC 141, RCB 593, and BFS 67) were identified as resistant to drought stress. Resistance to terminal drought stress was positively associated with EUW combined with increased dry matter partitioned to pod and seed production and negatively associated with days to flowering and days to physiological maturity. Differences in genotypic response were observed between grain CID and grain yield under irrigated and drought stress. Based on phenotypic differences in CID, leaf stomatal conductance, canopy biomass, and grain yield under drought stress, the lines tested were classified into two
Polania, Jose A.; Poschenrieder, Charlotte; Beebe, Stephen; Rao, Idupulapati M.
2016-01-01
Common bean (Phaseolus vulgaris L.) is the most important food legume in the diet of poor people in the tropics. Drought causes severe yield loss in this crop. Identification of traits associated with drought resistance contributes to improving the process of generating bean genotypes adapted to these conditions. Field studies were conducted at the International Center for Tropical Agriculture (CIAT), Palmira, Colombia, to determine the relationship between grain yield and different parameters such as effective use of water (EUW), canopy biomass, and dry partitioning indices (pod partitioning index, harvest index, and pod harvest index) in elite lines selected for drought resistance over the past decade. Carbon isotope discrimination (CID) was used for estimation of water use efficiency (WUE). The main objectives were: (i) to identify specific morpho-physiological traits that contribute to improved resistance to drought in lines developed over several cycles of breeding and that could be useful as selection criteria in breeding; and (ii) to identify genotypes with desirable traits that could serve as parents in the corresponding breeding programs. A set of 36 bean genotypes belonging to the Middle American gene pool were evaluated under field conditions with two levels of water supply (irrigated and drought) over two seasons. Eight bean lines (NCB 280, NCB 226, SEN 56, SCR 2, SCR 16, SMC 141, RCB 593, and BFS 67) were identified as resistant to drought stress. Resistance to terminal drought stress was positively associated with EUW combined with increased dry matter partitioned to pod and seed production and negatively associated with days to flowering and days to physiological maturity. Differences in genotypic response were observed between grain CID and grain yield under irrigated and drought stress. Based on phenotypic differences in CID, leaf stomatal conductance, canopy biomass, and grain yield under drought stress, the lines tested were classified into two
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…
Zhou, Feng; de la Torre, Fernando
2015-11-19
Graph matching (GM) is a fundamental problem in computer science, and it plays a central role to solve correspondence problems in computer vision. GM problems that incorporate pairwise constraints can be formulated as a quadratic assignment problem (QAP). Although widely used, solving the correspondence problem through GM has two main limitations: (1) the QAP is NP-hard and difficult to approximate; (2) GM algorithms do not incorporate geometric constraints between nodes that are natural in computer vision problems. To address aforementioned problems, this paper proposes factorized graph matching (FGM). FGM factorizes the large pairwise affinity matrix into smaller matrices that encode the local structure of each graph and the pairwise affinity between edges. Four are the benefits that follow from this factorization: (1) There is no need to compute the costly (in space and time) pairwise affinity matrix; (2) The factorization allows the use of a path-following optimization algorithm, that leads to improved optimization strategies and matching performance; (3) Given the factorization, it becomes straight-forward to incorporate geometric transformations (rigid and non-rigid) to the GM problem. (4) Using a matrix formulation for the GM problem and the factorization, it is easy to reveal commonalities and differences between different GM methods. The factorization also provides a clean connection with other matching algorithms such as iterative closest point; Experimental results on synthetic and real databases illustrate how FGM outperforms state-of-the-art algorithms for GM. The code is available at http://humansensing.cs.cmu.edu/fgm.
Huang, Xiaoke; Zhao, Ye; Yang, Jing; Zhang, Chong; Ma, Chao; Ye, Xinyue
2016-01-01
We propose TrajGraph, a new visual analytics method, for studying urban mobility patterns by integrating graph modeling and visual analysis with taxi trajectory data. A special graph is created to store and manifest real traffic information recorded by taxi trajectories over city streets. It conveys urban transportation dynamics which can be discovered by applying graph analysis algorithms. To support interactive, multiscale visual analytics, a graph partitioning algorithm is applied to create region-level graphs which have smaller size than the original street-level graph. Graph centralities, including Pagerank and betweenness, are computed to characterize the time-varying importance of different urban regions. The centralities are visualized by three coordinated views including a node-link graph view, a map view and a temporal information view. Users can interactively examine the importance of streets to discover and assess city traffic patterns. We have implemented a fully working prototype of this approach and evaluated it using massive taxi trajectories of Shenzhen, China. TrajGraph's capability in revealing the importance of city streets was evaluated by comparing the calculated centralities with the subjective evaluations from a group of drivers in Shenzhen. Feedback from a domain expert was collected. The effectiveness of the visual interface was evaluated through a formal user study. We also present several examples and a case study to demonstrate the usefulness of TrajGraph in urban transportation analysis.
Computing the isoperimetric number of a graph
Golovach, P.A.
1995-01-01
Let G be a finite graph. Denote by {partial_derivative}X, where X {contained_in} VG, the set of edges of the graph G with one end in X and the other end in the set VG{backslash}X. The ratio i(G) = min {vert_bar}{vert_bar}X{vert_bar}/{vert_bar}X{vert_bar}, where the minimum is over all nonempty subsets X of the set VG such that {vert_bar}X{vert_bar} {le} {vert_bar} VG {vert_bar}/2, is called the isoperimetric number of the graph G. It is easy to see that the isoperimetric number may be used as a {open_quotes}measure of connectivity{close_quotes} of the graph. The problem of determining the isoperimetric number is clearly linked with graph partition problems, which often arise in various applications. The isoperimetric number is also important for studying Riemann surfaces. These and other applications of the isoperimetric number justify the analysis of graphs of this kind. The properties of the isoperimetric number are presented in more detail elsewhere. It is shown elsewhere that the computation of the isoperimetric number is an NP-hard problem for graphs with multiple edges. We will show that the decision problem {open_quotes}given the graph G and two integers s and t decide if i(G) {le} s/t{close_quotes} is NP-complete even for simple graphs with vertex degrees not exceeding 3. Note that the isoperimetric number of a tree can be computed by a known polynomial-time algorithm.
Moren, Alexis; Hampton, David; Diggs, Brian; Kiraly, Laszlo; Fox, Erin; Holcomb, John; Rahbar, Mohammad; Brasel, Karen; Cohen, Mitchell; Bulger, Eileen; Schreiber, Martin
2015-01-01
Background Massive transfusion (MT) is classically defined as >10units of packed RBCs in 24 hours. This fails to capture the most severely injured patients. Extending the prior work of Savage and Rahbar, a rolling hourly rate-based definition of MT may more accurately define critically injured patients requiring early, aggressive resuscitation. Methods The Prospective Observational Multicenter Major Trauma Transfusion (PROMMTT) trial collected data from ten level-1 trauma centers. Patients were placed into rate-based transfusion groups by maximal number of PRBC's transfused in any hour within the first 6 hours. A nonparametric analysis using classification trees partitioned data according to mortality at 24-hours using a predictor variable of maximum number PRBC units transfused in an hour. Dichotomous variables significant in previous scores and models as predictors of MT were used to identify critically ill patients: a positive FAST exam, GCS <8, HR >120, SBP <90, penetrating mechanism of injury, INR >1.5, Hg <11 and BD >5. These critical indicators were then compared among the nodes of the classification tree. Patients omitted included those who did not receive PRBC's (n=24) and those who did not have all 8 critical indicators reported (n=449). Results In a population of 1245 patients, the classification tree included 772 patients. Analysis by recursive partitioning showed increased mortality among patients receiving greater than 13U/hr (73.9%, p<0.01). In those patients receiving ≤13U/hr, mortality was greater in patients who received more than 4U/hr (16.7% vs 6.0%; p<0.01) (Figure 1). Nodal analysis showed the median number of critical indicators for each node were: 3 (2,4) (≤4U/hr), 4(3,5) (>4U/hr and ≤13U/hr) and 5(4,5.5) (>13U/hr). Conclusions A rate-based transfusion definition identifies a difference in mortality in patients who receive >4U/hr of PRBC's. Redefining MT to >4U/hr allows early identification of patients with a significant mortality
Spectral graph optimization for instance reduction.
Nikolaidis, Konstantinos; Rodriguez-Martinez, Eduardo; Goulermas, John Yannis; Wu, Q H
2012-07-01
The operation of instance-based learning algorithms is based on storing a large set of prototypes in the system's database. However, such systems often experience issues with storage requirements, sensitivity to noise, and computational complexity, which result in high search and response times. In this brief, we introduce a novel framework that employs spectral graph theory to efficiently partition the dataset to border and internal instances. This is achieved by using a diverse set of border-discriminating features that capture the local friend and enemy profiles of the samples. The fused information from these features is then used via graph-cut modeling approach to generate the final dataset partitions of border and nonborder samples. The proposed method is referred to as the spectral instance reduction (SIR) algorithm. Experiments with a large number of datasets show that SIR performs competitively compared to many other reduction algorithms, in terms of both objectives of classification accuracy and data condensation.
Intrinsic graph structure estimation using graph Laplacian.
Noda, Atsushi; Hino, Hideitsu; Tatsuno, Masami; Akaho, Shotaro; Murata, Noboru
2014-07-01
A graph is a mathematical representation of a set of variables where some pairs of the variables are connected by edges. Common examples of graphs are railroads, the Internet, and neural networks. It is both theoretically and practically important to estimate the intensity of direct connections between variables. In this study, a problem of estimating the intrinsic graph structure from observed data is considered. The observed data in this study are a matrix with elements representing dependency between nodes in the graph. The dependency represents more than direct connections because it includes influences of various paths. For example, each element of the observed matrix represents a co-occurrence of events at two nodes or a correlation of variables corresponding to two nodes. In this setting, spurious correlations make the estimation of direct connection difficult. To alleviate this difficulty, a digraph Laplacian is used for characterizing a graph. A generative model of this observed matrix is proposed, and a parameter estimation algorithm for the model is also introduced. The notable advantage of the proposed method is its ability to deal with directed graphs, while conventional graph structure estimation methods such as covariance selections are applicable only to undirected graphs. The algorithm is experimentally shown to be able to identify the intrinsic graph structure.
Molecular graph convolutions: moving beyond fingerprints
NASA Astrophysics Data System (ADS)
Kearnes, Steven; McCloskey, Kevin; Berndl, Marc; Pande, Vijay; Riley, Patrick
2016-08-01
Molecular "fingerprints" encoding structural information are the workhorse of cheminformatics and machine learning in drug discovery applications. However, fingerprint representations necessarily emphasize particular aspects of the molecular structure while ignoring others, rather than allowing the model to make data-driven decisions. We describe molecular graph convolutions, a machine learning architecture for learning from undirected graphs, specifically small molecules. Graph convolutions use a simple encoding of the molecular graph—atoms, bonds, distances, etc.—which allows the model to take greater advantage of information in the graph structure. Although graph convolutions do not outperform all fingerprint-based methods, they (along with other graph-based methods) represent a new paradigm in ligand-based virtual screening with exciting opportunities for future improvement.
Convergence of Mayer and Virial expansions and the Penrose tree-graph identity
NASA Astrophysics Data System (ADS)
Procacci, Aldo; Yuhjtman, Sergio A.
2016-11-01
We establish new lower bounds for the convergence radius of the Mayer series and the Virial series of a continuous particle system interacting via a stable and tempered pair potential. Our bounds considerably improve those given by Penrose (J Math Phys 4:1312, 1963) and Ruelle (Ann Phys 5:109-120, 1963) for the Mayer series and by Lebowitz and Penrose (J Math Phys 7:841-847, 1964) for the Virial series. To get our results, we exploit the tree-graph identity given by Penrose (Statistical mechanics: foundations and applications. Benjamin, New York, 1967) using a new partition scheme based on minimum spanning trees.
Li, Qu; Yao, Min; Yang, Jianhua; Xu, Ning
2014-01-01
Online friend recommendation is a fast developing topic in web mining. In this paper, we used SVD matrix factorization to model user and item feature vector and used stochastic gradient descent to amend parameter and improve accuracy. To tackle cold start problem and data sparsity, we used KNN model to influence user feature vector. At the same time, we used graph theory to partition communities with fairly low time and space complexity. What is more, matrix factorization can combine online and offline recommendation. Experiments showed that the hybrid recommendation algorithm is able to recommend online friends with good accuracy.
Convergence of Mayer and Virial expansions and the Penrose tree-graph identity
NASA Astrophysics Data System (ADS)
Procacci, Aldo; Yuhjtman, Sergio A.
2017-01-01
We establish new lower bounds for the convergence radius of the Mayer series and the Virial series of a continuous particle system interacting via a stable and tempered pair potential. Our bounds considerably improve those given by Penrose (J Math Phys 4:1312, 1963) and Ruelle (Ann Phys 5:109-120, 1963) for the Mayer series and by Lebowitz and Penrose (J Math Phys 7:841-847, 1964) for the Virial series. To get our results, we exploit the tree-graph identity given by Penrose (Statistical mechanics: foundations and applications. Benjamin, New York, 1967) using a new partition scheme based on minimum spanning trees.
Labussière, Etienne; Dubois, Serge; van Milgen, Jaap; Noblet, Jean
2013-01-01
In growing pigs, the feed cost accounts for more than 60% of total production costs. The determination of efficiency of energy utilization through calorimetry measurements is of importance to sustain suitable feeding practice. The objective of this paper is to describe a methodology to correct daily heat production (HP) obtained from measurements in respiration chamber for the difference in energy expenditure related to physical activity between animals. The calculation is based on a preliminary published approach for partitioning HP between HP due to physical activity (AHP), thermic effect of feeding (TEF) and basal metabolic rate (fasting HP; FHP). Measurements with male growing pigs [mean body weight (BW): 115 kg] which were surgically castrated (SC), castrated through immunization against GnRH (IC), or kept as entire male (EM) were used as an example. Animals were fed the same diet ad-libitum and were housed individually in two 12-m3 open-circuit respiration chambers during 6 days when fed ad-libitum and one supplementary day when fasted. Physical activity was recorded through interruption of an infrared beam to detect standing and lying positions and with force transducers that recorded the mechanical force the animal exerted on the floor of the cage. Corrected AHP (AHPc), TEF (TEFc), and HP (HPc) were calculated to standardize the level of AHP between animals, assuming that the ratio between AHPc and ME intake should be constant. Inefficiency of energy utilization (sum of AHPc and TEFc) was lower than the inefficiency estimated from the slope of the classical relationship between HPc and ME intake but was associated with higher requirements for maintenance. Results indicate that EM pigs had higher FHP but lower TEFc than IC and SC pigs. These results agree with the higher contents in viscera of EM pigs that stimulate their basal metabolic rate and with the reduced utilization of dietary protein to provide energy for maintenance energy requirements and fat
Methods for fine registration of cadastre graphs to images.
Trias-Sanz, Roger; Pierrot-Deseilligny, Marc; Louchet, Jean; Stamon, Georges
2007-11-01
We propose two algorithms to match edges in a geometrically-imprecise graph to geometrically-precise strong boundaries in an image, where the graph is meant to give an a priori partition of the image into objects. This can be used to partition an image into objects described by imprecise external data, and thus to simplify the segmentation problem. We apply them to the problem of registering cadastre data to georeferenced aerial images, thus correcting the lack of geometrical detail of the cadastre data, and the fact that cadastre data gives information of a different nature than that found in images (fiscal information as opposed to actual land use).
Cognitive Aids for Guiding Graph Comprehension
ERIC Educational Resources Information Center
Mautone, Patricia D.; Mayer, Richard E.
2007-01-01
This study sought to improve students' comprehension of scientific graphs by adapting scaffolding techniques used to aid text comprehension. In 3 experiments involving 121 female and 88 male college students, some students were shown cognitive aids prior to viewing 4 geography graphs whereas others were not; all students were then asked to write a…
Identities between dimer partition functions on different surfaces
NASA Astrophysics Data System (ADS)
Cimasoni, David; Pham, Anh Minh
2016-10-01
Given a weighted graph G embedded in a non-orientable surface Σ , one can consider the corresponding weighted graph \\widetilde{G} embedded in the so-called orientation cover \\widetildeΣ of Σ . We prove identities relating twisted partition functions of the dimer model on these two graphs. When Σ is the Möbius strip or the Klein bottle, then \\widetildeΣ is the cylinder or the torus, respectively, and under some natural assumptions, these identities imply relations between the genuine dimer partition functions Z(G) and Z(\\widetilde{G}) . For example, we show that if G is a locally but not globally bipartite graph embedded in the Möbius strip, then Z(\\widetilde{G}) is equal to the square of Z(G). This extends results for the square lattice previously obtained by various authors.
Ensemble nonequivalence in random graphs with modular structure
NASA Astrophysics Data System (ADS)
Garlaschelli, Diego; den Hollander, Frank; Roccaverde, Andrea
2017-01-01
Breaking of equivalence between the microcanonical ensemble and the canonical ensemble, describing a large system subject to hard and soft constraints, respectively, was recently shown to occur in large random graphs. Hard constraints must be met by every graph, soft constraints must be met only on average, subject to maximal entropy. In Squartini, de Mol, den Hollander and Garlaschelli (2015 New J. Phys. 17 023052) it was shown that ensembles of random graphs are nonequivalent when the degrees of the nodes are constrained, in the sense of a non-zero limiting specific relative entropy as the number of nodes diverges. In that paper, the nodes were placed either on a single layer (uni-partite graphs) or on two layers (bi-partite graphs). In the present paper we consider an arbitrary number of intra-connected and inter-connected layers, thus allowing for modular graphs with a multi-partite, multiplex, time-varying, block-model or community structure. We give a full classification of ensemble equivalence in the sparse regime, proving that breakdown occurs as soon as the number of local constraints (i.e. the number of constrained degrees) is extensive in the number of nodes, irrespective of the layer structure. In addition, we derive an explicit formula for the specific relative entropy and provide an interpretation of this formula in terms of Poissonisation of the degrees.
ERIC Educational Resources Information Center
Albers, Craig A.; Hoffman, Alicia
2012-01-01
The increasing numbers of English language learners who are enrolled in schools across the nation, combined with the escalating academic demands placed on all students, warrant the evaluation of instructional strategies designed to improve English language learners' reading performance. In this study, the authors used a multiple baseline design…
On molecular graph comparison.
Melo, Jenny A; Daza, Edgar
2011-06-01
Since the last half of the nineteenth century, molecular graphs have been present in several branches of chemistry. When used for molecular structure representation, they have been compared after mapping the corresponding graphs into mathematical objects. However, direct molecular comparison of molecular graphs is a research field less explored. The goal of this mini-review is to show some distance and similarity coefficients which were proposed to directly compare molecular graphs or which could be useful to do so.
A Pfaffian Formula for Monomer-Dimer Partition Functions
NASA Astrophysics Data System (ADS)
Giuliani, Alessandro; Jauslin, Ian; Lieb, Elliott H.
2016-04-01
We consider the monomer-dimer partition function on arbitrary finite planar graphs and arbitrary monomer and dimer weights, with the restriction that the only non-zero monomer weights are those on the boundary. We prove a Pfaffian formula for the corresponding partition function. As a consequence of this result, multipoint boundary monomer correlation functions at close packing are shown to satisfy fermionic statistics. Our proof is based on the celebrated Kasteleyn theorem, combined with a theorem on Pfaffians proved by one of the authors, and a careful labeling and directing procedure of the vertices and edges of the graph.
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…
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…
Multipartite entanglement in four-qubit graph states
NASA Astrophysics Data System (ADS)
Jafarpour, Mojtaba; Assadi, Leila
2016-03-01
We consider a compendium of the non-trivial four-qubit graphs, derive their corresponding quantum states and classify them into equivalent classes. We use Meyer-Wallach measure and its generalizations to study block-partition and global entanglement in these states. We obtain several entanglement quantities for each graph state, which present a comprehensive characterization of the entanglement properties of the latter. As a result, a number of correlations between the graph structure and multipartite entanglement quantities have also been established.
Parallel algorithms for finding cliques in a graph
NASA Astrophysics Data System (ADS)
Szabó, S.
2011-01-01
A clique is a subgraph in a graph that is complete in the sense that each two of its nodes are connected by an edge. Finding cliques in a given graph is an important procedure in discrete mathematical modeling. The paper will show how concepts such as splitting partitions, quasi coloring, node and edge dominance are related to clique search problems. In particular we will discuss the connection with parallel clique search algorithms. These concepts also suggest practical guide lines to inspect a given graph before starting a large scale search.
Can Comparison of Contrastive Examples Facilitate Graph Understanding?
ERIC Educational Resources Information Center
Smith, Linsey A.; Gentner, Dedre
2011-01-01
The authors explore the role of comparison in improving graph fluency. The ability to use graphs fluently is crucial for STEM achievement, but graphs are challenging to interpret and produce because they often involve integration of multiple variables, continuous change in variables over time, and omission of certain details in order to highlight…
Partitioning Rectangular and Structurally Nonsymmetric Sparse Matrices for Parallel Processing
B. Hendrickson; T.G. Kolda
1998-09-01
A common operation in scientific computing is the multiplication of a sparse, rectangular or structurally nonsymmetric matrix and a vector. In many applications the matrix- transpose-vector product is also required. This paper addresses the efficient parallelization of these operations. We show that the problem can be expressed in terms of partitioning bipartite graphs. We then introduce several algorithms for this partitioning problem and compare their performance on a set of test matrices.
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.
Wong, Pak C.; Mackey, Patrick S.; Perrine, Kenneth A.; Foote, Harlan P.; Thomas, James J.
2008-12-23
Methods for visualizing a graph by automatically drawing elements of the graph as labels are disclosed. In one embodiment, the method comprises receiving node information and edge information from an input device and/or communication interface, constructing a graph layout based at least in part on that information, wherein the edges are automatically drawn as labels, and displaying the graph on a display device according to the graph layout. In some embodiments, the nodes are automatically drawn as labels instead of, or in addition to, the label-edges.
Coen, Paul M.; Menshikova, Elizabeth V.; Distefano, Giovanna; Zheng, Donghai; Tanner, Charles J.; Standley, Robert A.; Helbling, Nicole L.; Dubis, Gabriel S.; Ritov, Vladimir B.; Xie, Hui; Desimone, Marisa E.; Smith, Steven R.; Stefanovic-Racic, Maja; Toledo, Frederico G.S.; Houmard, Joseph A.
2015-01-01
Both Roux-en-Y gastric bypass (RYGB) surgery and exercise can improve insulin sensitivity in individuals with severe obesity. However, the impact of RYGB with or without exercise on skeletal muscle mitochondria, intramyocellular lipids, and insulin sensitivity index (SI) is unknown. We conducted a randomized exercise trial in patients (n = 101) who underwent RYGB surgery and completed either a 6-month moderate exercise (EX) or a health education control (CON) intervention. SI was determined by intravenous glucose tolerance test. Mitochondrial respiration and intramyocellular triglyceride, sphingolipid, and diacylglycerol content were measured in vastus lateralis biopsy specimens. We found that EX provided additional improvements in SI and that only EX improved cardiorespiratory fitness, mitochondrial respiration and enzyme activities, and cardiolipin profile with no change in mitochondrial content. Muscle triglycerides were reduced in type I fibers in CON, and sphingolipids decreased in both groups, with EX showing a further reduction in a number of ceramide species. In conclusion, exercise superimposed on bariatric surgery–induced weight loss enhances mitochondrial respiration, induces cardiolipin remodeling, reduces specific sphingolipids, and provides additional improvements in insulin sensitivity. PMID:26293505
Morrish, Jenna L E; Daugulis, Andrew J
2008-12-01
In an effort to improve reactor performance and process operability, the microbial biotransformation of (-)-trans-carveol to (R)-(-)-carvone by hydrophobic Rhodococcus erythropolis DCL14 was carried out in a two phase partitioning bioreactor (TPPB) with solid polymer beads acting as the partitioning phase. Previous work had demonstrated that the substrate and product become inhibitory to the organism at elevated aqueous concentrations and the use of an immiscible second phase in the bioreactor was intended to provide a reservoir for substrates to be delivered to the aqueous phase based on the metabolic rate of the cells, while also acting as a sink to uptake the product as it is produced. The biotransformation was previously undertaken in a two liquid phase TPPB with 1-dodecene and with silicone oil as the immiscible second phase and, although improvement in the reactor performance was obtained relative to a single phase system, the hydrophobic nature of the organism caused the formation of severe emulsions leading to significant operational challenges. In the present work, eight types of polymer beads were screened for their suitability for use in a solid-liquid TPPB for this biotransformation. The use of selected solid polymer beads as the second phase completely prevented emulsion formation and therefore improved overall operability of the reactor. Three modes of solid-liquid TPPB operation were considered: the use of a single polymer bead type (styrene/butadiene copolymer) in the reactor, the use of a mixture of polymer beads in the reactor (styrene/butadiene copolymer plus Hytrel(R) 8206), and the use of one type of polymer beads in the reactor (styrene/butadiene copolymer), and another bead type (Hytrel(R) 8206) in an external column through which fermentation medium was recirculated. This last configuration achieved the best reactor performance with 7 times more substrate being added throughout the biotransformation relative to a single aqueous phase
A Review of Big Graph Mining Research
NASA Astrophysics Data System (ADS)
Atastina, I.; Sitohang, B.; Saptawati, G. A. P.; Moertini, V. S.
2017-03-01
Big Graph Mining” is a continuously developing research that was started in 2009 until now. After 7 years, there are many researches that put this topic as the main concern. However, there is no mapping or summary concerning the important issues and solutions to explain this topic. This paper contains a summary of researches that have been conducted since 2009. The result is grouped based on the algorithms, built system and also preprocess techniques that have been developed. Based on survey, there are 11 algorithms and 6 distributed systems to analyse the Big Graph have been improved. While improved pre-process algorithm only covers: sampling and compression technique. These improving algorithms are usually aimed to frequent sub graphs discovery, whereas slightly those of is aimed to cluster Big Graph, and there is no algorithm to classify Big Graph. As a conclusion of this survey, there is a need for more researches to be conducted to improve a comprehensive Graph Mining System, especially for very big Graph.
Persona, Marek; Kutarov, Vladimir V; Kats, Boris M; Persona, Andrzej; Marczewska, Barbara
2007-01-01
The paper describes the new prediction method of octanol-water partition coefficient, which is based on molecular graph theory. The results obtained using the new method are well correlated with experimental values. These results were compared with the ones obtained by use of ten other structure correlated methods. The comparison shows that graph theory can be very useful in structure correlation research.
ERIC Educational Resources Information Center
Deniz, Hasan; Dulger, Mehmet F.
2012-01-01
This study examined to what extent inquiry-based instruction supported with real-time graphing technology improves fourth grader's ability to interpret graphs as representations of physical science concepts such as motion and temperature. This study also examined whether there is any difference between inquiry-based instruction supported with…
ERIC Educational Resources Information Center
Gültepe, Nejla
2016-01-01
Graphing subjects in chemistry has been used to provide alternatives to verbal and algorithmic descriptions of a subject by handing students another way of improving their manipulation of concepts. Teachers should therefore know the level of students' graphing skills. Studies have identified that students have difficulty making connections with…
NASA Technical Reports Server (NTRS)
Lieberman, R. N.
1972-01-01
Given a directed graph, a natural topology is defined and relationships between standard topological properties and graph theoretical concepts are studied. In particular, the properties of connectivity and separatedness are investigated. A metric is introduced which is shown to be related to separatedness. The topological notions of continuity and homeomorphism. A class of maps is studied which preserve both graph and topological properties. Applications involving strong maps and contractions are also presented.
Recognition of Probe Ptolemaic Graphs
NASA Astrophysics Data System (ADS)
Chang, Maw-Shang; Hung, Ling-Ju
Let G denote a graph class. An undirected graph G is called a probe G graph if one can make G a graph in G by adding edges between vertices in some independent set of G. By definition graph class G is a subclass of probe G graphs. Ptolemaic graphs are chordal and induced gem free. They form a subclass of both chordal graphs and distance-hereditary graphs. Many problems NP-hard on chordal graphs can be solved in polynomial time on ptolemaic graphs. We proposed an O(nm)-time algorithm to recognize probe ptolemaic graphs where n and m are the numbers of vertices and edges of the input graph respectively.
Lothian, Josh; Powers, Sarah S; Sullivan, Blair D; Baker, Matthew B; Schrock, Jonathan; Poole, Stephen W
2013-12-01
The benchmarking effort within the Extreme Scale Systems Center at Oak Ridge National Laboratory seeks to provide High Performance Computing benchmarks and test suites of interest to the DoD sponsor. The work described in this report is a part of the effort focusing on graph generation. A previously developed benchmark, SystemBurn, allowed the emulation of dierent application behavior profiles within a single framework. To complement this effort, similar capabilities are desired for graph-centric problems. This report examines existing synthetic graph generator implementations in preparation for further study on the properties of their generated synthetic graphs.
Frishman, Yaniv; Tal, Ayellet
2008-01-01
This paper presents an algorithm for drawing a sequence of graphs online. The algorithm strives to maintain the global structure of the graph and thus the user's mental map, while allowing arbitrary modifications between consecutive layouts. The algorithm works online and uses various execution culling methods in order to reduce the layout time and handle large dynamic graphs. Techniques for representing graphs on the GPU allow a speedup by a factor of up to 17 compared to the CPU implementation. The scalability of the algorithm across GPU generations is demonstrated. Applications of the algorithm to the visualization of discussion threads in Internet sites and to the visualization of social networks are provided.
Continuous-time quantum walks on directed bipartite graphs
NASA Astrophysics Data System (ADS)
Tödtli, Beat; Laner, Monika; Semenov, Jouri; Paoli, Beatrice; Blattner, Marcel; Kunegis, Jérôme
2016-11-01
This paper investigates continuous-time quantum walks on directed bipartite graphs based on a graph's adjacency matrix. We prove that on bipartite graphs, probability transport between the two node partitions can be completely suppressed by tuning a model parameter α . We provide analytic solutions to the quantum walks for the star and circulant graph classes that are valid for an arbitrary value of the number of nodes N , time t , and the model parameter α . We discuss quantitative and qualitative aspects of quantum walks based on directed graphs and their undirected counterparts. Numerical simulations of quantum walks on circulant graphs show complex interference phenomena and how complete suppression of transport is achieved near α =π /2 . By proving two mirror symmetries around α =0 and π /2 we show that these quantum walks have a period of π in α . We show that undirected edges lose their effect on the quantum walk at α =π /2 and present non-bipartite graphs that exhibit suppression of transport. Finally, we analytically compute the Hamiltonians of quantum walks on the directed ring graph.
Graphs, matrices, and the GraphBLAS: Seven good reasons
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
Graphs, matrices, and the GraphBLAS: Seven good reasons
Kepner, Jeremy; Bader, David; Buluç, Aydın; Gilbert, John; Mattson, Timothy; Meyerhenke, Henning
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 implement 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.
An iterated tabu search approach for the clique partitioning problem.
Palubeckis, Gintaras; Ostreika, Armantas; Tomkevičius, Arūnas
2014-01-01
Given an edge-weighted undirected graph with weights specifying dissimilarities between pairs of objects, represented by the vertices of the graph, the clique partitioning problem (CPP) is to partition the vertex set of the graph into mutually disjoint subsets such that the sum of the edge weights over all cliques induced by the subsets is as small as possible. We develop an iterated tabu search (ITS) algorithm for solving this problem. The proposed algorithm incorporates tabu search, local search, and solution perturbation procedures. We report computational results on CPP instances of size up to 2000 vertices. Performance comparisons of ITS against state-of-the-art methods from the literature demonstrate the competitiveness of our approach.
ERIC Educational Resources Information Center
Hirsch, Christian R.
1975-01-01
Using a set of worksheets, students will discover and apply Euler's formula regarding connected planar graphs and play and analyze the game of Sprouts. One sheet leads to the discovery of Euler's formula; another concerns traversability of a graph; another gives an example and a game involving these ideas. (Author/KM)
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…
ERIC Educational Resources Information Center
Petrosino, Anthony
2012-01-01
This article responds to arguments by Skidmore and Thompson (this issue of "Educational Researcher") that a graph published more than 10 years ago was erroneously reproduced and "gratuitously damaged" perceptions of the quality of education research. After describing the purpose of the original graph, the author counters assertions that the graph…
ERIC Educational Resources Information Center
Shen, Ji
2009-01-01
In the Walking Out Graphs Lesson described here, students experience several types of representations used to describe motion, including words, sentences, equations, graphs, data tables, and actions. The most important theme of this lesson is that students have to understand the consistency among these representations and form the habit of…
Graphing from Everyday Experience.
ERIC Educational Resources Information Center
Carraher, David; Schliemann, Analucia; Nemirousky, Ricardo
1995-01-01
Discusses the importance of teaching grounded in the everyday experiences and concerns of the learners. Studies how people with limited school experience can understand graphs and concludes that individuals with limited academic education can clarify the role of everyday experiences in learning about graphs. (ASK)
ERIC Educational Resources Information Center
Johnson, Millie
1997-01-01
Graphs from media sources and questions developed from them can be used in the middle school mathematics classroom. Graphs depict storage temperature on a milk carton; air pressure measurements on a package of shock absorbers; sleep-wake patterns of an infant; a dog's breathing patterns; and the angle, velocity, and radius of a leaning bicyclist…
ERIC Educational Resources Information Center
Doto, Julianne; Golbeck, Susan
2007-01-01
Collecting data and analyzing the results of experiments is difficult for children. The authors found a surprising way to help their third graders make graphs and draw conclusions from their data: digital photographs. The pictures bridged the gap between an abstract graph and the plants it represented. With the support of the photos, students…
GoFFish: A Sub-Graph Centric Framework for Large-Scale Graph Analytics1
Simmhan, Yogesh; Kumbhare, Alok; Wickramaarachchi, Charith; Nagarkar, Soonil; Ravi, Santosh; Raghavendra, Cauligi; Prasanna, Viktor
2014-08-25
Large scale graph processing is a major research area for Big Data exploration. Vertex centric programming models like Pregel are gaining traction due to their simple abstraction that allows for scalable execution on distributed systems naturally. However, there are limitations to this approach which cause vertex centric algorithms to under-perform due to poor compute to communication overhead ratio and slow convergence of iterative superstep. In this paper we introduce GoFFish a scalable sub-graph centric framework co-designed with a distributed persistent graph storage for large scale graph analytics on commodity clusters. We introduce a sub-graph centric programming abstraction that combines the scalability of a vertex centric approach with the flexibility of shared memory sub-graph computation. We map Connected Components, SSSP and PageRank algorithms to this model to illustrate its flexibility. Further, we empirically analyze GoFFish using several real world graphs and demonstrate its significant performance improvement, orders of magnitude in some cases, compared to Apache Giraph, the leading open source vertex centric implementation. We map Connected Components, SSSP and PageRank algorithms to this model to illustrate its flexibility. Further, we empirically analyze GoFFish using several real world graphs and demonstrate its significant performance improvement, orders of magnitude in some cases, compared to Apache Giraph, the leading open source vertex centric implementation.
Evolutionary stability on graphs
Ohtsuki, Hisashi; Nowak, Martin A.
2008-01-01
Evolutionary stability is a fundamental concept in evolutionary game theory. A strategy is called an evolutionarily stable strategy (ESS), if its monomorphic population rejects the invasion of any other mutant strategy. Recent studies have revealed that population structure can considerably affect evolutionary dynamics. Here we derive the conditions of evolutionary stability for games on graphs. We obtain analytical conditions for regular graphs of degree k > 2. Those theoretical predictions are compared with computer simulations for random regular graphs and for lattices. We study three different update rules: birth-death (BD), death-birth (DB), and imitation (IM) updating. Evolutionary stability on sparse graphs does not imply evolutionary stability in a well-mixed population, nor vice versa. We provide a geometrical interpretation of the ESS condition on graphs. PMID:18295801
NASA Astrophysics Data System (ADS)
Chen, Yiying; Ryder, James; Naudts, Kim; McGrath, Matthew J.; Otto, Juliane; Bastriko, Vladislav; Valade, Aude; Launiainen, Samuli; Ogée, Jérôme; Elbers, Jan A.; Foken, Thomas; Tiedemann, Frank; Heinesch, Bernard; Black, Andrew; Haverd, Vanessa; Loustau, Denis; Ottlé, Catherine; Peylin, Philippe; Polcher, Jan; Luyssaert, Sebastiaan
2015-04-01
Canopy structure is one of the most important vegetation characteristics for land-atmosphere interactions as it determines the energy and scalar exchanges between land surface and overlay air mass. In this study we evaluated the performance of a newly developed multi-layer energy budget (Ryder et al., 2014) in a land surface model, ORCHIDEE-CAN (Naudts et al., 2014), which simulates canopy structure and can be coupled to an atmospheric model using an implicit procedure. Furthermore, a vertical discrete drag parametrization scheme was also incorporated into this model, in order to obtain a better description of the sub-canopy wind profile simulation. Site level datasets, including the top-of-the-canopy and sub-canopy observations made available from eight flux observation sites, were collected in order to conduct this evaluation. The geo-location of the collected observation sites crossed climate zones from temperate to boreal and the vegetation types included deciduous, evergreen broad leaved and evergreen needle leaved forest with maximum LAI ranging from 2.1 to 7.0. First, we used long-term top-of-the-canopy measurements to analyze the performance of the current one-layer energy budget in ORCHIDEE-CAN. Three major processes were identified for improvement through the implementation of a multi-layer energy budget: 1) night time radiation balance, 2) energy partitioning during winter and 3) prediction of the ground heat flux. Short-term sub-canopy observations were used to calibrate the parameters in sub-canopy radiation, turbulence and resistances modules with an automatic tuning process following the maximum gradient of the user-defined objective function. The multi-layer model is able to capture the dynamic of sub-canopy turbulence, temperature and energy fluxes with imposed LAI profile and optimized parameter set at a site level calibration. The simulation result shows the improvement both on the nighttime energy balance and energy partitioning during winter
Community detection in directed acyclic graphs
NASA Astrophysics Data System (ADS)
Speidel, Leo; Takaguchi, Taro; Masuda, Naoki
2015-08-01
Some temporal networks, most notably citation networks, are naturally represented as directed acyclic graphs (DAGs). To detect communities in DAGs, we propose a modularity for DAGs by defining an appropriate null model (i.e., randomized network) respecting the order of nodes. We implement a spectral method to approximately maximize the proposed modularity measure and test the method on citation networks and other DAGs. We find that the attained values of the modularity for DAGs are similar for partitions that we obtain by maximizing the proposed modularity (designed for DAGs), the modularity for undirected networks and that for general directed networks. In other words, if we neglect the order imposed on nodes (and the direction of links) in a given DAG and maximize the conventional modularity measure, the obtained partition is close to the optimal one in the sense of the modularity for DAGs. Contribution to the Topical Issue "Temporal Network Theory and Applications", edited by Petter Holme.
Ridge network detection in crumpled paper via graph density maximization.
Hsu, Chiou-Ting; Huang, Marvin
2012-10-01
Crumpled sheets of paper tend to exhibit a specific and complex structure, which is described by physicists as ridge networks. Existing literature shows that the automation of ridge network detection in crumpled paper is very challenging because of its complex structure and measuring distortion. In this paper, we propose to model the ridge network as a weighted graph and formulate the ridge network detection as an optimization problem in terms of the graph density. First, we detect a set of graph nodes and then determine the edge weight between each pair of nodes to construct a complete graph. Next, we define a graph density criterion and formulate the detection problem to determine a subgraph with maximal graph density. Further, we also propose to refine the graph density by including a pairwise connectivity into the criterion to improve the connectivity of the detected ridge network. Our experimental results show that, with the density criterion, our proposed method effectively automates the ridge network detection.
Implementing Graph Pattern Queries on a Relational Database
Kaplan, I L; Abdulla, G M; Brugger, S T; Kohn, S R
2007-12-26
When a graph database is implemented on top of a relational database, queries in the graph query language are translated into relational SQL queries. Graph pattern queries are an important feature of a graph query language. Translating graph pattern queries into single SQL statements results in very poor query performance. By taking into account the pattern query structure and generating multiple SQL statements, pattern query performance can be dramatically improved. The performance problems encountered with the single SQL statements generated for pattern queries reflects a problem in the SQL query planner and optimizer. Addressing this problem would allow relational databases to better support semantic graph databases. Relational database systems that provide good support for graph databases may also be more flexible platforms for data warehouses.
Multi-level graph layout on the GPU.
Frishman, Yaniv; Tal, Ayellet
2007-01-01
This paper presents a new algorithm for force directed graph layout on the GPU. The algorithm, whose goal is to compute layouts accurately and quickly, has two contributions. The first contribution is proposing a general multi-level scheme, which is based on spectral partitioning. The second contribution is computing the layout on the GPU. Since the GPU requires a data parallel programming model, the challenge is devising a mapping of a naturally unstructured graph into a well-partitioned structured one. This is done by computing a balanced partitioning of a general graph. This algorithm provides a general multi-level scheme, which has the potential to be used not only for computation on the GPU, but also on emerging multi-core architectures. The algorithm manages to compute high quality layouts of large graphs in a fraction of the time required by existing algorithms of similar quality. An application for visualization of the topologies of ISP (Internet Service Provider) networks is presented.
Baxter, Jamie C; Funnell, Barbara E
2014-12-01
The stable maintenance of low-copy-number plasmids in bacteria is actively driven by partition mechanisms that are responsible for the positioning of plasmids inside the cell. Partition systems are ubiquitous in the microbial world and are encoded by many bacterial chromosomes as well as plasmids. These systems, although different in sequence and mechanism, typically consist of two proteins and a DNA partition site, or prokaryotic centromere, on the plasmid or chromosome. One protein binds site-specifically to the centromere to form a partition complex, and the other protein uses the energy of nucleotide binding and hydrolysis to transport the plasmid, via interactions with this partition complex inside the cell. For plasmids, this minimal cassette is sufficient to direct proper segregation in bacterial cells. There has been significant progress in the last several years in our understanding of partition mechanisms. Two general areas that have developed are (i) the structural biology of partition proteins and their interactions with DNA and (ii) the action and dynamics of the partition ATPases that drive the process. In addition, systems that use tubulin-like GTPases to partition plasmids have recently been identified. In this chapter, we concentrate on these recent developments and the molecular details of plasmid partition mechanisms.
The Effect of Using Graphing Calculators in Complex Function Graphs
ERIC Educational Resources Information Center
Ocak, Mehmet Akif
2008-01-01
This study investigates the role of graphing calculators in multiple representations for knowledge transfer and the omission of oversimplification in complex function graphs. The main aim is to examine whether graphing calculators were used efficiently to see different cases and multiple perspectives among complex function graphs, or whether…
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…
Understanding graphs with two independent variables
NASA Astrophysics Data System (ADS)
Cooper, Jennifer L.
Adults are not necessarily competent users of graphs with two independent variables, despite the frequency of this representational format. The three tasks in this thesis address the impact of interpretation statements and graph patterns. Interpretation statements were based on the statistical effects -- simple effects, main effects, and interactions. Graph patterns were systematically varied based on a novel classification scheme of graphs with two IVs. I suggest that the complexity of a graph's data pattern depends on the consistency of the simple effects' directions and magnitudes. In the first study, undergraduates constructed graphs based on statements about data patterns. Errors reflected a misunderstanding of how two IVs could be combined and represented graphically. When the experimental group had graph-relevant information added (variable labels spatially located on axes), the ability to represent the relationships among the IVs significantly increased. The ability to satisfy the constraints imposed by the statements was not affected. Adding labels specifically targeted skills relevant to graphical literacy. Transfer to a third trial was stronger for those of higher math abilities. The second study focused on the effect of an introductory statistics course. Overall, undergraduates performed well on statements describing the simple effects of the IVs. However, even though they improved from Time 1 to Time 2 for interaction statements, performance on statements about main effects and interactions still showed considerable room for improvement. In the third study, repeated trials of the 20 patterns proposed by the simple effects consistency model established that the proposed classification scheme addresses additional sources of variability in reasoning with graphs (i.e., sources not captured by traditional classification schemes). As the complexity level of the data pattern increased, performance (based on accuracy and RT) decreased, with parallel impacts on
Hajnal, A.
1971-01-01
If the continuum hypothesis is assumed, there is a graph G whose vertices form an ordered set of type ω12; G does not contain triangles or complete even graphs of form [[unk]0,[unk]0], and there is no independent subset of vertices of type ω12. PMID:16591893
Brandley, Matthew C; Schmitz, Andreas; Reeder, Tod W
2005-06-01
Partitioned Bayesian analyses of approximately 2.2 kb of nucleotide sequence data (mtDNA) were used to elucidate phylogenetic relationships among 30 scincid lizard genera. Few partitioned Bayesian analyses exist in the literature, resulting in a lack of methods to determine the appropriate number of and identity of partitions. Thus, a criterion, based on the Bayes factor, for selecting among competing partitioning strategies is proposed and tested. Improvements in both mean -lnL and estimated posterior probabilities were observed when specific models and parameter estimates were assumed for partitions of the total data set. This result is expected given that the 95% credible intervals of model parameter estimates for numerous partitions do not overlap and it reveals that different data partitions may evolve quite differently. We further demonstrate that how one partitions the data (by gene, codon position, etc.) is shown to be a greater concern than simply the overall number of partitions. Using the criterion of the 2 ln Bayes factor > 10, the phylogenetic analysis employing the largest number of partitions was decisively better than all other strategies. Strategies that partitioned the ND1 gene by codon position performed better than other partition strategies, regardless of the overall number of partitions. Scincidae, Acontinae, Lygosominae, east Asian and North American "Eumeces" + Neoseps; North African Eumeces, Scincus, and Scincopus, and a large group primarily from sub-Saharan Africa, Madagascar, and neighboring islands are monophyletic. Feylinia, a limbless group of previously uncertain relationships, is nested within a "scincine" clade from sub-Saharan Africa. We reject the hypothesis that the nearly limbless dibamids are derived from within the Scincidae, but cannot reject the hypothesis that they represent the sister taxon to skinks. Amphiglossus, Chalcides, the acontines Acontias and Typhlosaurus, and Scincinae are paraphyletic. The globally widespread
Tensor Spectral Clustering for Partitioning Higher-order Network Structures
Benson, Austin R.; Gleich, David F.; Leskovec, Jure
2016-01-01
Spectral graph theory-based methods represent an important class of tools for studying the structure of networks. Spectral methods are based on a first-order Markov chain derived from a random walk on the graph and thus they cannot take advantage of important higher-order network substructures such as triangles, cycles, and feed-forward loops. Here we propose a Tensor Spectral Clustering (TSC) algorithm that allows for modeling higher-order network structures in a graph partitioning framework. Our TSC algorithm allows the user to specify which higher-order network structures (cycles, feed-forward loops, etc.) should be preserved by the network clustering. Higher-order network structures of interest are represented using a tensor, which we then partition by developing a multilinear spectral method. Our framework can be applied to discovering layered flows in networks as well as graph anomaly detection, which we illustrate on synthetic networks. In directed networks, a higher-order structure of particular interest is the directed 3-cycle, which captures feedback loops in networks. We demonstrate that our TSC algorithm produces large partitions that cut fewer directed 3-cycles than standard spectral clustering algorithms. PMID:27812399
Tensor Spectral Clustering for Partitioning Higher-order Network Structures.
Benson, Austin R; Gleich, David F; Leskovec, Jure
2015-01-01
Spectral graph theory-based methods represent an important class of tools for studying the structure of networks. Spectral methods are based on a first-order Markov chain derived from a random walk on the graph and thus they cannot take advantage of important higher-order network substructures such as triangles, cycles, and feed-forward loops. Here we propose a Tensor Spectral Clustering (TSC) algorithm that allows for modeling higher-order network structures in a graph partitioning framework. Our TSC algorithm allows the user to specify which higher-order network structures (cycles, feed-forward loops, etc.) should be preserved by the network clustering. Higher-order network structures of interest are represented using a tensor, which we then partition by developing a multilinear spectral method. Our framework can be applied to discovering layered flows in networks as well as graph anomaly detection, which we illustrate on synthetic networks. In directed networks, a higher-order structure of particular interest is the directed 3-cycle, which captures feedback loops in networks. We demonstrate that our TSC algorithm produces large partitions that cut fewer directed 3-cycles than standard spectral clustering algorithms.
Burioni, Raffaella; Chibbaro, Sergio; Vergni, Davide; Vulpiani, Angelo
2012-11-01
We study reaction-diffusion processes on graphs through an extension of the standard reaction-diffusion equation starting from first principles. We focus on reaction spreading, i.e., on the time evolution of the reaction product M(t). At variance with pure diffusive processes, characterized by the spectral dimension d{s}, the important quantity for reaction spreading is found to be the connectivity dimension d{l}. Numerical data, in agreement with analytical estimates based on the features of n independent random walkers on the graph, show that M(t)∼t{d{l}}. In the case of Erdös-Renyi random graphs, the reaction product is characterized by an exponential growth M(t)e{αt} with α proportional to ln(k), where (k) is the average degree of the graph.
A Semantic Graph Query Language
Kaplan, I L
2006-10-16
Semantic graphs can be used to organize large amounts of information from a number of sources into one unified structure. A semantic query language provides a foundation for extracting information from the semantic graph. The graph query language described here provides a simple, powerful method for querying semantic graphs.
Assortativity of complementary graphs
NASA Astrophysics Data System (ADS)
Wang, H.; Winterbach, W.; van Mieghem, P.
2011-09-01
Newman's measure for (dis)assortativity, the linear degree correlationρD, is widely studied although analytic insight into the assortativity of an arbitrary network remains far from well understood. In this paper, we derive the general relation (2), (3) and Theorem 1 between the assortativity ρD(G) of a graph G and the assortativityρD(Gc) of its complement Gc. Both ρD(G) and ρD(Gc) are linearly related by the degree distribution in G. When the graph G(N,p) possesses a binomial degree distribution as in the Erdős-Rényi random graphs Gp(N), its complementary graph Gpc(N) = G1-p(N) follows a binomial degree distribution as in the Erdős-Rényi random graphs G1-p(N). We prove that the maximum and minimum assortativity of a class of graphs with a binomial distribution are asymptotically antisymmetric: ρmax(N,p) = -ρmin(N,p) for N → ∞. The general relation (3) nicely leads to (a) the relation (10) and (16) between the assortativity range ρmax(G)-ρmin(G) of a graph with a given degree distribution and the range ρmax(Gc)-ρmin(Gc) of its complementary graph and (b) new bounds (6) and (15) of the assortativity. These results together with our numerical experiments in over 30 real-world complex networks illustrate that the assortativity range ρmax-ρmin is generally large in sparse networks, which underlines the importance of assortativity as a network characterizer.
Commuting projections on graphs
Vassilevski, Panayot S.; Zikatanov, Ludmil T.
2013-02-19
For a given (connected) graph, we consider vector spaces of (discrete) functions defined on its vertices and its edges. These two spaces are related by a discrete gradient operator, Grad and its adjoint, ₋Div, referred to as (negative) discrete divergence. We also consider a coarse graph obtained by aggregation of vertices of the original one. Then a coarse vertex space is identified with the subspace of piecewise constant functions over the aggregates. We consider the ℓ_{2}-projection Q_{H} onto the space of these piecewise constants. In the present paper, our main result is the construction of a projection π _{H} from the original edge-space onto a properly constructed coarse edge-space associated with the edges of the coarse graph. The projections π _{H} and Q_{H} commute with the discrete divergence operator, i.e., we have div π _{H} = Q_{H} div. The respective pair of coarse edge-space and coarse vertexspace offer the potential to construct two-level, and by recursion, multilevel methods for the mixed formulation of the graph Laplacian which utilizes the discrete divergence operator. The performance of one two-level method with overlapping Schwarz smoothing and correction based on the constructed coarse spaces for solving such mixed graph Laplacian systems is illustrated on a number of graph examples.
Metabolic networks: beyond the graph.
Bernal, Andrés; Daza, Edgar
2011-06-01
Drugs are devised to enter into the metabolism of an organism in order to produce a desired effect. From the chemical point of view, cellular metabolism is constituted by a complex network of reactions transforming metabolites one in each other. Knowledge on the structure of this network could help to develop novel methods for drug design, and to comprehend the root of known unexpected side effects. Many large-scale studies on the structure of metabolic networks have been developed following models based on different kinds of graphs as the fundamental image of the reaction network. Graphs models, however, comport wrong assumptions regarding the structure of reaction networks that may lead into wrong conclusions if they are not taken into account. In this article we critically review some graph-theoretical approaches to the analysis of centrality, vulnerability and modularity of metabolic networks, analyzing their limitations in estimating these key network properties, consider some proposals explicit or implicitly based on directed hypergraphs regarding their ability to overcome these issues, and review some recent implementation improvements that make the application of these models in increasingly large networks a viable option.
NASA Astrophysics Data System (ADS)
Wichmann, A.; Jung, J.; Sohn, G.; Kada, M.; Ehlers, M.
2015-09-01
Recent approaches for the automatic reconstruction of 3D building models from airborne point cloud data integrate prior knowledge of roof shapes with the intention to improve the regularization of the resulting models without lessening the flexibility to generate all real-world occurring roof shapes. In this paper, we present a method to integrate building knowledge into the data-driven approach that uses binary space partitioning (BSP) for modeling the 3D building geometry. A retrospective regularization of polygons that emerge from the BSP tree is not without difficulty because it has to deal with the 2D BSP subdivision itself and the plane definitions of the resulting partition regions to ensure topological correctness. This is aggravated by the use of hyperplanes during the binary subdivision that often splits planar roof regions into several parts that are stored in different subtrees of the BSP tree. We therefore introduce the use of hyperpolylines in the generation of the BSP tree to avoid unnecessary spatial subdivisions, so that the spatial integrity of planar roof regions is better maintained. The hyperpolylines are shown to result from basic building roof knowledge that is extracted based on roof topology graphs. An adjustment of the underlying point segments ensures that the positions of the extracted hyperpolylines result in regularized 2D partitions as well as topologically correct 3D building models. The validity and limitations of the approach are demonstrated on real-world examples.
Proxy Graph: Visual Quality Metrics of Big Graph Sampling.
Nguyen, Quan-Hoang; Hong, Seok-Hee; Eades, Peter; Meidiana, Amyra
2017-02-24
Data sampling has been extensively studied for large scale graph mining. Many analyses and tasks become more efficient when performed on graph samples of much smaller size. The use of proxy objects is common in software engineering for analysis and interaction with heavy objects or systems. In this paper, we coin the term 'proxy graph' and empirically investigate how well a proxy graph visualization can represent a big graph. Our investigation focuses on proxy graphs obtained by sampling; this is one of the most common proxy approaches. Despite the plethora of data sampling studies, this is the first evaluation of sampling in the context of graph visualization. For an objective evaluation, we propose a new family of quality metrics for visual quality of proxy graphs. Our experiments cover popular sampling techniques. Our experimental results lead to guidelines for using sampling-based proxy graphs in visualization.
ERIC Educational Resources Information Center
Brusco, Michael; Steinley, Douglas
2010-01-01
Structural balance theory (SBT) has maintained a venerable status in the psychological literature for more than 5 decades. One important problem pertaining to SBT is the approximation of structural or generalized balance via the partitioning of the vertices of a signed graph into "K" clusters. This "K"-balance partitioning problem also has more…
Key-Node-Separated Graph Clustering and Layouts for Human Relationship Graph Visualization.
Itoh, Takayuki; Klein, Karsten
2015-01-01
Many graph-drawing methods apply node-clustering techniques based on the density of edges to find tightly connected subgraphs and then hierarchically visualize the clustered graphs. However, users may want to focus on important nodes and their connections to groups of other nodes for some applications. For this purpose, it is effective to separately visualize the key nodes detected based on adjacency and attributes of the nodes. This article presents a graph visualization technique for attribute-embedded graphs that applies a graph-clustering algorithm that accounts for the combination of connections and attributes. The graph clustering step divides the nodes according to the commonality of connected nodes and similarity of feature value vectors. It then calculates the distances between arbitrary pairs of clusters according to the number of connecting edges and the similarity of feature value vectors and finally places the clusters based on the distances. Consequently, the technique separates important nodes that have connections to multiple large clusters and improves the visibility of such nodes' connections. To test this technique, this article presents examples with human relationship graph datasets, including a coauthorship and Twitter communication network dataset.
Robust Spectral Clustering Using Statistical Sub-Graph Affinity Model
Eichel, Justin A.; Wong, Alexander; Fieguth, Paul; Clausi, David A.
2013-01-01
Spectral clustering methods have been shown to be effective for image segmentation. Unfortunately, the presence of image noise as well as textural characteristics can have a significant negative effect on the segmentation performance. To accommodate for image noise and textural characteristics, this study introduces the concept of sub-graph affinity, where each node in the primary graph is modeled as a sub-graph characterizing the neighborhood surrounding the node. The statistical sub-graph affinity matrix is then constructed based on the statistical relationships between sub-graphs of connected nodes in the primary graph, thus counteracting the uncertainty associated with the image noise and textural characteristics by utilizing more information than traditional spectral clustering methods. Experiments using both synthetic and natural images under various levels of noise contamination demonstrate that the proposed approach can achieve improved segmentation performance when compared to existing spectral clustering methods. PMID:24386111
A Graph Search Heuristic for Shortest Distance Paths
Chow, E
2005-03-24
This paper presents a heuristic for guiding A* search for finding the shortest distance path between two vertices in a connected, undirected, and explicitly stored graph. The heuristic requires a small amount of data to be stored at each vertex. The heuristic has application to quickly detecting relationships between two vertices in a large information or knowledge network. We compare the performance of this heuristic with breadth-first search on graphs with various topological properties. The results show that one or more orders of magnitude improvement in the number of vertices expanded is possible for large graphs, including Poisson random graphs.
Optimized Graph Search Using Multi-Level Graph Clustering
NASA Astrophysics Data System (ADS)
Kala, Rahul; Shukla, Anupam; Tiwari, Ritu
Graphs find a variety of use in numerous domains especially because of their capability to model common problems. The social networking graphs that are used for social networking analysis, a feature given by various social networking sites are an example of this. Graphs can also be visualized in the search engines to carry search operations and provide results. Various searching algorithms have been developed for searching in graphs. In this paper we propose that the entire network graph be clustered. The larger graphs are clustered to make smaller graphs. These smaller graphs can again be clustered to further reduce the size of graph. The search is performed on the smallest graph to identify the general path, which may be further build up to actual nodes by working on the individual clusters involved. Since many searches are carried out on the same graph, clustering may be done once and the data may be used for multiple searches over the time. If the graph changes considerably, only then we may re-cluster the graph.
Improving Design Efficiency for Large-Scale Heterogeneous Circuits
NASA Astrophysics Data System (ADS)
Gregerson, Anthony
Despite increases in logic density, many Big Data applications must still be partitioned across multiple computing devices in order to meet their strict performance requirements. Among the most demanding of these applications is high-energy physics (HEP), which uses complex computing systems consisting of thousands of FPGAs and ASICs to process the sensor data created by experiments at particles accelerators such as the Large Hadron Collider (LHC). Designing such computing systems is challenging due to the scale of the systems, the exceptionally high-throughput and low-latency performance constraints that necessitate application-specific hardware implementations, the requirement that algorithms are efficiently partitioned across many devices, and the possible need to update the implemented algorithms during the lifetime of the system. In this work, we describe our research to develop flexible architectures for implementing such large-scale circuits on FPGAs. In particular, this work is motivated by (but not limited in scope to) high-energy physics algorithms for the Compact Muon Solenoid (CMS) experiment at the LHC. To make efficient use of logic resources in multi-FPGA systems, we introduce Multi-Personality Partitioning, a novel form of the graph partitioning problem, and present partitioning algorithms that can significantly improve resource utilization on heterogeneous devices while also reducing inter-chip connections. To reduce the high communication costs of Big Data applications, we also introduce Information-Aware Partitioning, a partitioning method that analyzes the data content of application-specific circuits, characterizes their entropy, and selects circuit partitions that enable efficient compression of data between chips. We employ our information-aware partitioning method to improve the performance of the hardware validation platform for evaluating new algorithms for the CMS experiment. Together, these research efforts help to improve the efficiency
Chen, J.; Safro, I.
2011-01-01
Measuring the connection strength between a pair of vertices in a graph is one of the most important concerns in many graph applications. Simple measures such as edge weights may not be sufficient for capturing the effects associated with short paths of lengths greater than one. In this paper, we consider an iterative process that smooths an associated value for nearby vertices, and we present a measure of the local connection strength (called the algebraic distance; see [D. Ron, I. Safro, and A. Brandt, Multiscale Model. Simul., 9 (2011), pp. 407-423]) based on this process. The proposed measure is attractive in that the process is simple, linear, and easily parallelized. An analysis of the convergence property of the process reveals that the local neighborhoods play an important role in determining the connectivity between vertices. We demonstrate the practical effectiveness of the proposed measure through several combinatorial optimization problems on graphs and hypergraphs.
2002-04-15
path from a to (3 together with an edge (3 -+ a is called a (fully) directed cycle . An anterior path from a to f3 together with an edge (3 -+ a is...called a partially directed cycle . A directed acyclic graph (DA G) is a mixed graph in which all edges are directed, and there are no directed cycles . 3...regardless of whether a and "’f are adjacent). There are no directed cycles or pa’ltially directed cycles . 9 to Proof: follows because condition rules
1990-03-01
returns from a frequency swept microwave signal centred on the ship being measured. Each data set consists of 255 equally spaced points which represent...overlaid one over the other, or split into three windows where the hard black-lined top graph is the back chart and the thinner-lined lower graph is the...Borland’s Turbo Pascal Version 1.0 (Borland 1986) to edit and compile the main source code. Menu details, window specification, dialogue box and item
On Graph Isomorphism and the PageRank Algorithm
2008-09-01
International Conference on Robotics and Automation, IEEE, 2004. [Chu94] F. Chung . Spectral Graph Theory, Regional Conference Series in Mathematics, vol. 92...Enumeration of cospectral graphs”, European Journal of Combinatorics, 25:199–211, 2004. [HeL93] B. Hendrickson and R. Leland . “An improved spectral graph
NASA Astrophysics Data System (ADS)
Liu, Hongxia; Shi, Jiaqi; Liu, Hui; Wang, Zunyao
2013-10-01
The octanol/air partition coefficient (KOA) is a key physicochemical parameter for describing the partition of organic pollutants between air and environment organic phase. The development of appropriate method to estimate KOA is of great importance. In the present study, the steric, electrostatic, hydrophobic, hydrogen bond donor and acceptor descriptors were computed by comparative molecular field analysis (CoMFA) and comparative molecular similarity indices analysis (CoMSIA). On the basis of these parameters, the statistically quantitative structure-property relationship (QSPR) models for logKOA of hydroxylated polybrominated diphenyl ethers (OH-PBDEs) and methoxylated polybrominated diphenyl ethers (MeO-PBDEs) congeners were developed using partial least-squares (PLS) analysis, of which the R2 is about 0.980, 0.952 respectively. The electrostatic field was found to be main factors governing the logKOA. The results of validation indicate the models of this study exhibit optimum stability, and thus it is feasible to predict logKOA.
Reducing variance in batch partitioning measurements
Mariner, Paul E.
2010-08-11
The partitioning experiment is commonly performed with little or no attention to reducing measurement variance. Batch test procedures such as those used to measure K{sub d} values (e.g., ASTM D 4646 and EPA402 -R-99-004A) do not explain how to evaluate measurement uncertainty nor how to minimize measurement variance. In fact, ASTM D 4646 prescribes a sorbent:water ratio that prevents variance minimization. Consequently, the variance of a set of partitioning measurements can be extreme and even absurd. Such data sets, which are commonplace, hamper probabilistic modeling efforts. An error-savvy design requires adjustment of the solution:sorbent ratio so that approximately half of the sorbate partitions to the sorbent. Results of Monte Carlo simulations indicate that this simple step can markedly improve the precision and statistical characterization of partitioning uncertainty.
ERIC Educational Resources Information Center
Sokol, William
In this autoinstructional packet, the student is given an experimental situation which introduces him to the process of graphing. The lesson is presented for secondary school students in chemistry. Algebra I and a Del Mod System program (indicated as SE 018 020) are suggested prerequisites for the use of this program. Behavioral objectives are…
ERIC Educational Resources Information Center
Pitts Bannister, Vanessa R.; Jamar, Idorenyin; Mutegi, Jomo W.
2007-01-01
In this article, the learning progress of one fifth-grade student is examined with regard to the development of her graph interpretation skills as she participated in the Junior Science Institute (JSI), a two-week, science intensive summer camp in which participants engaged in microbiology research and application. By showcasing the student's…
Simmons, G.J.
1985-01-01
Given a graph G and an ordering phi of the vertices, V(G), we define a parsimonious proper coloring (PPC) of V(G) under phi to be a proper coloring of V(G) in the order phi, where a new color is introduced only when a vertex cannot be properly colored in its order with any of the colors already used.
2013-02-19
This library is used in several LLNL projects, including STAT (the Stack Trace Analysis Tool for scalable debugging) and some modules in P^nMPI (a tool MPI tool infrastructure). It can also be used standalone for creating and manipulationg graphs, but its API is primarily tuned to support these other projects
Coloring geographical threshold graphs
Bradonjic, Milan; Percus, Allon; Muller, Tobias
2008-01-01
We propose a coloring algorithm for sparse random graphs generated by the geographical threshold graph (GTG) model, a generalization of random geometric graphs (RGG). In a GTG, nodes are distributed in a Euclidean space, and edges are assigned according to a threshold function involving the distance between nodes as well as randomly chosen node weights. The motivation for analyzing this model is that many real networks (e.g., wireless networks, the Internet, etc.) need to be studied by using a 'richer' stochastic model (which in this case includes both a distance between nodes and weights on the nodes). Here, we analyze the GTG coloring algorithm together with the graph's clique number, showing formally that in spite of the differences in structure between GTG and RGG, the asymptotic behavior of the chromatic number is identical: {chi}1n 1n n / 1n n (1 + {omicron}(1)). Finally, we consider the leading corrections to this expression, again using the coloring algorithm and clique number to provide bounds on the chromatic number. We show that the gap between the lower and upper bound is within C 1n n / (1n 1n n){sup 2}, and specify the constant C.
ERIC Educational Resources Information Center
Nemirovsky, Ricardo; Tierney, Cornelia; Wright, Tracy
1998-01-01
Analyzed two children's use of a computer-based motion detector to make sense of symbolic expressions (Cartesian graphs). Found three themes: (1) tool perspectives, efforts to understand graphical responses to body motion; (2) fusion, emergent ways of talking and behaving that merge symbols and referents; and (3) graphical spaces, when changing…
ERIC Educational Resources Information Center
Donley, H. Edward; George, Elizabeth Ann
1993-01-01
Demonstrates how to construct rational, exponential, and sinusoidal functions that appear normal on one scale but exhibit interesting hidden behavior when viewed on another scale. By exploring these examples, students learn the importance of scale, window size, and resolution effects in computer and calculator graphing. (MAZ)
ERIC Educational Resources Information Center
Krueger, Tom
2010-01-01
In this article, the author shares one effective lesson idea on straight line graphs that he applied in his lower ability Y9 class. The author wanted something interesting for his class to do, something that was fun and engaging with direct feedback, and something that worked because someone else had tried it before. In a word, the author admits…
Temporal Representation in Semantic Graphs
Levandoski, J J; Abdulla, G M
2007-08-07
A wide range of knowledge discovery and analysis applications, ranging from business to biological, make use of semantic graphs when modeling relationships and concepts. Most of the semantic graphs used in these applications are assumed to be static pieces of information, meaning temporal evolution of concepts and relationships are not taken into account. Guided by the need for more advanced semantic graph queries involving temporal concepts, this paper surveys the existing work involving temporal representations in semantic graphs.
Quantum walks on quotient graphs
Krovi, Hari; Brun, Todd A.
2007-06-15
A discrete-time quantum walk on a graph {gamma} is the repeated application of a unitary evolution operator to a Hilbert space corresponding to the graph. If this unitary evolution operator has an associated group of symmetries, then for certain initial states the walk will be confined to a subspace of the original Hilbert space. Symmetries of the original graph, given by its automorphism group, can be inherited by the evolution operator. We show that a quantum walk confined to the subspace corresponding to this symmetry group can be seen as a different quantum walk on a smaller quotient graph. We give an explicit construction of the quotient graph for any subgroup H of the automorphism group and illustrate it with examples. The automorphisms of the quotient graph which are inherited from the original graph are the original automorphism group modulo the subgroup H used to construct it. The quotient graph is constructed by removing the symmetries of the subgroup H from the original graph. We then analyze the behavior of hitting times on quotient graphs. Hitting time is the average time it takes a walk to reach a given final vertex from a given initial vertex. It has been shown in earlier work [Phys. Rev. A 74, 042334 (2006)] that the hitting time for certain initial states of a quantum walks can be infinite, in contrast to classical random walks. We give a condition which determines whether the quotient graph has infinite hitting times given that they exist in the original graph. We apply this condition for the examples discussed and determine which quotient graphs have infinite hitting times. All known examples of quantum walks with hitting times which are short compared to classical random walks correspond to systems with quotient graphs much smaller than the original graph; we conjecture that the existence of a small quotient graph with finite hitting times is necessary for a walk to exhibit a quantum speedup.
A brief history of partitions of numbers, partition functions and their modern applications
NASA Astrophysics Data System (ADS)
Debnath, Lokenath
2016-04-01
A Visual Analytics Paradigm Enabling Trillion-Edge Graph Exploration
Wong, Pak C.; Haglin, David J.; Gillen, David S.; Chavarría-Miranda, Daniel; Castellana, Vito G.; Joslyn, Cliff A.; Chappell, Alan R.; Zhang, Song
2015-07-06
We present a visual analytics paradigm and a system prototype for exploring web-scale graphs. A web-scale graph is described as a graph with ~one trillion edges and ~50 billion vertices. While there is an aggressive R&D effort in processing and exploring web-scale graphs among internet vendors such as Facebook and Google, visualizing a graph of that scale still remains an underexplored R&D area. The paper describes a nontraditional peek-and-filter strategy that facilitates the exploration of a graph database of unprecedented size for visualization and analytics. We demonstrate that our system prototype can 1) preprocess a graph with ~25 billion edges in less than two hours and 2) support database query and visualization on the processed graph database afterward. Based on our computational performance results, we argue that we most likely will achieve the one trillion edge mark (a computational performance improvement of 40 times) for graph visual analytics in the near future.
Graph-state basis for Pauli channels
Chen Xiaoyu; Jiang Lizhen
2011-05-15
Quantum capacities of Pauli channels are not additive, a degenerate quantum code may improve the hashing bound of the capacity. The difficulty in approaching the capacity is how to calculate the coherent information of a generic degenerate quantum code. Using graph state basis, we greatly reduce the problem for the input of quantum error-correcting code. We show that for a graph diagonal state passing through a Pauli channel the output state is diagonalizable and the joint output state of the system and ancilla is block diagonalizable. When the input state is an equal probable mixture of codewords of a stabilizer code, the coherent information can be analytically obtained.
Recursive Feature Extraction in Graphs
2014-08-14
ReFeX extracts recursive topological features from graph data. The input is a graph as a csv file and the output is a csv file containing feature values for each node in the graph. The features are based on topological counts in the neighborhoods of each nodes, as well as recursive summaries of neighbors' features.
Mining and Indexing Graph Databases
ERIC Educational Resources Information Center
Yuan, Dayu
2013-01-01
Graphs are widely used to model structures and relationships of objects in various scientific and commercial fields. Chemical molecules, proteins, malware system-call dependencies and three-dimensional mechanical parts are all modeled as graphs. In this dissertation, we propose to mine and index those graph data to enable fast and scalable search.…
ERIC Educational Resources Information Center
Hopkins, Brian
2004-01-01
The interconnected world of actors and movies is a familiar, rich example for graph theory. This paper gives the history of the "Kevin Bacon Game" and makes extensive use of a Web site to analyze the underlying graph. The main content is the classroom development of the weighted average to determine the best choice of "center" for the graph. The…
ERIC Educational Resources Information Center
Skurnick, Ronald; Davi, Charles; Skurnick, Mia
2005-01-01
Since 1952, several well-known graph theorists have proven numerous results regarding Hamiltonian graphs. In fact, many elementary graph theory textbooks contain the theorems of Ore, Bondy and Chvatal, Chvatal and Erdos, Posa, and Dirac, to name a few. In this note, the authors state and prove some propositions of their own concerning Hamiltonian…
Winlaw, Manda; De Sterck, Hans; Sanders, Geoffrey
2015-10-26
In very simple terms a network can be de ned as a collection of points joined together by lines. Thus, networks can be used to represent connections between entities in a wide variety of elds including engi- neering, science, medicine, and sociology. Many large real-world networks share a surprising number of properties, leading to a strong interest in model development research and techniques for building synthetic networks have been developed, that capture these similarities and replicate real-world graphs. Modeling these real-world networks serves two purposes. First, building models that mimic the patterns and prop- erties of real networks helps to understand the implications of these patterns and helps determine which patterns are important. If we develop a generative process to synthesize real networks we can also examine which growth processes are plausible and which are not. Secondly, high-quality, large-scale network data is often not available, because of economic, legal, technological, or other obstacles [7]. Thus, there are many instances where the systems of interest cannot be represented by a single exemplar network. As one example, consider the eld of cybersecurity, where systems require testing across diverse threat scenarios and validation across diverse network structures. In these cases, where there is no single exemplar network, the systems must instead be modeled as a collection of networks in which the variation among them may be just as important as their common features. By developing processes to build synthetic models, so-called graph generators, we can build synthetic networks that capture both the essential features of a system and realistic variability. Then we can use such synthetic graphs to perform tasks such as simulations, analysis, and decision making. We can also use synthetic graphs to performance test graph analysis algorithms, including clustering algorithms and anomaly detection algorithms.
Towards Scalable Graph Computation on Mobile Devices
Chen, Yiqi; Lin, Zhiyuan; Pienta, Robert; Kahng, Minsuk; Chau, Duen Horng
2015-01-01
Mobile devices have become increasingly central to our everyday activities, due to their portability, multi-touch capabilities, and ever-improving computational power. Such attractive features have spurred research interest in leveraging mobile devices for computation. We explore a novel approach that aims to use a single mobile device to perform scalable graph computation on large graphs that do not fit in the device's limited main memory, opening up the possibility of performing on-device analysis of large datasets, without relying on the cloud. Based on the familiar memory mapping capability provided by today's mobile operating systems, our approach to scale up computation is powerful and intentionally kept simple to maximize its applicability across the iOS and Android platforms. Our experiments demonstrate that an iPad mini can perform fast computation on large real graphs with as many as 272 million edges (Google+ social graph), at a speed that is only a few times slower than a 13″ Macbook Pro. Through creating a real world iOS app with this technique, we demonstrate the strong potential application for scalable graph computation on a single mobile device using our approach. PMID:25859564
Towards Scalable Graph Computation on Mobile Devices.
Chen, Yiqi; Lin, Zhiyuan; Pienta, Robert; Kahng, Minsuk; Chau, Duen Horng
2014-10-01
Mobile devices have become increasingly central to our everyday activities, due to their portability, multi-touch capabilities, and ever-improving computational power. Such attractive features have spurred research interest in leveraging mobile devices for computation. We explore a novel approach that aims to use a single mobile device to perform scalable graph computation on large graphs that do not fit in the device's limited main memory, opening up the possibility of performing on-device analysis of large datasets, without relying on the cloud. Based on the familiar memory mapping capability provided by today's mobile operating systems, our approach to scale up computation is powerful and intentionally kept simple to maximize its applicability across the iOS and Android platforms. Our experiments demonstrate that an iPad mini can perform fast computation on large real graphs with as many as 272 million edges (Google+ social graph), at a speed that is only a few times slower than a 13″ Macbook Pro. Through creating a real world iOS app with this technique, we demonstrate the strong potential application for scalable graph computation on a single mobile device using our approach.
Orthocomplemented complete lattices and graphs
NASA Astrophysics Data System (ADS)
Ollech, Astrid
1995-08-01
The problem I consider originates from Dörfler, who found a construction to assign an Orthocomplemented lattice H(G) to a graph G. By Dörfler it is known that for every finite Orthocomplemented lattice L there exists a graph G such that H(G)=L. Unfortunately, we can find more than one graph G with this property, i.e., orthocomplemented lattices which belong to different graphs can be isomorphic. I show some conditions under which two graphs have the same orthocomplemented lattice.
Spectral fluctuations of quantum graphs
Pluhař, Z.; Weidenmüller, H. A.
2014-10-15
We prove the Bohigas-Giannoni-Schmit conjecture in its most general form for completely connected simple graphs with incommensurate bond lengths. We show that for graphs that are classically mixing (i.e., graphs for which the spectrum of the classical Perron-Frobenius operator possesses a finite gap), the generating functions for all (P,Q) correlation functions for both closed and open graphs coincide (in the limit of infinite graph size) with the corresponding expressions of random-matrix theory, both for orthogonal and for unitary symmetry.
Prostate cancer grading: use of graph cut and spatial arrangement of nuclei.
Nguyen, Kien; Sarkar, Anindya; Jain, Anil K
2014-12-01
Tissue image grading is one of the most important steps in prostate cancer diagnosis, where the pathologist relies on the gland structure to assign a Gleason grade to the tissue image. In this grading scheme, the discrimination between grade 3 and grade 4 is the most difficult, and receives the most attention from researchers. In this study, we propose a novel method (called nuclei-based method) that 1) utilizes graph theory techniques to segment glands and 2) computes a gland-score (based on the spatial arrangement of nuclei) to estimate how similar a segmented region is to a gland. Next, we create a fusion method by combining this nuclei-based method with the lumen-based method presented in our previous work to improve the performance of grade 3 versus grade 4 classification problem (the accuracy is now improved to 87.3% compared to 81.1% of the lumen-based method alone). To segment glands, we build a graph of nuclei and lumina in the image, and use the normalized cut method to partition the graph into different components, each corresponding to a gland. Unlike most state-of-the-art lumen-based gland segmentation method, the nuclei-based method is able to segment glands without lumen or glands with multiple lumina. Moreover, another important contribution in this research is the development of a set of measures to exploit the difference in nuclei spatial arrangement between grade 3 images (where nuclei form closed chain structure on the gland boundary) and grade 4 image (where nuclei distribute more randomly in the gland). These measures are combined to generate a single gland-score value, which estimates how similar a segmented region (which is a set of nuclei and lumina) is to a gland.
A new graph drawing scheme for social network.
Wang, Eric Ke; Zou, Futai
2014-01-01
With the development of social networks, people have started to use social network tools to record their life and work more and more frequently. How to analyze social networks to explore potential characteristics and trend of social events has been a hot research topic. In order to analyze it effectively, a kind of techniques called information visualization is employed to extract the potential information from the large scale of social network data and present the information briefly as visualized graphs. In the process of information visualization, graph drawing is a crucial part. In this paper, we study the graph layout algorithms and propose a new graph drawing scheme combining multilevel and single-level drawing approaches, including the graph division method based on communities and refining approach based on partitioning strategy. Besides, we compare the effectiveness of our scheme and FM(3) in experiments. The experiment results show that our scheme can achieve a clearer diagram and effectively extract the community structure of the social network to be applied to drawing schemes.
Exact Algorithms for Coloring Graphs While Avoiding Monochromatic Cycles
NASA Astrophysics Data System (ADS)
Talla Nobibon, Fabrice; Hurkens, Cor; Leus, Roel; Spieksma, Frits C. R.
We consider the problem of deciding whether a given directed graph can be vertex partitioned into two acyclic subgraphs. Applications of this problem include testing rationality of collective consumption behavior, a subject in micro-economics. We identify classes of directed graphs for which the problem is easy and prove that the existence of a constant factor approximation algorithm is unlikely for an optimization version which maximizes the number of vertices that can be colored using two colors while avoiding monochromatic cycles. We present three exact algorithms, namely an integer-programming algorithm based on cycle identification, a backtracking algorithm, and a branch-and-check algorithm. We compare these three algorithms both on real-life instances and on randomly generated graphs. We find that for the latter set of graphs, every algorithm solves instances of considerable size within few seconds; however, the CPU time of the integer-programming algorithm increases with the number of vertices in the graph while that of the two other procedures does not. For every algorithm, we also study empirically the transition from a high to a low probability of YES answer as function of a parameter of the problem. For real-life instances, the integer-programming algorithm fails to solve the largest instance after one hour while the other two algorithms solve it in about ten minutes.
Complete graph model for community detection
NASA Astrophysics Data System (ADS)
Sun, Peng Gang; Sun, Xiya
2017-04-01
Community detection brings plenty of considerable problems, which has attracted more attention for many years. This paper develops a new framework, which tries to measure the interior and the exterior of a community based on a same metric, complete graph model. In particular, the exterior is modeled as a complete bipartite. We partition a network into subnetworks by maximizing the difference between the interior and the exterior of the subnetworks. In addition, we compare our approach with some state of the art methods on computer-generated networks based on the LFR benchmark as well as real-world networks. The experimental results indicate that our approach obtains better results for community detection, is capable of splitting irregular networks and achieves perfect results on the karate network and the dolphin network.
2010-12-02
evaluating the function ΘP (A) for any fixed A,P is equivalent to solving the so-called Quadratic Assignment Problem ( QAP ), and thus we can employ various...tractable linear programming, spectral, and SDP relaxations of QAP [40, 11, 33]. In particular we discuss recent work [14] on exploiting group...symmetry in SDP relaxations of QAP , which is useful for approximately computing elementary convex graph invariants in many interesting cases. Finally in
ERIC Educational Resources Information Center
Syed, M. Qasim; Lovatt, Ian
2014-01-01
This paper is an addition to the series of papers on the exponential function begun by Albert Bartlett. In particular, we ask how the graph of the exponential function y = e[superscript -t/t] would appear if y were plotted versus ln t rather than the normal practice of plotting ln y versus t. In answering this question, we find a new way to…
An asynchronous traversal engine for graph-based rich metadata management
Dai, Dong; Carns, Philip; Ross, Robert B.; Jenkins, John; Muirhead, Nicholas; Chen, Yong
2016-06-23
and execution merging) necessary for efficient performance. We further explore the effect of different graph partitioning strategies on the traversal performance for both synchronous and asynchronous traversal engines. Our experiments show that the asynchronous graph traversal engine is more efficient than its synchronous counterpart in the case of HPC rich metadata processing, where more servers are involved and larger traversals are needed. Furthermore, the asynchronous traversal engine is more adaptive to different graph partitioning strategies.
An asynchronous traversal engine for graph-based rich metadata management
Dai, Dong; Carns, Philip; Ross, Robert B.; ...
2016-06-23
-affiliate caching and execution merging) necessary for efficient performance. We further explore the effect of different graph partitioning strategies on the traversal performance for both synchronous and asynchronous traversal engines. Our experiments show that the asynchronous graph traversal engine is more efficient than its synchronous counterpart in the case of HPC rich metadata processing, where more servers are involved and larger traversals are needed. Furthermore, the asynchronous traversal engine is more adaptive to different graph partitioning strategies.« less
Iron Partitioning in Ferropericlase
NASA Astrophysics Data System (ADS)
Braithwaite, J. W. H.; Stixrude, L. P.; Pinilla, C.; Holmstrom, E.
2015-12-01
Ferropericlase, (Mg,Fe)O, is the second most abundant mineral in the Earth's lower mantle. Whether iron favours the liquid or solid phase of (Mg,Fe)O has important implications for the Earth's mantle, both chemically and dynamically. As iron is much heavier than magnesium, the partitioning of iron between liquid and solid will lead to a contrast in densities. This difference in density will lead one phase to be more buoyant than the other and would help, in part, to explain how the mantle crystallised from the magma ocean of the Hadean eon to its current state. The partitioning of iron between the two phases is characterized by partition coefficients. Using ab-initio methods, thermodynamic integration and adiabatic switching these coefficients have been determined. Results are presented for pressures encompassing the region between the upper mantle and the core-mantle boundary (10-140GPa).
NASA Technical Reports Server (NTRS)
Vanalstine, James M.
1993-01-01
Project NAS8-36955 D.O. #100 initially involved the following tasks: (1) evaluation of various coatings' ability to control wall wetting and surface zeta potential expression; (2) testing various methods to mix and control the demixing of phase systems; and (3) videomicroscopic investigation of cell partition. Three complementary areas were identified for modification and extension of the original contract. They were: (1) identification of new supports for column cell partition; (2) electrokinetic detection of protein adsorption; and (3) emulsion studies related to bioseparations.
Fast clique minor generation in Chimera qubit connectivity graphs
NASA Astrophysics Data System (ADS)
Boothby, Tomas; King, Andrew D.; Roy, Aidan
2016-01-01
The current generation of D-Wave quantum annealing processor is designed to minimize the energy of an Ising spin configuration whose pairwise interactions lie on the edges of a Chimera graph C_{M,N,L}. In order to solve an Ising spin problem with arbitrary pairwise interaction structure, the corresponding graph must be minor-embedded into a Chimera graph. We define a combinatorial class of native clique minors in Chimera graphs with vertex images of uniform, near minimal size and provide a polynomial-time algorithm that finds a maximum native clique minor in a given induced subgraph of a Chimera graph. These minors allow improvement over recent work and have immediate practical applications in the field of quantum annealing.
Eigenvector synchronization, graph rigidity and the molecule problem.
Cucuringu, Mihai; Singer, Amit; Cowburn, David
2012-12-01
The graph realization problem has received a great deal of attention in recent years, due to its importance in applications such as wireless sensor networks and structural biology. In this paper, we extend the previous work and propose the 3D-As-Synchronized-As-Possible (3D-ASAP) algorithm, for the graph realization problem in ℝ(3), given a sparse and noisy set of distance measurements. 3D-ASAP is a divide and conquer, non-incremental and non-iterative algorithm, which integrates local distance information into a global structure determination. Our approach starts with identifying, for every node, a subgraph of its 1-hop neighborhood graph, which can be accurately embedded in its own coordinate system. In the noise-free case, the computed coordinates of the sensors in each patch must agree with their global positioning up to some unknown rigid motion, that is, up to translation, rotation and possibly reflection. In other words, to every patch, there corresponds an element of the Euclidean group, Euc(3), of rigid transformations in ℝ(3), and the goal was to estimate the group elements that will properly align all the patches in a globally consistent way. Furthermore, 3D-ASAP successfully incorporates information specific to the molecule problem in structural biology, in particular information on known substructures and their orientation. In addition, we also propose 3D-spectral-partitioning (SP)-ASAP, a faster version of 3D-ASAP, which uses a spectral partitioning algorithm as a pre-processing step for dividing the initial graph into smaller subgraphs. Our extensive numerical simulations show that 3D-ASAP and 3D-SP-ASAP are very robust to high levels of noise in the measured distances and to sparse connectivity in the measurement graph, and compare favorably with similar state-of-the-art localization algorithms.
Thermodynamic characterization of networks using graph polynomials
NASA Astrophysics Data System (ADS)
Ye, Cheng; Comin, César H.; Peron, Thomas K. DM.; Silva, Filipi N.; Rodrigues, Francisco A.; Costa, Luciano da F.; Torsello, Andrea; Hancock, Edwin R.
2015-09-01
In this paper, we present a method for characterizing the evolution of time-varying complex networks by adopting a thermodynamic representation of network structure computed from a polynomial (or algebraic) characterization of graph structure. Commencing from a representation of graph structure based on a characteristic polynomial computed from the normalized Laplacian matrix, we show how the polynomial is linked to the Boltzmann partition function of a network. This allows us to compute a number of thermodynamic quantities for the network, including the average energy and entropy. Assuming that the system does not change volume, we can also compute the temperature, defined as the rate of change of entropy with energy. All three thermodynamic variables can be approximated using low-order Taylor series that can be computed using the traces of powers of the Laplacian matrix, avoiding explicit computation of the normalized Laplacian spectrum. These polynomial approximations allow a smoothed representation of the evolution of networks to be constructed in the thermodynamic space spanned by entropy, energy, and temperature. We show how these thermodynamic variables can be computed in terms of simple network characteristics, e.g., the total number of nodes and node degree statistics for nodes connected by edges. We apply the resulting thermodynamic characterization to real-world time-varying networks representing complex systems in the financial and biological domains. The study demonstrates that the method provides an efficient tool for detecting abrupt changes and characterizing different stages in network evolution.
Evaluation of Graph Pattern Matching Workloads in Graph Analysis Systems
Hong, Seokyong; Lee, Sangkeun; Lim, Seung-Hwan; Sukumar, Sreenivas Rangan; Vatsavai, Raju
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: 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.
A significance test for graph-constrained estimation.
Zhao, Sen; Shojaie, Ali
2016-06-01
Graph-constrained estimation methods encourage similarities among neighboring covariates presented as nodes of a graph, and can result in more accurate estimates, especially in high-dimensional settings. Variable selection approaches can then be utilized to select a subset of variables that are associated with the response. However, existing procedures do not provide measures of uncertainty of estimates. Further, the vast majority of existing approaches assume that available graph accurately captures the association among covariates; violations to this assumption could severely hurt the reliability of the resulting estimates. In this article, we present a new inference framework, called the Grace test, which produces coefficient estimates and corresponding p-values by incorporating the external graph information. We show, both theoretically and via numerical studies, that the proposed method asymptotically controls the type-I error rate regardless of the choice of the graph. We also show that when the underlying graph is informative, the Grace test is asymptotically more powerful than similar tests that ignore the external information. We study the power properties of the proposed test when the graph is not fully informative and develop a more powerful Grace-ridge test for such settings. Our numerical studies show that as long as the graph is reasonably informative, the proposed inference procedures deliver improved statistical power over existing methods that ignore external information.
Robust deformable and occluded object tracking with dynamic graph.
Cai, Zhaowei; Wen, Longyin; Lei, Zhen; Vasconcelos, Nuno; Li, Stan Z
2014-12-01
While some efforts have been paid to handle deformation and occlusion in visual tracking, they are still great challenges. In this paper, a dynamic graph-based tracker (DGT) is proposed to address these two challenges in a unified framework. In the dynamic target graph, nodes are the target local parts encoding appearance information, and edges are the interactions between nodes encoding inner geometric structure information. This graph representation provides much more information for tracking in the presence of deformation and occlusion. The target tracking is then formulated as tracking this dynamic undirected graph, which is also a matching problem between the target graph and the candidate graph. The local parts within the candidate graph are separated from the background with Markov random field, and spectral clustering is used to solve the graph matching. The final target state is determined through a weighted voting procedure according to the reliability of part correspondence, and refined with recourse to a foreground/background segmentation. An effective online updating mechanism is proposed to update the model, allowing DGT to robustly adapt to variations of target structure. Experimental results show improved performance over several state-of-the-art trackers, in various challenging scenarios.
Automated Program Recognition by Graph Parsing
1992-07-01
programs are represented as attributed dataflow graphs and a library of clichis is encoded as an attributed graph grammar . Graph parsing is used to...recognition. Second, we investigate the expressiveness of our graph grammar formalism for capturing pro- gramming cliches. Third, we empirically and...library of cliches is encoded as an attributed graph grammar . Graph parsing is used to recognize clich6s in the code. We demonstrate that this graph
Liu, Qian; Chen, Yi-Ping Phoebe; Li, Jinyan
2014-01-07
Many studies are aimed at identifying dense clusters/subgraphs from protein-protein interaction (PPI) networks for protein function prediction. However, the prediction performance based on the dense clusters is actually worse than a simple guilt-by-association method using neighbor counting ideas. This indicates that the local topological structures and properties of PPI networks are still open to new theoretical investigation and empirical exploration. We introduce a novel topological structure called k-partite cliques of protein interactions-a functionally coherent but not-necessarily dense subgraph topology in PPI networks-to study PPI networks. A k-partite protein clique is a maximal k-partite clique comprising two or more nonoverlapping protein subsets between any two of which full interactions are exhibited. In the detection of PPI's maximal k-partite cliques, we propose to transform PPI networks into induced K-partite graphs where edges exist only between the partites. Then, we present a maximal k-partite clique mining (MaCMik) algorithm to enumerate maximal k-partite cliques from K-partite graphs. Our MaCMik algorithm is then applied to a yeast PPI network. We observed interesting and unusually high functional coherence in k-partite protein cliques-the majority of the proteins in k-partite protein cliques, especially those in the same partites, share the same functions, although k-partite protein cliques are not restricted to be dense compared with dense subgraph patterns or (quasi-)cliques. The idea of k-partite protein cliques provides a novel approach of characterizing PPI networks, and so it will help function prediction for unknown proteins.
Graph Coarsening for Path Finding in Cybersecurity Graphs
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 of being used by adversaries.
New methods for analyzing semantic graph based assessments in science education
NASA Astrophysics Data System (ADS)
Vikaros, Lance Steven
This research investigated how the scoring of semantic graphs (known by many as concept maps) could be improved and automated in order to address issues of inter-rater reliability and scalability. As part of the NSF funded SENSE-IT project to introduce secondary school science students to sensor networks (NSF Grant No. 0833440), semantic graphs illustrating how temperature change affects water ecology were collected from 221 students across 16 schools. The graphing task did not constrain students' use of terms, as is often done with semantic graph based assessment due to coding and scoring concerns. The graphing software used provided real-time feedback to help students learn how to construct graphs, stay on topic and effectively communicate ideas. The collected graphs were scored by human raters using assessment methods expected to boost reliability, which included adaptations of traditional holistic and propositional scoring methods, use of expert raters, topical rubrics, and criterion graphs. High levels of inter-rater reliability were achieved, demonstrating that vocabulary constraints may not be necessary after all. To investigate a new approach to automating the scoring of graphs, thirty-two different graph features characterizing graphs' structure, semantics, configuration and process of construction were then used to predict human raters' scoring of graphs in order to identify feature patterns correlated to raters' evaluations of graphs' topical accuracy and complexity. Results led to the development of a regression model able to predict raters' scoring with 77% accuracy, with 46% accuracy expected when used to score new sets of graphs, as estimated via cross-validation tests. Although such performance is comparable to other graph and essay based scoring systems, cross-context testing of the model and methods used to develop it would be needed before it could be recommended for widespread use. Still, the findings suggest techniques for improving the
Zu, Baokai; Xia, Kewen; Pan, Yongke; Niu, Wenjia
2017-01-01
Semisupervised Discriminant Analysis (SDA) is a semisupervised dimensionality reduction algorithm, which can easily resolve the out-of-sample problem. Relative works usually focus on the geometric relationships of data points, which are not obvious, to enhance the performance of SDA. Different from these relative works, the regularized graph construction is researched here, which is important in the graph-based semisupervised learning methods. In this paper, we propose a novel graph for Semisupervised Discriminant Analysis, which is called combined low-rank and k-nearest neighbor (LRKNN) graph. In our LRKNN graph, we map the data to the LR feature space and then the kNN is adopted to satisfy the algorithmic requirements of SDA. Since the low-rank representation can capture the global structure and the k-nearest neighbor algorithm can maximally preserve the local geometrical structure of the data, the LRKNN graph can significantly improve the performance of SDA. Extensive experiments on several real-world databases show that the proposed LRKNN graph is an efficient graph constructor, which can largely outperform other commonly used baselines.
Pan, Yongke; Niu, Wenjia
2017-01-01
Semisupervised Discriminant Analysis (SDA) is a semisupervised dimensionality reduction algorithm, which can easily resolve the out-of-sample problem. Relative works usually focus on the geometric relationships of data points, which are not obvious, to enhance the performance of SDA. Different from these relative works, the regularized graph construction is researched here, which is important in the graph-based semisupervised learning methods. In this paper, we propose a novel graph for Semisupervised Discriminant Analysis, which is called combined low-rank and k-nearest neighbor (LRKNN) graph. In our LRKNN graph, we map the data to the LR feature space and then the kNN is adopted to satisfy the algorithmic requirements of SDA. Since the low-rank representation can capture the global structure and the k-nearest neighbor algorithm can maximally preserve the local geometrical structure of the data, the LRKNN graph can significantly improve the performance of SDA. Extensive experiments on several real-world databases show that the proposed LRKNN graph is an efficient graph constructor, which can largely outperform other commonly used baselines. PMID:28316616
An Efficient Algorithm for Partitioning and Authenticating Problem-Solutions of eLeaming Contents
ERIC Educational Resources Information Center
Dewan, Jahangir; Chowdhury, Morshed; Batten, Lynn
2013-01-01
Content authenticity and correctness is one of the important challenges in eLearning as there can be many solutions to one specific problem in cyber space. Therefore, the authors feel it is necessary to map problems to solutions using graph partition and weighted bipartite matching. This article proposes an efficient algorithm to partition…
ERIC Educational Resources Information Center
Brusco, Michael J.; Kohn, Hans-Friedrich
2009-01-01
The clique partitioning problem (CPP) requires the establishment of an equivalence relation for the vertices of a graph such that the sum of the edge costs associated with the relation is minimized. The CPP has important applications for the social sciences because it provides a framework for clustering objects measured on a collection of nominal…
1973-10-01
The theory of strongly regular graphs was introduced by Bose r7 1 in 1963, in connection with partial geometries and 2 class association schemes. One...non adjacent vertices is constant and equal to ~. We shall denote by ~(p) (reap.r(p)) the set of vertices adjacent (resp.non adjacent) to a vertex p...is the complement of .2’ if the set of vertices of ~ is the set of vertices of .2’ and if two vertices in .2’ are adjacent if and only if they were
Eigensolutions of dodecahedron graphs
NASA Astrophysics Data System (ADS)
Ghosh, Piyali; Karmakar, Somnath; Mandal, Bholanath
2014-02-01
Eigensolutions of 20-vertex cage (i.e. dodecahedron) have been determined with the use of fivefold rotational symmetry. For homo-dodecahedron the eigensolutions become analytical but for the hetero-dodecahedron having two different types of atoms ((C,N),(C,B),(B,N)) the eigensolutions are found to be factored out into five 4-degree polynomials with one corresponding to nondegenerate and other four corresponding to two degenerate eigensolutions. Eigenspectra and total π-electron energies of homo- and hetero-dodecahedron graphs have been calculated.
NASA Technical Reports Server (NTRS)
Burleigh, Scott C.
2011-01-01
Contact Graph Routing (CGR) is a dynamic routing system that computes routes through a time-varying topology of scheduled communication contacts in a network based on the DTN (Delay-Tolerant Networking) architecture. It is designed to enable dynamic selection of data transmission routes in a space network based on DTN. This dynamic responsiveness in route computation should be significantly more effective and less expensive than static routing, increasing total data return while at the same time reducing mission operations cost and risk. The basic strategy of CGR is to take advantage of the fact that, since flight mission communication operations are planned in detail, the communication routes between any pair of bundle agents in a population of nodes that have all been informed of one another's plans can be inferred from those plans rather than discovered via dialogue (which is impractical over long one-way-light-time space links). Messages that convey this planning information are used to construct contact graphs (time-varying models of network connectivity) from which CGR automatically computes efficient routes for bundles. Automatic route selection increases the flexibility and resilience of the space network, simplifying cross-support and reducing mission management costs. Note that there are no routing tables in Contact Graph Routing. The best route for a bundle destined for a given node may routinely be different from the best route for a different bundle destined for the same node, depending on bundle priority, bundle expiration time, and changes in the current lengths of transmission queues for neighboring nodes; routes must be computed individually for each bundle, from the Bundle Protocol agent's current network connectivity model for the bundle s destination node (the contact graph). Clearly this places a premium on optimizing the implementation of the route computation algorithm. The scalability of CGR to very large networks remains a research topic
Noncommutative Riemannian geometry on graphs
NASA Astrophysics Data System (ADS)
Majid, Shahn
2013-07-01
We show that arising out of noncommutative geometry is a natural family of edge Laplacians on the edges of a graph. The family includes a canonical edge Laplacian associated to the graph, extending the usual graph Laplacian on vertices, and we find its spectrum. We show that for a connected graph its eigenvalues are strictly positive aside from one mandatory zero mode, and include all the vertex degrees. Our edge Laplacian is not the graph Laplacian on the line graph but rather it arises as the noncommutative Laplace-Beltrami operator on differential 1-forms, where we use the language of differential algebras to functorially interpret a graph as providing a 'finite manifold structure' on the set of vertices. We equip any graph with a canonical 'Euclidean metric' and a canonical bimodule connection, and in the case of a Cayley graph we construct a metric compatible connection for the Euclidean metric. We make use of results on bimodule connections on inner calculi on algebras, which we prove, including a general relation between zero curvature and the braid relations.
Hinz, Andreas M.
2012-01-01
The appropriate mathematical model for the problem space of tower transformation tasks is the state graph representing positions of discs or balls and their moves. Graph theoretical quantities like distance, eccentricities or degrees of vertices and symmetries of graphs support the choice of problems, the selection of tasks and the analysis of performance of subjects whose solution paths can be projected onto the graph. The mathematical model is also at the base of a computerized test tool to administer various types of tower tasks. PMID:22207419
Ionic partitioning and stomatal regulation
Sanoubar, Rabab; Orsini, Francesco; Gianquinto, Giorgio Prosdocimi
2013-01-01
Vegetable grafting is commonly claimed to improve crop’s tolerance to biotic and abiotic stresses, including salinity. Although the use of inter-specific graftings is relatively common, whether the improved salt tolerance should be attributed to the genotypic background rather than the grafting per se is a matter of discussion among scientists. It is clear that most of published research has to date overlooked the issue, with the mutual presence of self-grafted and non-grafted controls resulting to be quite rare within experimental evidences. It was recently demonstrated that the genotype of the rootstock and grafting per se are responsible respectively for the differential ion accumulation and partitioning as well as to the stomatal adaptation to the stress. The present paper contributes to the ongoing discussion with further data on the differences associated to salinity response in a range of grafted melon combinations. PMID:24309549
Graph Visualization for RDF Graphs with SPARQL-EndPoints
Sukumar, Sreenivas R; Bond, Nathaniel
2014-07-11
RDF graphs are hard to visualize as triples. This software module is a web interface that connects to a SPARQL endpoint and retrieves graph data that the user can explore interactively and seamlessly. The software written in python and JavaScript has been tested to work on screens as little as the smart phones to large screens such as EVEREST.
NASA Astrophysics Data System (ADS)
Kupavskii, A. B.
2014-02-01
We study distance graphs with exponentially large chromatic numbers and without k-cliques, that is, complete subgraphs of size k. Explicit constructions of such graphs use vectors in the integer lattice. For a large class of graphs we find a sharp threshold for containing a k-clique. This enables us to improve the lower bounds for the maximum of the chromatic numbers of such graphs. We give a new probabilistic approach to the construction of distance graphs without k-cliques, and this yields better lower bounds for the maximum of the chromatic numbers for large k.
Kirkpatrick, Bonnie; Reshef, Yakir; Finucane, Hilary; Jiang, Haitao; Zhu, Binhai; Karp, Richard M
2012-09-01
Pedigree graphs, or family trees, are typically constructed by an expensive process of examining genealogical records to determine which pairs of individuals are parent and child. New methods to automate this process take as input genetic data from a set of extant individuals and reconstruct ancestral individuals. There is a great need to evaluate the quality of these methods by comparing the estimated pedigree to the true pedigree. In this article, we consider two main pedigree comparison problems. The first is the pedigree isomorphism problem, for which we present a linear-time algorithm for leaf-labeled pedigrees. The second is the pedigree edit distance problem, for which we present (1) several algorithms that are fast and exact in various special cases, and (2) a general, randomized heuristic algorithm. In the negative direction, we first prove that the pedigree isomorphism problem is as hard as the general graph isomorphism problem, and that the sub-pedigree isomorphism problem is NP-hard. We then show that the pedigree edit distance problem is APX-hard in general and NP-hard on leaf-labeled pedigrees. We use simulated pedigrees to compare our edit-distance algorithms to each other as well as to a branch-and-bound algorithm that always finds an optimal solution.
Maunz, Peter Lukas Wilhelm; Sterk, Jonathan David; Lobser, Daniel; Parekh, Ojas D.; Ryan-Anderson, Ciaran
2016-01-01
In recent years, advanced network analytics have become increasingly important to na- tional security with applications ranging from cyber security to detection and disruption of ter- rorist networks. While classical computing solutions have received considerable investment, the development of quantum algorithms to address problems, such as data mining of attributed relational graphs, is a largely unexplored space. Recent theoretical work has shown that quan- tum algorithms for graph analysis can be more efficient than their classical counterparts. Here, we have implemented a trapped-ion-based two-qubit quantum information proces- sor to address these goals. Building on Sandia's microfabricated silicon surface ion traps, we have designed, realized and characterized a quantum information processor using the hyperfine qubits encoded in two 171 Yb + ions. We have implemented single qubit gates using resonant microwave radiation and have employed Gate set tomography (GST) to characterize the quan- tum process. For the first time, we were able to prove that the quantum process surpasses the fault tolerance thresholds of some quantum codes by demonstrating a diamond norm distance of less than 1 . 9 x 10 [?] 4 . We used Raman transitions in order to manipulate the trapped ions' motion and realize two-qubit gates. We characterized the implemented motion sensitive and insensitive single qubit processes and achieved a maximal process infidelity of 6 . 5 x 10 [?] 5 . We implemented the two-qubit gate proposed by Molmer and Sorensen and achieved a fidelity of more than 97 . 7%.
Quantization of gauge fields, graph polynomials and graph homology
Kreimer, Dirk; 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. -- 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.
High performance genetic algorithm for VLSI circuit partitioning
NASA Astrophysics Data System (ADS)
Dinu, Simona
2016-12-01
Partitioning is one of the biggest challenges in computer-aided design for VLSI circuits (very large-scale integrated circuits). This work address the min-cut balanced circuit partitioning problem- dividing the graph that models the circuit into almost equal sized k sub-graphs while minimizing the number of edges cut i.e. minimizing the number of edges connecting the sub-graphs. The problem may be formulated as a combinatorial optimization problem. Experimental studies in the literature have shown the problem to be NP-hard and thus it is important to design an efficient heuristic algorithm to solve it. The approach proposed in this study is a parallel implementation of a genetic algorithm, namely an island model. The information exchange between the evolving subpopulations is modeled using a fuzzy controller, which determines an optimal balance between exploration and exploitation of the solution space. The results of simulations show that the proposed algorithm outperforms the standard sequential genetic algorithm both in terms of solution quality and convergence speed. As a direction for future study, this research can be further extended to incorporate local search operators which should include problem-specific knowledge. In addition, the adaptive configuration of mutation and crossover rates is another guidance for future research.
Dependence Graphs for Information Assurance of Systems
2003-06-01
in sequential programs using dependence analysis, which provides a sound basis for understanding such information flows. The goal was to develop...the design of extensions to the dependence analysis to support concurrency and asynchronous transfer of control. To improve accuracy, it was necessary...achieving results in the area of dependence -graph representations, and queries for software assurance. The results of the research are described in the appendices.
Blind Identification of Graph Filters
NASA Astrophysics Data System (ADS)
Segarra, Santiago; Mateos, Gonzalo; Marques, Antonio G.; Ribeiro, Alejandro
2017-03-01
Network processes are often represented as signals defined on the vertices of a graph. To untangle the latent structure of such signals, one can view them as outputs of linear graph filters modeling underlying network dynamics. This paper deals with the problem of joint identification of a graph filter and its input signal, thus broadening the scope of classical blind deconvolution of temporal and spatial signals to the less-structured graph domain. Given a graph signal $\\mathbf{y}$ modeled as the output of a graph filter, the goal is to recover the vector of filter coefficients $\\mathbf{h}$, and the input signal $\\mathbf{x}$ which is assumed to be sparse. While $\\mathbf{y}$ is a bilinear function of $\\mathbf{x}$ and $\\mathbf{h}$, the filtered graph signal is also a linear combination of the entries of the lifted rank-one, row-sparse matrix $\\mathbf{x} \\mathbf{h}^T$. The blind graph-filter identification problem can thus be tackled via rank and sparsity minimization subject to linear constraints, an inverse problem amenable to convex relaxations offering provable recovery guarantees under simplifying assumptions. Numerical tests using both synthetic and real-world networks illustrate the merits of the proposed algorithms, as well as the benefits of leveraging multiple signals to aid the blind identification task.
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.
ERIC Educational Resources Information Center
Axtell, M.; Stickles, J.
2010-01-01
The last ten years have seen an explosion of research in the zero-divisor graphs of commutative rings--by professional mathematicians "and" undergraduates. The objective is to find algebraic information within the geometry of these graphs. This topic is approachable by anyone with one or two semesters of abstract algebra. This article gives the…
Graphs as Statements of Belief.
ERIC Educational Resources Information Center
Lake, David
2002-01-01
Identifies points where beliefs are important when making decisions about how graphs are drawn. Describes a simple case of the reaction between 'bicarb soda' and orange or lemon juice and discusses how drawing a graph becomes a statement of belief. (KHR)
In-Memory Graph Databases for Web-Scale Data
Castellana, Vito G.; Morari, Alessandro; Weaver, Jesse R.; Tumeo, Antonino; Haglin, David J.; Villa, Oreste; Feo, John
2015-03-01
RDF databases have emerged as one of the most relevant way for organizing, integrating, and managing expo- nentially growing, often heterogeneous, and not rigidly structured data for a variety of scientific and commercial fields. In this paper we discuss the solutions integrated in GEMS (Graph database Engine for Multithreaded Systems), a software framework for implementing RDF databases on commodity, distributed-memory high-performance clusters. Unlike the majority of current RDF databases, GEMS has been designed from the ground up to primarily employ graph-based methods. This is reflected in all the layers of its stack. The GEMS framework is composed of: a SPARQL-to-C++ compiler, a library of data structures and related methods to access and modify them, and a custom runtime providing lightweight software multithreading, network messages aggregation and a partitioned global address space. We provide an overview of the framework, detailing its component and how they have been closely designed and customized to address issues of graph methods applied to large-scale datasets on clusters. We discuss in details the principles that enable automatic translation of the queries (expressed in SPARQL, the query language of choice for RDF databases) to graph methods, and identify differences with respect to other RDF databases.
Experimental quantum annealing: case study involving the graph isomorphism problem
Zick, Kenneth M.; Shehab, Omar; French, Matthew
2015-01-01
Quantum annealing is a proposed combinatorial optimization technique meant to exploit quantum mechanical effects such as tunneling and entanglement. Real-world quantum annealing-based solvers require a combination of annealing and classical pre- and post-processing; at this early stage, little is known about how to partition and optimize the processing. This article presents an experimental case study of quantum annealing and some of the factors involved in real-world solvers, using a 504-qubit D-Wave Two machine and the graph isomorphism problem. To illustrate the role of classical pre-processing, a compact Hamiltonian is presented that enables a reduced Ising model for each problem instance. On random N-vertex graphs, the median number of variables is reduced from N2 to fewer than N log2 N and solvable graph sizes increase from N = 5 to N = 13. Additionally, error correction via classical post-processing majority voting is evaluated. While the solution times are not competitive with classical approaches to graph isomorphism, the enhanced solver ultimately classified correctly every problem that was mapped to the processor and demonstrated clear advantages over the baseline approach. The results shed some light on the nature of real-world quantum annealing and the associated hybrid classical-quantum solvers. PMID:26053973
Inexact Matching of Ontology Graphs Using Expectation-Maximization
Doshi, Prashant; Kolli, Ravikanth; Thomas, Christopher
2009-01-01
We present a new method for mapping ontology schemas that address similar domains. The problem of ontology matching is crucial since we are witnessing a decentralized development and publication of ontological data. We formulate the problem of inferring a match between two ontologies as a maximum likelihood problem, and solve it using the technique of expectation-maximization (EM). Specifically, we adopt directed graphs as our model for ontology schemas and use a generalized version of EM to arrive at a map between the nodes of the graphs. We exploit the structural, lexical and instance similarity between the graphs, and differ from the previous approaches in the way we utilize them to arrive at, a possibly inexact, match. Inexact matching is the process of finding a best possible match between the two graphs when exact matching is not possible or is computationally difficult. In order to scale the method to large ontologies, we identify the computational bottlenecks and adapt the generalized EM by using a memory bounded partitioning scheme. We provide comparative experimental results in support of our method on two well-known ontology alignment benchmarks and discuss their implications. PMID:20160892
A Collection of Features for Semantic Graphs
Eliassi-Rad, T; Fodor, I K; Gallagher, B
2007-05-02
Semantic graphs are commonly used to represent data from one or more data sources. Such graphs extend traditional graphs by imposing types on both nodes and links. This type information defines permissible links among specified nodes and can be represented as a graph commonly referred to as an ontology or schema graph. Figure 1 depicts an ontology graph for data from National Association of Securities Dealers. Each node type and link type may also have a list of attributes. To capture the increased complexity of semantic graphs, concepts derived for standard graphs have to be extended. This document explains briefly features commonly used to characterize graphs, and their extensions to semantic graphs. This document is divided into two sections. Section 2 contains the feature descriptions for static graphs. Section 3 extends the features for semantic graphs that vary over time.
TIFF Image Writer patch for OpenSceneGraph
Eldridge, Bryce
2012-01-05
This software consists of code modifications to the open-source OpenSceneGraph software package to enable the creation of TlFF images containing 16 bit unsigned data. They also allow the user to disable compression and set the DPI tags in the resulting TIFF Images. Some image analysis programs require uncompressed, 16 bit unsigned input data. These code modifications allow programs based on OpenSceneGraph to write out such images, improving connectivity between applications.
Raberto, Marco; Rapallo, Fabio; Scalas, Enrico
2011-01-01
In this paper, we outline a model of graph (or network) dynamics based on two ingredients. The first ingredient is a Markov chain on the space of possible graphs. The second ingredient is a semi-Markov counting process of renewal type. The model consists in subordinating the Markov chain to the semi-Markov counting process. In simple words, this means that the chain transitions occur at random time instants called epochs. The model is quite rich and its possible connections with algebraic geometry are briefly discussed. Moreover, for the sake of simplicity, we focus on the space of undirected graphs with a fixed number of nodes. However, in an example, we present an interbank market model where it is meaningful to use directed graphs or even weighted graphs. PMID:21887245
Graph states of prime-power dimension from generalized CNOT quantum circuit
Chen, Lin; Zhou, D. L.
2016-01-01
We construct multipartite graph states whose dimension is the power of a prime number. This is realized by the finite field, as well as the generalized controlled-NOT quantum circuit acting on two qudits. We propose the standard form of graph states up to local unitary transformations and particle permutations. The form greatly simplifies the classification of graph states as we illustrate up to five qudits. We also show that some graph states are multipartite maximally entangled states in the sense that any bipartition of the system produces a bipartite maximally entangled state. We further prove that 4-partite maximally entangled states exist when the dimension is an odd number at least three or a multiple of four. PMID:27272401
Graph states of prime-power dimension from generalized CNOT quantum circuit.
Chen, Lin; Zhou, D L
2016-06-07
We construct multipartite graph states whose dimension is the power of a prime number. This is realized by the finite field, as well as the generalized controlled-NOT quantum circuit acting on two qudits. We propose the standard form of graph states up to local unitary transformations and particle permutations. The form greatly simplifies the classification of graph states as we illustrate up to five qudits. We also show that some graph states are multipartite maximally entangled states in the sense that any bipartition of the system produces a bipartite maximally entangled state. We further prove that 4-partite maximally entangled states exist when the dimension is an odd number at least three or a multiple of four.
Exploring and Making Sense of Large Graphs
2015-08-01
our fast algorithmic methodologies, we also contribute graph-theoretical ideas and models, and real-world applications in two main areas ??? Single ...Graph Exploration: We show how to interpretably summarize a single graph by identifying its important graph structures. We complement summarization with...effectively learn information about the unknown entities. ??? Multiple-Graph Exploration: We extend the idea of single -graph summarization to time
Completeness and regularity of generalized fuzzy graphs.
Samanta, Sovan; Sarkar, Biswajit; Shin, Dongmin; Pal, Madhumangal
2016-01-01
Fuzzy graphs are the backbone of many real systems like networks, image, scheduling, etc. But, due to some restriction on edges, fuzzy graphs are limited to represent for some systems. Generalized fuzzy graphs are appropriate to avoid such restrictions. In this study generalized fuzzy graphs are introduced. In this study, matrix representation of generalized fuzzy graphs is described. Completeness and regularity are two important parameters of graph theory. Here, regular and complete generalized fuzzy graphs are introduced. Some properties of them are discussed. After that, effective regular graphs are exemplified.
Comparison and enumeration of chemical graphs.
Akutsu, Tatsuya; Nagamochi, Hiroshi
2013-01-01
Chemical compounds are usually represented as graph structured data in computers. In this review article, we overview several graph classes relevant to chemical compounds and the computational complexities of several fundamental problems for these graph classes. In particular, we consider the following problems: determining whether two chemical graphs are identical, determining whether one input chemical graph is a part of the other input chemical graph, finding a maximum common part of two input graphs, finding a reaction atom mapping, enumerating possible chemical graphs, and enumerating stereoisomers. We also discuss the relationship between the fifth problem and kernel functions for chemical compounds.
MTC: A Fast and Robust Graph-Based Transductive Learning Method.
Zhang, Yan-Ming; Huang, Kaizhu; Geng, Guang-Gang; Liu, Cheng-Lin
2015-09-01
Despite the great success of graph-based transductive learning methods, most of them have serious problems in scalability and robustness. In this paper, we propose an efficient and robust graph-based transductive classification method, called minimum tree cut (MTC), which is suitable for large-scale data. Motivated from the sparse representation of graph, we approximate a graph by a spanning tree. Exploiting the simple structure, we develop a linear-time algorithm to label the tree such that the cut size of the tree is minimized. This significantly improves graph-based methods, which typically have a polynomial time complexity. Moreover, we theoretically and empirically show that the performance of MTC is robust to the graph construction, overcoming another big problem of traditional graph-based methods. Extensive experiments on public data sets and applications on web-spam detection and interactive image segmentation demonstrate our method's advantages in aspect of accuracy, speed, and robustness.
GRAPH III: a digitizing and graph plotting program
Selleck, C.B.
1986-03-01
GRAPH is an interactive program that allows the user to perform two functions. The first is to plot two dimensional graphs and the second is to digitize graphs or plots to create data files of points. The program is designed to allow the user to get results quickly and easily. It is written in RATIV (a FORTRAN preprocessor) and is currently in use at Sandia under VMS on a VAX computer and CTSS on a Cray supercomputer. The program provides graphical output through all of the Sandia Virtual Device Interface (VDI) graphics devices. 2 refs., 3 figs., 3 tabs.
On the Exact Evaluation of Certain Instances of the Potts Partition Function by Quantum Computers
NASA Astrophysics Data System (ADS)
Geraci, Joseph; Lidar, Daniel A.
2008-05-01
We present an efficient quantum algorithm for the exact evaluation of either the fully ferromagnetic or anti-ferromagnetic q-state Potts partition function Z for a family of graphs related to irreducible cyclic codes. This problem is related to the evaluation of the Jones and Tutte polynomials. We consider the connection between the weight enumerator polynomial from coding theory and Z and exploit the fact that there exists a quantum algorithm for efficiently estimating Gauss sums in order to obtain the weight enumerator for a certain class of linear codes. In this way we demonstrate that for a certain class of sparse graphs, which we call Irreducible Cyclic Cocycle Code (ICCCɛ) graphs, quantum computers provide a polynomial speed up in the difference between the number of edges and vertices of the graph, and an exponential speed up in q, over the best classical algorithms known to date.
Adaptive graph construction for Isomap manifold learning
NASA Astrophysics Data System (ADS)
Tran, Loc; Zheng, Zezhong; Zhou, Guoqing; Li, Jiang
2015-03-01
Isomap is a classical manifold learning approach that preserves geodesic distance of nonlinear data sets. One of the main drawbacks of this method is that it is susceptible to leaking, where a shortcut appears between normally separated portions of a manifold. We propose an adaptive graph construction approach that is based upon the sparsity property of the l1 norm. The l1 enhanced graph construction method replaces k-nearest neighbors in the classical approach. The proposed algorithm is first tested on the data sets from the UCI data base repository which showed that the proposed approach performs better than the classical approach. Next, the proposed approach is applied to two image data sets and achieved improved performances over standard Isomap.
Local quality functions for graph clustering with non-negative matrix factorization
NASA Astrophysics Data System (ADS)
van Laarhoven, Twan; Marchiori, Elena
2014-12-01
Many graph clustering quality functions suffer from a resolution limit, namely the inability to find small clusters in large graphs. So-called resolution-limit-free quality functions do not have this limit. This property was previously introduced for hard clustering, that is, graph partitioning. We investigate the resolution-limit-free property in the context of non-negative matrix factorization (NMF) for hard and soft graph clustering. To use NMF in the hard clustering setting, a common approach is to assign each node to its highest membership cluster. We show that in this case symmetric NMF is not resolution-limit free, but that it becomes so when hardness constraints are used as part of the optimization. The resulting function is strongly linked to the constant Potts model. In soft clustering, nodes can belong to more than one cluster, with varying degrees of membership. In this setting resolution-limit free turns out to be too strong a property. Therefore we introduce locality, which roughly states that changing one part of the graph does not affect the clustering of other parts of the graph. We argue that this is a desirable property, provide conditions under which NMF quality functions are local, and propose a novel class of local probabilistic NMF quality functions for soft graph clustering.
Schmidt, Deena R; Thomas, Peter J
2014-04-17
Mathematical models of cellular physiological mechanisms often involve random walks on graphs representing transitions within networks of functional states. Schmandt and Galán recently introduced a novel stochastic shielding approximation as a fast, accurate method for generating approximate sample paths from a finite state Markov process in which only a subset of states are observable. For example, in ion-channel models, such as the Hodgkin-Huxley or other conductance-based neural models, a nerve cell has a population of ion channels whose states comprise the nodes of a graph, only some of which allow a transmembrane current to pass. The stochastic shielding approximation consists of neglecting fluctuations in the dynamics associated with edges in the graph not directly affecting the observable states. We consider the problem of finding the optimal complexity reducing mapping from a stochastic process on a graph to an approximate process on a smaller sample space, as determined by the choice of a particular linear measurement functional on the graph. The partitioning of ion-channel states into conducting versus nonconducting states provides a case in point. In addition to establishing that Schmandt and Galán's approximation is in fact optimal in a specific sense, we use recent results from random matrix theory to provide heuristic error estimates for the accuracy of the stochastic shielding approximation for an ensemble of random graphs. Moreover, we provide a novel quantitative measure of the contribution of individual transitions within the reaction graph to the accuracy of the approximate process.
Flying through Graphs: An Introduction to Graph Theory.
ERIC Educational Resources Information Center
McDuffie, Amy Roth
2001-01-01
Presents an activity incorporating basic terminology, concepts, and solution methods of graph theory in the context of solving problems related to air travel. Discusses prerequisite knowledge and resources and includes a teacher's guide with a student worksheet. (KHR)
A Graph Based Backtracking Algorithm for Solving General CSPs
NASA Technical Reports Server (NTRS)
Pang, Wanlin; Goodwin, Scott D.
2003-01-01
Many AI tasks can be formalized as constraint satisfaction problems (CSPs), which involve finding values for variables subject to constraints. While solving a CSP is an NP-complete task in general, tractable classes of CSPs have been identified based on the structure of the underlying constraint graphs. Much effort has been spent on exploiting structural properties of the constraint graph to improve the efficiency of finding a solution. These efforts contributed to development of a class of CSP solving algorithms called decomposition algorithms. The strength of CSP decomposition is that its worst-case complexity depends on the structural properties of the constraint graph and is usually better than the worst-case complexity of search methods. Its practical application is limited, however, since it cannot be applied if the CSP is not decomposable. In this paper, we propose a graph based backtracking algorithm called omega-CDBT, which shares merits and overcomes the weaknesses of both decomposition and search approaches.
TopoLayout: multilevel graph layout by topological features.
Archambault, Daniel; Munzner, Tamara; Auber, David
2007-01-01
We describe TopoLayout, a feature-based, multilevel algorithm that draws undirected graphs based on the topological features they contain. Topological features are detected recursively inside the graph, and their subgraphs are collapsed into single nodes, forming a graph hierarchy. Each feature is drawn with an algorithm tuned for its topology. As would be expected from a feature-based approach, the runtime and visual quality of TopoLayout depends on the number and types of topological features present in the graph. We show experimental results comparing speed and visual quality for TopoLayout against four other multilevel algorithms on a variety of data sets with a range of connectivities and sizes. TopoLayout frequently improves the results in terms of speed and visual quality on these data sets.
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
DNA Rearrangements through Spatial Graphs
NASA Astrophysics Data System (ADS)
Jonoska, Nataša; Saito, Masahico
The paper is a short overview of a recent model of homologous DNA recombination events guided by RNA templates that have been observed in certain species of ciliates. This model uses spatial graphs to describe DNA rearrangements and show how gene recombination can be modeled as topological braiding of the DNA. We show that a graph structure, which we refer to as an assembly graph, containing only 1- and 4-valent rigid vertices can provide a physical representation of the DNA at the time of recombination. With this representation, 4-valent vertices correspond to the alignment of the recombination sites, and we model the actual recombination event as smoothing of these vertices.
Uncluttering graph layouts using anisotropic diffusion and mass transport.
Frishman, Yaniv; Tal, Ayellet
2009-01-01
Many graph layouts include very dense areas, making the layout difficult to understand. In this paper, we propose a technique for modifying an existing layout in order to reduce the clutter in dense areas. A physically inspired evolution process based on a modified heat equation is used to create an improved layout density image, making better use of available screen space. Using results from optimal mass transport problems, a warp to the improved density image is computed. The graph nodes are displaced according to the warp. The warp maintains the overall structure of the graph, thus limiting disturbances to the mental map, while reducing the clutter in dense areas of the layout. The complexity of the algorithm depends mainly on the resolution of the image visualizing the graph and is linear in the size of the graph. This allows scaling the computation according to required running times. It is demonstrated how the algorithm can be significantly accelerated using a graphics processing unit (GPU), resulting in the ability to handle large graphs in a matter of seconds. Results on several layout algorithms and applications are demonstrated.
Structural pursuit over multiple undirected graphs*
Zhu, Yunzhang; Shen, Xiaotong; Pan, Wei
2014-01-01
Summary Gaussian graphical models are useful to analyze and visualize conditional dependence relationships between interacting units. Motivated from network analysis under di erent experimental conditions, such as gene networks for disparate cancer subtypes, we model structural changes over multiple networks with possible heterogeneities. In particular, we estimate multiple precision matrices describing dependencies among interacting units through maximum penalized likelihood. Of particular interest are homogeneous groups of similar entries across and zero-entries of these matrices, referred to as clustering and sparseness structures, respectively. A non-convex method is proposed to seek a sparse representation for each matrix and identify clusters of the entries across the matrices. Computationally, we develop an e cient method on the basis of di erence convex programming, the augmented Lagrangian method and the block-wise coordinate descent method, which is scalable to hundreds of graphs of thousands nodes through a simple necessary and sufficient partition rule, which divides nodes into smaller disjoint subproblems excluding zero-coe cients nodes for arbitrary graphs with convex relaxation. Theoretically, a finite-sample error bound is derived for the proposed method to reconstruct the clustering and sparseness structures. This leads to consistent reconstruction of these two structures simultaneously, permitting the number of unknown parameters to be exponential in the sample size, and yielding the optimal performance of the oracle estimator as if the true structures were given a priori. Simulation studies suggest that the method enjoys the benefit of pursuing these two disparate kinds of structures, and compares favorably against its convex counterpart in the accuracy of structure pursuit and parameter estimation. PMID:25642006
Chemical amplification based on fluid partitioning
Anderson, Brian L.; Colston, Jr., Billy W.; Elkin, Chris
2006-05-09
A system for nucleic acid amplification of a sample comprises partitioning the sample into partitioned sections and performing PCR on the partitioned sections of the sample. Another embodiment of the invention provides a system for nucleic acid amplification and detection of a sample comprising partitioning the sample into partitioned sections, performing PCR on the partitioned sections of the sample, and detecting and analyzing the partitioned sections of the sample.
NASA Astrophysics Data System (ADS)
Gibbard, Philip L.; Lewin, John
2016-11-01
We review the historical purposes and procedures for stratigraphical division and naming within the Quaternary, and summarize the current requirements for formal partitioning through the International Commission on Stratigraphy (ICS). A raft of new data and evidence has impacted traditional approaches: quasi-continuous records from ocean sediments and ice cores, new numerical dating techniques, and alternative macro-models, such as those provided through Sequence Stratigraphy and Earth-System Science. The practical usefulness of division remains, but there is now greater appreciation of complex Quaternary detail and the modelling of time continua, the latter also extending into the future. There are problems both of commission (what is done, but could be done better) and of omission (what gets left out) in partitioning the Quaternary. These include the challenge set by the use of unconformities as stage boundaries, how to deal with multiphase records in ocean and terrestrial sediments, what happened at the 'Early-Mid- (Middle) Pleistocene Transition', dealing with trends that cross phase boundaries, and the current controversial focus on how to subdivide the Holocene and formally define an 'Anthropocene'.
Unsupervised segmentation of MRI knees using image partition forests
NASA Astrophysics Data System (ADS)
Marčan, Marija; Voiculescu, Irina
2016-03-01
Nowadays many people are affected by arthritis, a condition of the joints with limited prevention measures, but with various options of treatment the most radical of which is surgical. In order for surgery to be successful, it can make use of careful analysis of patient-based models generated from medical images, usually by manual segmentation. In this work we show how to automate the segmentation of a crucial and complex joint -- the knee. To achieve this goal we rely on our novel way of representing a 3D voxel volume as a hierarchical structure of partitions which we have named Image Partition Forest (IPF). The IPF contains several partition layers of increasing coarseness, with partitions nested across layers in the form of adjacency graphs. On the basis of a set of properties (size, mean intensity, coordinates) of each node in the IPF we classify nodes into different features. Values indicating whether or not any particular node belongs to the femur or tibia are assigned through node filtering and node-based region growing. So far we have evaluated our method on 15 MRI knee images. Our unsupervised segmentation compared against a hand-segmented gold standard has achieved an average Dice similarity coefficient of 0.95 for femur and 0.93 for tibia, and an average symmetric surface distance of 0.98 mm for femur and 0.73 mm for tibia. The paper also discusses ways to introduce stricter morphological and spatial conditioning in the bone labelling process.
Iterative cross section sequence graph for handwritten character segmentation.
Dawoud, Amer
2007-08-01
The iterative cross section sequence graph (ICSSG) is an algorithm for handwritten character segmentation. It expands the cross section sequence graph concept by applying it iteratively at equally spaced thresholds. The iterative thresholding reduces the effect of information loss associated with image binarization. ICSSG preserves the characters' skeletal structure by preventing the interference of pixels that causes flooding of adjacent characters' segments. Improving the structural quality of the characters' skeleton facilitates better feature extraction and classification, which improves the overall performance of optical character recognition (OCR). Experimental results showed significant improvements in OCR recognition rates compared to other well-established segmentation algorithms.
A Ranking Approach on Large-Scale Graph With Multidimensional Heterogeneous Information.
Wei, Wei; Gao, Bin; Liu, Tie-Yan; Wang, Taifeng; Li, Guohui; Li, Hang
2016-04-01
Graph-based ranking has been extensively studied and frequently applied in many applications, such as webpage ranking. It aims at mining potentially valuable information from the raw graph-structured data. Recently, with the proliferation of rich heterogeneous information (e.g., node/edge features and prior knowledge) available in many real-world graphs, how to effectively and efficiently leverage all information to improve the ranking performance becomes a new challenging problem. Previous methods only utilize part of such information and attempt to rank graph nodes according to link-based methods, of which the ranking performances are severely affected by several well-known issues, e.g., over-fitting or high computational complexity, especially when the scale of graph is very large. In this paper, we address the large-scale graph-based ranking problem and focus on how to effectively exploit rich heterogeneous information of the graph to improve the ranking performance. Specifically, we propose an innovative and effective semi-supervised PageRank (SSP) approach to parameterize the derived information within a unified semi-supervised learning framework (SSLF-GR), then simultaneously optimize the parameters and the ranking scores of graph nodes. Experiments on the real-world large-scale graphs demonstrate that our method significantly outperforms the algorithms that consider such graph information only partially.
Graph anomalies in cyber communications
Vander Wiel, Scott A; Storlie, Curtis B; Sandine, Gary; Hagberg, Aric A; Fisk, Michael
2011-01-11
Enterprises monitor cyber traffic for viruses, intruders and stolen information. Detection methods look for known signatures of malicious traffic or search for anomalies with respect to a nominal reference model. Traditional anomaly detection focuses on aggregate traffic at central nodes or on user-level monitoring. More recently, however, traffic is being viewed more holistically as a dynamic communication graph. Attention to the graph nature of the traffic has expanded the types of anomalies that are being sought. We give an overview of several cyber data streams collected at Los Alamos National Laboratory and discuss current work in modeling the graph dynamics of traffic over the network. We consider global properties and local properties within the communication graph. A method for monitoring relative entropy on multiple correlated properties is discussed in detail.
Constructing Dense Graphs with Unique Hamiltonian Cycles
ERIC Educational Resources Information Center
Lynch, Mark A. M.
2012-01-01
It is not difficult to construct dense graphs containing Hamiltonian cycles, but it is difficult to generate dense graphs that are guaranteed to contain a unique Hamiltonian cycle. This article presents an algorithm for generating arbitrarily large simple graphs containing "unique" Hamiltonian cycles. These graphs can be turned into dense graphs…
The Replica Symmetric Solution for Potts Models on d-Regular Graphs
NASA Astrophysics Data System (ADS)
Dembo, Amir; Montanari, Andrea; Sly, Allan; Sun, Nike
2014-04-01
We establish an explicit formula for the limiting free energy density (log-partition function divided by the number of vertices) for ferromagnetic Potts models on uniformly sparse graph sequences converging locally to the d-regular tree for d even, covering all temperature regimes. This formula coincides with the Bethe free energy functional evaluated at a suitable fixed point of the belief propagation recursion on the d-regular tree, the so-called replica symmetric solution. For uniformly random d-regular graphs we further show that the replica symmetric Bethe formula is an upper bound for the asymptotic free energy for any model with permissive interactions.
CUDA Enabled Graph Subset Examiner
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 vertices 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.
Chromatic polynomials of random graphs
NASA Astrophysics Data System (ADS)
Van Bussel, Frank; Ehrlich, Christoph; Fliegner, Denny; Stolzenberg, Sebastian; Timme, Marc
2010-04-01
Chromatic polynomials and related graph invariants are central objects in both graph theory and statistical physics. Computational difficulties, however, have so far restricted studies of such polynomials to graphs that were either very small, very sparse or highly structured. Recent algorithmic advances (Timme et al 2009 New J. Phys. 11 023001) now make it possible to compute chromatic polynomials for moderately sized graphs of arbitrary structure and number of edges. Here we present chromatic polynomials of ensembles of random graphs with up to 30 vertices, over the entire range of edge density. We specifically focus on the locations of the zeros of the polynomial in the complex plane. The results indicate that the chromatic zeros of random graphs have a very consistent layout. In particular, the crossing point, the point at which the chromatic zeros with non-zero imaginary part approach the real axis, scales linearly with the average degree over most of the density range. While the scaling laws obtained are purely empirical, if they continue to hold in general there are significant implications: the crossing points of chromatic zeros in the thermodynamic limit separate systems with zero ground state entropy from systems with positive ground state entropy, the latter an exception to the third law of thermodynamics.
Graph Matching: Relax at Your Own Risk
Lyzinski, Vince; Fishkind, Donniell E.; Fiori, Marcelo; Vogelstein, Joshua T.; Priebe, Carey E.; Sapiro, Guillermo
2015-01-01
Graph matching—aligning a pair of graphs to minimize their edge disagreements—has received wide-spread attention from both theoretical and applied communities over the past several decades, including combinatorics, computer vision, and connectomics. Its attention can be partially attributed to its computational difficulty. Although many heuristics have previously been proposed in the literature to approximately solve graph matching, very few have any theoretical support for their performance. A common technique is to relax the discrete problem to a continuous problem, therefore enabling practitioners to bring gradient-descent-type algorithms to bear. We prove that an indefinite relaxation (when solved exactly) almost always discovers the optimal permutation, while a common convex relaxation almost always fails to discover the optimal permutation. These theoretical results suggest that initializing the indefinite algorithm with the convex optimum might yield improved practical performance. Indeed, experimental results illuminate and corroborate these theoretical findings, demonstrating that excellent results are achieved in both benchmark and real data problems by amalgamating the two approaches. PMID:26656578
Hendriks, P.W.; Kirkegaard, J.A.; Lilley, J.M.; Gregory, P.J.; Rebetzke, G.J.
2016-01-01
Genetic modification of shoot and root morphology has potential to improve water and nutrient uptake of wheat crops in rainfed environments. Near-isogenic lines (NILs) varying for a tillering inhibition (tin) gene and representing multiple genetic backgrounds were phenotyped in contrasting, controlled environments for shoot and root growth. Leaf area, shoot and root biomass were similar until tillering, whereupon reduced tillering in tin-containing NILs produced reductions of up to 60% in total leaf area and biomass, and increases in total root length of up to 120% and root biomass to 145%. Together, the root-to-shoot ratio increased two-fold with the tin gene. The influence of tin on shoot and root growth was greatest in the cv. Banks genetic background, particularly in the biculm-selected NIL, and was typically strongest in cooler environments. A separate de-tillering study confirmed greater root-to-shoot ratios with regular tiller removal in non-tin-containing genotypes. In validating these observations in a rainfed field study, the tin allele had a negligible effect on seedling growth but was associated with significantly (P<0.05) reduced tiller number (–37%), leaf area index (–26%), and spike number (–35%) to reduce plant biomass (–19%) at anthesis. Root biomass, root-to-shoot ratio at early stem elongation, and root depth at maturity were all increased in tin-containing NILs. Soil water use was slowed in tin-containing NILs, resulting in greater water availability, greater stomatal conductance, cooler canopy temperatures, and maintenance of green leaf area during grain-filling. Together these effects contributed to increases in harvest index and grain yield. In both the controlled and field environments, the tin gene was commonly associated with increased root length and biomass, but the significant influence of genetic background and environment suggests careful assessment of tin-containing progeny in selection for genotypic increases in root growth
Khovanov homology of graph-links
Nikonov, Igor M
2012-08-31
Graph-links arise as the intersection graphs of turning chord diagrams of links. Speaking informally, graph-links provide a combinatorial description of links up to mutations. Many link invariants can be reformulated in the language of graph-links. Khovanov homology, a well-known and useful knot invariant, is defined for graph-links in this paper (in the case of the ground field of characteristic two). Bibliography: 14 titles.
Partition Density Functional Theory
NASA Astrophysics Data System (ADS)
Wasserman, Adam
2012-02-01
Partition Density Functional Theory (PDFT) is a formally exact method for obtaining molecular properties from self-consistent calculations on isolated fragments [1,2]. For a given choice of fragmentation, PDFT outputs the (in principle exact) molecular energy and density, as well as fragment densities that sum to the correct molecular density. I describe our progress understanding the behavior of the fragment energies as a function of fragment occupations, derivative discontinuities, practical implementation, and applications of PDFT to small molecules. I also discuss implications for ground-state Density Functional Theory, such as the promise of PDFT to circumvent the delocalization error of approximate density functionals. [4pt] [1] M.H. Cohen and A. Wasserman, J. Phys. Chem. A, 111, 2229(2007).[0pt] [2] P. Elliott, K. Burke, M.H. Cohen, and A. Wasserman, Phys. Rev. A 82, 024501 (2010).
Partitioning: splitting fact from fiction.
Pike, Brian
2012-05-01
Many larger hospitals are sprawling complexes with endless corridors and rooms of varying purpose. While cleanliness and infection control are, understandably, leading considerations in any hospital building, fire safety also plays a crucial role. Here Brian Pike MBE, technical consultant at partitioning system designer and manufacturer, Komfort Workspace, looks at how current fire guidelines impact on the use of partitioning systems in hospital premises.
Using Correlation to Compute Better Probability Estimates in Plan Graphs
NASA Technical Reports Server (NTRS)
Bryce, Daniel; Smith, David E.
2006-01-01
Plan graphs are commonly used in planning to help compute heuristic "distance" estimates between states and goals. A few authors have also attempted to use plan graphs in probabilistic planning to compute estimates of the probability that propositions can be achieved and actions can be performed. This is done by propagating probability information forward through the plan graph from the initial conditions through each possible action to the action effects, and hence to the propositions at the next layer of the plan graph. The problem with these calculations is that they make very strong independence assumptions - in particular, they usually assume that the preconditions for each action are independent of each other. This can lead to gross overestimates in probability when the plans for those preconditions interfere with each other. It can also lead to gross underestimates of probability when there is synergy between the plans for two or more preconditions. In this paper we introduce a notion of the binary correlation between two propositions and actions within a plan graph, show how to propagate this information within a plan graph, and show how this improves probability estimates for planning. This notion of correlation can be thought of as a continuous generalization of the notion of mutual exclusion (mutex) often used in plan graphs. At one extreme (correlation=0) two propositions or actions are completely mutex. With correlation = 1, two propositions or actions are independent, and with correlation > 1, two propositions or actions are synergistic. Intermediate values can and do occur indicating different degrees to which propositions and action interfere or are synergistic. We compare this approach with another recent approach by Bryce that computes probability estimates using Monte Carlo simulation of possible worlds in plan graphs.
Principal Graph and Structure Learning Based on Reversed Graph Embedding.
Mao, Qi; Wang, Li; Tsang, Ivor; Sun, Yijun
2016-12-05
Many scientific datasets are of high dimension, and the analysis usually requires retaining the most important structures of data. Principal curve is a widely used approach for this purpose. However, many existing methods work only for data with structures that are mathematically formulated by curves, which is quite restrictive for real applications. A few methods can overcome the above problem, but they either require complicated human-made rules for a specific task with lack of adaption flexibility to different tasks, or cannot obtain explicit structures of data. To address these issues, we develop a novel principal graph and structure learning framework that captures the local information of the underlying graph structure based on reversed graph embedding. As showcases, models that can learn a spanning tree or a weighted undirected `1 graph are proposed, and a new learning algorithm is developed that learns a set of principal points and a graph structure from data, simultaneously. The new algorithm is simple with guaranteed convergence. We then extend the proposed framework to deal with large-scale data. Experimental results on various synthetic and six real world datasets show that the proposed method compares favorably with baselines and can uncover the underlying structure correctly.
Private Graphs - Access Rights on Graphs for Seamless Navigation
NASA Astrophysics Data System (ADS)
Dorner, W.; Hau, F.; Pagany, R.
2016-06-01
After the success of GNSS (Global Navigational Satellite Systems) and navigation services for public streets, indoor seems to be the next big development in navigational services, relying on RTLS - Real Time Locating Services (e.g. WIFI) and allowing seamless navigation. In contrast to navigation and routing services on public streets, seamless navigation will cause an additional challenge: how to make routing data accessible to defined users or restrict access rights for defined areas or only to parts of the graph to a defined user group? The paper will present case studies and data from literature, where seamless and especially indoor navigation solutions are presented (hospitals, industrial complexes, building sites), but the problem of restricted access rights was only touched from a real world, but not a technical perspective. The analysis of case studies will show, that the objective of navigation and the different target groups for navigation solutions will demand well defined access rights and require solutions, how to make only parts of a graph to a user or application available to solve a navigational task. The paper will therefore introduce the concept of private graphs, which is defined as a graph for navigational purposes covering the street, road or floor network of an area behind a public street and suggest different approaches how to make graph data for navigational purposes available considering access rights and data protection, privacy and security issues as well.
Sharing Teaching Ideas: Graphing Families of Curves Using Transformations of Reference Graphs
ERIC Educational Resources Information Center
Kukla, David
2007-01-01
This article provides for a fast extremely accurate approach to graphing functions that is based on learning function reference graphs and then applying algebraic transformations to these reference graphs.
Indoor scene reconstruction using feature sensitive primitive extraction and graph-cut
NASA Astrophysics Data System (ADS)
Oesau, Sven; Lafarge, Florent; Alliez, Pierre
2014-04-01
We present a method for automatic reconstruction of permanent structures, such as walls, floors and ceilings, given a raw point cloud of an indoor scene. The main idea behind our approach is a graph-cut formulation to solve an inside/outside labeling of a space partitioning. We first partition the space in order to align the reconstructed models with permanent structures. The horizontal structures are located through analysis of the vertical point distribution, while vertical wall structures are detected through feature preserving multi-scale line fitting, followed by clustering in a Hough transform space. The final surface is extracted through a graph-cut formulation that trades faithfulness to measurement data for geometric complexity. A series of experiments show watertight surface meshes reconstructed from point clouds measured on multi-level buildings.
Graph classification by means of Lipschitz embedding.
Riesen, Kaspar; Bunke, Horst
2009-12-01
In pattern recognition and related fields, graph-based representations offer a versatile alternative to the widely used feature vectors. Therefore, an emerging trend of representing objects by graphs can be observed. This trend is intensified by the development of novel approaches in graph-based machine learning, such as graph kernels or graph-embedding techniques. These procedures overcome a major drawback of graphs, which consists of a serious lack of algorithms for classification. This paper is inspired by the idea of representing graphs through dissimilarities and extends our previous work to the more general setting of Lipschitz embeddings. In an experimental evaluation, we empirically confirm that classifiers that rely on the original graph distances can be outperformed by a classification system using the Lipschitz embedded graphs.
Use of graph theory measures to identify errors in record linkage.
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.
Cluster Consensus of Nonlinearly Coupled Multi-Agent Systems in Directed Graphs
NASA Astrophysics Data System (ADS)
Lu, Xiao-Qing; Francis, Austin; Chen, Shi-Hua
2010-05-01
We investigate the cluster consensus problem in directed networks of nonlinearly coupled multi-agent systems by using pinning control. Depending on the community structure generated by the group partition of the underlying digraph, various clusters can be made coherently independent by applying feedback injections to a fraction of the agents. Sufficient conditions for cluster consensus are obtained using algebraic graph theory and matrix theory and some simulations results are included to illustrate the method.
Detecting labor using graph theory on connectivity matrices of uterine EMG.
Al-Omar, S; Diab, A; Nader, N; Khalil, M; Karlsson, B; Marque, C
2015-08-01
Premature labor is one of the most serious health problems in the developed world. One of the main reasons for this is that no good way exists to distinguish true labor from normal pregnancy contractions. The aim of this paper is to investigate if the application of graph theory techniques to multi-electrode uterine EMG signals can improve the discrimination between pregnancy contractions and labor. To test our methods we first applied them to synthetic graphs where we detected some differences in the parameters results and changes in the graph model from pregnancy-like graphs to labor-like graphs. Then, we applied the same methods to real signals. We obtained the best differentiation between pregnancy and labor through the same parameters. Major improvements in differentiating between pregnancy and labor were obtained using a low pass windowing preprocessing step. Results show that real graphs generally became more organized when moving from pregnancy, where the graph showed random characteristics, to labor where the graph became a more small-world like graph.
Partitioning ecosystems for sustainability.
Murray, Martyn G
2016-03-01
Decline in the abundance of renewable natural resources (RNRs) coupled with increasing demands of an expanding human population will greatly intensify competition for Earth's natural resources during this century, yet curiously, analytical approaches to the management of productive ecosystems (ecological theory of wildlife harvesting, tragedy of the commons, green economics, and bioeconomics) give only peripheral attention to the driving influence of competition on resource exploitation. Here, I apply resource competition theory (RCT) to the exploitation of RNRs and derive four general policies in support of their sustainable and equitable use: (1) regulate resource extraction technology to avoid damage to the resource base; (2) increase efficiency of resource use and reduce waste at every step in the resource supply chain and distribution network; (3) partition ecosystems with the harvesting niche as the basic organizing principle for sustainable management of natural resources by multiple users; and (4) increase negative feedback between consumer and resource to bring about long-term sustainable use. A simple policy framework demonstrates how RCT integrates with other elements of sustainability science to better manage productive ecosystems. Several problem areas of RNR management are discussed in the light of RCT, including tragedy of the commons, overharvesting, resource collapse, bycatch, single species quotas, and simplification of ecosystems.
Algebraic connectivity and graph robustness.
Feddema, John Todd; Byrne, Raymond Harry; Abdallah, Chaouki T.
2009-07-01
Recent papers have used Fiedler's definition of algebraic connectivity to show that network robustness, as measured by node-connectivity and edge-connectivity, can be increased by increasing the algebraic connectivity of the network. By the definition of algebraic connectivity, the second smallest eigenvalue of the graph Laplacian is a lower bound on the node-connectivity. In this paper we show that for circular random lattice graphs and mesh graphs algebraic connectivity is a conservative lower bound, and that increases in algebraic connectivity actually correspond to a decrease in node-connectivity. This means that the networks are actually less robust with respect to node-connectivity as the algebraic connectivity increases. However, an increase in algebraic connectivity seems to correlate well with a decrease in the characteristic path length of these networks - which would result in quicker communication through the network. Applications of these results are then discussed for perimeter security.
Graph Analytics for Signature Discovery
Hogan, Emilie A.; Johnson, John R.; Halappanavar, Mahantesh; Lo, Chaomei
2013-06-01
Within large amounts of seemingly unstructured data it can be diffcult to find signatures of events. In our work we transform unstructured data into a graph representation. By doing this we expose underlying structure in the data and can take advantage of existing graph analytics capabilities, as well as develop new capabilities. Currently we focus on applications in cybersecurity and communication domains. Within cybersecurity we aim to find signatures for perpetrators using the pass-the-hash attack, and in communications we look for emails or phone calls going up or down a chain of command. In both of these areas, and in many others, the signature we look for is a path with certain temporal properties. In this paper we discuss our methodology for finding these temporal paths within large graphs.
Graph modeling systems and methods
Neergaard, Mike
2015-10-13
An apparatus and a method for vulnerability and reliability modeling are provided. The method generally includes constructing a graph model of a physical network using a computer, the graph model including a plurality of terminating vertices to represent nodes in the physical network, a plurality of edges to represent transmission paths in the physical network, and a non-terminating vertex to represent a non-nodal vulnerability along a transmission path in the physical network. The method additionally includes evaluating the vulnerability and reliability of the physical network using the constructed graph model, wherein the vulnerability and reliability evaluation includes a determination of whether each terminating and non-terminating vertex represents a critical point of failure. The method can be utilized to evaluate wide variety of networks, including power grid infrastructures, communication network topologies, and fluid distribution systems.
Sequential visibility-graph motifs
NASA Astrophysics Data System (ADS)
Iacovacci, Jacopo; Lacasa, Lucas
2016-04-01
Visibility algorithms transform time series into graphs and encode dynamical information in their topology, paving the way for graph-theoretical time series analysis as well as building a bridge between nonlinear dynamics and network science. In this work we introduce and study the concept of sequential visibility-graph motifs, smaller substructures of n consecutive nodes that appear with characteristic frequencies. We develop a theory to compute in an exact way the motif profiles associated with general classes of deterministic and stochastic dynamics. We find that this simple property is indeed a highly informative and computationally efficient feature capable of distinguishing among different dynamics and robust against noise contamination. We finally confirm that it can be used in practice to perform unsupervised learning, by extracting motif profiles from experimental heart-rate series and being able, accordingly, to disentangle meditative from other relaxation states. Applications of this general theory include the automatic classification and description of physical, biological, and financial time series.
NASA Astrophysics Data System (ADS)
Algor, Ilan
1988-03-01
The problem concerns the minimum time in which a number of messages can be transmitted through a communication network in which each node can transmit to many other nodes simultaneously but can receive only one message at a time. In the undirected version of the problem, the graphs, G, representing the messages are finite, undirected and simple; the messages transmitted in unit time form a subgraph which is a star. The star aboricity, st(G) of a graph G is the minimum number of star forests whose union covers all edges of G. A maximum value is derived for the star aboricity of any d-regular graph G, and is proved through probabilistic arguments.
Optimal preparation of graph states
Cabello, Adan; Lopez-Tarrida, Antonio J.; Danielsen, Lars Eirik; Portillo, Jose R.
2011-04-15
We show how to prepare any graph state of up to 12 qubits with (a) the minimum number of controlled-Z gates and (b) the minimum preparation depth. We assume only one-qubit and controlled-Z gates. The method exploits the fact that any graph state belongs to an equivalence class under local Clifford operations. We extend up to 12 qubits the classification of graph states according to their entanglement properties, and identify each class using only a reduced set of invariants. For any state, we provide a circuit with both properties (a) and (b), if it does exist, or, if it does not, one circuit with property (a) and one with property (b), including the explicit one-qubit gates needed.
Rosmanis, Ansis
2011-02-15
I introduce a continuous-time quantum walk on graphs called the quantum snake walk, the basis states of which are fixed-length paths (snakes) in the underlying graph. First, I analyze the quantum snake walk on the line, and I show that, even though most states stay localized throughout the evolution, there are specific states that most likely move on the line as wave packets with momentum inversely proportional to the length of the snake. Next, I discuss how an algorithm based on the quantum snake walk might potentially be able to solve an extended version of the glued trees problem, which asks to find a path connecting both roots of the glued trees graph. To the best of my knowledge, no efficient quantum algorithm solving this problem is known yet.
Dynamic criteria for partitioning and transmutation
Lu, A.H. )
1991-11-01
Because of the slow progress being made in the national geologic repository program, the idea of partitioning and transmuting (P-T) long-lived radionuclides resurfaces as a potential improvement in high-level radioactive waste management. It seems theoretically possible to reduce the overall problems of radioactive waste by repeatedly partitioning and recycling wastes into actinide-free wastes, but there are recognizable difficulties and negative consequences that may overshadow the long-term benefits. This paper addresses some of the criteria that might be used to achieve an optimal P-T concept development, i.e., to minimize the negative short-term impact and to maximize both short-term and long-term benefits.
Interacting particle systems on graphs
NASA Astrophysics Data System (ADS)
Sood, Vishal
In this dissertation, the dynamics of socially or biologically interacting populations are investigated. The individual members of the population are treated as particles that interact via links on a social or biological network represented as a graph. The effect of the structure of the graph on the properties of the interacting particle system is studied using statistical physics techniques. In the first chapter, the central concepts of graph theory and social and biological networks are presented. Next, interacting particle systems that are drawn from physics, mathematics and biology are discussed in the second chapter. In the third chapter, the random walk on a graph is studied. The mean time for a random walk to traverse between two arbitrary sites of a random graph is evaluated. Using an effective medium approximation it is found that the mean first-passage time between pairs of sites, as well as all moments of this first-passage time, are insensitive to the density of links in the graph. The inverse of the mean-first passage time varies non-monotonically with the density of links near the percolation transition of the random graph. Much of the behavior can be understood by simple heuristic arguments. Evolutionary dynamics, by which mutants overspread an otherwise uniform population on heterogeneous graphs, are studied in the fourth chapter. Such a process underlies' epidemic propagation, emergence of fads, social cooperation or invasion of an ecological niche by a new species. The first part of this chapter is devoted to neutral dynamics, in which the mutant genotype does not have a selective advantage over the resident genotype. The time to extinction of one of the two genotypes is derived. In the second part of this chapter, selective advantage or fitness is introduced such that the mutant genotype has a higher birth rate or a lower death rate. This selective advantage leads to a dynamical competition in which selection dominates for large populations
Synchronizability of random rectangular graphs
Estrada, Ernesto Chen, Guanrong
2015-08-15
Random rectangular graphs (RRGs) represent a generalization of the random geometric graphs in which the nodes are embedded into hyperrectangles instead of on hypercubes. The synchronizability of RRG model is studied. Both upper and lower bounds of the eigenratio of the network Laplacian matrix are determined analytically. It is proven that as the rectangular network is more elongated, the network becomes harder to synchronize. The synchronization processing behavior of a RRG network of chaotic Lorenz system nodes is numerically investigated, showing complete consistence with the theoretical results.
Link community detection based on line graphs with a novel link similarity measure
NASA Astrophysics Data System (ADS)
Wang, Guishen; Huang, Lan; Wang, Yan; Pang, Wei; Ma, Qin
2016-02-01
Link community gradually unfolds its capacity in complex network research. In this paper, a novel link similarity measure on line graphs is proposed. This measure can be adapted to different types of networks with an adjustable parameter. We prove its value converges to a limit on line graphs with the relationship of the nonneighbor links taken into account. Based on this similarity measure, we propose a novel link community detection algorithm for link clustering on line graphs. The detection algorithm combines the novel link similarity measure with the classic Markov Cluster (MCL) Algorithm and determines the link community partitions by calculating an extended modularity measure. Extensive experiments on two types of complex networks demonstrate the effectiveness, reliability and rationality of our solution in contrast to the other two classical algorithms.
Multibody Graph Transformations and Analysis Part II: Closed-chain constraint embedding
Jain, Abhinandan
2011-01-01
This is the second part of a two-part paper that develops graph theoretic techniques for the topological transformation and analysis of multibody system dynamics. The first part focused on tree systems, and developed systematic and rigorous techniques for the partitioning, aggregation and sub-structuring of multibody dynamics models. This second part, uses the aggregation techniques as the foundation to develop the constraint-embedding technique that enables the transformation of the non-tree system graphs into tree graphs. This enables the application of a large family of analytical and computational techniques for trees to closed-chain systems. This is illustrated through an extension of the low-order articulated-body forward dynamics algorithm for tree systems to closed-chain systems. PMID:22267894
Boosting for multi-graph classification.
Wu, Jia; Pan, Shirui; Zhu, Xingquan; Cai, Zhihua
2015-03-01
In this paper, we formulate a novel graph-based learning problem, multi-graph classification (MGC), which aims to learn a classifier from a set of labeled bags each containing a number of graphs inside the bag. A bag is labeled positive, if at least one graph in the bag is positive, and negative otherwise. Such a multi-graph representation can be used for many real-world applications, such as webpage classification, where a webpage can be regarded as a bag with texts and images inside the webpage being represented as graphs. This problem is a generalization of multi-instance learning (MIL) but with vital differences, mainly because instances in MIL share a common feature space whereas no feature is available to represent graphs in a multi-graph bag. To solve the problem, we propose a boosting based multi-graph classification framework (bMGC). Given a set of labeled multi-graph bags, bMGC employs dynamic weight adjustment at both bag- and graph-levels to select one subgraph in each iteration as a weak classifier. In each iteration, bag and graph weights are adjusted such that an incorrectly classified bag will receive a higher weight because its predicted bag label conflicts to the genuine label, whereas an incorrectly classified graph will receive a lower weight value if the graph is in a positive bag (or a higher weight if the graph is in a negative bag). Accordingly, bMGC is able to differentiate graphs in positive and negative bags to derive effective classifiers to form a boosting model for MGC. Experiments and comparisons on real-world multi-graph learning tasks demonstrate the algorithm performance.
Approximate Graph Edit Distance in Quadratic Time.
Riesen, Kaspar; Ferrer, Miquel; Bunke, Horst
2015-09-14
Graph edit distance is one of the most flexible and general graph matching models available. The major drawback of graph edit distance, however, is its computational complexity that restricts its applicability to graphs of rather small size. Recently the authors of the present paper introduced a general approximation framework for the graph edit distance problem. The basic idea of this specific algorithm is to first compute an optimal assignment of independent local graph structures (including substitutions, deletions, and insertions of nodes and edges). This optimal assignment is complete and consistent with respect to the involved nodes of both graphs and can thus be used to instantly derive an admissible (yet suboptimal) solution for the original graph edit distance problem in O(n3) time. For large scale graphs or graph sets, however, the cubic time complexity may still be too high. Therefore, we propose to use suboptimal algorithms with quadratic rather than cubic time for solving the basic assignment problem. In particular, the present paper introduces five different greedy assignment algorithms in the context of graph edit distance approximation. In an experimental evaluation we show that these methods have great potential for further speeding up the computation of graph edit distance while the approximated distances remain sufficiently accurate for graph based pattern classification.
Hierarchical image feature extraction by an irregular pyramid of polygonal partitions
Skurikhin, Alexei N
2008-01-01
We present an algorithmic framework for hierarchical image segmentation and feature extraction. We build a successive fine-to-coarse hierarchy of irregular polygonal partitions of the original image. This multiscale hierarchy forms the basis for object-oriented image analysis. The framework incorporates the Gestalt principles of visual perception, such as proximity and closure, and exploits spectral and textural similarities of polygonal partitions, while iteratively grouping them until dissimilarity criteria are exceeded. Seed polygons are built upon a triangular mesh composed of irregular sized triangles, whose spatial arrangement is adapted to the image content. This is achieved by building the triangular mesh on the top of detected spectral discontinuities (such as edges), which form a network of constraints for the Delaunay triangulation. The image is then represented as a spatial network in the form of a graph with vertices corresponding to the polygonal partitions and edges reflecting their relations. The iterative agglomeration of partitions into object-oriented segments is formulated as Minimum Spanning Tree (MST) construction. An important characteristic of the approach is that the agglomeration of polygonal partitions is constrained by the detected edges; thus the shapes of agglomerated partitions are more likely to correspond to the outlines of real-world objects. The constructed partitions and their spatial relations are characterized using spectral, textural and structural features based on proximity graphs. The framework allows searching for object-oriented features of interest across multiple levels of details of the built hierarchy and can be generalized to the multi-criteria MST to account for multiple criteria important for an application.
Comparison Graph of Sea Ice Minimum - 2010
This animated graph tracks the retreat of sea ice, measured in millions of square kilometers, averaged from the start of the satellite record in 1979 through 2000 (white). Next, the graph follows t...
Mathematical Minute: Rotating a Function Graph
ERIC Educational Resources Information Center
Bravo, Daniel; Fera, Joseph
2013-01-01
Using calculus only, we find the angles you can rotate the graph of a differentiable function about the origin and still obtain a function graph. We then apply the solution to odd and even degree polynomials.
Standard Distributions: One Graph Fits All
ERIC Educational Resources Information Center
Wagner, Clifford H.
2007-01-01
Standard distributions are ubiquitous but not unique. With suitable scaling, the graph of a standard distribution serves as the graph for every distribution in the family. The standard exponential can easily be taught in elementary statistics courses.
Graphing and Social Studies: An Interdisciplinary Activity.
ERIC Educational Resources Information Center
Brehm, Julia L.
1996-01-01
Describes a graphing activity that promotes mathematical connections with social studies lessons. Students should be familiar with graphing on the Cartesian coordinate system to play this variation of the game Battleship on maps of various regions of the world. (AIM)
Torsional rigidity, isospectrality and quantum graphs
NASA Astrophysics Data System (ADS)
Colladay, Don; Kaganovskiy, Leon; McDonald, Patrick
2017-01-01
We study torsional rigidity for graph and quantum graph analogs of well-known pairs of isospectral non-isometric planar domains. We prove that such isospectral pairs are distinguished by torsional rigidity.
Humidity Graphs for All Seasons.
ERIC Educational Resources Information Center
Esmael, F.
1982-01-01
In a previous article in this journal (Vol. 17, p358, 1979), a wet-bulb depression table was recommended for two simple experiments to determine relative humidity. However, the use of a graph is suggested because it gives the relative humidity directly from the wet and dry bulb readings. (JN)
NASA Astrophysics Data System (ADS)
Prudente, Matthew James
Given a graph G with pebbles on the vertices, we define a pebbling move as removing two pebbles from a vertex u, placing one pebble on a neighbor v, and discarding the other pebble, like a toll. The pebbling number pi( G) is the least number of pebbles needed so that every arrangement of pi(G) pebbles can place a pebble on any vertex through a sequence of pebbling moves. We introduce a new variation on graph pebbling called two-player pebbling. In this, players called the mover and the defender alternate moves, with the stipulation that the defender cannot reverse the previous move. The mover wins only if they can place a pebble on a specified vertex and the defender wins if the mover cannot. We define η(G), analogously, as the minimum number of pebbles such that given every configuration of the η( G) pebbles and every specified vertex r, the mover has a winning strategy. First, we will investigate upper bounds for η( G) on various classes of graphs and find a certain structure for which the defender has a winning strategy, no matter how many pebbles are in a configuration. Then, we characterize winning configurations for both players on a special class of diameter 2 graphs. Finally, we show winning configurations for the mover on paths using a recursive argument.
Graphs and Enhancing Maple Multiplication.
ERIC Educational Resources Information Center
Cecil, David R.; Wang, Rongdong
2002-01-01
Description of a technique in Maple programming language that automatically prints all paths of any desired length along with the name of each vertex, proceeding in order from the beginning vertex to the ending vertex for a given graph. (Author/MM)
Fibonacci Identities, Matrices, and Graphs
ERIC Educational Resources Information Center
Huang, Danrun
2005-01-01
General strategies used to help discover, prove, and generalize identities for Fibonacci numbers are described along with some properties about the determinants of square matrices. A matrix proof for identity (2) that has received immense attention from many branches of mathematics, like linear algebra, dynamical systems, graph theory and others…
Ancestral Genres of Mathematical Graphs
ERIC Educational Resources Information Center
Gerofsky, Susan
2011-01-01
Drawing from sources in gesture studies, cognitive science, the anthropology of religion and art/architecture history, this article explores cultural, bodily and cosmological resonances carried (unintentionally) by mathematical graphs on Cartesian coordinates. Concepts of asymmetric bodily spaces, grids, orthogonality, mapping and sacred spaces…
Situating Graphs as Workplace Knowledge
ERIC Educational Resources Information Center
Noss, Richard; Bakker, Arthur; Hoyles, Celia; Kent, Phillip
2007-01-01
We investigate the use and knowledge of graphs in the context of a large industrial factory. We are particularly interested in the question of "transparency", a question that has been extensively considered in the general literature on tool use and, more recently, by Michael Roth and his colleagues in the context of scientific work. Roth uses the…
Conceptual graphs for semantics and knowledge processing
Fargues, J.; Landau, M.C.; Dugourd, A.; Catach, L.
1986-01-01
This paper discusses the representational and algorithmic power of the conceptual graph model for natural language semantics and knowledge processing. Also described is a Prolog-like resolution method for conceptual graphs, which allows to perform deduction on very large semantic domains. The interpreter developed is similar to a Prolog interpreter in which the terms are any conceptual graphs and in which the unification algorithm is replaced by a specialized algorithm for conceptual graphs.
Claw-Free Maximal Planar Graphs
1989-01-01
0, 1,2 and 3 points of degree 6 respectively.) Now suppose G,. has no claws for 3 < r < i and consider graph G ,+,. Graph G,+ 1 is obtained from Gr by...adjacent to a point v by N(v) and call the induced subgraph GiN(v)] the neighborhood graph of v in G . Graph G is said to be locally n-connected if for all
ERIC Educational Resources Information Center
Vinberg, Anders
Although computer graphics professionals usually consider only technical graphic design issues, recent improvements may make the only limiting design factors the user's purpose, imagination, style, and taste rather than computer hardware or software technology. Computer graphics designers can be helped to avoid pitfalls by understanding the visual…
Chemical Applications of Graph Theory: Part II. Isomer Enumeration.
ERIC Educational Resources Information Center
Hansen, Peter J.; Jurs, Peter C.
1988-01-01
Discusses the use of graph theory to aid in the depiction of organic molecular structures. Gives a historical perspective of graph theory and explains graph theory terminology with organic examples. Lists applications of graph theory to current research projects. (ML)
Ivanciuc, Ovidiu
2013-06-01
Chemical and molecular graphs have fundamental applications in chemoinformatics, quantitative structureproperty relationships (QSPR), quantitative structure-activity relationships (QSAR), virtual screening of chemical libraries, and computational drug design. Chemoinformatics applications of graphs include chemical structure representation and coding, database search and retrieval, and physicochemical property prediction. QSPR, QSAR and virtual screening are based on the structure-property principle, which states that the physicochemical and biological properties of chemical compounds can be predicted from their chemical structure. Such structure-property correlations are usually developed from topological indices and fingerprints computed from the molecular graph and from molecular descriptors computed from the three-dimensional chemical structure. We present here a selection of the most important graph descriptors and topological indices, including molecular matrices, graph spectra, spectral moments, graph polynomials, and vertex topological indices. These graph descriptors are used to define several topological indices based on molecular connectivity, graph distance, reciprocal distance, distance-degree, distance-valency, spectra, polynomials, and information theory concepts. The molecular descriptors and topological indices can be developed with a more general approach, based on molecular graph operators, which define a family of graph indices related by a common formula. Graph descriptors and topological indices for molecules containing heteroatoms and multiple bonds are computed with weighting schemes based on atomic properties, such as the atomic number, covalent radius, or electronegativity. The correlation in QSPR and QSAR models can be improved by optimizing some parameters in the formula of topological indices, as demonstrated for structural descriptors based on atomic connectivity and graph distance.
Multiple directed graph large-class multi-spectral processor
NASA Technical Reports Server (NTRS)
Casasent, David; Liu, Shiaw-Dong; Yoneyama, Hideyuki
1988-01-01
Numerical analysis techniques for the interpretation of high-resolution imaging-spectrometer data are described and demonstrated. The method proposed involves the use of (1) a hierarchical classifier with a tree structure generated automatically by a Fisher linear-discriminant-function algorithm and (2) a novel multiple-directed-graph scheme which reduces the local maxima and the number of perturbations required. Results for a 500-class test problem involving simulated imaging-spectrometer data are presented in tables and graphs; 100-percent-correct classification is achieved with an improvement factor of 5.
Collaborative Robotic Instruction: A Graph Teaching Experience
ERIC Educational Resources Information Center
Mitnik, Ruben; Recabarren, Matias; Nussbaum, Miguel; Soto, Alvaro
2009-01-01
Graphing is a key skill in the study of Physics. Drawing and interpreting graphs play a key role in the understanding of science, while the lack of these has proved to be a handicap and a limiting factor in the learning of scientific concepts. It has been observed that despite the amount of previous graph-working experience, students of all ages…
47 CFR 80.761 - Conversion graphs.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 47 Telecommunication 5 2012-10-01 2012-10-01 false Conversion graphs. 80.761 Section 80.761... MARITIME SERVICES Standards for Computing Public Coast Station VHF Coverage § 80.761 Conversion graphs. The following graphs must be employed where conversion from one to the other of the indicated types of units...
Positive and Unlabeled Multi-Graph Learning.
Wu, Jia; Pan, Shirui; Zhu, Xingquan; Zhang, Chengqi; Wu, Xindong
2016-03-23
In this paper, we advance graph classification to handle multi-graph learning for complicated objects, where each object is represented as a bag of graphs and the label is only available to each bag but not individual graphs. In addition, when training classifiers, users are only given a handful of positive bags and many unlabeled bags, and the learning objective is to train models to classify previously unseen graph bags with maximum accuracy. To achieve the goal, we propose a positive and unlabeled multi-graph learning (puMGL) framework to first select informative subgraphs to convert graphs into a feature space. To utilize unlabeled bags for learning, puMGL assigns a confidence weight to each bag and dynamically adjusts its weight value to select "reliable negative bags." A number of representative graphs, selected from positive bags and identified reliable negative graph bags, form a "margin graph pool" which serves as the base for deriving subgraph patterns, training graph classifiers, and further updating the bag weight values. A closed-loop iterative process helps discover optimal subgraphs from positive and unlabeled graph bags for learning. Experimental comparisons demonstrate the performance of puMGL for classifying real-world complicated objects.
47 CFR 80.761 - Conversion graphs.
Code of Federal Regulations, 2013 CFR
2013-10-01
... 47 Telecommunication 5 2013-10-01 2013-10-01 false Conversion graphs. 80.761 Section 80.761... MARITIME SERVICES Standards for Computing Public Coast Station VHF Coverage § 80.761 Conversion graphs. The following graphs must be employed where conversion from one to the other of the indicated types of units...
47 CFR 80.761 - Conversion graphs.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 47 Telecommunication 5 2010-10-01 2010-10-01 false Conversion graphs. 80.761 Section 80.761... MARITIME SERVICES Standards for Computing Public Coast Station VHF Coverage § 80.761 Conversion graphs. The following graphs must be employed where conversion from one to the other of the indicated types of units...
ERIC Educational Resources Information Center
McMillen, Sue; McMillen, Beth
2010-01-01
Connecting stories to qualitative coordinate graphs has been suggested as an effective instructional strategy. Even students who are able to "create" bar graphs may struggle to correctly "interpret" them. Giving children opportunities to work with qualitative graphs can help them develop the skills to interpret, describe, and compare information…
So Many Graphs, So Little Time
ERIC Educational Resources Information Center
Wall, Jennifer J.; Benson, Christine C.
2009-01-01
Interpreting graphs found in various content areas is an important skill for students, especially in light of high-stakes testing. In addition, reading and understanding graphs is an important part of numeracy, or numeric literacy, a skill necessary for informed citizenry. This article explores the different categories of graphs, provides…
47 CFR 80.761 - Conversion graphs.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 47 Telecommunication 5 2011-10-01 2011-10-01 false Conversion graphs. 80.761 Section 80.761... MARITIME SERVICES Standards for Computing Public Coast Station VHF Coverage § 80.761 Conversion graphs. The following graphs must be employed where conversion from one to the other of the indicated types of units...
47 CFR 80.761 - Conversion graphs.
Code of Federal Regulations, 2014 CFR
2014-10-01
... 47 Telecommunication 5 2014-10-01 2014-10-01 false Conversion graphs. 80.761 Section 80.761... MARITIME SERVICES Standards for Computing Public Coast Station VHF Coverage § 80.761 Conversion graphs. The following graphs must be employed where conversion from one to the other of the indicated types of units...
Some Applications of Graph Theory to Clustering
ERIC Educational Resources Information Center
Hubert, Lawrence J.
1974-01-01
The connection between graph theory and clustering is reviewed and extended. Major emphasis is on restating, in a graph-theoretic context, selected past work in clustering, and conversely, developing alternative strategies from several standard concepts used in graph theory per se. (Author/RC)
Visual Exploratory Search of Relationship Graphs on Smartphones
Ouyang, Jianquan; Zheng, Hao; Kong, Fanbin; Liu, Tianming
2013-01-01
This paper presents a novel framework for Visual Exploratory Search of Relationship Graphs on Smartphones (VESRGS) that is composed of three major components: inference and representation of semantic relationship graphs on the Web via meta-search, visual exploratory search of relationship graphs through both querying and browsing strategies, and human-computer interactions via the multi-touch interface and mobile Internet on smartphones. In comparison with traditional lookup search methodologies, the proposed VESRGS system is characterized with the following perceived advantages. 1) It infers rich semantic relationships between the querying keywords and other related concepts from large-scale meta-search results from Google, Yahoo! and Bing search engines, and represents semantic relationships via graphs; 2) the exploratory search approach empowers users to naturally and effectively explore, adventure and discover knowledge in a rich information world of interlinked relationship graphs in a personalized fashion; 3) it effectively takes the advantages of smartphones’ user-friendly interfaces and ubiquitous Internet connection and portability. Our extensive experimental results have demonstrated that the VESRGS framework can significantly improve the users’ capability of seeking the most relevant relationship information to their own specific needs. We envision that the VESRGS framework can be a starting point for future exploration of novel, effective search strategies in the mobile Internet era. PMID:24223936
Plan-graph Based Heuristics for Conformant Probabilistic Planning
NASA Technical Reports Server (NTRS)
Ramakrishnan, Salesh; Pollack, Martha E.; Smith, David E.
2004-01-01
In this paper, we introduce plan-graph based heuristics to solve a variation of the conformant probabilistic planning (CPP) problem. In many real-world problems, it is the case that the sensors are unreliable or take too many resources to provide knowledge about the environment. These domains are better modeled as conformant planning problems. POMDP based techniques are currently the most successful approach for solving CPP but have the limitation of state- space explosion. Recent advances in deterministic and conformant planning have shown that plan-graphs can be used to enhance the performance significantly. We show that this enhancement can also be translated to CPP. We describe our process for developing the plan-graph heuristics and estimating the probability of a partial plan. We compare the performance of our planner PVHPOP when used with different heuristics. We also perform a comparison with a POMDP solver to show over a order of magnitude improvement in performance.
Hybridization of GA and ANN to Solve Graph Coloring
NASA Astrophysics Data System (ADS)
Maitra, Timir; Pal, Anindya J.; Choi, Minkyu; Kim, Taihoon
A recent and very promising approach for combinatorial optimization is to embed local search into the framework of evolutionary algorithms. In this paper, we present one efficient hybrid algorithms for the graph coloring problem. Here we have considered the hybridization of Boltzmann Machine (BM) of Artificial Neural Network with Genetic Algorithms. Genetic algorithm we have used to generate different coloration of a graph quickly on which we have applied boltzmann machine approach. Unlike traditional approaches of GA and ANN the proposed hybrid algorithm is guranteed to have 100% convergence rate to valid solution with no parameter tuning. Experiments of such a hybrid algorithm are carried out on large DIMACS Challenge benchmark graphs. Results prove very competitive. Analysis of the behavior of the algorithm sheds light on ways to further improvement.
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.
Liu, Yuangang; Guo, Qingsheng; Sun, Yageng; Ma, Xiaoya
2014-01-01
Scale reduction from source to target maps inevitably leads to conflicts of map symbols in cartography and geographic information systems (GIS). Displacement is one of the most important map generalization operators and it can be used to resolve the problems that arise from conflict among two or more map objects. In this paper, we propose a combined approach based on constraint Delaunay triangulation (CDT) skeleton and improved elastic beam algorithm for automated building displacement. In this approach, map data sets are first partitioned. Then the displacement operation is conducted in each partition as a cyclic and iterative process of conflict detection and resolution. In the iteration, the skeleton of the gap spaces is extracted using CDT. It then serves as an enhanced data model to detect conflicts and construct the proximity graph. Then, the proximity graph is adjusted using local grouping information. Under the action of forces derived from the detected conflicts, the proximity graph is deformed using the improved elastic beam algorithm. In this way, buildings are displaced to find an optimal compromise between related cartographic constraints. To validate this approach, two topographic map data sets (i.e., urban and suburban areas) were tested. The results were reasonable with respect to each constraint when the density of the map was not extremely high. In summary, the improvements include (1) an automated parameter-setting method for elastic beams, (2) explicit enforcement regarding the positional accuracy constraint, added by introducing drag forces, (3) preservation of local building groups through displacement over an adjusted proximity graph, and (4) an iterative strategy that is more likely to resolve the proximity conflicts than the one used in the existing elastic beam algorithm.
Liu, Yuangang; Guo, Qingsheng; Sun, Yageng; Ma, Xiaoya
2014-01-01
Scale reduction from source to target maps inevitably leads to conflicts of map symbols in cartography and geographic information systems (GIS). Displacement is one of the most important map generalization operators and it can be used to resolve the problems that arise from conflict among two or more map objects. In this paper, we propose a combined approach based on constraint Delaunay triangulation (CDT) skeleton and improved elastic beam algorithm for automated building displacement. In this approach, map data sets are first partitioned. Then the displacement operation is conducted in each partition as a cyclic and iterative process of conflict detection and resolution. In the iteration, the skeleton of the gap spaces is extracted using CDT. It then serves as an enhanced data model to detect conflicts and construct the proximity graph. Then, the proximity graph is adjusted using local grouping information. Under the action of forces derived from the detected conflicts, the proximity graph is deformed using the improved elastic beam algorithm. In this way, buildings are displaced to find an optimal compromise between related cartographic constraints. To validate this approach, two topographic map data sets (i.e., urban and suburban areas) were tested. The results were reasonable with respect to each constraint when the density of the map was not extremely high. In summary, the improvements include (1) an automated parameter-setting method for elastic beams, (2) explicit enforcement regarding the positional accuracy constraint, added by introducing drag forces, (3) preservation of local building groups through displacement over an adjusted proximity graph, and (4) an iterative strategy that is more likely to resolve the proximity conflicts than the one used in the existing elastic beam algorithm. PMID:25470727
Dense Trivalent Graphs for Processor Interconnection,
1981-01-01
this paper is organized as follows: Sec- tion 2 introduces notation and defines the new family of graphs, which we call Moebius graphs. Section 3...the shuffle exchange [9].) Let Id denote the identity function on 2 The Moebius graph of order n (so named because the function f introduces a loop...We will write vk = p(v ). 3. DIAMETER OF THE MOEBIUS GRAPH In this section we will show that the diameter of the Moe- bius graph is bounded by L3/2 nj
Stability Properties of Inclusive Connectivity for Graphs
1993-12-01
of G . Graphs illustrating the two possible relationships between the three inclusive connectivity parameters for edges are shown in Figures 2.12 and...For simplicity in this section, we will call this graph G the "internal G graph " due to its location in the figures, and the "K4 with one edge doubly...to one copy of the subdivided K4 producing the graph in Figure 5.25. 117 1(4 with one edge Internal G graph K4 with one edge Figure 5.24 The
Proving relations between modular graph functions
NASA Astrophysics Data System (ADS)
Basu, Anirban
2016-12-01
We consider modular graph functions that arise in the low energy expansion of the four graviton amplitude in type II string theory. The vertices of these graphs are the positions of insertions of vertex operators on the toroidal worldsheet, while the links are the scalar Green functions connecting the vertices. Graphs with four and five links satisfy several non-trivial relations, which have been proved recently. We prove these relations by using elementary properties of Green functions and the details of the graphs. We also prove a relation between modular graph functions with six links.
Spatial partitions systematize visual search and enhance target memory.
Solman, Grayden J F; Kingstone, Alan
2017-02-01
Humans are remarkably capable of finding desired objects in the world, despite the scale and complexity of naturalistic environments. Broadly, this ability is supported by an interplay between exploratory search and guidance from episodic memory for previously observed target locations. Here we examined how the environment itself may influence this interplay. In particular, we examined how partitions in the environment-like buildings, rooms, and furniture-can impact memory during repeated search. We report that the presence of partitions in a display, independent of item configuration, reliably improves episodic memory for item locations. Repeated search through partitioned displays was faster overall and was characterized by more rapid ballistic orienting in later repetitions. Explicit recall was also both faster and more accurate when displays were partitioned. Finally, we found that search paths were more regular and systematic when displays were partitioned. Given the ubiquity of partitions in real-world environments, these results provide important insights into the mechanisms of naturalistic search and its relation to memory.
High Pressure/Temperature Metal Silicate Partitioning of Tungsten
NASA Technical Reports Server (NTRS)
Shofner, G. A.; Danielson, L.; Righter, K.; Campbell, A. J.
2010-01-01
The behavior of chemical elements during metal/silicate segregation and their resulting distribution in Earth's mantle and core provide insight into core formation processes. Experimental determination of partition coefficients allows calculations of element distributions that can be compared to accepted values of element abundances in the silicate (mantle) and metallic (core) portions of the Earth. Tungsten (W) is a moderately siderophile element and thus preferentially partitions into metal versus silicate under many planetary conditions. The partitioning behavior has been shown to vary with temperature, silicate composition, oxygen fugacity, and pressure. Most of the previous work on W partitioning has been conducted at 1-bar conditions or at relatively low pressures, i.e. <10 GPa, and in two cases at or near 20 GPa. According to those data, the stronger influences on the distribution coefficient of W are temperature, composition, and oxygen fugacity with a relatively slight influence in pressure. Predictions based on extrapolation of existing data and parameterizations suggest an increased pressured dependence on metal/ silicate partitioning of W at higher pressures 5. However, the dependence on pressure is not as well constrained as T, fO2, and silicate composition. This poses a problem because proposed equilibration pressures for core formation range from 27 to 50 GPa, falling well outside the experimental range, therefore requiring exptrapolation of a parametereized model. Higher pressure data are needed to improve our understanding of W partitioning at these more extreme conditions.
Generalized graph states based on Hadamard matrices
Cui, Shawn X.; Yu, Nengkun; Zeng, Bei
2015-07-15
Graph states are widely used in quantum information theory, including entanglement theory, quantum error correction, and one-way quantum computing. Graph states have a nice structure related to a certain graph, which is given by either a stabilizer group or an encoding circuit, both can be directly given by the graph. To generalize graph states, whose stabilizer groups are abelian subgroups of the Pauli group, one approach taken is to study non-abelian stabilizers. In this work, we propose to generalize graph states based on the encoding circuit, which is completely determined by the graph and a Hadamard matrix. We study the entanglement structures of these generalized graph states and show that they are all maximally mixed locally. We also explore the relationship between the equivalence of Hadamard matrices and local equivalence of the corresponding generalized graph states. This leads to a natural generalization of the Pauli (X, Z) pairs, which characterizes the local symmetries of these generalized graph states. Our approach is also naturally generalized to construct graph quantum codes which are beyond stabilizer codes.
Constrained Graph Optimization: Interdiction and Preservation Problems
Schild, Aaron V
2012-07-30
The maximum flow, shortest path, and maximum matching problems are a set of basic graph problems that are critical in theoretical computer science and applications. Constrained graph optimization, a variation of these basic graph problems involving modification of the underlying graph, is equally important but sometimes significantly harder. In particular, one can explore these optimization problems with additional cost constraints. In the preservation case, the optimizer has a budget to preserve vertices or edges of a graph, preventing them from being deleted. The optimizer wants to find the best set of preserved edges/vertices in which the cost constraints are satisfied and the basic graph problems are optimized. For example, in shortest path preservation, the optimizer wants to find a set of edges/vertices within which the shortest path between two predetermined points is smallest. In interdiction problems, one deletes vertices or edges from the graph with a particular cost in order to impede the basic graph problems as much as possible (for example, delete edges/vertices to maximize the shortest path between two predetermined vertices). Applications of preservation problems include optimal road maintenance, power grid maintenance, and job scheduling, while interdiction problems are related to drug trafficking prevention, network stability assessment, and counterterrorism. Computational hardness results are presented, along with heuristic methods for approximating solutions to the matching interdiction problem. Also, efficient algorithms are presented for special cases of graphs, including on planar graphs. The graphs in many of the listed applications are planar, so these algorithms have important practical implications.
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.
Efficient Graph Sequence Mining Using Reverse Search
NASA Astrophysics Data System (ADS)
Inokuchi, Akihiro; Ikuta, Hiroaki; Washio, Takashi
The mining of frequent subgraphs from labeled graph data has been studied extensively. Furthermore, much attention has recently been paid to frequent pattern mining from graph sequences. A method, called GTRACE, has been proposed to mine frequent patterns from graph sequences under the assumption that changes in graphs are gradual. Although GTRACE mines the frequent patterns efficiently, it still needs substantial computation time to mine the patterns from graph sequences containing large graphs and long sequences. In this paper, we propose a new version of GTRACE that permits efficient mining of frequent patterns based on the principle of a reverse search. The underlying concept of the reverse search is a general scheme for designing efficient algorithms for hard enumeration problems. Our performance study shows that the proposed method is efficient and scalable for mining both long and large graph sequence patterns and is several orders of magnitude faster than the original GTRACE.
Fast Approximate Quadratic Programming for Graph Matching
Vogelstein, Joshua T.; Conroy, John M.; Lyzinski, Vince; Podrazik, Louis J.; Kratzer, Steven G.; Harley, Eric T.; Fishkind, Donniell E.; Vogelstein, R. Jacob; Priebe, Carey E.
2015-01-01
Quadratic assignment problems arise in a wide variety of domains, spanning operations research, graph theory, computer vision, and neuroscience, to name a few. The graph matching problem is a special case of the quadratic assignment problem, and graph matching is increasingly important as graph-valued data is becoming more prominent. With the aim of efficiently and accurately matching the large graphs common in big data, we present our graph matching algorithm, the Fast Approximate Quadratic assignment algorithm. We empirically demonstrate that our algorithm is faster and achieves a lower objective value on over 80% of the QAPLIB benchmark library, compared with the previous state-of-the-art. Applying our algorithm to our motivating example, matching C. elegans connectomes (brain-graphs), we find that it efficiently achieves performance. PMID:25886624
The Feynman Identity for Planar Graphs
NASA Astrophysics Data System (ADS)
da Costa, G. A. T. F.
2016-08-01
The Feynman identity (FI) of a planar graph relates the Euler polynomial of the graph to an infinite product over the equivalence classes of closed nonperiodic signed cycles in the graph. The main objectives of this paper are to compute the number of equivalence classes of nonperiodic cycles of given length and sign in a planar graph and to interpret the data encoded by the FI in the context of free Lie superalgebras. This solves in the case of planar graphs a problem first raised by Sherman and sets the FI as the denominator identity of a free Lie superalgebra generated from a graph. Other results are obtained. For instance, in connection with zeta functions of graphs.
Fast approximate quadratic programming for graph matching.
Vogelstein, Joshua T; Conroy, John M; Lyzinski, Vince; Podrazik, Louis J; Kratzer, Steven G; Harley, Eric T; Fishkind, Donniell E; Vogelstein, R Jacob; Priebe, Carey E
2015-01-01
Quadratic assignment problems arise in a wide variety of domains, spanning operations research, graph theory, computer vision, and neuroscience, to name a few. The graph matching problem is a special case of the quadratic assignment problem, and graph matching is increasingly important as graph-valued data is becoming more prominent. With the aim of efficiently and accurately matching the large graphs common in big data, we present our graph matching algorithm, the Fast Approximate Quadratic assignment algorithm. We empirically demonstrate that our algorithm is faster and achieves a lower objective value on over 80% of the QAPLIB benchmark library, compared with the previous state-of-the-art. Applying our algorithm to our motivating example, matching C. elegans connectomes (brain-graphs), we find that it efficiently achieves performance.
Hierarchical structure of the logical Internet graph
NASA Astrophysics Data System (ADS)
Ge, Zihui; Figueiredo, Daniel R.; Jaiswal, Sharad; Gao, Lixin
2001-07-01
The study of the Internet topology has recently received much attention from the research community. In particular, the observation that the network graph has interesting properties, such as power laws, that might be explored in a myriad of ways. Most of the work in characterizing the Internet graph is based on the physical network graph, i.e., the connectivity graph. In this paper we investigate how logical relationships between nodes of the AS graph can be used to gain insight to its structure. We characterize the logical graph using various metrics and identify the presence of power laws in the number of customers that a provider has. Using these logical relationships we define a structural model of the AS graph. The model highlights the hierarchical nature of logical relationships and the preferential connection to larger providers. We also investigate the consistency of this model over time and observe interesting properties of the hierarchical structure.
Graph theoretical similarity approach to compare molecular electrostatic potentials.
Marín, Ray M; Aguirre, Nestor F; Daza, Edgar E
2008-01-01
In this work we introduce a graph theoretical method to compare MEPs, which is independent of molecular alignment. It is based on the edit distance of weighted rooted trees, which encode the geometrical and topological information of Negative Molecular Isopotential Surfaces. A meaningful chemical classification of a set of 46 molecules with different functional groups was achieved. Structure--activity relationships for the corticosteroid binding affinity (CBG) of 31 steroids by means of hierarchical clustering resulted in a clear partitioning in high, intermediate, and low activity groups, whereas the results from quantitative structure--activity relationships, obtained from a partial least-squares analysis, showed comparable or better cross-validated correlation coefficients than the ones reported for previous methods based solely in the MEP.
Graph distance for complex networks
NASA Astrophysics Data System (ADS)
Shimada, Yutaka; Hirata, Yoshito; Ikeguchi, Tohru; Aihara, Kazuyuki
2016-10-01
Networks are widely used as a tool for describing diverse real complex systems and have been successfully applied to many fields. The distance between networks is one of the most fundamental concepts for properly classifying real networks, detecting temporal changes in network structures, and effectively predicting their temporal evolution. However, this distance has rarely been discussed in the theory of complex networks. Here, we propose a graph distance between networks based on a Laplacian matrix that reflects the structural and dynamical properties of networked dynamical systems. Our results indicate that the Laplacian-based graph distance effectively quantifies the structural difference between complex networks. We further show that our approach successfully elucidates the temporal properties underlying temporal networks observed in the context of face-to-face human interactions.
Graph distance for complex networks
Shimada, Yutaka; Hirata, Yoshito; Ikeguchi, Tohru; Aihara, Kazuyuki
2016-01-01
Networks are widely used as a tool for describing diverse real complex systems and have been successfully applied to many fields. The distance between networks is one of the most fundamental concepts for properly classifying real networks, detecting temporal changes in network structures, and effectively predicting their temporal evolution. However, this distance has rarely been discussed in the theory of complex networks. Here, we propose a graph distance between networks based on a Laplacian matrix that reflects the structural and dynamical properties of networked dynamical systems. Our results indicate that the Laplacian-based graph distance effectively quantifies the structural difference between complex networks. We further show that our approach successfully elucidates the temporal properties underlying temporal networks observed in the context of face-to-face human interactions. PMID:27725690
Graph Embedded Extreme Learning Machine.
Iosifidis, Alexandros; Tefas, Anastasios; Pitas, Ioannis
2016-01-01
In this paper, we propose a novel extension of the extreme learning machine (ELM) algorithm for single-hidden layer feedforward neural network training that is able to incorporate subspace learning (SL) criteria on the optimization process followed for the calculation of the network's output weights. The proposed graph embedded ELM (GEELM) algorithm is able to naturally exploit both intrinsic and penalty SL criteria that have been (or will be) designed under the graph embedding framework. In addition, we extend the proposed GEELM algorithm in order to be able to exploit SL criteria in arbitrary (even infinite) dimensional ELM spaces. We evaluate the proposed approach on eight standard classification problems and nine publicly available datasets designed for three problems related to human behavior analysis, i.e., the recognition of human face, facial expression, and activity. Experimental results denote the effectiveness of the proposed approach, since it outperforms other ELM-based classification schemes in all the cases.
Line graphs as social networks
NASA Astrophysics Data System (ADS)
Krawczyk, M. J.; Muchnik, L.; Mańka-Krasoń, A.; Kułakowski, K.
2011-07-01
It was demonstrated recently that the line graphs are clustered and assortative. These topological features are known to characterize some social networks [M.E.J. Newman, Y. Park, Why social networks are different from other types of networks, Phys. Rev. E 68 (2003) 036122]; it was argued that this similarity reveals their cliquey character. In the model proposed here, a social network is the line graph of an initial network of families, communities, interest groups, school classes and small companies. These groups play the role of nodes, and individuals are represented by links between these nodes. The picture is supported by the data on the LiveJournal network of about 8×10 6 people.
Temporal Partitioning on Multicore Platform
NASA Astrophysics Data System (ADS)
Mahmud Pathan, Ristat; Hashi, Feysal; Stenstrom, Per; Green, Lars-Goran; Hult, Torbjorn; Sandin, Patrik
2014-08-01
This paper addresses the problem of ensuring temporal partitioning according to the ARINC-653 standard for integrating multiple applications on the same multicore platform. To employ temporal partitioning, we propose the design and analysis of a hierarchical scheduling framework (HSF) for multicore platform. In HSF, each application has a server task, which is mapped to one of the physical cores of the multicore platform. The HSF framework is based on scheduling at two-levels: (i) a system-level scheduler for each core schedules the server tasks that are mapped to that core, and (ii) a task- level scheduler for each application schedules the tasks of the application. This paper presents the design and analysis of this two-level HSF that can be used to ensure temporal partitioning and meeting all the deadlines of each application tasks. The effectiveness of our technique is demonstrated using real-world space applications provided by RUAG Space Sweden AB.
Relativity on Rotated Graph Paper
NASA Astrophysics Data System (ADS)
Salgado, Roberto
2011-11-01
We present visual calculations in special relativity using spacetime diagrams drawn on graph paper that has been rotated by 45 degrees. The rotated lines represent lightlike directions in Minkowski spacetime, and the boxes in the grid (called light-clock diamonds) represent ticks of an inertial observer's lightclock. We show that many quantitative results can be read off a spacetime diagram by counting boxes, using a minimal amount of algebra.
Dynamic molecular graphs: "hopping" structures.
Cortés-Guzmán, Fernando; Rocha-Rinza, Tomas; Guevara-Vela, José Manuel; Cuevas, Gabriel; Gómez, Rosa María
2014-05-05
This work aims to contribute to the discussion about the suitability of bond paths and bond-critical points as indicators of chemical bonding defined within the theoretical framework of the quantum theory of atoms in molecules. For this purpose, we consider the temporal evolution of the molecular structure of [Fe{C(CH2 )3 }(CO)3 ] throughout Born-Oppenheimer molecular dynamics (BOMD), which illustrates the changing behaviour of the molecular graph (MG) of an electronic system. Several MGs with significant lifespans are observed across the BOMD simulations. The bond paths between the trimethylenemethane and the metallic core are uninterruptedly formed and broken. This situation is reminiscent of a "hopping" ligand over the iron atom. The molecular graph wherein the bonding between trimethylenemethane and the iron atom takes place only by means of the tertiary carbon atom has the longest lifespan of all the considered structures, which is consistent with the MG found by X-ray diffraction experiments and quantum chemical calculations. In contrast, the η(4) complex predicted by molecular-orbital theory has an extremely brief lifetime. The lifespan of different molecular structures is related to bond descriptors on the basis of the topology of the electron density such as the ellipticities at the FeCH2 bond-critical points and electron delocalisation indices. This work also proposes the concept of a dynamic molecular graph composed of the different structures found throughout the BOMD trajectories in analogy to a resonance hybrid of Lewis structures. It is our hope that the notion of dynamic molecular graphs will prove useful in the discussion of electronic systems, in particular for those in which analysis on the basis of static structures leads to controversial conclusions.
Topological structure of dictionary graphs
NASA Astrophysics Data System (ADS)
Fukś, Henryk; Krzemiński, Mark
2009-09-01
We investigate the topological structure of the subgraphs of dictionary graphs constructed from WordNet and Moby thesaurus data. In the process of learning a foreign language, the learner knows only a subset of all words of the language, corresponding to a subgraph of a dictionary graph. When this subgraph grows with time, its topological properties change. We introduce the notion of the pseudocore and argue that the growth of the vocabulary roughly follows decreasing pseudocore numbers—that is, one first learns words with a high pseudocore number followed by smaller pseudocores. We also propose an alternative strategy for vocabulary growth, involving decreasing core numbers as opposed to pseudocore numbers. We find that as the core or pseudocore grows in size, the clustering coefficient first decreases, then reaches a minimum and starts increasing again. The minimum occurs when the vocabulary reaches a size between 103 and 104. A simple model exhibiting similar behavior is proposed. The model is based on a generalized geometric random graph. Possible implications for language learning are discussed.
What is the difference between the breakpoint graph and the de Bruijn graph?
Lin, Yu; Nurk, Sergey; Pevzner, Pavel A
2014-01-01
The breakpoint graph and the de Bruijn graph are two key data structures in the studies of genome rearrangements and genome assembly. However, the classical breakpoint graphs are defined on two genomes (represented as sequences of synteny blocks), while the classical de Bruijn graphs are defined on a single genome (represented as DNA strings). Thus, the connection between these two graph models is not explicit. We generalize the notions of both the breakpoint graph and the de Bruijn graph, and make it transparent that the breakpoint graph and the de Bruijn graph are mathematically equivalent. The explicit description of the connection between these important data structures provides a bridge between two previously separated bioinformatics communities studying genome rearrangements and genome assembly.
2014-01-01
Mathematical models of cellular physiological mechanisms often involve random walks on graphs representing transitions within networks of functional states. Schmandt and Galán recently introduced a novel stochastic shielding approximation as a fast, accurate method for generating approximate sample paths from a finite state Markov process in which only a subset of states are observable. For example, in ion-channel models, such as the Hodgkin–Huxley or other conductance-based neural models, a nerve cell has a population of ion channels whose states comprise the nodes of a graph, only some of which allow a transmembrane current to pass. The stochastic shielding approximation consists of neglecting fluctuations in the dynamics associated with edges in the graph not directly affecting the observable states. We consider the problem of finding the optimal complexity reducing mapping from a stochastic process on a graph to an approximate process on a smaller sample space, as determined by the choice of a particular linear measurement functional on the graph. The partitioning of ion-channel states into conducting versus nonconducting states provides a case in point. In addition to establishing that Schmandt and Galán’s approximation is in fact optimal in a specific sense, we use recent results from random matrix theory to provide heuristic error estimates for the accuracy of the stochastic shielding approximation for an ensemble of random graphs. Moreover, we provide a novel quantitative measure of the contribution of individual transitions within the reaction graph to the accuracy of the approximate process. PMID:24742077
Helping Students Make Sense of Graphs: An Experimental Trial of SmartGraphs Software
NASA Astrophysics Data System (ADS)
Zucker, Andrew; Kay, Rachel; Staudt, Carolyn
2014-06-01
Graphs are commonly used in science, mathematics, and social sciences to convey important concepts; yet students at all ages demonstrate difficulties interpreting graphs. This paper reports on an experimental study of free, Web-based software called SmartGraphs that is specifically designed to help students overcome their misconceptions regarding graphs. SmartGraphs allows students to interact with graphs and provides hints and scaffolding to help students, if they need help. SmartGraphs activities can be authored to be useful in teaching and learning a variety of topics that use graphs (such as slope, velocity, half-life, and global warming). A 2-year experimental study in physical science classrooms was conducted with dozens of teachers and thousands of students. In the first year, teachers were randomly assigned to experimental or control conditions. Data show that students of teachers who use SmartGraphs as a supplement to normal instruction make greater gains understanding graphs than control students studying the same content using the same textbooks, but without SmartGraphs. Additionally, teachers believe that the SmartGraphs activities help students meet learning goals in the physical science course, and a great majority reported they would use the activities with students again. In the second year of the study, several specific variations of SmartGraphs were researched to help determine what makes SmartGraphs effective.
Many-core graph analytics using accelerated sparse linear algebra routines
NASA Astrophysics Data System (ADS)
Kozacik, Stephen; Paolini, Aaron L.; Fox, Paul; Kelmelis, Eric
2016-05-01
Graph analytics is a key component in identifying emerging trends and threats in many real-world applications. Largescale graph analytics frameworks provide a convenient and highly-scalable platform for developing algorithms to analyze large datasets. Although conceptually scalable, these techniques exhibit poor performance on modern computational hardware. Another model of graph computation has emerged that promises improved performance and scalability by using abstract linear algebra operations as the basis for graph analysis as laid out by the GraphBLAS standard. By using sparse linear algebra as the basis, existing highly efficient algorithms can be adapted to perform computations on the graph. This approach, however, is often less intuitive to graph analytics experts, who are accustomed to vertex-centric APIs such as Giraph, GraphX, and Tinkerpop. We are developing an implementation of the high-level operations supported by these APIs in terms of linear algebra operations. This implementation is be backed by many-core implementations of the fundamental GraphBLAS operations required, and offers the advantages of both the intuitive programming model of a vertex-centric API and the performance of a sparse linear algebra implementation. This technology can reduce the number of nodes required, as well as the run-time for a graph analysis problem, enabling customers to perform more complex analysis with less hardware at lower cost. All of this can be accomplished without the requirement for the customer to make any changes to their analytics code, thanks to the compatibility with existing graph APIs.
Brusco, Michael; Steinley, Douglas
2010-06-01
Structural balance theory (SBT) has maintained a venerable status in the psychological literature for more than 5 decades. One important problem pertaining to SBT is the approximation of structural or generalized balance via the partitioning of the vertices of a signed graph into K clusters. This K-balance partitioning problem also has more general psychological applications associated with the analysis of similarity/dissimilarity relationships among stimuli. Accordingly, K-balance partitioning can be gainfully used in a wide variety of SBT applications, such as attraction and child development, evaluation of group membership, marketing and consumer issues, and other psychological contexts not necessarily related to SBT. We present a branch-and-bound algorithm for the K-balance partitioning problem. This new algorithm is applied to 2 synthetic numerical examples as well as to several real-world data sets from the behavioral sciences literature.
Fast Dynamic Meshing Method Based on Delaunay Graph and Inverse Distance Weighting Interpolation
NASA Astrophysics Data System (ADS)
Wang, Yibin; Qin, Ning; Zhao, Ning
2016-06-01
A novel mesh deformation technique is developed based on the Delaunay graph mapping method and the inverse distance weighting (IDW) interpolation. The algorithm maintains the advantages of the efficiency of Delaunay-graph-mapping mesh deformation while possess the ability for better controlling the near surface mesh quality. The Delaunay graph is used to divide the mesh domain into a number of sub-domains. On each of the sub-domains, the inverse distance weighting interpolation is applied to build a much smaller sized translation matrix between the original mesh and the deformed mesh, resulting a similar efficiency for the mesh deformation as compared to the fast Delaunay graph mapping method. The paper will show how the near-wall mesh quality is controlled and improved by the new method while the computational time is compared with the original Delaunay graph mapping method.
Time Domain Partitioning of Electricity Production Cost Simulations
Barrows, C.; Hummon, M.; Jones, W.; Hale, E.
2014-01-01
Production cost models are often used for planning by simulating power system operations over long time horizons. The simulation of a day-ahead energy market can take several weeks to compute. Tractability improvements are often made through model simplifications, such as: reductions in transmission modeling detail, relaxation of commitment variable integrality, reductions in cost modeling detail, etc. One common simplification is to partition the simulation horizon so that weekly or monthly horizons can be simulated in parallel. However, horizon partitions are often executed with overlap periods of arbitrary and sometimes zero length. We calculate the time domain persistence of historical unit commitment decisions to inform time domain partitioning of production cost models. The results are implemented using PLEXOS production cost modeling software in an HPC environment to improve the computation time of simulations while maintaining solution integrity.
Expanding our understanding of students' use of graphs for learning physics
NASA Astrophysics Data System (ADS)
Laverty, James T.
It is generally agreed that the ability to visualize functional dependencies or physical relationships as graphs is an important step in modeling and learning. However, several studies in Physics Education Research (PER) have shown that many students in fact do not master this form of representation and even have misconceptions about the meaning of graphs that impede learning physics concepts. Working with graphs in classroom settings has been shown to improve student abilities with graphs, particularly when the students can interact with them. We introduce a novel problem type in an online homework system, which requires students to construct the graphs themselves in free form, and requires no hand-grading by instructors. A study of pre/post-test data using the Test of Understanding Graphs in Kinematics (TUG-K) over several semesters indicates that students learn significantly more from these graph construction problems than from the usual graph interpretation problems, and that graph interpretation alone may not have any significant effect. The interpretation of graphs, as well as the representation translation between textual, mathematical, and graphical representations of physics scenarios, are frequently listed among the higher order thinking skills we wish to convey in an undergraduate course. But to what degree do we succeed? Do students indeed employ higher order thinking skills when working through graphing exercises? We investigate students working through a variety of graph problems, and, using a think-aloud protocol, aim to reconstruct the cognitive processes that the students go through. We find that to a certain degree, these problems become commoditized and do not trigger the desired higher order thinking processes; simply translating ``textbook-like'' problems into the graphical realm will not achieve any additional educational goals. Whether the students have to interpret or construct a graph makes very little difference in the methods used by the
Computing Information Value from RDF Graph Properties
al-Saffar, Sinan; Heileman, Gregory
2010-11-08
Information value has been implicitly utilized and mostly non-subjectively computed in information retrieval (IR) systems. We explicitly define and compute the value of an information piece as a function of two parameters, the first is the potential semantic impact the target information can subjectively have on its recipient's world-knowledge, and the second parameter is trust in the information source. We model these two parameters as properties of RDF graphs. Two graphs are constructed, a target graph representing the semantics of the target body of information and a context graph representing the context of the consumer of that information. We compute information value subjectively as a function of both potential change to the context graph (impact) and the overlap between the two graphs (trust). Graph change is computed as a graph edit distance measuring the dissimilarity between the context graph before and after the learning of the target graph. A particular application of this subjective information valuation is in the construction of a personalized ranking component in Web search engines. Based on our method, we construct a Web re-ranking system that personalizes the information experience for the information-consumer.
Inferring Pedigree Graphs from Genetic Distances
NASA Astrophysics Data System (ADS)
Tamura, Takeyuki; Ito, Hiro
In this paper, we study a problem of inferring blood relationships which satisfy a given matrix of genetic distances between all pairs of n nodes. Blood relationships are represented by our proposed graph class, which is called a pedigree graph. A pedigree graph is a directed acyclic graph in which the maximum indegree is at most two. We show that the number of pedigree graphs which satisfy the condition of given genetic distances may be exponential, but they can be represented by one directed acyclic graph with n nodes. Moreover, an O(n3) time algorithm which solves the problem is also given. Although phylogenetic trees and phylogenetic networks are similar data structures to pedigree graphs, it seems that inferring methods for phylogenetic trees and networks cannot be applied to infer pedigree graphs since nodes of phylogenetic trees and networks represent species whereas nodes of pedigree graphs represent individuals. We also show an O(n2) time algorithm which detects a contradiction between a given pedigreee graph and distance matrix of genetic distances.
Motifs in triadic random graphs based on Steiner triple systems
NASA Astrophysics Data System (ADS)
Winkler, Marco; Reichardt, Jörg
2013-08-01
Conventionally, pairwise relationships between nodes are considered to be the fundamental building blocks of complex networks. However, over the last decade, the overabundance of certain subnetwork patterns, i.e., the so-called motifs, has attracted much attention. It has been hypothesized that these motifs, instead of links, serve as the building blocks of network structures. Although the relation between a network's topology and the general properties of the system, such as its function, its robustness against perturbations, or its efficiency in spreading information, is the central theme of network science, there is still a lack of sound generative models needed for testing the functional role of subgraph motifs. Our work aims to overcome this limitation. We employ the framework of exponential random graph models (ERGMs) to define models based on triadic substructures. The fact that only a small portion of triads can actually be set independently poses a challenge for the formulation of such models. To overcome this obstacle, we use Steiner triple systems (STSs). These are partitions of sets of nodes into pair-disjoint triads, which thus can be specified independently. Combining the concepts of ERGMs and STSs, we suggest generative models capable of generating ensembles of networks with nontrivial triadic Z-score profiles. Further, we discover inevitable correlations between the abundance of triad patterns, which occur solely for statistical reasons and need to be taken into account when discussing the functional implications of motif statistics. Moreover, we calculate the degree distributions of our triadic random graphs analytically.
JavaGenes: Evolving Graphs with Crossover
NASA Technical Reports Server (NTRS)
Globus, Al; Atsatt, Sean; Lawton, John; Wipke, Todd
2000-01-01
Genetic algorithms usually use string or tree representations. We have developed a novel crossover operator for a directed and undirected graph representation, and used this operator to evolve molecules and circuits. Unlike strings or trees, a single point in the representation cannot divide every possible graph into two parts, because graphs may contain cycles. Thus, the crossover operator is non-trivial. A steady-state, tournament selection genetic algorithm code (JavaGenes) was written to implement and test the graph crossover operator. All runs were executed by cycle-scavagging on networked workstations using the Condor batch processing system. The JavaGenes code has evolved pharmaceutical drug molecules and simple digital circuits. Results to date suggest that JavaGenes can evolve moderate sized drug molecules and very small circuits in reasonable time. The algorithm has greater difficulty with somewhat larger circuits, suggesting that directed graphs (circuits) are more difficult to evolve than undirected graphs (molecules), although necessary differences in the crossover operator may also explain the results. In principle, JavaGenes should be able to evolve other graph-representable systems, such as transportation networks, metabolic pathways, and computer networks. However, large graphs evolve significantly slower than smaller graphs, presumably because the space-of-all-graphs explodes combinatorially with graph size. Since the representation strongly affects genetic algorithm performance, adding graphs to the evolutionary programmer's bag-of-tricks should be beneficial. Also, since graph evolution operates directly on the phenotype, the genotype-phenotype translation step, common in genetic algorithm work, is eliminated.
Integrating GIS and genetic algorithms for automating land partitioning
NASA Astrophysics Data System (ADS)
Demetriou, Demetris; See, Linda; Stillwell, John
2014-08-01
Land consolidation is considered to be the most effective land management planning approach for controlling land fragmentation and hence improving agricultural efficiency. Land partitioning is a basic process of land consolidation that involves the subdivision of land into smaller sub-spaces subject to a number of constraints. This paper explains the development of a module called LandParcelS (Land Parcelling System) that integrates geographical information systems and a genetic algorithm to automate the land partitioning process by designing and optimising land parcels in terms of their shape, size and value. This new module has been applied to two land blocks that are part of a larger case study area in Cyprus. Partitioning is carried out by guiding a Thiessen polygon process within ArcGIS and it is treated as a multiobjective problem. The results suggest that a step forward has been made in solving this complex spatial problem, although further research is needed to improve the algorithm. The contribution of this research extends land partitioning and space partitioning in general, since these approaches may have relevance to other spatial processes that involve single or multi-objective problems that could be solved in the future by spatial evolutionary algorithms.
Understanding Partitive Division of Fractions.
ERIC Educational Resources Information Center
Ott, Jack M.; And Others
1991-01-01
Concrete experience should be a first step in the development of new abstract concepts and their symbolization. Presents concrete activities based on Hyde and Nelson's work with egg cartons and Steiner's work with money to develop students' understanding of partitive division when using fractions. (MDH)
METAL PARTITIONING IN COMBUSTION PROCESSES
This article summarizes ongoing research efforts at the National Risk Management Research Laboratory of the U.S. Environmental Protection Agency examining [high temperature] metal behavior within combustion environments. The partitioning of non-volatile (Cr and Ni), semi-volatil...
Correlation of tissue, blood, and air partition coefficients of volatile organic chemicals.
Paterson, S; Mackay, D
1989-01-01
The physical chemical factors controlling partition coefficients between air, water, blood, and various tissues are discussed. It is suggested that improved insights into the relations between partition coefficients, which are frequently expressed as correlations, may be obtained by viewing the partition coefficients as ratios of solubilities or pseudosolubilities. A simple, novel correlation approach is developed and applied to 24 volatile organic chemicals, which enables tissue/blood, tissue/air, and blood/air partition coefficients to be estimated from water solubility and vapour pressure. An illustration is presented in which these solubilities are used to calculate the equilibrium distribution of dichloromethane between air, blood, and various tissues. PMID:2751930
Mays, E.T.; Feldhoff, R.C.; Nettleton, G.S.
1984-10-01
In phase partition fixation tissue is immersed in an organic solvent at equilibrium with an aqueous phase containing a fixing agent. By using radioisotope labeling techniques the effects of phase partition fixation on protein retention during fixation of tissue with formalin and glutaraldehyde have been determined and compared with those of standard aqueous fixation using these fixatives. It has been shown that retention of protein in tissue during phase partition fixation was as good or better than during aqueous fixation. Improved retention provides further evidence that phase partition fixation may be a useful alternative to aqueous fixation.
Fast dual graph-based hotspot detection
NASA Astrophysics Data System (ADS)
Kahng, Andrew B.; Park, Chul-Hong; Xu, Xu
2006-10-01
features or "L-shaped" features; (2) face-level detection finds the pattern-related hotspots which span several close features; and (3) merged-face-level detection finds hotspots with more complex patterns. To find the merged faces which capture the pattern-related hotspots, we propose to convert the layout into a planar graph G. We then construct its dual graph G D and sort the dual nodes according to their weights. We merge the sorted dual nodes (i.e., the faces in G) that share a given feature, in sequence. We have tested our flow on several industry testcases. The experimental results show that our method is promising: for a 90nm metal layer with 17 hotspots detected by commercial optical rule check (ORC) tools, our method can detect all of them while the overall runtime improvement is more than 287X.
A mesh partitioning algorithm for preserving spatial locality in arbitrary geometries
NASA Astrophysics Data System (ADS)
Nivarti, Girish V.; Salehi, M. Mahdi; Bushe, W. Kendal
2015-01-01
A space-filling curve (SFC) is a proximity preserving linear mapping of any multi-dimensional space and is widely used as a clustering tool. Equi-sized partitioning of an SFC ignores the loss in clustering quality that occurs due to inaccuracies in the mapping. Often, this results in poor locality within partitions, especially for the conceptually simple, Morton order curves. We present a heuristic that improves partition locality in arbitrary geometries by slicing a Morton order curve at points where spatial locality is sacrificed. In addition, we develop algorithms that evenly distribute points to the extent possible while maintaining spatial locality. A metric is defined to estimate relative inter-partition contact as an indicator of communication in parallel computing architectures. Domain partitioning tests have been conducted on geometries relevant to turbulent reactive flow simulations. The results obtained highlight the performance of our method as an unsupervised and computationally inexpensive domain partitioning tool.
API Requirements for Dynamic Graph Prediction
Gallagher, B; Eliassi-Rad, T
2006-10-13
Given a large-scale time-evolving multi-modal and multi-relational complex network (a.k.a., a large-scale dynamic semantic graph), we want to implement algorithms that discover patterns of activities on the graph and learn predictive models of those discovered patterns. This document outlines the application programming interface (API) requirements for fast prototyping of feature extraction, learning, and prediction algorithms on large dynamic semantic graphs. Since our algorithms must operate on large-scale dynamic semantic graphs, we have chosen to use the graph API developed in the CASC Complex Networks Project. This API is supported on the back end by a semantic graph database (developed by Scott Kohn and his team). The advantages of using this API are (i) we have full-control of its development and (ii) the current API meets almost all of the requirements outlined in this document.
Fast generation of sparse random kernel graphs
Hagberg, Aric; Lemons, Nathan; Du, Wen -Bo
2015-09-10
The development of kernel-based inhomogeneous random graphs has provided models that are flexible enough to capture many observed characteristics of real networks, and that are also mathematically tractable. We specify a class of inhomogeneous random graph models, called random kernel graphs, that produces sparse graphs with tunable graph properties, and we develop an efficient generation algorithm to sample random instances from this model. As real-world networks are usually large, it is essential that the run-time of generation algorithms scales better than quadratically in the number of vertices n. We show that for many practical kernels our algorithm runs in time at most ο(n(logn)²). As an example, we show how to generate samples of power-law degree distribution graphs with tunable assortativity.
Fast generation of sparse random kernel graphs
Hagberg, Aric; Lemons, Nathan; Du, Wen -Bo
2015-09-10
The development of kernel-based inhomogeneous random graphs has provided models that are flexible enough to capture many observed characteristics of real networks, and that are also mathematically tractable. We specify a class of inhomogeneous random graph models, called random kernel graphs, that produces sparse graphs with tunable graph properties, and we develop an efficient generation algorithm to sample random instances from this model. As real-world networks are usually large, it is essential that the run-time of generation algorithms scales better than quadratically in the number of vertices n. We show that for many practical kernels our algorithm runs in timemore » at most ο(n(logn)²). As an example, we show how to generate samples of power-law degree distribution graphs with tunable assortativity.« less
Replica methods for loopy sparse random graphs
NASA Astrophysics Data System (ADS)
Coolen, ACC
2016-03-01
I report on the development of a novel statistical mechanical formalism for the analysis of random graphs with many short loops, and processes on such graphs. The graphs are defined via maximum entropy ensembles, in which both the degrees (via hard constraints) and the adjacency matrix spectrum (via a soft constraint) are prescribed. The sum over graphs can be done analytically, using a replica formalism with complex replica dimensions. All known results for tree-like graphs are recovered in a suitable limit. For loopy graphs, the emerging theory has an appealing and intuitive structure, suggests how message passing algorithms should be adapted, and what is the structure of theories describing spin systems on loopy architectures. However, the formalism is still largely untested, and may require further adjustment and refinement. This paper is dedicated to the memory of our colleague and friend Jun-Ichi Inoue, with whom the author has had the great pleasure and privilege of collaborating.
Traxl, Dominik; Boers, Niklas; Kurths, Jürgen
2016-06-01
Network theory has proven to be a powerful tool in describing and analyzing systems by modelling the relations between their constituent objects. Particularly in recent years, a great progress has been made by augmenting "traditional" network theory in order to account for the multiplex nature of many networks, multiple types of connections between objects, the time-evolution of networks, networks of networks and other intricacies. However, existing network representations still lack crucial features in order to serve as a general data analysis tool. These include, most importantly, an explicit association of information with possibly heterogeneous types of objects and relations, and a conclusive representation of the properties of groups of nodes as well as the interactions between such groups on different scales. In this paper, we introduce a collection of definitions resulting in a framework that, on the one hand, entails and unifies existing network representations (e.g., network of networks and multilayer networks), and on the other hand, generalizes and extends them by incorporating the above features. To implement these features, we first specify the nodes and edges of a finite graph as sets of properties (which are permitted to be arbitrary mathematical objects). Second, the mathematical concept of partition lattices is transferred to the network theory in order to demonstrate how partitioning the node and edge set of a graph into supernodes and superedges allows us to aggregate, compute, and allocate information on and between arbitrary groups of nodes. The derived partition lattice of a graph, which we denote by deep graph, constitutes a concise, yet comprehensive representation that enables the expression and analysis of heterogeneous properties, relations, and interactions on all scales of a complex system in a self-contained manner. Furthermore, to be able to utilize existing network-based methods and models, we derive different representations of
Spectral correlations of individual quantum graphs
Gnutzmann, Sven; Altland, Alexander
2005-11-01
We investigate the spectral properties of chaotic quantum graphs. We demonstrate that the energy-average over the spectrum of individual graphs can be traded for the functional average over a supersymmetric nonlinear {sigma}-model action. This proves that spectral correlations of individual quantum graphs behave according to the predictions of Wigner-Dyson random matrix theory. We explore the stability of the universal random matrix behavior with regard to perturbations, and discuss the crossover between different types of symmetries.
NASA Technical Reports Server (NTRS)
Collins, Oliver (Inventor); Dolinar, Jr., Samuel J. (Inventor); Hus, In-Shek (Inventor); Bozzola, Fabrizio P. (Inventor); Olson, Erlend M. (Inventor); Statman, Joseph I. (Inventor); Zimmerman, George A. (Inventor)
1991-01-01
A method of formulating and packaging decision-making elements into a long constraint length Viterbi decoder which involves formulating the decision-making processors as individual Viterbi butterfly processors that are interconnected in a deBruijn graph configuration. A fully distributed architecture, which achieves high decoding speeds, is made feasible by novel wiring and partitioning of the state diagram. This partitioning defines universal modules, which can be used to build any size decoder, such that a large number of wires is contained inside each module, and a small number of wires is needed to connect modules. The total system is modular and hierarchical, and it implements a large proportion of the required wiring internally within modules and may include some external wiring to fully complete the deBruijn graph. pg,14.
NASA Astrophysics Data System (ADS)
Sui, Xiukai; Wu, Bin; Wang, Long
2015-12-01
The likelihood that a mutant fixates in the wild population, i.e., fixation probability, has been intensively studied in evolutionary game theory, where individuals' fitness is frequency dependent. However, it is of limited interest when it takes long to take over. Thus the speed of evolution becomes an important issue. In general, it is still unclear how fixation times are affected by the population structure, although the fixation times have already been addressed in the well-mixed populations. Here we theoretically address this issue by pair approximation and diffusion approximation on regular graphs. It is shown (i) that under neutral selection, both unconditional and conditional fixation time are shortened by increasing the number of neighbors; (ii) that under weak selection, for the simplified prisoner's dilemma game, if benefit-to-cost ratio exceeds the degree of the graph, then the unconditional fixation time of a single cooperator is slower than that in the neutral case; and (iii) that under weak selection, for the conditional fixation time, limited neighbor size dilutes the counterintuitive stochastic slowdown which was found in well-mixed populations. Interestingly, we find that all of our results can be interpreted as that in the well-mixed population with a transformed payoff matrix. This interpretation is also valid for both death-birth and birth-death processes on graphs. This interpretation bridges the fixation time in the structured population and that in the well-mixed population. Thus it opens the avenue to investigate the challenging fixation time in structured populations by the known results in well-mixed populations.
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.
NASA Astrophysics Data System (ADS)
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), 10.1103/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.
The alignment-distribution graph
NASA Technical Reports Server (NTRS)
Chatterjee, Siddhartha; Gilbert, John R.; Schreiber, Robert
1993-01-01
Implementing a data-parallel language such as Fortran 90 on a distributed-memory parallel computer requires distributing aggregate data objects (such as arrays) among the memory modules attached to the processors. The mapping of objects to the machine determines the amount of residual communication needed to bring operands of parallel operations into alignment with each other. We present a program representation called the alignment-distribution graph that makes these communication requirements explicit. We describe the details of the representation, show how to model communication cost in this framework, and outline several algorithms for determining object mappings that approximately minimize residual communication.
The alignment-distribution graph
NASA Technical Reports Server (NTRS)
Chatterjee, Siddhartha; Gilbert, John R.; Schreiber, Robert
1993-01-01
Implementing a data-parallel language such as Fortran 90 on a distributed-memory parallel computer requires distributing aggregate data objects (such as arrays) among the memory modules attached to the processors. The mapping of objects to the machine determines the amount of residual communication needed to bring operands of parallel operations into alignment with each other. We present a program representation called the alignment distribution graph that makes these communication requirements explicit. We describe the details of the representation, show how to model communication cost in this framework, and outline several algorithms for determining object mappings that approximately minimize residual communication.
NASA Astrophysics Data System (ADS)
Gosti, Giorgio; Batchelder, William H.
We address how the structure of a social communication system affects language coordination. The naming game is an abstraction of lexical acquisition dynamics, in which N agents try to find an agreement on the names to give to objects. Most results on naming games are specific to certain communication network topologies. We present two important results that are general to any graph topology: the first proves that under certain topologies the system always converges to a name-object agreement; the second proves that if these conditions are not met the system may end up in a state in which sub-networks with different competing object-name associations coexist.
Simple scale interpolator facilitates reading of graphs
NASA Technical Reports Server (NTRS)
Fetterman, D. E., Jr.
1965-01-01
Simple transparent overlay with interpolation scale facilitates accurate, rapid reading of graph coordinate points. This device can be used for enlarging drawings and locating points on perspective drawings.
Evolutionary Games of Multiplayer Cooperation on Graphs
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
Graph algorithms in the titan toolkit.
McLendon, William Clarence, III; Wylie, Brian Neil
2009-10-01
Graph algorithms are a key component in a wide variety of intelligence analysis activities. The Graph-Based Informatics for Non-Proliferation and Counter-Terrorism project addresses the critical need of making these graph algorithms accessible to Sandia analysts in a manner that is both intuitive and effective. Specifically we describe the design and implementation of an open source toolkit for doing graph analysis, informatics, and visualization that provides Sandia with novel analysis capability for non-proliferation and counter-terrorism.
Some Recent Results on Graph Matching,
1987-06-01
extendable graphs In Section 2 of this paper we saw how the brick decomposition procedure can be carried out on an arbitrary 1-extendable graph and that...in fact, the procedure is "canonical" in the sense that the final list of bricks so obtained is an invariant of the graph. Furthermore, we saw how...JACKSON, P. KATERINIS and A. SAITO, Toughness and the existence of k-factors, J. Graph Theory 9, 1985, 87-95. [G1] T. GALLAI, Kritische Graphen II
Bandlimited graph signal reconstruction by diffusion operator
NASA Astrophysics Data System (ADS)
Yang, Lishan; You, Kangyong; Guo, Wenbin
2016-12-01
Signal processing on graphs extends signal processing concepts and methodologies from the classical signal processing theory to data indexed by general graphs. For a bandlimited graph signal, the unknown data associated with unsampled vertices can be reconstructed from the sampled data by exploiting the spatial relationship of graph signal. In this paper, we propose a generalized analytical framework of unsampled graph signal and introduce a concept of diffusion operator which consists of local-mean and global-bias diffusion operator. Then, a diffusion operator-based iterative algorithm is proposed to reconstruct bandlimited graph signal from sampled data. In each iteration, the reconstructed residuals associated with the sampled vertices are diffused to all the unsampled vertices for accelerating the convergence. We then prove that the proposed reconstruction strategy converges to the original graph signal. The simulation results demonstrate the effectiveness of the proposed reconstruction strategy with various downsampling patterns, fluctuation of graph cut-off frequency, robustness on the classic graph structures, and noisy scenarios.
Generation of graph-state streams
Ballester, Daniel; Cho, Jaeyoon; Kim, M. S.
2011-01-15
We propose a protocol to generate a stream of mobile qubits in a graph state through a single stationary parent qubit and discuss two types of its physical implementation, namely, the generation of photonic graph states through an atomlike qubit and the generation of flying atoms through a cavity-mode photonic qubit. The generated graph states fall into an important class that can hugely reduce the resource requirement of fault-tolerant linear optics quantum computation, which was previously known to be far from realistic. In regard to the flying atoms, we also propose a heralded generation scheme, which allows for high-fidelity graph states even under the photon loss.
A strand graph semantics for DNA-based computation.
Petersen, Rasmus L; Lakin, Matthew R; Phillips, Andrew
2016-06-13
DNA nanotechnology is a promising approach for engineering computation at the nanoscale, with potential applications in biofabrication and intelligent nanomedicine. DNA strand displacement is a general strategy for implementing a broad range of nanoscale computations, including any computation that can be expressed as a chemical reaction network. Modelling and analysis of DNA strand displacement systems is an important part of the design process, prior to experimental realisation. As experimental techniques improve, it is important for modelling languages to keep pace with the complexity of structures that can be realised experimentally. In this paper we present a process calculus for modelling DNA strand displacement computations involving rich secondary structures, including DNA branches and loops. We prove that our calculus is also sufficiently expressive to model previous work on non-branching structures, and propose a mapping from our calculus to a canonical strand graph representation, in which vertices represent DNA strands, ordered sites represent domains, and edges between sites represent bonds between domains. We define interactions between strands by means of strand graph rewriting, and prove the correspondence between the process calculus and strand graph behaviours. Finally, we propose a mapping from strand graphs to an efficient implementation, which we use to perform modelling and simulation of DNA strand displacement systems with rich secondary structure.
Optimized replica gas estimation of absolute integrals and partition functions
NASA Astrophysics Data System (ADS)
Minh, David D. L.
2010-09-01
In contrast with most Monte Carlo integration algorithms, which are used to estimate ratios, the replica gas identities recently introduced by Adib enable the estimation of absolute integrals and partition functions using multiple copies of a system and normalized transition functions. Here, an optimized form is presented. After generalizing a replica gas identity with an arbitrary weighting function, we obtain a functional form that has the minimal asymptotic variance for samples from two replicas and is provably good for a larger number. This equation is demonstrated to improve the convergence of partition function estimates in a two-dimensional Ising model.
Optimized replica gas estimation of absolute integrals and partition functions.
Minh, D.
2010-01-01
In contrast with most Monte Carlo integration algorithms, which are used to estimate ratios, the replica gas identities recently introduced by Adib enable the estimation of absolute integrals and partition functions using multiple copies of a system and normalized transition functions. Here, an optimized form is presented. After generalizing a replica gas identity with an arbitrary weighting function, we obtain a functional form that has the minimal asymptotic variance for samples from two replicas and is provably good for a larger number. This equation is demonstrated to improve the convergence of partition function estimates in a two-dimensional Ising model.
Smalter, Aaron; Huan, Jun Luke; Jia, Yi; Lushington, Gerald
2010-01-01
Graph data mining is an active research area. Graphs are general modeling tools to organize information from heterogeneous sources and have been applied in many scientific, engineering, and business fields. With the fast accumulation of graph data, building highly accurate predictive models for graph data emerges as a new challenge that has not been fully explored in the data mining community. In this paper, we demonstrate a novel technique called graph pattern diffusion (GPD) kernel. Our idea is to leverage existing frequent pattern discovery methods and to explore the application of kernel classifier (e.g., support vector machine) in building highly accurate graph classification. In our method, we first identify all frequent patterns from a graph database. We then map subgraphs to graphs in the graph database and use a process we call "pattern diffusion" to label nodes in the graphs. Finally, we designed a graph alignment algorithm to compute the inner product of two graphs. We have tested our algorithm using a number of chemical structure data. The experimental results demonstrate that our method is significantly better than competing methods such as those kernel functions based on paths, cycles, and subgraphs.
ERIC Educational Resources Information Center
Xi, Xiaoming
2010-01-01
Motivated by cognitive theories of graph comprehension, this study systematically manipulated characteristics of a line graph description task in a speaking test in ways to mitigate the influence of graph familiarity, a potential source of construct-irrelevant variance. It extends Xi (2005), which found that the differences in holistic scores on…
Helping Students Make Sense of Graphs: An Experimental Trial of SmartGraphs Software
ERIC Educational Resources Information Center
Zucker, Andrew; Kay, Rachel; Staudt, Carolyn
2014-01-01
Graphs are commonly used in science, mathematics, and social sciences to convey important concepts; yet students at all ages demonstrate difficulties interpreting graphs. This paper reports on an experimental study of free, Web-based software called SmartGraphs that is specifically designed to help students overcome their misconceptions regarding…
Exotic equilibria of Harary graphs and a new minimum degree lower bound for synchronization
NASA Astrophysics Data System (ADS)
Canale, Eduardo A.; Monzón, Pablo
2015-02-01
This work is concerned with stability of equilibria in the homogeneous (equal frequencies) Kuramoto model of weakly coupled oscillators. In 2012 [R. Taylor, J. Phys. A: Math. Theor. 45, 1-15 (2012)], a sufficient condition for almost global synchronization was found in terms of the minimum degree-order ratio of the graph. In this work, a new lower bound for this ratio is given. The improvement is achieved by a concrete infinite sequence of regular graphs. Besides, non standard unstable equilibria of the graphs studied in Wiley et al. [Chaos 16, 015103 (2006)] are shown to exist as conjectured in that work.
Exotic equilibria of Harary graphs and a new minimum degree lower bound for synchronization
Canale, Eduardo A.; Monzón, Pablo
2015-02-15
This work is concerned with stability of equilibria in the homogeneous (equal frequencies) Kuramoto model of weakly coupled oscillators. In 2012 [R. Taylor, J. Phys. A: Math. Theor. 45, 1–15 (2012)], a sufficient condition for almost global synchronization was found in terms of the minimum degree–order ratio of the graph. In this work, a new lower bound for this ratio is given. The improvement is achieved by a concrete infinite sequence of regular graphs. Besides, non standard unstable equilibria of the graphs studied in Wiley et al. [Chaos 16, 015103 (2006)] are shown to exist as conjectured in that work.
Clique percolation in random graphs
NASA Astrophysics Data System (ADS)
Li, Ming; Deng, Youjin; Wang, Bing-Hong
2015-10-01
As a generation of the classical percolation, clique percolation focuses on the connection of cliques in a graph, where the connection of two k cliques means that they share at least l
Clique percolation in random graphs.
Li, Ming; Deng, Youjin; Wang, Bing-Hong
2015-10-01
As a generation of the classical percolation, clique percolation focuses on the connection of cliques in a graph, where the connection of two k cliques means that they share at least l
Feature Tracking Using Reeb Graphs
Weber, Gunther H.; Bremer, Peer-Timo; Day, Marcus S.; Bell, John B.; Pascucci, Valerio
2010-08-02
Tracking features and exploring their temporal dynamics can aid scientists in identifying interesting time intervals in a simulation and serve as basis for performing quantitative analyses of temporal phenomena. In this paper, we develop a novel approach for tracking subsets of isosurfaces, such as burning regions in simulated flames, which are defined as areas of high fuel consumption on a temperature isosurface. Tracking such regions as they merge and split over time can provide important insights into the impact of turbulence on the combustion process. However, the convoluted nature of the temperature isosurface and its rapid movement make this analysis particularly challenging. Our approach tracks burning regions by extracting a temperature isovolume from the four-dimensional space-time temperature field. It then obtains isosurfaces for the original simulation time steps and labels individual connected 'burning' regions based on the local fuel consumption value. Based on this information, a boundary surface between burning and non-burning regions is constructed. The Reeb graph of this boundary surface is the tracking graph for burning regions.
Enabling Graph Appliance for Genome Assembly
Singh, Rina; Graves, Jeffrey A; Lee, Sangkeun; Sukumar, Sreenivas R; Shankar, Mallikarjun
2015-01-01
In recent years, there has been a huge growth in the amount of genomic data available as reads generated from various genome sequencers. The number of reads generated can be huge, ranging from hundreds to billions of nucleotide, each varying in size. Assembling such large amounts of data is one of the challenging computational problems for both biomedical and data scientists. Most of the genome assemblers developed have used de Bruijn graph techniques. A de Bruijn graph represents a collection of read sequences by billions of vertices and edges, which require large amounts of memory and computational power to store and process. This is the major drawback to de Bruijn graph assembly. Massively parallel, multi-threaded, shared memory systems can be leveraged to overcome some of these issues. The objective of our research is to investigate the feasibility and scalability issues of de Bruijn graph assembly on Cray s Urika-GD system; Urika-GD is a high performance graph appliance with a large shared memory and massively multithreaded custom processor designed for executing SPARQL queries over large-scale RDF data sets. However, to the best of our knowledge, there is no research on representing a de Bruijn graph as an RDF graph or finding Eulerian paths in RDF graphs using SPARQL for potential genome discovery. In this paper, we address the issues involved in representing a de Bruin graphs as RDF graphs and propose an iterative querying approach for finding Eulerian paths in large RDF graphs. We evaluate the performance of our implementation on real world ebola genome datasets and illustrate how genome assembly can be accomplished with Urika-GD using iterative SPARQL queries.
Partitioning in parallel processing of production systems
Oflazer, K.
1987-01-01
This thesis presents research on certain issues related to parallel processing of production systems. It first presents a parallel production system interpreter that has been implemented on a four-processor multiprocessor. This parallel interpreter is based on Forgy's OPS5 interpreter and exploits production-level parallelism in production systems. Runs on the multiprocessor system indicate that it is possible to obtain speed-up of around 1.7 in the match computation for certain production systems when productions are split into three sets that are processed in parallel. The next issue addressed is that of partitioning a set of rules to processors in a parallel interpreter with production-level parallelism, and the extent of additional improvement in performance. The partitioning problem is formulated and an algorithm for approximate solutions is presented. The thesis next presents a parallel processing scheme for OPS5 production systems that allows some redundancy in the match computation. This redundancy enables the processing of a production to be divided into units of medium granularity each of which can be processed in parallel. Subsequently, a parallel processor architecture for implementing the parallel processing algorithm is presented.
Partitioning sparse rectangular matrices for parallel processing
Kolda, T.G.
1998-05-01
The authors are interested in partitioning sparse rectangular matrices for parallel processing. The partitioning problem has been well-studied in the square symmetric case, but the rectangular problem has received very little attention. They will formalize the rectangular matrix partitioning problem and discuss several methods for solving it. They will extend the spectral partitioning method for symmetric matrices to the rectangular case and compare this method to three new methods -- the alternating partitioning method and two hybrid methods. The hybrid methods will be shown to be best.
Feynman graph generation and calculations in the Hopf algebra of Feynman graphs
NASA Astrophysics Data System (ADS)
Borinsky, Michael
2014-12-01
Two programs for the computation of perturbative expansions of quantum field theory amplitudes are provided. feyngen can be used to generate Feynman graphs for Yang-Mills, QED and φk theories. Using dedicated graph theoretic tools feyngen can generate graphs of comparatively high loop orders. feyncop implements the Hopf algebra of those Feynman graphs which incorporates the renormalization procedure necessary to calculate finite results in perturbation theory of the underlying quantum field theory. feyngen is validated by comparison to explicit calculations of zero dimensional quantum field theories and feyncop is validated using a combinatorial identity on the Hopf algebra of graphs.
Generative Graph Prototypes from Information Theory.
Han, Lin; Wilson, Richard C; Hancock, Edwin R
2015-10-01
In this paper we present a method for constructing a generative prototype for a set of graphs by adopting a minimum description length approach. The method is posed in terms of learning a generative supergraph model from which the new samples can be obtained by an appropriate sampling mechanism. We commence by constructing a probability distribution for the occurrence of nodes and edges over the supergraph. We encode the complexity of the supergraph using an approximate Von Neumann entropy. A variant of the EM algorithm is developed to minimize the description length criterion in which the structure of the supergraph and the node correspondences between the sample graphs and the supergraph are treated as missing data. To generate new graphs, we assume that the nodes and edges of graphs arise under independent Bernoulli distributions and sample new graphs according to their node and edge occurrence probabilities. Empirical evaluations on real-world databases demonstrate the practical utility of the proposed algorithm and show the effectiveness of the generative model for the tasks of graph classification, graph clustering and generating new sample graphs.
Graphing as a Problem-Solving Strategy.
ERIC Educational Resources Information Center
Cohen, Donald
1984-01-01
The focus is on how line graphs can be used to approximate solutions to rate problems and to suggest equations that offer exact algebraic solutions to the problem. Four problems requiring progressively greater graphing sophistication are presented plus four exercises. (MNS)
Qualitative Graphing: A Construction in Mathematics.
ERIC Educational Resources Information Center
Narode, Ronald
This document argues that qualitative graphing is an effective introduction to mathematics as a construction for communication of ideas involving quantitative relationships. It is suggested that with little or no prior knowledge of Cartesian coordinates or analytic descriptions of graphs using equations students can successfully grasp concepts of…
Developing Data Graph Comprehension. Third Edition
ERIC Educational Resources Information Center
Curcio, Frances
2010-01-01
Since the dawn of civilization, pictorial representations and symbols have been used to communicate simple statistics. Efficient and effective, they are still used today in the form of pictures and graphs to record and present data. Who can tie their shoes? How many calories are in your favorite food? Make data and graphs relevant and interesting…
A Ring Construction Using Finite Directed Graphs
ERIC Educational Resources Information Center
Bardzell, Michael
2012-01-01
In this paper we discuss an interesting class of noncommutative rings which can be constructed using finite directed graphs. This construction also creates a vector space. These structures provide undergraduate students connections between ring theory and graph theory and, among other things, allow them to see a ring unity element that looks quite…
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…
Pattern Perception and the Comprehension of Graphs.
ERIC Educational Resources Information Center
Pinker, Steven
Three experiments tested the hypothesis that graphs convey information effectively because they can display global trends as geometric patterns that visual systems encode easily. A novel type of graph was invented in which angles/lengths of line segments joined end-to-end represented variables of rainfall and temperature of a set of months. It was…
Body Motion and Graphing. Working Paper.
ERIC Educational Resources Information Center
Nemirovsky, Ricardo; Tierney, Cornelia; Wright, Tracey
This paper explores children's efforts to make sense of graphs by analyzing two students' use of a computer-based motion detector. The analysis focuses on the students' growing understanding of the motion detector which enables them to plan their movements in order to create graphs and interpret them in terms of kinesthetic actions. Students…
ON CLUSTERING TECHNIQUES OF CITATION GRAPHS.
ERIC Educational Resources Information Center
CHIEN, R.T.; PREPARATA, F.P.
ONE OF THE PROBLEMS ENCOUNTERED IN CLUSTERING TECHNIQUES AS APPLIED TO DOCUMENT RETRIEVAL SYSTEMS USING BIBLIOGRAPHIC COUPLING DEVICES IS THAT THE COMPUTATIONAL EFFORT REQUIRED GROWS ROUGHLY AS THE SQUARE OF THE COLLECTION SIZE. IN THIS STUDY GRAPH THEORY IS APPLIED TO THIS PROBLEM BY FIRST MAPPING THE CITATION GRAPH OF THE DOCUMENT COLLECTION…
Using a Microcomputer for Graphing Practice.
ERIC Educational Resources Information Center
Beichner, Robert J.
1986-01-01
Describes a laboratory exercise that introduces physics students to graphing. Presents the program format and sample output of a computer simulation of an experiment which tests the effects of sound intensity on the crawling speed of a snail. Provides students with practice in making exponential or logarithmic graphs. (ML)
Teaching Discrete Mathematics with Graphing Calculators.
ERIC Educational Resources Information Center
Masat, Francis E.
Graphing calculator use is often thought of in terms of pre-calculus or continuous topics in mathematics. This paper contains examples and activities that demonstrate useful, interesting, and easy ways to use a graphing calculator with discrete topics. Examples are given for each of the following topics: functions, mathematical induction and…
Pattern vectors from algebraic graph theory.
Wilson, Richard C; Hancock, Edwin R; Luo, Bin
2005-07-01
Graph structures have proven computationally cumbersome for pattern analysis. The reason for this is that, before graphs can be converted to pattern vectors, correspondences must be established between the nodes of structures which are potentially of different size. To overcome this problem, in this paper, we turn to the spectral decomposition of the Laplacian matrix. We show how the elements of the spectral matrix for the Laplacian can be used to construct symmetric polynomials that are permutation invariants. The coefficients of these polynomials can be used as graph features which can be encoded in a vectorial manner. We extend this representation to graphs in which there are unary attributes on the nodes and binary attributes on the edges by using the spectral decomposition of a Hermitian property matrix that can be viewed as a complex analogue of the Laplacian. To embed the graphs in a pattern space, we explore whether the vectors of invariants can be embedded in a low-dimensional space using a number of alternative strategies, including principal components analysis (PCA), multidimensional scaling (MDS), and locality preserving projection (LPP). Experimentally, we demonstrate that the embeddings result in well-defined graph clusters. Our experiments with the spectral representation involve both synthetic and real-world data. The experiments with synthetic data demonstrate that the distances between spectral feature vectors can be used to discriminate between graphs on the basis of their structure. The real-world experiments show that the method can be used to locate clusters of graphs.
Universal spectral statistics in quantum graphs.
Gnutzmann, Sven; Altland, Alexander
2004-11-05
We prove that the spectrum of an individual chaotic quantum graph shows universal spectral correlations, as predicted by random-matrix theory. The stability of these correlations with regard to nonuniversal corrections is analyzed in terms of the linear operator governing the classical dynamics on the graph.
Sequential motif profile of natural visibility graphs
NASA Astrophysics Data System (ADS)
Iacovacci, Jacopo; Lacasa, Lucas
2016-11-01
The concept of sequential visibility graph motifs—subgraphs appearing with characteristic frequencies in the visibility graphs associated to time series—has been advanced recently along with a theoretical framework to compute analytically the motif profiles associated to horizontal visibility graphs (HVGs). Here we develop a theory to compute the profile of sequential visibility graph motifs in the context of natural visibility graphs (VGs). This theory gives exact results for deterministic aperiodic processes with a smooth invariant density or stochastic processes that fulfill the Markov property and have a continuous marginal distribution. The framework also allows for a linear time numerical estimation in the case of empirical time series. A comparison between the HVG and the VG case (including evaluation of their robustness for short series polluted with measurement noise) is also presented.
Vortices and superfields on a graph
NASA Astrophysics Data System (ADS)
Kan, Nahomi; Kobayashi, Koichiro; Shiraishi, Kiyoshi
2009-08-01
We extend the dimensional deconstruction by utilizing the knowledge of graph theory. In the dimensional deconstruction, one uses the moose diagram to exhibit the structure of the “theory space.” We generalize the moose diagram to a general graph with oriented edges. In the present paper, we consider only the U(1) gauge symmetry. We also introduce supersymmetry into our model by use of superfields. We suppose that vector superfields reside at the vertices and chiral superfields at the edges of a given graph. Then we can consider multivector, multi-Higgs models. In our model, [U(1)]p (where p is the number of vertices) is broken to a single U(1). Therefore, for specific graphs, we get vortexlike classical solutions in our model. We show some examples of the graphs admitting the vortex solutions of simple structure as the Bogomolnyi solution.
Vortices and superfields on a graph
Kan, Nahomi; Kobayashi, Koichiro; Shiraishi, Kiyoshi
2009-08-15
We extend the dimensional deconstruction by utilizing the knowledge of graph theory. In the dimensional deconstruction, one uses the moose diagram to exhibit the structure of the 'theory space'. We generalize the moose diagram to a general graph with oriented edges. In the present paper, we consider only the U(1) gauge symmetry. We also introduce supersymmetry into our model by use of superfields. We suppose that vector superfields reside at the vertices and chiral superfields at the edges of a given graph. Then we can consider multivector, multi-Higgs models. In our model, [U(1)]{sup p} (where p is the number of vertices) is broken to a single U(1). Therefore, for specific graphs, we get vortexlike classical solutions in our model. We show some examples of the graphs admitting the vortex solutions of simple structure as the Bogomolnyi solution.
Graph Mining Meets the Semantic Web
Lee, Sangkeun; Sukumar, Sreenivas R; Lim, Seung-Hwan
2015-01-01
The Resource Description Framework (RDF) and SPARQL Protocol and RDF Query Language (SPARQL) were introduced about a decade ago to enable flexible schema-free data interchange on the Semantic Web. Today, data scientists use the framework as a scalable graph representation for integrating, querying, exploring and analyzing data sets hosted at different sources. With increasing adoption, the need for graph mining capabilities for the Semantic Web has emerged. We address that need through implementation of three popular iterative Graph Mining algorithms (Triangle count, Connected component analysis, and PageRank). We implement these algorithms as SPARQL queries, wrapped within Python scripts. We evaluate the performance of our implementation on 6 real world data sets and show graph mining algorithms (that have a linear-algebra formulation) can indeed be unleashed on data represented as RDF graphs using the SPARQL query interface.
Quantum graphs and random-matrix theory
NASA Astrophysics Data System (ADS)
Pluhař, Z.; Weidenmüller, H. A.
2015-07-01
For simple connected graphs with incommensurate bond lengths and with unitary symmetry we prove the Bohigas-Giannoni-Schmit (BGS) conjecture in its most general form. Using supersymmetry and taking the limit of infinite graph size, we show that the generating function for every (P,Q) correlation function for both closed and open graphs coincides with the corresponding expression of random-matrix theory. We show that the classical Perron-Frobenius operator is bistochastic and possesses a single eigenvalue +1. In the quantum case that implies the existence of a zero (or massless) mode of the effective action. That mode causes universal fluctuation properties. Avoiding the saddle-point approximation we show that for graphs that are classically mixing (i.e. for which the spectrum of the classical Perron-Frobenius operator possesses a finite gap) and that do not carry a special class of bound states, the zero mode dominates in the limit of infinite graph size.
GraphReduce: Processing Large-Scale Graphs on Accelerator-Based Systems
Sengupta, Dipanjan; Song, Shuaiwen; Agarwal, Kapil; Schwan, Karsten
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 and device.
GraphReduce: Large-Scale Graph Analytics on Accelerator-Based HPC Systems
Sengupta, Dipanjan; Agarwal, Kapil; Song, Shuaiwen; Schwan, Karsten
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 host and the device.
Sacchet, Matthew D.; Prasad, Gautam; Foland-Ross, Lara C.; Thompson, Paul M.; Gotlib, Ian H.
2015-01-01
Recently, there has been considerable interest in understanding brain networks in major depressive disorder (MDD). Neural pathways can be tracked in the living brain using diffusion-weighted imaging (DWI); graph theory can then be used to study properties of the resulting fiber networks. To date, global abnormalities have not been reported in tractography-based graph metrics in MDD, so we used a machine learning approach based on “support vector machines” to differentiate depressed from healthy individuals based on multiple brain network properties. We also assessed how important specific graph metrics were for this differentiation. Finally, we conducted a local graph analysis to identify abnormal connectivity at specific nodes of the network. We were able to classify depression using whole-brain graph metrics. Small-worldness was the most useful graph metric for classification. The right pars orbitalis, right inferior parietal cortex, and left rostral anterior cingulate all showed abnormal network connectivity in MDD. This is the first use of structural global graph metrics to classify depressed individuals. These findings highlight the importance of future research to understand network properties in depression across imaging modalities, improve classification results, and relate network alterations to psychiatric symptoms, medication, and comorbidities. PMID:25762941
Scarselli, Franco; Tsoi, Ah Chung; Hagenbuchner, Markus; Noi, Lucia Di
2013-12-01
This paper proposes the combination of two state-of-the-art algorithms for processing graph input data, viz., the probabilistic mapping graph self organizing map, an unsupervised learning approach, and the graph neural network, a supervised learning approach. We organize these two algorithms in a cascade architecture containing a probabilistic mapping graph self organizing map, and a graph neural network. We show that this combined approach helps us to limit the long-term dependency problem that exists when training the graph neural network resulting in an overall improvement in performance. This is demonstrated in an application to a benchmark problem requiring the detection of spam in a relatively large set of web sites. It is found that the proposed method produces results which reach the state of the art when compared with some of the best results obtained by others using quite different approaches. A particular strength of our method is its applicability towards any input domain which can be represented as a graph.
Sacchet, Matthew D; Prasad, Gautam; Foland-Ross, Lara C; Thompson, Paul M; Gotlib, Ian H
2015-01-01
Recently, there has been considerable interest in understanding brain networks in major depressive disorder (MDD). Neural pathways can be tracked in the living brain using diffusion-weighted imaging (DWI); graph theory can then be used to study properties of the resulting fiber networks. To date, global abnormalities have not been reported in tractography-based graph metrics in MDD, so we used a machine learning approach based on "support vector machines" to differentiate depressed from healthy individuals based on multiple brain network properties. We also assessed how important specific graph metrics were for this differentiation. Finally, we conducted a local graph analysis to identify abnormal connectivity at specific nodes of the network. We were able to classify depression using whole-brain graph metrics. Small-worldness was the most useful graph metric for classification. The right pars orbitalis, right inferior parietal cortex, and left rostral anterior cingulate all showed abnormal network connectivity in MDD. This is the first use of structural global graph metrics to classify depressed individuals. These findings highlight the importance of future research to understand network properties in depression across imaging modalities, improve classification results, and relate network alterations to psychiatric symptoms, medication, and comorbidities.
Relativity on rotated graph paper
NASA Astrophysics Data System (ADS)
Salgado, Roberto B.
2016-05-01
We demonstrate a method for constructing spacetime diagrams for special relativity on graph paper that has been rotated by 45°. The diagonal grid lines represent light-flash worldlines in Minkowski spacetime, and the boxes in the grid (called "clock diamonds") represent units of measurement corresponding to the ticks of an inertial observer's light clock. We show that many quantitative results can be read off a spacetime diagram simply by counting boxes, with very little algebra. In particular, we show that the squared interval between two events is equal to the signed area of the parallelogram on the grid (called the "causal diamond") with opposite vertices corresponding to those events. We use the Doppler effect—without explicit use of the Doppler formula—to motivate the method.
Join-Graph Propagation Algorithms
Mateescu, Robert; Kask, Kalev; Gogate, Vibhav; Dechter, Rina
2010-01-01
The paper investigates parameterized approximate message-passing schemes that are based on bounded inference and are inspired by Pearl's belief propagation algorithm (BP). We start with the bounded inference mini-clustering algorithm and then move to the iterative scheme called Iterative Join-Graph Propagation (IJGP), that combines both iteration and bounded inference. Algorithm IJGP belongs to the class of Generalized Belief Propagation algorithms, a framework that allowed connections with approximate algorithms from statistical physics and is shown empirically to surpass the performance of mini-clustering and belief propagation, as well as a number of other state-of-the-art algorithms on several classes of networks. We also provide insight into the accuracy of iterative BP and IJGP by relating these algorithms to well known classes of constraint propagation schemes. PMID:20740057
Overlapped partitioning for ensemble classifiers of P300-based brain-computer interfaces.
Onishi, Akinari; Natsume, Kiyohisa
2014-01-01
A P300-based brain-computer interface (BCI) enables a wide range of people to control devices that improve their quality of life. Ensemble classifiers with naive partitioning were recently applied to the P300-based BCI and these classification performances were assessed. However, they were usually trained on a large amount of training data (e.g., 15300). In this study, we evaluated ensemble linear discriminant analysis (LDA) classifiers with a newly proposed overlapped partitioning method using 900 training data. In addition, the classification performances of the ensemble classifier with naive partitioning and a single LDA classifier were compared. One of three conditions for dimension reduction was applied: the stepwise method, principal component analysis (PCA), or none. The results show that an ensemble stepwise LDA (SWLDA) classifier with overlapped partitioning achieved a better performance than the commonly used single SWLDA classifier and an ensemble SWLDA classifier with naive partitioning. This result implies that the performance of the SWLDA is improved by overlapped partitioning and the ensemble classifier with overlapped partitioning requires less training data than that with naive partitioning. This study contributes towards reducing the required amount of training data and achieving better classification performance.
Degree distribution and assortativity in line graphs of complex networks
NASA Astrophysics Data System (ADS)
Wang, Xiangrong; Trajanovski, Stojan; Kooij, Robert E.; Van Mieghem, Piet
2016-03-01
Topological characteristics of links of complex networks influence the dynamical processes executed on networks triggered by links, such as cascading failures triggered by links in power grids and epidemic spread due to link infection. The line graph transforms links in the original graph into nodes. In this paper, we investigate how graph metrics in the original graph are mapped into those for its line graph. In particular, we study the degree distribution and the assortativity of a graph and its line graph. Specifically, we show, both analytically and numerically, the degree distribution of the line graph of an Erdős-Rényi graph follows the same distribution as its original graph. We derive a formula for the assortativity of line graphs and indicate that the assortativity of a line graph is not linearly related to its original graph. Additionally, line graphs of various graphs, e.g. Erdős-Rényi graphs, scale-free graphs, show positive assortativity. In contrast, we find certain types of trees and non-trees whose line graphs have negative assortativity.
Partitioned-Interval Quantum Optical Communications Receiver
NASA Technical Reports Server (NTRS)
Vilnrotter, Victor A.
2013-01-01
The proposed quantum receiver in this innovation partitions each binary signal interval into two unequal segments: a short "pre-measurement" segment in the beginning of the symbol interval used to make an initial guess with better probability than 50/50 guessing, and a much longer segment used to make the high-sensitivity signal detection via field-cancellation and photon-counting detection. It was found that by assigning as little as 10% of the total signal energy to the pre-measurement segment, the initial 50/50 guess can be improved to about 70/30, using the best available measurements such as classical coherent or "optimized Kennedy" detection.
Uncertainty in source partitioning using stable isotopes.
Phillips, D L; Gregg, J W
2001-04-01
Stable isotope analyses are often used to quantify the contribution of multiple sources to a mixture, such as proportions of food sources in an animal's diet, or C3 and C4 plant inputs to soil organic carbon. Linear mixing models can be used to partition two sources with a single isotopic signature (e.g., δ(13)C) or three sources with a second isotopic signature (e.g., δ(15)N). Although variability of source and mixture signatures is often reported, confidence interval calculations for source proportions typically use only the mixture variability. We provide examples showing that omission of source variability can lead to underestimation of the variability of source proportion estimates. For both two- and three-source mixing models, we present formulas for calculating variances, standard errors (SE), and confidence intervals for source proportion estimates that account for the observed variability in the isotopic signatures for the sources as well as the mixture. We then performed sensitivity analyses to assess the relative importance of: (1) the isotopic signature difference between the sources, (2) isotopic signature standard deviations (SD) in the source and mixture populations, (3) sample size, (4) analytical SD, and (5) the evenness of the source proportions, for determining the variability (SE) of source proportion estimates. The proportion SEs varied inversely with the signature difference between sources, so doubling the source difference from 2‰ to 4‰ reduced the SEs by half. Source and mixture signature SDs had a substantial linear effect on source proportion SEs. However, the population variability of the sources and the mixture are fixed and the sampling error component can be changed only by increasing sample size. Source proportion SEs varied inversely with the square root of sample size, so an increase from 1 to 4 samples per population cut the SE in half. Analytical SD had little effect over the range examined since it was generally
Laser system with partitioned prism
Nettleton, J. E.; Barr, D. N.
1985-03-26
An array of optical frequency-sensitive elements such as diffraction gratings or interference filters are arranged in a row, and the optical path of the laser cavity can be directed to include one of these elements. A partitioned optical prism consisting of a triangular portion and one or more paralleogramatic portions are used to direct the path. Between the portions are piezoelectric elements which, when energized, expand to provide an air gap between the portions and to allow total reflection of an optical ray at the surface of the prism next to the gap.
Graph-based segmentation of abnormal nuclei in cervical cytology.
Zhang, Ling; Kong, Hui; Liu, Shaoxiong; Wang, Tianfu; Chen, Siping; Sonka, Milan
2017-03-01
A general method is reported for improving the segmentation of abnormal cell nuclei in cervical cytology images. In automation-assisted reading of cervical cytology, one of the essential steps is the segmentation of nuclei. Despite some progress, there is a need to improve the sensitivity, particularly the segmentation of abnormal nuclei. Our method starts with pre-segmenting the nucleus to define the coarse center and size of nucleus, which is used to construct a graph by image unfolding that maps ellipse-like border in the Cartesian coordinate system to lines in the polar coordinate system. The cost function jointly reflects properties of nucleus border and nucleus region. The prior constraints regarding the context of nucleus-cytoplasm position are utilized to modify the local cost functions. The globally optimal path in the constructed graph is then identified by dynamic programming with an iterative approach ensuring an optimal closed contour. Validation of our method was performed on abnormal nuclei from two cervical cell image datasets, Herlev and H&E stained manual liquid-based cytology (HEMLBC). Compared with five state-of-the-art approaches, our graph-search based method shows superior performance.
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.
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.
A Graph Syntax for Processes and Services
NASA Astrophysics Data System (ADS)
Bruni, Roberto; Gadducci, Fabio; Lafuente, Alberto Lluch
We propose a class of hierarchical graphs equipped with a simple algebraic syntax as a convenient way to describe configurations in languages with inherently hierarchical features such as sessions, fault- handling scopes or transactions. The graph syntax can be seen as an intermediate representation language, that facilitates the encoding of structured specifications and, in particular, of process calculi, since it provides primitives for nesting, name restriction and parallel composition. The syntax is based on an algebraic presentation that faithfully characterises families of hierarchical graphs, meaning that each term of the language uniquely identifies an equivalence class of graphs (modulo graph isomorphism). Proving soundness and completeness of an encoding (i.e. proving that structurally equivalent processes are mapped to isomorphic graphs) is then facilitated and can be done by structural induction. Summing up, the graph syntax facilitates the definition of faithful encodings, yet allowing a precise visual representation. We illustrate our work with an application to a workflow language and a service-oriented calculus.
Pathfinder: Visual Analysis of Paths in Graphs
Partl, C.; Gratzl, S.; Streit, M.; Wassermann, A. M.; Pfister, H.; Schmalstieg, D.; Lex, A.
2016-01-01
The analysis of paths in graphs is highly relevant in many domains. Typically, path-related tasks are performed in node-link layouts. Unfortunately, graph layouts often do not scale to the size of many real world networks. Also, many networks are multivariate, i.e., contain rich attribute sets associated with the nodes and edges. These attributes are often critical in judging paths, but directly visualizing attributes in a graph layout exacerbates the scalability problem. In this paper, we present visual analysis solutions dedicated to path-related tasks in large and highly multivariate graphs. We show that by focusing on paths, we can address the scalability problem of multivariate graph visualization, equipping analysts with a powerful tool to explore large graphs. We introduce Pathfinder (Figure 1), a technique that provides visual methods to query paths, while considering various constraints. The resulting set of paths is visualized in both a ranked list and as a node-link diagram. For the paths in the list, we display rich attribute data associated with nodes and edges, and the node-link diagram provides topological context. The paths can be ranked based on topological properties, such as path length or average node degree, and scores derived from attribute data. Pathfinder is designed to scale to graphs with tens of thousands of nodes and edges by employing strategies such as incremental query results. We demonstrate Pathfinder's fitness for use in scenarios with data from a coauthor network and biological pathways. PMID:27942090
Object Discovery: Soft Attributed Graph Mining.
Zhang, Quanshi; Song, Xuan; Shao, Xiaowei; Zhao, Huijing; Shibasaki, Ryosuke
2016-03-01
We categorize this research in terms of its contribution to both graph theory and computer vision. From the theoretical perspective, this study can be considered as the first attempt to formulate the idea of mining maximal frequent subgraphs in the challenging domain of messy visual data, and as a conceptual extension to the unsupervised learning of graph matching. We define a soft attributed pattern (SAP) to represent the common subgraph pattern among a set of attributed relational graphs (ARGs), considering both their structure and attributes. Regarding the differences between ARGs with fuzzy attributes and conventional labeled graphs, we propose a new mining strategy that directly extracts the SAP with the maximal graph size without applying node enumeration. Given an initial graph template and a number of ARGs, we develop an unsupervised method to modify the graph template into the maximal-size SAP. From a practical perspective, this research develops a general platform for learning the category model (i.e., the SAP) from cluttered visual data (i.e., the ARGs) without labeling "what is where," thereby opening the possibility for a series of applications in the era of big visual data. Experiments demonstrate the superior performance of the proposed method on RGB/RGB-D images and videos.
Sketch Matching on Topology Product Graph.
Liang, Shuang; Luo, Jun; Liu, Wenyin; Wei, Yichen
2015-08-01
Sketch matching is the fundamental problem in sketch based interfaces. After years of study, it remains challenging when there exists large irregularity and variations in the hand drawn sketch shapes. While most existing works exploit topology relations and graph representations for this problem, they are usually limited by the coarse topology exploration and heuristic (thus suboptimal) similarity metrics between graphs. We present a new sketch matching method with two novel contributions. We introduce a comprehensive definition of topology relations, which results in a rich and informative graph representation of sketches. For graph matching, we propose topology product graph that retains the full correspondence for matching two graphs. Based on it, we derive an intuitive sketch similarity metric whose exact solution is easy to compute. In addition, the graph representation and new metric naturally support partial matching, an important practical problem that received less attention in the literature. Extensive experimental results on a real challenging dataset and the superior performance of our method show that it outperforms the state-of-the-art.
Approximate von Neumann entropy for directed graphs.
Ye, Cheng; Wilson, Richard C; Comin, César H; Costa, Luciano da F; Hancock, Edwin R
2014-05-01
In this paper, we develop an entropy measure for assessing the structural complexity of directed graphs. Although there are many existing alternative measures for quantifying the structural properties of undirected graphs, there are relatively few corresponding measures for directed graphs. To fill this gap in the literature, we explore an alternative technique that is applicable to directed graphs. We commence by using Chung's generalization of the Laplacian of a directed graph to extend the computation of von Neumann entropy from undirected to directed graphs. We provide a simplified form of the entropy which can be expressed in terms of simple node in-degree and out-degree statistics. Moreover, we find approximate forms of the von Neumann entropy that apply to both weakly and strongly directed graphs, and that can be used to characterize network structure. We illustrate the usefulness of these simplified entropy forms defined in this paper on both artificial and real-world data sets, including structures from protein databases and high energy physics theory citation networks.
Massive graph visualization : LDRD final report.
Wylie, Brian Neil; Moreland, Kenneth D.
2007-10-01
Graphs are a vital way of organizing data with complex correlations. A good visualization of a graph can fundamentally change human understanding of the data. Consequently, there is a rich body of work on graph visualization. Although there are many techniques that are effective on small to medium sized graphs (tens of thousands of nodes), there is a void in the research for visualizing massive graphs containing millions of nodes. Sandia is one of the few entities in the world that has the means and motivation to handle data on such a massive scale. For example, homeland security generates graphs from prolific media sources such as television, telephone, and the Internet. The purpose of this project is to provide the groundwork for visualizing such massive graphs. The research provides for two major feature gaps: a parallel, interactive visualization framework and scalable algorithms to make the framework usable to a practical application. Both the frameworks and algorithms are designed to run on distributed parallel computers, which are already available at Sandia. Some features are integrated into the ThreatView{trademark} application and future work will integrate further parallel algorithms.
Poor Textural Image Matching Based on Graph Theory
NASA Astrophysics Data System (ADS)
Chen, Shiyu; Yuan, Xiuxiao; Yuan, Wei; Cai, Yang
2016-06-01
Image matching lies at the heart of photogrammetry and computer vision. For poor textural images, the matching result is affected by low contrast, repetitive patterns, discontinuity or occlusion, few or homogeneous textures. Recently, graph matching became popular for its integration of geometric and radiometric information. Focused on poor textural image matching problem, it is proposed an edge-weight strategy to improve graph matching algorithm. A series of experiments have been conducted including 4 typical landscapes: Forest, desert, farmland, and urban areas. And it is experimentally found that our new algorithm achieves better performance. Compared to SIFT, doubled corresponding points were acquired, and the overall recall rate reached up to 68%, which verifies the feasibility and effectiveness of the algorithm.
Got Graphs? An Assessment of Data Visualization Tools
NASA Technical Reports Server (NTRS)
Schaefer, C. M.; Foy, M.
2015-01-01
Graphs are powerful tools for simplifying complex data. They are useful for quickly assessing patterns and relationships among one or more variables from a dataset. As the amount of data increases, it becomes more difficult to visualize potential associations. Lifetime Surveillance of Astronaut Health (LSAH) was charged with assessing its current visualization tools along with others on the market to determine whether new tools would be useful for supporting NASA's occupational surveillance effort. It was concluded by members of LSAH that the current tools hindered their ability to provide quick results to researchers working with the department. Due to the high volume of data requests and the many iterations of visualizations requested by researchers, software with a better ability to replicate graphs and edit quickly could improve LSAH's efficiency and lead to faster research results.
Graph Laplace for occluded face completion and recognition.
Deng, Yue; Dai, Qionghai; Zhang, Zengke
2011-08-01
This paper proposes a spectral-graph-based algorithm for face image repairing, which can improve the recognition performance on occluded faces. The face completion algorithm proposed in this paper includes three main procedures: 1) sparse representation for partially occluded face classification; 2) image-based data mining; and 3) graph Laplace (GL) for face image completion. The novel part of the proposed framework is GL, as named from graphical models and the Laplace equation, and can achieve a high-quality repairing of damaged or occluded faces. The relationship between the GL and the traditional Poisson equation is proven. We apply our face repairing algorithm to produce completed faces, and use face recognition to evaluate the performance of the algorithm. Experimental results verify the effectiveness of the GL method for occluded face completion.
Enabling Graph Mining in RDF Triplestores using SPARQL for Holistic In-situ Graph Analysis
Lee, Sangkeun; Sukumar, Sreenivas R; Hong, Seokyong; Lim, Seung-Hwan
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 existing 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.
Enabling Graph Mining in RDF Triplestores using SPARQL for Holistic In-situ Graph Analysis
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
The MultiThreaded Graph Library (MTGL)
Berry, Jonathan; Leung, Vitus; McLendon, III, William; & Madduri, Kamesh
2008-07-17
The MultiThreaded Graph Library (MTGL) is a set of header files that implement graph algorithm in such a way that they can run on massively multithreaded architectures. It is based upon the Boost Graph Library, but doesnÃÂÃÂ¢ÃÂÃÂÃÂÃÂt use Boost since the latter doesnÃÂÃÂ¢ÃÂÃÂÃÂÃÂt run well on these architectures.
Identifying Codes on Directed De Bruijn Graphs
2014-12-19
ar X iv :1 41 2. 58 42 v1 [ m at h. C O ] 1 8 D ec 2 01 4 Identifying Codes on Directed De Bruijn Graphs Debra Boutin ∗ Department of...Mathematics Hamilton College Victoria Horan † Air Force Research Laboratory Information Directorate December 19, 2014 Abstract For a directed graph G, a t...length at most t is both non-empty and unique. A graph is called t-identifiable if there exists a t-identifying code. This paper shows that the de
A heterogeneous graph-based recommendation simulator
Yeonchan, Ahn; Sungchan, Park; Lee, Matt Sangkeun; Sang-goo, Lee
2013-01-01
Heterogeneous graph-based recommendation frameworks have flexibility in that they can incorporate various recommendation algorithms and various kinds of information to produce better results. In this demonstration, we present a heterogeneous graph-based recommendation simulator which enables participants to experience the flexibility of a heterogeneous graph-based recommendation method. With our system, participants can simulate various recommendation semantics by expressing the semantics via meaningful paths like User Movie User Movie. The simulator then returns the recommendation results on the fly based on the user-customized semantics using a fast Monte Carlo algorithm.
Identifying Codes on Directed De Bruijn Graphs
2015-08-27
JOURNAL ARTICLE (POST PRINT) 3. DATES COVERED (From - To) JUN 2013 – AUG 2015 4. TITLE AND SUBTITLE IDENTIFYING CODES ON DIRECTED DE BRUIJN GRAPHS 5a...owner. 14. ABSTRACT For a directed graph G, a t-identifying code is a subset S ⊆ V (G) with the property that for each vertex v ∈ V (G) the set of...t-identifying code . This paper shows that the directed de Bruijn graph B(d, n) is t- identifiable for n ≥ 2t−1, and is not t-identifiable for n ≤ 2t
The Total Interval of a Graph.
1988-01-01
definitions for all of these clases . A Husimi tree is a graph for which every block is a clique. A cactus is a graph for which every edge is in at most one...proportion of graphs with n vertices that we can represent with q(n) intervals is at most n-2 and this approaches zero as n gets large . Hence the...representations will have relatively few intervals of small depth and relatively many intervals of large depth. It is nevertheless often useful to restrict
Prime Graph Components of Finite Simple Groups
NASA Astrophysics Data System (ADS)
Kondrat'ev, A. S.
1990-02-01
Let G be a finite group and π(G) the set of prime factors of its order. The prime graph of G is the graph with vertex-set π(G), two vertices p and q being joined by an edge whenever G contains an element of order pq. This article contains an explicit description of the primes in each of the connected components of the prime graphs of the finite simple groups of Lie type of even characteristic. This solves question 9.16 of the Kourovka Notebook. Bibliography: 15 titles.
Finite Frames and Graph Theoretic Uncertainty Principles
NASA Astrophysics Data System (ADS)
Koprowski, Paul J.
The subject of analytical uncertainty principles is an important field within harmonic analysis, quantum physics, and electrical engineering. We explore uncertainty principles in the context of the graph Fourier transform, and we prove additive results analogous to the multiplicative version of the classical uncertainty principle. We establish additive uncertainty principles for finite Parseval frames. Lastly, we examine the feasibility region of simultaneous values of the norms of a graph differential operator acting on a function f ∈ l2(G) and its graph Fourier transform.
Implementation aspects of Graph Neural Networks
NASA Astrophysics Data System (ADS)
Barcz, A.; Szymański, Z.; Jankowski, S.
2013-10-01
This article summarises the results of implementation of a Graph Neural Network classi er. The Graph Neural Network model is a connectionist model, capable of processing various types of structured data, including non- positional and cyclic graphs. In order to operate correctly, the GNN model must implement a transition function being a contraction map, which is assured by imposing a penalty on model weights. This article presents research results concerning the impact of the penalty parameter on the model training process and the practical decisions that were made during the GNN implementation process.
Supporting interactive graph exploration using edge plucking
NASA Astrophysics Data System (ADS)
Wong, Nelson; Carpendale, Sheelagh
2007-01-01
Excessive edge density in graphs can cause serious readability issues, which in turn can make the graphs difficult to understand or even misleading. Recently, we introduced the idea of providing tools that offer interactive edge bending as a method by which edge congestion can be disambiguated. We extend this direction, presenting a new tool, Edge Plucking, which offers new interactive methods to clarify node-edge relationships. Edge Plucking expands the number of situations in which interactive graph exploration tools can be used to address edge congestion.
Line graphs for a multiplex network.
Criado, Regino; Flores, Julio; García Del Amo, Alejandro; Romance, Miguel; Barrena, Eva; Mesa, Juan A
2016-06-01
It is well known that line graphs offer a good summary of the graphs properties, which make them easier to analyze and highlight the desired properties. We extend the concept of line graph to multiplex networks in order to analyze multi-plexed and multi-layered networked systems. As these structures are very rich, different approaches to this notion are required to capture a variety of situations. Some relationships between these approaches are established. Finally, by means of some simulations, the potential utility of this concept is illustrated.
Rapid graph layout using space filling curves.
Muelder, Chris; Ma, Kwan-Liu
2008-01-01
Network data frequently arises in a wide variety of fields, and node-link diagrams are a very natural and intuitive representation of such data. In order for a node-link diagram to be effective, the nodes must be arranged well on the screen. While many graph layout algorithms exist for this purpose, they often have limitations such as high computational complexity or node colocation. This paper proposes a new approach to graph layout through the use of space filling curves which is very fast and guarantees that there will be no nodes that are colocated. The resulting layout is also aesthetic and satisfies several criteria for graph layout effectiveness.
Intelligent Graph Layout Using Many Users' Input.
Yuan, Xiaoru; Che, Limei; Hu, Yifan; Zhang, Xin
2012-12-01
In this paper, we propose a new strategy for graph drawing utilizing layouts of many sub-graphs supplied by a large group of people in a crowd sourcing manner. We developed an algorithm based on Laplacian constrained distance embedding to merge subgraphs submitted by different users, while attempting to maintain the topological information of the individual input layouts. To facilitate collection of layouts from many people, a light-weight interactive system has been designed to enable convenient dynamic viewing, modification and traversing between layouts. Compared with other existing graph layout algorithms, our approach can achieve more aesthetic and meaningful layouts with high user preference.
Integer sequence discovery from small graphs
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
Loops in Reeb Graphs of 2-Manifolds
Cole-McLaughlin, K; Edelsbrunner, H; Harer, J; Natarajan, V; Pascucci, V
2003-02-11
Given a Morse function f over a 2-manifold with or without boundary, the Reeb graph is obtained by contracting the connected components of the level sets to points. We prove tight upper and lower bounds on the number of loops in the Reeb graph that depend on the genus, the number of boundary components, and whether or not the 2-manifold is orientable. We also give an algorithm that constructs the Reeb graph in time O(n log n), where n is the number of edges in the triangulation used to represent the 2-manifold and the Morse function.