A multicolour graph as a complete topological invariant for \\Omega-stable flows without periodic trajectories on surfaces

NASA Astrophysics Data System (ADS)

Kruglov, V. E.; Malyshev, D. S.; Pochinka, O. V.

2018-01-01

Studying the dynamics of a flow on surfaces by partitioning the phase space into cells with the same limit behaviour of trajectories within a cell goes back to the classical papers of Andronov, Pontryagin, Leontovich and Maier. The types of cells (the number of which is finite) and how the cells adjoin one another completely determine the topological equivalence class of a flow with finitely many special trajectories. If one trajectory is chosen in every cell of a rough flow without periodic orbits, then the cells are partitioned into so-called triangular regions of the same type. A combinatorial description of such a partition gives rise to the three-colour Oshemkov-Sharko graph, the vertices of which correspond to the triangular regions, and the edges to separatrices connecting them. Oshemkov and Sharko proved that such flows are topologically equivalent if and only if the three-colour graphs of the flows are isomorphic, and described an algorithm of distinguishing three-colour graphs. But their algorithm is not efficient with respect to graph theory. In the present paper, we describe the dynamics of Ω-stable flows without periodic trajectories on surfaces in the language of four-colour graphs, present an efficient algorithm for distinguishing such graphs, and develop a realization of a flow from some abstract graph. Bibliography: 17 titles.

Dynamic airspace configuration algorithms for next generation air transportation system

NASA Astrophysics Data System (ADS)

Wei, Jian

The National Airspace System (NAS) is under great pressure to safely and efficiently handle the record-high air traffic volume nowadays, and will face even greater challenge to keep pace with the steady increase of future air travel demand, since the air travel demand is projected to increase to two to three times the current level by 2025. The inefficiency of traffic flow management initiatives causes severe airspace congestion and frequent flight delays, which cost billions of economic losses every year. To address the increasingly severe airspace congestion and delays, the Next Generation Air Transportation System (NextGen) is proposed to transform the current static and rigid radar based system to a dynamic and flexible satellite based system. New operational concepts such as Dynamic Airspace Configuration (DAC) have been under development to allow more flexibility required to mitigate the demand-capacity imbalances in order to increase the throughput of the entire NAS. In this dissertation, we address the DAC problem in the en route and terminal airspace under the framework of NextGen. We develop a series of algorithms to facilitate the implementation of innovative concepts relevant with DAC in both the en route and terminal airspace. We also develop a performance evaluation framework for comprehensive benefit analyses on different aspects of future sector design algorithms. First, we complete a graph based sectorization algorithm for DAC in the en route airspace, which models the underlying air route network with a weighted graph, converts the sectorization problem into the graph partition problem, partitions the weighted graph with an iterative spectral bipartition method, and constructs the sectors from the partitioned graph. The algorithm uses a graph model to accurately capture the complex traffic patterns of the real flights, and generates sectors with high efficiency while evenly distributing the workload among the generated sectors. We further improve the robustness and efficiency of the graph based DAC algorithm by incorporating the Multilevel Graph Partitioning (MGP) method into the graph model, and develop a MGP based sectorization algorithm for DAC in the en route airspace. In a comprehensive benefit analysis, the performance of the proposed algorithms are tested in numerical simulations with Enhanced Traffic Management System (ETMS) data. Simulation results demonstrate that the algorithmically generated sectorizations outperform the current sectorizations in different sectors for different time periods. Secondly, based on our experience with DAC in the en route airspace, we further study the sectorization problem for DAC in the terminal airspace. The differences between the en route and terminal airspace are identified, and their influence on the terminal sectorization is analyzed. After adjusting the graph model to better capture the unique characteristics of the terminal airspace and the requirements of terminal sectorization, we develop a graph based geometric sectorization algorithm for DAC in the terminal airspace. Moreover, the graph based model is combined with the region based sector design method to better handle the complicated geometric and operational constraints in the terminal sectorization problem. In the benefit analysis, we identify the contributing factors to terminal controller workload, define evaluation metrics, and develop a bebefit analysis framework for terminal sectorization evaluation. With the evaluation framework developed, we demonstrate the improvements on the current sectorizations with real traffic data collected from several major international airports in the U.S., and conduct a detailed analysis on the potential benefits of dynamic reconfiguration in the terminal airspace. Finally, in addition to the research on the macroscopic behavior of a large number of aircraft, we also study the dynamical behavior of individual aircraft from the perspective of traffic flow management. We formulate the mode-confusion problem as hybrid estimation problem, and develop a state estimation algorithm for the linear hybrid system with continuous-state-dependent transitions based on sparse observations. We also develop an estimated time of arrival prediction algorithm based on the state-dependent transition hybrid estimation algorithm, whose performance is demonstrated with simulations on the landing procedure following the Continuous Descend Approach (CDA) profile.

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

PubMed Central

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

2014-01-01

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

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

PubMed

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

2014-11-01

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

INDDGO: Integrated Network Decomposition & Dynamic programming for Graph Optimization

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

Groer, Christopher S; Sullivan, Blair D; Weerapurage, Dinesh P

2012-10-01

It is well-known that dynamic programming algorithms can utilize tree decompositions to provide a way to solve some \\emph{NP}-hard problems on graphs where the complexity is polynomial in the number of nodes and edges in the graph, but exponential in the width of the underlying tree decomposition. However, there has been relatively little computational work done to determine the practical utility of such dynamic programming algorithms. We have developed software to construct tree decompositions using various heuristics and have created a fast, memory-efficient dynamic programming implementation for solving maximum weighted independent set. We describe our software and the algorithms wemore » have implemented, focusing on memory saving techniques for the dynamic programming. We compare the running time and memory usage of our implementation with other techniques for solving maximum weighted independent set, including a commercial integer programming solver and a semi-definite programming solver. Our results indicate that it is possible to solve some instances where the underlying decomposition has width much larger than suggested by the literature. For certain types of problems, our dynamic programming code runs several times faster than these other methods.« less

Dynamic Load Balancing for Adaptive Computations on Distributed-Memory Machines

NASA Technical Reports Server (NTRS)

1999-01-01

Dynamic load balancing is central to adaptive mesh-based computations on large-scale parallel computers. The principal investigator has investigated various issues on the dynamic load balancing problem under NASA JOVE and JAG rants. The major accomplishments of the project are two graph partitioning algorithms and a load balancing framework. The S-HARP dynamic graph partitioner is known to be the fastest among the known dynamic graph partitioners to date. It can partition a graph of over 100,000 vertices in 0.25 seconds on a 64- processor Cray T3E distributed-memory multiprocessor while maintaining the scalability of over 16-fold speedup. Other known and widely used dynamic graph partitioners take over a second or two while giving low scalability of a few fold speedup on 64 processors. These results have been published in journals and peer-reviewed flagship conferences.

Visibility graphs and symbolic dynamics

NASA Astrophysics Data System (ADS)

Lacasa, Lucas; Just, Wolfram

2018-07-01

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

Method for concurrent execution of primitive operations by dynamically assigning operations based upon computational marked graph and availability of data

NASA Technical Reports Server (NTRS)

Mielke, Roland V. (Inventor); Stoughton, John W. (Inventor)

1990-01-01

Computationally complex primitive operations of an algorithm are executed concurrently in a plurality of functional units under the control of an assignment manager. The algorithm is preferably defined as a computationally marked graph contianing data status edges (paths) corresponding to each of the data flow edges. The assignment manager assigns primitive operations to the functional units and monitors completion of the primitive operations to determine data availability using the computational marked graph of the algorithm. All data accessing of the primitive operations is performed by the functional units independently of the assignment manager.

An annealed chaotic maximum neural network for bipartite subgraph problem.

PubMed

Wang, Jiahai; Tang, Zheng; Wang, Ronglong

2004-04-01

In this paper, based on maximum neural network, we propose a new parallel algorithm that can help the maximum neural network escape from local minima by including a transient chaotic neurodynamics for bipartite subgraph problem. The goal of the bipartite subgraph problem, which is an NP- complete problem, is to remove the minimum number of edges in a given graph such that the remaining graph is a bipartite graph. Lee et al. presented a parallel algorithm using the maximum neural model (winner-take-all neuron model) for this NP- complete problem. The maximum neural model always guarantees a valid solution and greatly reduces the search space without a burden on the parameter-tuning. However, the model has a tendency to converge to a local minimum easily because it is based on the steepest descent method. By adding a negative self-feedback to the maximum neural network, we proposed a new parallel algorithm that introduces richer and more flexible chaotic dynamics and can prevent the network from getting stuck at local minima. After the chaotic dynamics vanishes, the proposed algorithm is then fundamentally reined by the gradient descent dynamics and usually converges to a stable equilibrium point. The proposed algorithm has the advantages of both the maximum neural network and the chaotic neurodynamics. A large number of instances have been simulated to verify the proposed algorithm. The simulation results show that our algorithm finds the optimum or near-optimum solution for the bipartite subgraph problem superior to that of the best existing parallel algorithms.

Graph Theoretic Foundations of Multibody Dynamics Part I: Structural Properties

PubMed Central

Jain, Abhinandan

2011-01-01

This is the first part of two papers that use concepts from graph theory to obtain a deeper understanding of the mathematical foundations of multibody dynamics. The key contribution is the development of a unifying framework that shows that key analytical results and computational algorithms in multibody dynamics are a direct consequence of structural properties and require minimal assumptions about the specific nature of the underlying multibody system. This first part focuses on identifying the abstract graph theoretic structural properties of spatial operator techniques in multibody dynamics. The second part paper exploits these structural properties to develop a broad spectrum of analytical results and computational algorithms. Towards this, we begin with the notion of graph adjacency matrices and generalize it to define block-weighted adjacency (BWA) matrices and their 1-resolvents. Previously developed spatial operators are shown to be special cases of such BWA matrices and their 1-resolvents. These properties are shown to hold broadly for serial and tree topology multibody systems. Specializations of the BWA and 1-resolvent matrices are referred to as spatial kernel operators (SKO) and spatial propagation operators (SPO). These operators and their special properties provide the foundation for the analytical and algorithmic techniques developed in the companion paper. We also use the graph theory concepts to study the topology induced sparsity structure of these operators and the system mass matrix. Similarity transformations of these operators are also studied. While the detailed development is done for the case of rigid-link multibody systems, the extension of these techniques to a broader class of systems (e.g. deformable links) are illustrated. PMID:22102790

User-Assisted Store Recycling for Dynamic Task Graph Schedulers

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

Kurt, Mehmet Can; Krishnamoorthy, Sriram; Agrawal, Gagan

The emergence of the multi-core era has led to increased interest in designing effective yet practical parallel programming models. Models based on task graphs that operate on single-assignment data are attractive in several ways: they can support dynamic applications and precisely represent the available concurrency. However, they also require nuanced algorithms for scheduling and memory management for efficient execution. In this paper, we consider memory-efficient dynamic scheduling of task graphs. Specifically, we present a novel approach for dynamically recycling the memory locations assigned to data items as they are produced by tasks. We develop algorithms to identify memory-efficient store recyclingmore » functions by systematically evaluating the validity of a set of (user-provided or automatically generated) alternatives. Because recycling function can be input data-dependent, we have also developed support for continued correct execution of a task graph in the presence of a potentially incorrect store recycling function. Experimental evaluation demonstrates that our approach to automatic store recycling incurs little to no overheads, achieves memory usage comparable to the best manually derived solutions, often produces recycling functions valid across problem sizes and input parameters, and efficiently recovers from an incorrect choice of store recycling functions.« less

A flocking algorithm for multi-agent systems with connectivity preservation under hybrid metric-topological interactions.

PubMed

He, Chenlong; Feng, Zuren; Ren, Zhigang

2018-01-01

In this paper, we propose a connectivity-preserving flocking algorithm for multi-agent systems in which the neighbor set of each agent is determined by the hybrid metric-topological distance so that the interaction topology can be represented as the range-limited Delaunay graph, which combines the properties of the commonly used disk graph and Delaunay graph. As a result, the proposed flocking algorithm has the following advantages over the existing ones. First, range-limited Delaunay graph is sparser than the disk graph so that the information exchange among agents is reduced significantly. Second, some links irrelevant to the connectivity can be dynamically deleted during the evolution of the system. Thus, the proposed flocking algorithm is more flexible than existing algorithms, where links are not allowed to be disconnected once they are created. Finally, the multi-agent system spontaneously generates a regular quasi-lattice formation without imposing the constraint on the ratio of the sensing range of the agent to the desired distance between two adjacent agents. With the interaction topology induced by the hybrid distance, the proposed flocking algorithm can still be implemented in a distributed manner. We prove that the proposed flocking algorithm can steer the multi-agent system to a stable flocking motion, provided the initial interaction topology of multi-agent systems is connected and the hysteresis in link addition is smaller than a derived upper bound. The correctness and effectiveness of the proposed algorithm are verified by extensive numerical simulations, where the flocking algorithms based on the disk and Delaunay graph are compared.

A flocking algorithm for multi-agent systems with connectivity preservation under hybrid metric-topological interactions

PubMed Central

Feng, Zuren; Ren, Zhigang

2018-01-01

In this paper, we propose a connectivity-preserving flocking algorithm for multi-agent systems in which the neighbor set of each agent is determined by the hybrid metric-topological distance so that the interaction topology can be represented as the range-limited Delaunay graph, which combines the properties of the commonly used disk graph and Delaunay graph. As a result, the proposed flocking algorithm has the following advantages over the existing ones. First, range-limited Delaunay graph is sparser than the disk graph so that the information exchange among agents is reduced significantly. Second, some links irrelevant to the connectivity can be dynamically deleted during the evolution of the system. Thus, the proposed flocking algorithm is more flexible than existing algorithms, where links are not allowed to be disconnected once they are created. Finally, the multi-agent system spontaneously generates a regular quasi-lattice formation without imposing the constraint on the ratio of the sensing range of the agent to the desired distance between two adjacent agents. With the interaction topology induced by the hybrid distance, the proposed flocking algorithm can still be implemented in a distributed manner. We prove that the proposed flocking algorithm can steer the multi-agent system to a stable flocking motion, provided the initial interaction topology of multi-agent systems is connected and the hysteresis in link addition is smaller than a derived upper bound. The correctness and effectiveness of the proposed algorithm are verified by extensive numerical simulations, where the flocking algorithms based on the disk and Delaunay graph are compared. PMID:29462217

Parallel Algorithms for Switching Edges in Heterogeneous Graphs☆

PubMed Central

Khan, Maleq; Chen, Jiangzhuo; Marathe, Madhav

2017-01-01

An edge switch is an operation on a graph (or network) where two edges are selected randomly and one of their end vertices are swapped with each other. Edge switch operations have important applications in graph theory and network analysis, such as in generating random networks with a given degree sequence, modeling and analyzing dynamic networks, and in studying various dynamic phenomena over a network. The recent growth of real-world networks motivates the need for efficient parallel algorithms. The dependencies among successive edge switch operations and the requirement to keep the graph simple (i.e., no self-loops or parallel edges) as the edges are switched lead to significant challenges in designing a parallel algorithm. Addressing these challenges requires complex synchronization and communication among the processors leading to difficulties in achieving a good speedup by parallelization. In this paper, we present distributed memory parallel algorithms for switching edges in massive networks. These algorithms provide good speedup and scale well to a large number of processors. A harmonic mean speedup of 73.25 is achieved on eight different networks with 1024 processors. One of the steps in our edge switch algorithms requires the computation of multinomial random variables in parallel. This paper presents the first non-trivial parallel algorithm for the problem, achieving a speedup of 925 using 1024 processors. PMID:28757680

Information Dynamics in Networks: Models and Algorithms

DTIC Science & Technology

2016-09-13

Twitter ; we investigated how to detect spam accounts on Facebook and other social networks by graph analytics; and finally we investigated how to design...networks. We investigated the appropriateness of existing mathematical models for explaining the structure of retweet cascades on Twitter ; we investigated...Received Paper 1.00 2.00 3.00 . A Note on Modeling Retweet Cascades on Twitter , Workshop on Algorithms and Models for the Web Graph. 09-DEC-15

Dynamic programming and graph algorithms in computer vision.

PubMed

Felzenszwalb, Pedro F; Zabih, Ramin

2011-04-01

Optimization is a powerful paradigm for expressing and solving problems in a wide range of areas, and has been successfully applied to many vision problems. Discrete optimization techniques are especially interesting since, by carefully exploiting problem structure, they often provide nontrivial guarantees concerning solution quality. In this paper, we review dynamic programming and graph algorithms, and discuss representative examples of how these discrete optimization techniques have been applied to some classical vision problems. We focus on the low-level vision problem of stereo, the mid-level problem of interactive object segmentation, and the high-level problem of model-based recognition.

Enumerating Substituted Benzene Isomers of Tree-Like Chemical Graphs.

PubMed

Li, Jinghui; Nagamochi, Hiroshi; Akutsu, Tatsuya

2018-01-01

Enumeration of chemical structures is useful for drug design, which is one of the main targets of computational biology and bioinformatics. A chemical graph with no other cycles than benzene rings is called tree-like, and becomes a tree possibly with multiple edges if we contract each benzene ring into a single virtual atom of valence 6. All tree-like chemical graphs with a given tree representation are called the substituted benzene isomers of . When we replace each virtual atom in with a benzene ring to obtain a substituted benzene isomer, distinct isomers of are caused by the difference in arrangements of atom groups around a benzene ring. In this paper, we propose an efficient algorithm that enumerates all substituted benzene isomers of a given tree representation . Our algorithm first counts the number of all the isomers of the tree representation by a dynamic programming method. To enumerate all the isomers, for each , our algorithm then generates the th isomer by backtracking the counting phase of the dynamic programming. We also implemented our algorithm for computational experiments.

Combinatorial-topological framework for the analysis of global dynamics.

PubMed

Bush, Justin; Gameiro, Marcio; Harker, Shaun; Kokubu, Hiroshi; Mischaikow, Konstantin; Obayashi, Ippei; Pilarczyk, Paweł

2012-12-01

We discuss an algorithmic framework based on efficient graph algorithms and algebraic-topological computational tools. The framework is aimed at automatic computation of a database of global dynamics of a given m-parameter semidynamical system with discrete time on a bounded subset of the n-dimensional phase space. We introduce the mathematical background, which is based upon Conley's topological approach to dynamics, describe the algorithms for the analysis of the dynamics using rectangular grids both in phase space and parameter space, and show two sample applications.

Combinatorial-topological framework for the analysis of global dynamics

NASA Astrophysics Data System (ADS)

Bush, Justin; Gameiro, Marcio; Harker, Shaun; Kokubu, Hiroshi; Mischaikow, Konstantin; Obayashi, Ippei; Pilarczyk, Paweł

2012-12-01

We discuss an algorithmic framework based on efficient graph algorithms and algebraic-topological computational tools. The framework is aimed at automatic computation of a database of global dynamics of a given m-parameter semidynamical system with discrete time on a bounded subset of the n-dimensional phase space. We introduce the mathematical background, which is based upon Conley's topological approach to dynamics, describe the algorithms for the analysis of the dynamics using rectangular grids both in phase space and parameter space, and show two sample applications.

Faster Parameterized Algorithms for Minor Containment

NASA Astrophysics Data System (ADS)

Adler, Isolde; Dorn, Frederic; Fomin, Fedor V.; Sau, Ignasi; Thilikos, Dimitrios M.

The theory of Graph Minors by Robertson and Seymour is one of the deepest and significant theories in modern Combinatorics. This theory has also a strong impact on the recent development of Algorithms, and several areas, like Parameterized Complexity, have roots in Graph Minors. Until very recently it was a common belief that Graph Minors Theory is mainly of theoretical importance. However, it appears that many deep results from Robertson and Seymour's theory can be also used in the design of practical algorithms. Minor containment testing is one of algorithmically most important and technical parts of the theory, and minor containment in graphs of bounded branchwidth is a basic ingredient of this algorithm. In order to implement minor containment testing on graphs of bounded branchwidth, Hicks [NETWORKS 04] described an algorithm, that in time O(3^{k^2}\\cdot (h+k-1)!\\cdot m) decides if a graph G with m edges and branchwidth k, contains a fixed graph H on h vertices as a minor. That algorithm follows the ideas introduced by Robertson and Seymour in [J'CTSB 95]. In this work we improve the dependence on k of Hicks' result by showing that checking if H is a minor of G can be done in time O(2^{(2k +1 )\\cdot log k} \\cdot h^{2k} \\cdot 2^{2h^2} \\cdot m). Our approach is based on a combinatorial object called rooted packing, which captures the properties of the potential models of subgraphs of H that we seek in our dynamic programming algorithm. This formulation with rooted packings allows us to speed up the algorithm when G is embedded in a fixed surface, obtaining the first single-exponential algorithm for minor containment testing. Namely, it runs in time 2^{O(k)} \\cdot h^{2k} \\cdot 2^{O(h)} \\cdot n, with n = |V(G)|. Finally, we show that slight modifications of our algorithm permit to solve some related problems within the same time bounds, like induced minor or contraction minor containment.

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

PubMed

Blin, Guillaume; Sikora, Florian; Vialette, Stéphane

2010-01-01

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

Dynamic Programming and Graph Algorithms in Computer Vision*

PubMed Central

Felzenszwalb, Pedro F.; Zabih, Ramin

2013-01-01

Optimization is a powerful paradigm for expressing and solving problems in a wide range of areas, and has been successfully applied to many vision problems. Discrete optimization techniques are especially interesting, since by carefully exploiting problem structure they often provide non-trivial guarantees concerning solution quality. In this paper we briefly review dynamic programming and graph algorithms, and discuss representative examples of how these discrete optimization techniques have been applied to some classical vision problems. We focus on the low-level vision problem of stereo; the mid-level problem of interactive object segmentation; and the high-level problem of model-based recognition. PMID:20660950

Interference graph-based dynamic frequency reuse in optical attocell networks

NASA Astrophysics Data System (ADS)

Liu, Huanlin; Xia, Peijie; Chen, Yong; Wu, Lan

2017-11-01

Indoor optical attocell network may achieve higher capacity than radio frequency (RF) or Infrared (IR)-based wireless systems. It is proposed as a special type of visible light communication (VLC) system using Light Emitting Diodes (LEDs). However, the system spectral efficiency may be severely degraded owing to the inter-cell interference (ICI), particularly for dense deployment scenarios. To address these issues, we construct the spectral interference graph for indoor optical attocell network, and propose the Dynamic Frequency Reuse (DFR) and Weighted Dynamic Frequency Reuse (W-DFR) algorithms to decrease ICI and improve the spectral efficiency performance. The interference graph makes LEDs can transmit data without interference and select the minimum sub-bands needed for frequency reuse. Then, DFR algorithm reuses the system frequency equally across service-providing cells to mitigate spectrum interference. While W-DFR algorithm can reuse the system frequency by using the bandwidth weight (BW), which is defined based on the number of service users. Numerical results show that both of the proposed schemes can effectively improve the average spectral efficiency (ASE) of the system. Additionally, improvement of the user data rate is also obtained by analyzing its cumulative distribution function (CDF).

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.

Post-processing interstitialcy diffusion from molecular dynamics simulations

NASA Astrophysics Data System (ADS)

Bhardwaj, U.; Bukkuru, S.; Warrier, M.

2016-01-01

An algorithm to rigorously trace the interstitialcy diffusion trajectory in crystals is developed. The algorithm incorporates unsupervised learning and graph optimization which obviate the need to input extra domain specific information depending on crystal or temperature of the simulation. The algorithm is implemented in a flexible framework as a post-processor to molecular dynamics (MD) simulations. We describe in detail the reduction of interstitialcy diffusion into known computational problems of unsupervised clustering and graph optimization. We also discuss the steps, computational efficiency and key components of the algorithm. Using the algorithm, thermal interstitialcy diffusion from low to near-melting point temperatures is studied. We encapsulate the algorithms in a modular framework with functionality to calculate diffusion coefficients, migration energies and other trajectory properties. The study validates the algorithm by establishing the conformity of output parameters with experimental values and provides detailed insights for the interstitialcy diffusion mechanism. The algorithm along with the help of supporting visualizations and analysis gives convincing details and a new approach to quantifying diffusion jumps, jump-lengths, time between jumps and to identify interstitials from lattice atoms.

Post-processing interstitialcy diffusion from molecular dynamics simulations

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

Bhardwaj, U., E-mail: haptork@gmail.com; Bukkuru, S.; Warrier, M.

2016-01-15

An algorithm to rigorously trace the interstitialcy diffusion trajectory in crystals is developed. The algorithm incorporates unsupervised learning and graph optimization which obviate the need to input extra domain specific information depending on crystal or temperature of the simulation. The algorithm is implemented in a flexible framework as a post-processor to molecular dynamics (MD) simulations. We describe in detail the reduction of interstitialcy diffusion into known computational problems of unsupervised clustering and graph optimization. We also discuss the steps, computational efficiency and key components of the algorithm. Using the algorithm, thermal interstitialcy diffusion from low to near-melting point temperatures ismore » studied. We encapsulate the algorithms in a modular framework with functionality to calculate diffusion coefficients, migration energies and other trajectory properties. The study validates the algorithm by establishing the conformity of output parameters with experimental values and provides detailed insights for the interstitialcy diffusion mechanism. The algorithm along with the help of supporting visualizations and analysis gives convincing details and a new approach to quantifying diffusion jumps, jump-lengths, time between jumps and to identify interstitials from lattice atoms. -- Graphical abstract:.« less

All-Optical Implementation of the Ant Colony Optimization Algorithm

PubMed Central

Hu, Wenchao; Wu, Kan; Shum, Perry Ping; Zheludev, Nikolay I.; Soci, Cesare

2016-01-01

We report all-optical implementation of the optimization algorithm for the famous “ant colony” problem. Ant colonies progressively optimize pathway to food discovered by one of the ants through identifying the discovered route with volatile chemicals (pheromones) secreted on the way back from the food deposit. Mathematically this is an important example of graph optimization problem with dynamically changing parameters. Using an optical network with nonlinear waveguides to represent the graph and a feedback loop, we experimentally show that photons traveling through the network behave like ants that dynamically modify the environment to find the shortest pathway to any chosen point in the graph. This proof-of-principle demonstration illustrates how transient nonlinearity in the optical system can be exploited to tackle complex optimization problems directly, on the hardware level, which may be used for self-routing of optical signals in transparent communication networks and energy flow in photonic systems. PMID:27222098

A graph based algorithm for adaptable dynamic airspace configuration for NextGen

NASA Astrophysics Data System (ADS)

Savai, Mehernaz P.

The National Airspace System (NAS) is a complicated large-scale aviation network, consisting of many static sectors wherein each sector is controlled by one or more controllers. The main purpose of the NAS is to enable safe and prompt air travel in the U.S. However, such static configuration of sectors will not be able to handle the continued growth of air travel which is projected to be more than double the current traffic by 2025. Under the initiative of the Next Generation of Air Transportation system (NextGen), the main objective of Adaptable Dynamic Airspace Configuration (ADAC) is that the sectors should change to the changing traffic so as to reduce the controller workload variance with time while increasing the throughput. Change in the resectorization should be such that there is a minimal increase in exchange of air traffic among controllers. The benefit of a new design (improvement in workload balance, etc.) should sufficiently exceed the transition cost, in order to deserve a change. This leads to the analysis of the concept of transition workload which is the cost associated with a transition from one sectorization to another. Given two airspace configurations, a transition workload metric which considers the air traffic as well as the geometry of the airspace is proposed. A solution to reduce this transition workload is also discussed. The algorithm is specifically designed to be implemented for the Dynamic Airspace Configuration (DAC) Algorithm. A graph model which accurately represents the air route structure and air traffic in the NAS is used to formulate the airspace configuration problem. In addition, a multilevel graph partitioning algorithm is developed for Dynamic Airspace Configuration which partitions the graph model of airspace with given user defined constraints and hence provides the user more flexibility and control over various partitions. In terms of air traffic management, vertices represent airports and waypoints. Some of the major (busy) airports need to be given more importance and hence treated separately. Thus the algorithm takes into account the air route structure while finding a balance between sector workloads. The performance of the proposed algorithms and performance metrics is validated with the Enhanced Traffic Management System (ETMS) air traffic data.

Final Report: Sampling-Based Algorithms for Estimating Structure in Big Data.

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

Matulef, Kevin Michael

The purpose of this project was to develop sampling-based algorithms to discover hidden struc- ture in massive data sets. Inferring structure in large data sets is an increasingly common task in many critical national security applications. These data sets come from myriad sources, such as network traffic, sensor data, and data generated by large-scale simulations. They are often so large that traditional data mining techniques are time consuming or even infeasible. To address this problem, we focus on a class of algorithms that do not compute an exact answer, but instead use sampling to compute an approximate answer using fewermore » resources. The particular class of algorithms that we focus on are streaming algorithms , so called because they are designed to handle high-throughput streams of data. Streaming algorithms have only a small amount of working storage - much less than the size of the full data stream - so they must necessarily use sampling to approximate the correct answer. We present two results: * A streaming algorithm called HyperHeadTail , that estimates the degree distribution of a graph (i.e., the distribution of the number of connections for each node in a network). The degree distribution is a fundamental graph property, but prior work on estimating the degree distribution in a streaming setting was impractical for many real-world application. We improve upon prior work by developing an algorithm that can handle streams with repeated edges, and graph structures that evolve over time. * An algorithm for the task of maintaining a weighted subsample of items in a stream, when the items must be sampled according to their weight, and the weights are dynamically changing. To our knowledge, this is the first such algorithm designed for dynamically evolving weights. We expect it may be useful as a building block for other streaming algorithms on dynamic data sets.« less

Multifractal analysis of multiparticle emission data in the framework of visibility graph and sandbox algorithm

NASA Astrophysics Data System (ADS)

Mali, P.; Manna, S. K.; Mukhopadhyay, A.; Haldar, P. K.; Singh, G.

2018-03-01

Multiparticle emission data in nucleus-nucleus collisions are studied in a graph theoretical approach. The sandbox algorithm used to analyze complex networks is employed to characterize the multifractal properties of the visibility graphs associated with the pseudorapidity distribution of charged particles produced in high-energy heavy-ion collisions. Experimental data on 28Si+Ag/Br interaction at laboratory energy Elab = 14 . 5 A GeV, and 16O+Ag/Br and 32S+Ag/Br interactions both at Elab = 200 A GeV, are used in this analysis. We observe a scale free nature of the degree distributions of the visibility and horizontal visibility graphs associated with the event-wise pseudorapidity distributions. Equivalent event samples simulated by ultra-relativistic quantum molecular dynamics, produce degree distributions that are almost identical to the respective experiment. However, the multifractal variables obtained by using sandbox algorithm for the experiment to some extent differ from the respective simulated results.

Feedback topology and XOR-dynamics in Boolean networks with varying input structure

NASA Astrophysics Data System (ADS)

Ciandrini, L.; Maffi, C.; Motta, A.; Bassetti, B.; Cosentino Lagomarsino, M.

2009-08-01

We analyze a model of fixed in-degree random Boolean networks in which the fraction of input-receiving nodes is controlled by the parameter γ . We investigate analytically and numerically the dynamics of graphs under a parallel XOR updating scheme. This scheme is interesting because it is accessible analytically and its phenomenology is at the same time under control and as rich as the one of general Boolean networks. We give analytical formulas for the dynamics on general graphs, showing that with a XOR-type evolution rule, dynamic features are direct consequences of the topological feedback structure, in analogy with the role of relevant components in Kauffman networks. Considering graphs with fixed in-degree, we characterize analytically and numerically the feedback regions using graph decimation algorithms (Leaf Removal). With varying γ , this graph ensemble shows a phase transition that separates a treelike graph region from one in which feedback components emerge. Networks near the transition point have feedback components made of disjoint loops, in which each node has exactly one incoming and one outgoing link. Using this fact, we provide analytical estimates of the maximum period starting from topological considerations.

Feedback topology and XOR-dynamics in Boolean networks with varying input structure.

PubMed

Ciandrini, L; Maffi, C; Motta, A; Bassetti, B; Cosentino Lagomarsino, M

2009-08-01

We analyze a model of fixed in-degree random Boolean networks in which the fraction of input-receiving nodes is controlled by the parameter gamma. We investigate analytically and numerically the dynamics of graphs under a parallel XOR updating scheme. This scheme is interesting because it is accessible analytically and its phenomenology is at the same time under control and as rich as the one of general Boolean networks. We give analytical formulas for the dynamics on general graphs, showing that with a XOR-type evolution rule, dynamic features are direct consequences of the topological feedback structure, in analogy with the role of relevant components in Kauffman networks. Considering graphs with fixed in-degree, we characterize analytically and numerically the feedback regions using graph decimation algorithms (Leaf Removal). With varying gamma , this graph ensemble shows a phase transition that separates a treelike graph region from one in which feedback components emerge. Networks near the transition point have feedback components made of disjoint loops, in which each node has exactly one incoming and one outgoing link. Using this fact, we provide analytical estimates of the maximum period starting from topological considerations.

Multi-A Graph Patrolling and Partitioning

NASA Astrophysics Data System (ADS)

Elor, Y.; Bruckstein, A. M.

2012-12-01

We introduce a novel multi agent patrolling algorithm inspired by the behavior of gas filled balloons. Very low capability ant-like agents are considered with the task of patrolling an unknown area modeled as a graph. While executing the proposed algorithm, the agents dynamically partition the graph between them using simple local interactions, every agent assuming the responsibility for patrolling his subgraph. Balanced graph partition is an emergent behavior due to the local interactions between the agents in the swarm. Extensive simulations on various graphs (environments) showed that the average time to reach a balanced partition is linear with the graph size. The simulations yielded a convincing argument for conjecturing that if the graph being patrolled contains a balanced partition, the agents will find it. However, we could not prove this. Nevertheless, we have proved that if a balanced partition is reached, the maximum time lag between two successive visits to any vertex using the proposed strategy is at most twice the optimal so the patrol quality is at least half the optimal. In case of weighted graphs the patrol quality is at least (1)/(2){lmin}/{lmax} of the optimal where lmax (lmin) is the longest (shortest) edge in the graph.

The Dynamics of Germinal Centre Selection as Measured by Graph-Theoretical Analysis of Mutational Lineage Trees

PubMed Central

Dunn-Walters, Deborah K.; Belelovsky, Alex; Edelman, Hanna; Banerjee, Monica; Mehr, Ramit

2002-01-01

We have developed a rigorous graph-theoretical algorithm for quantifying the shape properties of mutational lineage trees. We show that information about the dynamics of hypermutation and antigen-driven clonal selection during the humoral immune response is contained in the shape of mutational lineage trees deduced from the responding clones. Age and tissue related differences in the selection process can be studied using this method. Thus, tree shape analysis can be used as a means of elucidating humoral immune response dynamics in various situations. PMID:15144020

Application of dynamic uncertain causality graph in spacecraft fault diagnosis: Logic cycle

NASA Astrophysics Data System (ADS)

Yao, Quanying; Zhang, Qin; Liu, Peng; Yang, Ping; Zhu, Ma; Wang, Xiaochen

2017-04-01

Intelligent diagnosis system are applied to fault diagnosis in spacecraft. Dynamic Uncertain Causality Graph (DUCG) is a new probability graphic model with many advantages. In the knowledge expression of spacecraft fault diagnosis, feedback among variables is frequently encountered, which may cause directed cyclic graphs (DCGs). Probabilistic graphical models (PGMs) such as bayesian network (BN) have been widely applied in uncertain causality representation and probabilistic reasoning, but BN does not allow DCGs. In this paper, DUGG is applied to fault diagnosis in spacecraft: introducing the inference algorithm for the DUCG to deal with feedback. Now, DUCG has been tested in 16 typical faults with 100% diagnosis accuracy.

Optimizing spread dynamics on graphs by message passing

NASA Astrophysics Data System (ADS)

Altarelli, F.; Braunstein, A.; Dall'Asta, L.; Zecchina, R.

2013-09-01

Cascade processes are responsible for many important phenomena in natural and social sciences. Simple models of irreversible dynamics on graphs, in which nodes activate depending on the state of their neighbors, have been successfully applied to describe cascades in a large variety of contexts. Over the past decades, much effort has been devoted to understanding the typical behavior of the cascades arising from initial conditions extracted at random from some given ensemble. However, the problem of optimizing the trajectory of the system, i.e. of identifying appropriate initial conditions to maximize (or minimize) the final number of active nodes, is still considered to be practically intractable, with the only exception being models that satisfy a sort of diminishing returns property called submodularity. Submodular models can be approximately solved by means of greedy strategies, but by definition they lack cooperative characteristics which are fundamental in many real systems. Here we introduce an efficient algorithm based on statistical physics for the optimization of trajectories in cascade processes on graphs. We show that for a wide class of irreversible dynamics, even in the absence of submodularity, the spread optimization problem can be solved efficiently on large networks. Analytic and algorithmic results on random graphs are complemented by the solution of the spread maximization problem on a real-world network (the Epinions consumer reviews network).

TrajGraph: A Graph-Based Visual Analytics Approach to Studying Urban Network Centralities Using Taxi Trajectory Data.

PubMed

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.

Visibility graph analysis on quarterly macroeconomic series of China based on complex network theory

NASA Astrophysics Data System (ADS)

Wang, Na; Li, Dong; Wang, Qiwen

2012-12-01

The visibility graph approach and complex network theory provide a new insight into time series analysis. The inheritance of the visibility graph from the original time series was further explored in the paper. We found that degree distributions of visibility graphs extracted from Pseudo Brownian Motion series obtained by the Frequency Domain algorithm exhibit exponential behaviors, in which the exponential exponent is a binomial function of the Hurst index inherited in the time series. Our simulations presented that the quantitative relations between the Hurst indexes and the exponents of degree distribution function are different for different series and the visibility graph inherits some important features of the original time series. Further, we convert some quarterly macroeconomic series including the growth rates of value-added of three industry series and the growth rates of Gross Domestic Product series of China to graphs by the visibility algorithm and explore the topological properties of graphs associated from the four macroeconomic series, namely, the degree distribution and correlations, the clustering coefficient, the average path length, and community structure. Based on complex network analysis we find degree distributions of associated networks from the growth rates of value-added of three industry series are almost exponential and the degree distributions of associated networks from the growth rates of GDP series are scale free. We also discussed the assortativity and disassortativity of the four associated networks as they are related to the evolutionary process of the original macroeconomic series. All the constructed networks have “small-world” features. The community structures of associated networks suggest dynamic changes of the original macroeconomic series. We also detected the relationship among government policy changes, community structures of associated networks and macroeconomic dynamics. We find great influences of government policies in China on the changes of dynamics of GDP and the three industries adjustment. The work in our paper provides a new way to understand the dynamics of economic development.

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

DTIC Science & Technology

2017-07-01

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

Graph Theory Roots of Spatial Operators for Kinematics and Dynamics

NASA Technical Reports Server (NTRS)

Jain, Abhinandan

2011-01-01

Spatial operators have been used to analyze the dynamics of robotic multibody systems and to develop novel computational dynamics algorithms. Mass matrix factorization, inversion, diagonalization, and linearization are among several new insights obtained using such operators. While initially developed for serial rigid body manipulators, the spatial operators and the related mathematical analysis have been shown to extend very broadly including to tree and closed topology systems, to systems with flexible joints, links, etc. This work uses concepts from graph theory to explore the mathematical foundations of spatial operators. The goal is to study and characterize the properties of the spatial operators at an abstract level so that they can be applied to a broader range of dynamics problems. The rich mathematical properties of the kinematics and dynamics of robotic multibody systems has been an area of strong research interest for several decades. These properties are important to understand the inherent physical behavior of systems, for stability and control analysis, for the development of computational algorithms, and for model development of faithful models. Recurring patterns in spatial operators leads one to ask the more abstract question about the properties and characteristics of spatial operators that make them so broadly applicable. The idea is to step back from the specific application systems, and understand more deeply the generic requirements and properties of spatial operators, so that the insights and techniques are readily available across different kinematics and dynamics problems. In this work, techniques from graph theory were used to explore the abstract basis for the spatial operators. The close relationship between the mathematical properties of adjacency matrices for graphs and those of spatial operators and their kernels were established. The connections hold across very basic requirements on the system topology, the nature of the component bodies, the indexing schemes, etc. The relationship of the underlying structure is intimately connected with efficient, recursive computational algorithms. The results provide the foundational groundwork for a much broader look at the key problems in kinematics and dynamics. The properties of general graphs and trees of nodes and edge were examined, as well as the properties of adjacency matrices that are used to describe graph connectivity. The nilpotency property of such matrices for directed trees was reviewed, and the adjacency matrices were generalized to the notion of block weighted adjacency matrices that support block matrix elements. This leads us to the development of the notion of Spatial Kernel Operator SKO kernels. These kernels provide the basis for the development of SKO resolvent operators.

An algorithm for finding a similar subgraph of all Hamiltonian cycles

NASA Astrophysics Data System (ADS)

Wafdan, R.; Ihsan, M.; Suhaimi, D.

2018-01-01

This paper discusses an algorithm to find a similar subgraph called findSimSubG algorithm. A similar subgraph is a subgraph with a maximum number of edges, contains no isolated vertex and is contained in every Hamiltonian cycle of a Hamiltonian Graph. The algorithm runs only on Hamiltonian graphs with at least two Hamiltonian cycles. The algorithm works by examining whether the initial subgraph of the first Hamiltonian cycle is a subgraph of comparison graphs. If the initial subgraph is not in comparison graphs, the algorithm will remove edges and vertices of the initial subgraph that are not in comparison graphs. There are two main processes in the algorithm, changing Hamiltonian cycle into a cycle graph and removing edges and vertices of the initial subgraph that are not in comparison graphs. The findSimSubG algorithm can find the similar subgraph without using backtracking method. The similar subgraph cannot be found on certain graphs, such as an n-antiprism graph, complete bipartite graph, complete graph, 2n-crossed prism graph, n-crown graph, n-möbius ladder, prism graph, and wheel graph. The complexity of this algorithm is O(m|V|), where m is the number of Hamiltonian cycles and |V| is the number of vertices of a Hamiltonian graph.

Dynamic extension of the Simulation Problem Analysis Kernel (SPANK)

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

Sowell, E.F.; Buhl, W.F.

1988-07-15

The Simulation Problem Analysis Kernel (SPANK) is an object-oriented simulation environment for general simulation purposes. Among its unique features is use of the directed graph as the primary data structure, rather than the matrix. This allows straightforward use of graph algorithms for matching variables and equations, and reducing the problem graph for efficient numerical solution. The original prototype implementation demonstrated the principles for systems of algebraic equations, allowing simulation of steady-state, nonlinear systems (Sowell 1986). This paper describes how the same principles can be extended to include dynamic objects, allowing simulation of general dynamic systems. The theory is developed andmore » an implementation is described. An example is taken from the field of building energy system simulation. 2 refs., 9 figs.« less

Exact numerical calculation of fixation probability and time on graphs.

PubMed

Hindersin, Laura; Möller, Marius; Traulsen, Arne; Bauer, Benedikt

2016-12-01

The Moran process on graphs is a popular model to study the dynamics of evolution in a spatially structured population. Exact analytical solutions for the fixation probability and time of a new mutant have been found for only a few classes of graphs so far. Simulations are time-expensive and many realizations are necessary, as the variance of the fixation times is high. We present an algorithm that numerically computes these quantities for arbitrary small graphs by an approach based on the transition matrix. The advantage over simulations is that the calculation has to be executed only once. Building the transition matrix is automated by our algorithm. This enables a fast and interactive study of different graph structures and their effect on fixation probability and time. We provide a fast implementation in C with this note (Hindersin et al., 2016). Our code is very flexible, as it can handle two different update mechanisms (Birth-death or death-Birth), as well as arbitrary directed or undirected graphs. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

A New Augmentation Based Algorithm for Extracting Maximal Chordal Subgraphs.

PubMed

Bhowmick, Sanjukta; Chen, Tzu-Yi; Halappanavar, Mahantesh

2015-02-01

A graph is chordal if every cycle of length greater than three contains an edge between non-adjacent vertices. Chordal graphs are of interest both theoretically, since they admit polynomial time solutions to a range of NP-hard graph problems, and practically, since they arise in many applications including sparse linear algebra, computer vision, and computational biology. A maximal chordal subgraph is a chordal subgraph that is not a proper subgraph of any other chordal subgraph. Existing algorithms for computing maximal chordal subgraphs depend on dynamically ordering the vertices, which is an inherently sequential process and therefore limits the algorithms' parallelizability. In this paper we explore techniques to develop a scalable parallel algorithm for extracting a maximal chordal subgraph. We demonstrate that an earlier attempt at developing a parallel algorithm may induce a non-optimal vertex ordering and is therefore not guaranteed to terminate with a maximal chordal subgraph. We then give a new algorithm that first computes and then repeatedly augments a spanning chordal subgraph. After proving that the algorithm terminates with a maximal chordal subgraph, we then demonstrate that this algorithm is more amenable to parallelization and that the parallel version also terminates with a maximal chordal subgraph. That said, the complexity of the new algorithm is higher than that of the previous parallel algorithm, although the earlier algorithm computes a chordal subgraph which is not guaranteed to be maximal. We experimented with our augmentation-based algorithm on both synthetic and real-world graphs. We provide scalability results and also explore the effect of different choices for the initial spanning chordal subgraph on both the running time and on the number of edges in the maximal chordal subgraph.

Inference of Spatio-Temporal Functions Over Graphs via Multikernel Kriged Kalman Filtering

NASA Astrophysics Data System (ADS)

Ioannidis, Vassilis N.; Romero, Daniel; Giannakis, Georgios B.

2018-06-01

Inference of space-time varying signals on graphs emerges naturally in a plethora of network science related applications. A frequently encountered challenge pertains to reconstructing such dynamic processes, given their values over a subset of vertices and time instants. The present paper develops a graph-aware kernel-based kriged Kalman filter that accounts for the spatio-temporal variations, and offers efficient online reconstruction, even for dynamically evolving network topologies. The kernel-based learning framework bypasses the need for statistical information by capitalizing on the smoothness that graph signals exhibit with respect to the underlying graph. To address the challenge of selecting the appropriate kernel, the proposed filter is combined with a multi-kernel selection module. Such a data-driven method selects a kernel attuned to the signal dynamics on-the-fly within the linear span of a pre-selected dictionary. The novel multi-kernel learning algorithm exploits the eigenstructure of Laplacian kernel matrices to reduce computational complexity. Numerical tests with synthetic and real data demonstrate the superior reconstruction performance of the novel approach relative to state-of-the-art alternatives.

Real-time path planning in dynamic virtual environments using multiagent navigation graphs.

PubMed

Sud, Avneesh; Andersen, Erik; Curtis, Sean; Lin, Ming C; Manocha, Dinesh

2008-01-01

We present a novel approach for efficient path planning and navigation of multiple virtual agents in complex dynamic scenes. We introduce a new data structure, Multi-agent Navigation Graph (MaNG), which is constructed using first- and second-order Voronoi diagrams. The MaNG is used to perform route planning and proximity computations for each agent in real time. Moreover, we use the path information and proximity relationships for local dynamics computation of each agent by extending a social force model [Helbing05]. We compute the MaNG using graphics hardware and present culling techniques to accelerate the computation. We also address undersampling issues and present techniques to improve the accuracy of our algorithm. Our algorithm is used for real-time multi-agent planning in pursuit-evasion, terrain exploration and crowd simulation scenarios consisting of hundreds of moving agents, each with a distinct goal.

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

PubMed

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

2006-01-15

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

Graph regularized nonnegative matrix factorization for temporal link prediction in dynamic networks

NASA Astrophysics Data System (ADS)

Ma, Xiaoke; Sun, Penggang; Wang, Yu

2018-04-01

Many networks derived from society and nature are temporal and incomplete. The temporal link prediction problem in networks is to predict links at time T + 1 based on a given temporal network from time 1 to T, which is essential to important applications. The current algorithms either predict the temporal links by collapsing the dynamic networks or collapsing features derived from each network, which are criticized for ignoring the connection among slices. to overcome the issue, we propose a novel graph regularized nonnegative matrix factorization algorithm (GrNMF) for the temporal link prediction problem without collapsing the dynamic networks. To obtain the feature for each network from 1 to t, GrNMF factorizes the matrix associated with networks by setting the rest networks as regularization, which provides a better way to characterize the topological information of temporal links. Then, the GrNMF algorithm collapses the feature matrices to predict temporal links. Compared with state-of-the-art methods, the proposed algorithm exhibits significantly improved accuracy by avoiding the collapse of temporal networks. Experimental results of a number of artificial and real temporal networks illustrate that the proposed method is not only more accurate but also more robust than state-of-the-art approaches.

A new augmentation based algorithm for extracting maximal chordal subgraphs

DOE PAGES

Bhowmick, Sanjukta; Chen, Tzu-Yi; Halappanavar, Mahantesh

2014-10-18

If every cycle of a graph is chordal length greater than three then it contains an edge between non-adjacent vertices. Chordal graphs are of interest both theoretically, since they admit polynomial time solutions to a range of NP-hard graph problems, and practically, since they arise in many applications including sparse linear algebra, computer vision, and computational biology. A maximal chordal subgraph is a chordal subgraph that is not a proper subgraph of any other chordal subgraph. Existing algorithms for computing maximal chordal subgraphs depend on dynamically ordering the vertices, which is an inherently sequential process and therefore limits the algorithms’more » parallelizability. In our paper we explore techniques to develop a scalable parallel algorithm for extracting a maximal chordal subgraph. We demonstrate that an earlier attempt at developing a parallel algorithm may induce a non-optimal vertex ordering and is therefore not guaranteed to terminate with a maximal chordal subgraph. We then give a new algorithm that first computes and then repeatedly augments a spanning chordal subgraph. After proving that the algorithm terminates with a maximal chordal subgraph, we then demonstrate that this algorithm is more amenable to parallelization and that the parallel version also terminates with a maximal chordal subgraph. That said, the complexity of the new algorithm is higher than that of the previous parallel algorithm, although the earlier algorithm computes a chordal subgraph which is not guaranteed to be maximal. Finally, we experimented with our augmentation-based algorithm on both synthetic and real-world graphs. We provide scalability results and also explore the effect of different choices for the initial spanning chordal subgraph on both the running time and on the number of edges in the maximal chordal subgraph.« less

Distributed Containment Control for Multiple Unknown Second-Order Nonlinear Systems With Application to Networked Lagrangian Systems.

PubMed

Mei, Jie; Ren, Wei; Li, Bing; Ma, Guangfu

2015-09-01

In this paper, we consider the distributed containment control problem for multiagent systems with unknown nonlinear dynamics. More specifically, we focus on multiple second-order nonlinear systems and networked Lagrangian systems. We first study the distributed containment control problem for multiple second-order nonlinear systems with multiple dynamic leaders in the presence of unknown nonlinearities and external disturbances under a general directed graph that characterizes the interaction among the leaders and the followers. A distributed adaptive control algorithm with an adaptive gain design based on the approximation capability of neural networks is proposed. We present a necessary and sufficient condition on the directed graph such that the containment error can be reduced as small as desired. As a byproduct, the leaderless consensus problem is solved with asymptotical convergence. Because relative velocity measurements between neighbors are generally more difficult to obtain than relative position measurements, we then propose a distributed containment control algorithm without using neighbors' velocity information. A two-step Lyapunov-based method is used to study the convergence of the closed-loop system. Next, we apply the ideas to deal with the containment control problem for networked unknown Lagrangian systems under a general directed graph. All the proposed algorithms are distributed and can be implemented using only local measurements in the absence of communication. Finally, simulation examples are provided to show the effectiveness of the proposed control algorithms.

PathFinder: reconstruction and dynamic visualization of metabolic pathways.

PubMed

Goesmann, Alexander; Haubrock, Martin; Meyer, Folker; Kalinowski, Jörn; Giegerich, Robert

2002-01-01

Beyond methods for a gene-wise annotation and analysis of sequenced genomes new automated methods for functional analysis on a higher level are needed. The identification of realized metabolic pathways provides valuable information on gene expression and regulation. Detection of incomplete pathways helps to improve a constantly evolving genome annotation or discover alternative biochemical pathways. To utilize automated genome analysis on the level of metabolic pathways new methods for the dynamic representation and visualization of pathways are needed. PathFinder is a tool for the dynamic visualization of metabolic pathways based on annotation data. Pathways are represented as directed acyclic graphs, graph layout algorithms accomplish the dynamic drawing and visualization of the metabolic maps. A more detailed analysis of the input data on the level of biochemical pathways helps to identify genes and detect improper parts of annotations. As an Relational Database Management System (RDBMS) based internet application PathFinder reads a list of EC-numbers or a given annotation in EMBL- or Genbank-format and dynamically generates pathway graphs.

Graph-based analysis of kinetics on multidimensional potential-energy surfaces.

PubMed

Okushima, T; Niiyama, T; Ikeda, K S; Shimizu, Y

2009-09-01

The aim of this paper is twofold: one is to give a detailed description of an alternative graph-based analysis method, which we call saddle connectivity graph, for analyzing the global topography and the dynamical properties of many-dimensional potential-energy landscapes and the other is to give examples of applications of this method in the analysis of the kinetics of realistic systems. A Dijkstra-type shortest path algorithm is proposed to extract dynamically dominant transition pathways by kinetically defining transition costs. The applicability of this approach is first confirmed by an illustrative example of a low-dimensional random potential. We then show that a coarse-graining procedure tailored for saddle connectivity graphs can be used to obtain the kinetic properties of 13- and 38-atom Lennard-Jones clusters. The coarse-graining method not only reduces the complexity of the graphs, but also, with iterative use, reveals a self-similar hierarchical structure in these clusters. We also propose that the self-similarity is common to many-atom Lennard-Jones clusters.

Array distribution in data-parallel programs

NASA Technical Reports Server (NTRS)

Chatterjee, Siddhartha; Gilbert, John R.; Schreiber, Robert; Sheffler, Thomas J.

1994-01-01

We consider distribution at compile time of the array data in a distributed-memory implementation of a data-parallel program written in a language like Fortran 90. We allow dynamic redistribution of data and define a heuristic algorithmic framework that chooses distribution parameters to minimize an estimate of program completion time. We represent the program as an alignment-distribution graph. We propose a divide-and-conquer algorithm for distribution that initially assigns a common distribution to each node of the graph and successively refines this assignment, taking computation, realignment, and redistribution costs into account. We explain how to estimate the effect of distribution on computation cost and how to choose a candidate set of distributions. We present the results of an implementation of our algorithms on several test problems.

Diffusion-based recommendation with trust relations on tripartite graphs

NASA Astrophysics Data System (ADS)

Wang, Ximeng; Liu, Yun; Zhang, Guangquan; Xiong, Fei; Lu, Jie

2017-08-01

The diffusion-based recommendation approach is a vital branch in recommender systems, which successfully applies physical dynamics to make recommendations for users on bipartite or tripartite graphs. Trust links indicate users’ social relations and can provide the benefit of reducing data sparsity. However, traditional diffusion-based algorithms only consider rating links when making recommendations. In this paper, the complementarity of users’ implicit and explicit trust is exploited, and a novel resource-allocation strategy is proposed, which integrates these two kinds of trust relations on tripartite graphs. Through empirical studies on three benchmark datasets, our proposed method obtains better performance than most of the benchmark algorithms in terms of accuracy, diversity and novelty. According to the experimental results, our method is an effective and reasonable way to integrate additional features into the diffusion-based recommendation approach.

GBS 1.0

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

2010-09-30

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

Dynamical modeling and analysis of large cellular regulatory networks

NASA Astrophysics Data System (ADS)

Bérenguier, D.; Chaouiya, C.; Monteiro, P. T.; Naldi, A.; Remy, E.; Thieffry, D.; Tichit, L.

2013-06-01

The dynamical analysis of large biological regulatory networks requires the development of scalable methods for mathematical modeling. Following the approach initially introduced by Thomas, we formalize the interactions between the components of a network in terms of discrete variables, functions, and parameters. Model simulations result in directed graphs, called state transition graphs. We are particularly interested in reachability properties and asymptotic behaviors, which correspond to terminal strongly connected components (or "attractors") in the state transition graph. A well-known problem is the exponential increase of the size of state transition graphs with the number of network components, in particular when using the biologically realistic asynchronous updating assumption. To address this problem, we have developed several complementary methods enabling the analysis of the behavior of large and complex logical models: (i) the definition of transition priority classes to simplify the dynamics; (ii) a model reduction method preserving essential dynamical properties, (iii) a novel algorithm to compact state transition graphs and directly generate compressed representations, emphasizing relevant transient and asymptotic dynamical properties. The power of an approach combining these different methods is demonstrated by applying them to a recent multilevel logical model for the network controlling CD4+ T helper cell response to antigen presentation and to a dozen cytokines. This model accounts for the differentiation of canonical Th1 and Th2 lymphocytes, as well as of inflammatory Th17 and regulatory T cells, along with many hybrid subtypes. All these methods have been implemented into the software GINsim, which enables the definition, the analysis, and the simulation of logical regulatory graphs.

Optimal Quantum Spatial Search on Random Temporal Networks

NASA Astrophysics Data System (ADS)

Chakraborty, Shantanav; Novo, Leonardo; Di Giorgio, Serena; Omar, Yasser

2017-12-01

To investigate the performance of quantum information tasks on networks whose topology changes in time, we study the spatial search algorithm by continuous time quantum walk to find a marked node on a random temporal network. We consider a network of n nodes constituted by a time-ordered sequence of Erdös-Rényi random graphs G (n ,p ), where p is the probability that any two given nodes are connected: After every time interval τ , a new graph G (n ,p ) replaces the previous one. We prove analytically that, for any given p , there is always a range of values of τ for which the running time of the algorithm is optimal, i.e., O (√{n }), even when search on the individual static graphs constituting the temporal network is suboptimal. On the other hand, there are regimes of τ where the algorithm is suboptimal even when each of the underlying static graphs are sufficiently connected to perform optimal search on them. From this first study of quantum spatial search on a time-dependent network, it emerges that the nontrivial interplay between temporality and connectivity is key to the algorithmic performance. Moreover, our work can be extended to establish high-fidelity qubit transfer between any two nodes of the network. Overall, our findings show that one can exploit temporality to achieve optimal quantum information tasks on dynamical random networks.

A Probabilistic Framework for Constructing Temporal Relations in Replica Exchange Molecular Trajectories.

PubMed

Chattopadhyay, Aditya; Zheng, Min; Waller, Mark Paul; Priyakumar, U Deva

2018-05-23

Knowledge of the structure and dynamics of biomolecules is essential for elucidating the underlying mechanisms of biological processes. Given the stochastic nature of many biological processes, like protein unfolding, it's almost impossible that two independent simulations will generate the exact same sequence of events, which makes direct analysis of simulations difficult. Statistical models like Markov Chains, transition networks etc. help in shedding some light on the mechanistic nature of such processes by predicting long-time dynamics of these systems from short simulations. However, such methods fall short in analyzing trajectories with partial or no temporal information, for example, replica exchange molecular dynamics or Monte Carlo simulations. In this work we propose a probabilistic algorithm, borrowing concepts from graph theory and machine learning, to extract reactive pathways from molecular trajectories in the absence of temporal data. A suitable vector representation was chosen to represent each frame in the macromolecular trajectory (as a series of interaction and conformational energies) and dimensionality reduction was performed using principal component analysis (PCA). The trajectory was then clustered using a density-based clustering algorithm, where each cluster represents a metastable state on the potential energy surface (PES) of the biomolecule under study. A graph was created with these clusters as nodes with the edges learnt using an iterative expectation maximization algorithm. The most reactive path is conceived as the widest path along this graph. We have tested our method on RNA hairpin unfolding trajectory in aqueous urea solution. Our method makes the understanding of the mechanism of unfolding in RNA hairpin molecule more tractable. As this method doesn't rely on temporal data it can be used to analyze trajectories from Monte Carlo sampling techniques and replica exchange molecular dynamics (REMD).

Unsupervised Spatial Event Detection in Targeted Domains with Applications to Civil Unrest Modeling

PubMed Central

Zhao, Liang; Chen, Feng; Dai, Jing; Hua, Ting; Lu, Chang-Tien; Ramakrishnan, Naren

2014-01-01

Twitter has become a popular data source as a surrogate for monitoring and detecting events. Targeted domains such as crime, election, and social unrest require the creation of algorithms capable of detecting events pertinent to these domains. Due to the unstructured language, short-length messages, dynamics, and heterogeneity typical of Twitter data streams, it is technically difficult and labor-intensive to develop and maintain supervised learning systems. We present a novel unsupervised approach for detecting spatial events in targeted domains and illustrate this approach using one specific domain, viz. civil unrest modeling. Given a targeted domain, we propose a dynamic query expansion algorithm to iteratively expand domain-related terms, and generate a tweet homogeneous graph. An anomaly identification method is utilized to detect spatial events over this graph by jointly maximizing local modularity and spatial scan statistics. Extensive experiments conducted in 10 Latin American countries demonstrate the effectiveness of the proposed approach. PMID:25350136

Aligning Biomolecular Networks Using Modular Graph Kernels

NASA Astrophysics Data System (ADS)

Towfic, Fadi; Greenlee, M. Heather West; Honavar, Vasant

Comparative analysis of biomolecular networks constructed using measurements from different conditions, tissues, and organisms offer a powerful approach to understanding the structure, function, dynamics, and evolution of complex biological systems. We explore a class of algorithms for aligning large biomolecular networks by breaking down such networks into subgraphs and computing the alignment of the networks based on the alignment of their subgraphs. The resulting subnetworks are compared using graph kernels as scoring functions. We provide implementations of the resulting algorithms as part of BiNA, an open source biomolecular network alignment toolkit. Our experiments using Drosophila melanogaster, Saccharomyces cerevisiae, Mus musculus and Homo sapiens protein-protein interaction networks extracted from the DIP repository of protein-protein interaction data demonstrate that the performance of the proposed algorithms (as measured by % GO term enrichment of subnetworks identified by the alignment) is competitive with some of the state-of-the-art algorithms for pair-wise alignment of large protein-protein interaction networks. Our results also show that the inter-species similarity scores computed based on graph kernels can be used to cluster the species into a species tree that is consistent with the known phylogenetic relationships among the species.

Fast and asymptotic computation of the fixation probability for Moran processes on graphs.

PubMed

Alcalde Cuesta, F; González Sequeiros, P; Lozano Rojo, Á

2015-03-01

Evolutionary dynamics has been classically studied for homogeneous populations, but now there is a growing interest in the non-homogeneous case. One of the most important models has been proposed in Lieberman et al. (2005), adapting to a weighted directed graph the process described in Moran (1958). The Markov chain associated with the graph can be modified by erasing all non-trivial loops in its state space, obtaining the so-called Embedded Markov chain (EMC). The fixation probability remains unchanged, but the expected time to absorption (fixation or extinction) is reduced. In this paper, we shall use this idea to compute asymptotically the average fixation probability for complete bipartite graphs K(n,m). To this end, we firstly review some recent results on evolutionary dynamics on graphs trying to clarify some points. We also revisit the 'Star Theorem' proved in Lieberman et al. (2005) for the star graphs K(1,m). Theoretically, EMC techniques allow fast computation of the fixation probability, but in practice this is not always true. Thus, in the last part of the paper, we compare this algorithm with the standard Monte Carlo method for some kind of complex networks. Copyright © 2015 Elsevier Ireland Ltd. All rights reserved.

A matrix-algebraic formulation of distributed-memory maximal cardinality matching algorithms in bipartite graphs

DOE PAGES

Azad, Ariful; Buluç, Aydın

2016-05-16

We describe parallel algorithms for computing maximal cardinality matching in a bipartite graph on distributed-memory systems. Unlike traditional algorithms that match one vertex at a time, our algorithms process many unmatched vertices simultaneously using a matrix-algebraic formulation of maximal matching. This generic matrix-algebraic framework is used to develop three efficient maximal matching algorithms with minimal changes. The newly developed algorithms have two benefits over existing graph-based algorithms. First, unlike existing parallel algorithms, cardinality of matching obtained by the new algorithms stays constant with increasing processor counts, which is important for predictable and reproducible performance. Second, relying on bulk-synchronous matrix operations,more » these algorithms expose a higher degree of parallelism on distributed-memory platforms than existing graph-based algorithms. We report high-performance implementations of three maximal matching algorithms using hybrid OpenMP-MPI and evaluate the performance of these algorithm using more than 35 real and randomly generated graphs. On real instances, our algorithms achieve up to 200 × speedup on 2048 cores of a Cray XC30 supercomputer. Even higher speedups are obtained on larger synthetically generated graphs where our algorithms show good scaling on up to 16,384 cores.« less

Probabilistic fusion of stereo with color and contrast for bilayer segmentation.

PubMed

Kolmogorov, Vladimir; Criminisi, Antonio; Blake, Andrew; Cross, Geoffrey; Rother, Carsten

2006-09-01

This paper describes models and algorithms for the real-time segmentation of foreground from background layers in stereo video sequences. Automatic separation of layers from color/contrast or from stereo alone is known to be error-prone. Here, color, contrast, and stereo matching information are fused to infer layers accurately and efficiently. The first algorithm, Layered Dynamic Programming (LDP), solves stereo in an extended six-state space that represents both foreground/background layers and occluded regions. The stereo-match likelihood is then fused with a contrast-sensitive color model that is learned on-the-fly and stereo disparities are obtained by dynamic programming. The second algorithm, Layered Graph Cut (LGC), does not directly solve stereo. Instead, the stereo match likelihood is marginalized over disparities to evaluate foreground and background hypotheses and then fused with a contrast-sensitive color model like the one used in LDP. Segmentation is solved efficiently by ternary graph cut. Both algorithms are evaluated with respect to ground truth data and found to have similar performance, substantially better than either stereo or color/ contrast alone. However, their characteristics with respect to computational efficiency are rather different. The algorithms are demonstrated in the application of background substitution and shown to give good quality composite video output.

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

PubMed

Aaron, Catherine

2006-01-01

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

Scalable Static and Dynamic Community Detection Using Grappolo

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

Halappanavar, Mahantesh; Lu, Hao; Kalyanaraman, Anantharaman

Graph clustering, popularly known as community detection, is a fundamental kernel for several applications of relevance to the Defense Advanced Research Projects Agency’s (DARPA) Hierarchical Identify Verify Exploit (HIVE) Pro- gram. Clusters or communities represent natural divisions within a network that are densely connected within a cluster and sparsely connected to the rest of the network. The need to compute clustering on large scale data necessitates the development of efficient algorithms that can exploit modern architectures that are fundamentally parallel in nature. How- ever, due to their irregular and inherently sequential nature, many of the current algorithms for community detectionmore » are challenging to parallelize. In response to the HIVE Graph Challenge, we present several parallelization heuristics for fast community detection using the Louvain method as the serial template. We implement all the heuristics in a software library called Grappolo. Using the inputs from the HIVE Challenge, we demonstrate superior performance and high quality solutions based on four parallelization heuristics. We use Grappolo on static graphs as the first step towards community detection on streaming graphs.« less

Graphing trillions of triangles.

PubMed

Burkhardt, Paul

2017-07-01

The increasing size of Big Data is often heralded but how data are transformed and represented is also profoundly important to knowledge discovery, and this is exemplified in Big Graph analytics. Much attention has been placed on the scale of the input graph but the product of a graph algorithm can be many times larger than the input. This is true for many graph problems, such as listing all triangles in a graph. Enabling scalable graph exploration for Big Graphs requires new approaches to algorithms, architectures, and visual analytics. A brief tutorial is given to aid the argument for thoughtful representation of data in the context of graph analysis. Then a new algebraic method to reduce the arithmetic operations in counting and listing triangles in graphs is introduced. Additionally, a scalable triangle listing algorithm in the MapReduce model will be presented followed by a description of the experiments with that algorithm that led to the current largest and fastest triangle listing benchmarks to date. Finally, a method for identifying triangles in new visual graph exploration technologies is proposed.

Mathematics of Web science: structure, dynamics and incentives.

PubMed

Chayes, Jennifer

2013-03-28

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

The Container Problem in Bubble-Sort Graphs

NASA Astrophysics Data System (ADS)

Suzuki, Yasuto; Kaneko, Keiichi

Bubble-sort graphs are variants of Cayley graphs. A bubble-sort graph is suitable as a topology for massively parallel systems because of its simple and regular structure. Therefore, in this study, we focus on n-bubble-sort graphs and propose an algorithm to obtain n-1 disjoint paths between two arbitrary nodes in time bounded by a polynomial in n, the degree of the graph plus one. We estimate the time complexity of the algorithm and the sum of the path lengths after proving the correctness of the algorithm. In addition, we report the results of computer experiments evaluating the average performance of the algorithm.

Graphs, matrices, and the GraphBLAS: Seven good reasons

DOE PAGES

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

2015-01-01

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

Enhancements and Algorithms for Avionic Information Processing System Design Methodology.

DTIC Science & Technology

1982-06-16

programming algorithm is enhanced by incorporating task precedence constraints and hardware failures. Stochastic network methods are used to analyze...allocations in the presence of random fluctuations. Graph theoretic methods are used to analyze hardware designs, and new designs are constructed with...There, spatial dynamic programming (SDP) was used to solve a static, deterministic software allocation problem. Under the current contract the SDP

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

PubMed Central

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

2016-01-01

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

Multi-layer service function chaining scheduling based on auxiliary graph in IP over optical network

NASA Astrophysics Data System (ADS)

Li, Yixuan; Li, Hui; Liu, Yuze; Ji, Yuefeng

2017-10-01

Software Defined Optical Network (SDON) can be considered as extension of Software Defined Network (SDN) in optical networks. SDON offers a unified control plane and makes optical network an intelligent transport network with dynamic flexibility and service adaptability. For this reason, a comprehensive optical transmission service, able to achieve service differentiation all the way down to the optical transport layer, can be provided to service function chaining (SFC). IP over optical network, as a promising networking architecture to interconnect data centers, is the most widely used scenarios of SFC. In this paper, we offer a flexible and dynamic resource allocation method for diverse SFC service requests in the IP over optical network. To do so, we firstly propose the concept of optical service function (OSF) and a multi-layer SFC model. OSF represents the comprehensive optical transmission service (e.g., multicast, low latency, quality of service, etc.), which can be achieved in multi-layer SFC model. OSF can also be considered as a special SF. Secondly, we design a resource allocation algorithm, which we call OSF-oriented optical service scheduling algorithm. It is able to address multi-layer SFC optical service scheduling and provide comprehensive optical transmission service, while meeting multiple optical transmission requirements (e.g., bandwidth, latency, availability). Moreover, the algorithm exploits the concept of Auxiliary Graph. Finally, we compare our algorithm with the Baseline algorithm in simulation. And simulation results show that our algorithm achieves superior performance than Baseline algorithm in low traffic load condition.

Hierarchical graphs for rule-based modeling of biochemical systems

PubMed Central

2011-01-01

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

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.

Survey of Approaches to Generate Realistic Synthetic Graphs

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

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

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

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

PubMed

Grady, Leo; Jolly, Marie-Pierre

2008-01-01

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

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

PubMed

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

2010-11-15

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

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.

Graphing trillions of triangles

PubMed Central

Burkhardt, Paul

2016-01-01

The increasing size of Big Data is often heralded but how data are transformed and represented is also profoundly important to knowledge discovery, and this is exemplified in Big Graph analytics. Much attention has been placed on the scale of the input graph but the product of a graph algorithm can be many times larger than the input. This is true for many graph problems, such as listing all triangles in a graph. Enabling scalable graph exploration for Big Graphs requires new approaches to algorithms, architectures, and visual analytics. A brief tutorial is given to aid the argument for thoughtful representation of data in the context of graph analysis. Then a new algebraic method to reduce the arithmetic operations in counting and listing triangles in graphs is introduced. Additionally, a scalable triangle listing algorithm in the MapReduce model will be presented followed by a description of the experiments with that algorithm that led to the current largest and fastest triangle listing benchmarks to date. Finally, a method for identifying triangles in new visual graph exploration technologies is proposed. PMID:28690426

Topological properties of the limited penetrable horizontal visibility graph family

NASA Astrophysics Data System (ADS)

Wang, Minggang; Vilela, André L. M.; Du, Ruijin; Zhao, Longfeng; Dong, Gaogao; Tian, Lixin; Stanley, H. Eugene

2018-05-01

The limited penetrable horizontal visibility graph algorithm was recently introduced to map time series in complex networks. In this work, we extend this algorithm to create a directed-limited penetrable horizontal visibility graph and an image-limited penetrable horizontal visibility graph. We define two algorithms and provide theoretical results on the topological properties of these graphs associated with different types of real-value series. We perform several numerical simulations to check the accuracy of our theoretical results. Finally, we present an application of the directed-limited penetrable horizontal visibility graph to measure real-value time series irreversibility and an application of the image-limited penetrable horizontal visibility graph that discriminates noise from chaos. We also propose a method to measure the systematic risk using the image-limited penetrable horizontal visibility graph, and the empirical results show the effectiveness of our proposed algorithms.

Building occupancy simulation and data assimilation using a graph-based agent-oriented model

NASA Astrophysics Data System (ADS)

Rai, Sanish; Hu, Xiaolin

2018-07-01

Building occupancy simulation and estimation simulates the dynamics of occupants and estimates their real-time spatial distribution in a building. It requires a simulation model and an algorithm for data assimilation that assimilates real-time sensor data into the simulation model. Existing building occupancy simulation models include agent-based models and graph-based models. The agent-based models suffer high computation cost for simulating large numbers of occupants, and graph-based models overlook the heterogeneity and detailed behaviors of individuals. Recognizing the limitations of existing models, this paper presents a new graph-based agent-oriented model which can efficiently simulate large numbers of occupants in various kinds of building structures. To support real-time occupancy dynamics estimation, a data assimilation framework based on Sequential Monte Carlo Methods is also developed and applied to the graph-based agent-oriented model to assimilate real-time sensor data. Experimental results show the effectiveness of the developed model and the data assimilation framework. The major contributions of this work are to provide an efficient model for building occupancy simulation that can accommodate large numbers of occupants and an effective data assimilation framework that can provide real-time estimations of building occupancy from sensor data.

Search Problems in Mission Planning and Navigation of Autonomous Aircraft. M.S. Thesis

NASA Technical Reports Server (NTRS)

Krozel, James A.

1988-01-01

An architecture for the control of an autonomous aircraft is presented. The architecture is a hierarchical system representing an anthropomorphic breakdown of the control problem into planner, navigator, and pilot systems. The planner system determines high level global plans from overall mission objectives. This abstract mission planning is investigated by focusing on the Traveling Salesman Problem with variations on local and global constraints. Tree search techniques are applied including the breadth first, depth first, and best first algorithms. The minimum-column and row entries for the Traveling Salesman Problem cost matrix provides a powerful heuristic to guide these search techniques. Mission planning subgoals are directed from the planner to the navigator for planning routes in mountainous terrain with threats. Terrain/threat information is abstracted into a graph of possible paths for which graph searches are performed. It is shown that paths can be well represented by a search graph based on the Voronoi diagram of points representing the vertices of mountain boundaries. A comparison of Dijkstra's dynamic programming algorithm and the A* graph search algorithm from artificial intelligence/operations research is performed for several navigation path planning examples. These examples illustrate paths that minimize a combination of distance and exposure to threats. Finally, the pilot system synthesizes the flight trajectory by creating the control commands to fly the aircraft.

An Adiabatic Quantum Algorithm for Determining Gracefulness of a Graph

NASA Astrophysics Data System (ADS)

Hosseini, Sayed Mohammad; Davoudi Darareh, Mahdi; Janbaz, Shahrooz; Zaghian, Ali

2017-07-01

Graph labelling is one of the noticed contexts in combinatorics and graph theory. Graceful labelling for a graph G with e edges, is to label the vertices of G with 0, 1, ℒ, e such that, if we specify to each edge the difference value between its two ends, then any of 1, 2, ℒ, e appears exactly once as an edge label. For a given graph, there are still few efficient classical algorithms that determine either it is graceful or not, even for trees - as a well-known class of graphs. In this paper, we introduce an adiabatic quantum algorithm, which for a graceful graph G finds a graceful labelling. Also, this algorithm can determine if G is not graceful. Numerical simulations of the algorithm reveal that its time complexity has a polynomial behaviour with the problem size up to the range of 15 qubits. A general sufficient condition for a combinatorial optimization problem to have a satisfying adiabatic solution is also derived.

Graph-based structural change detection for rotating machinery monitoring

NASA Astrophysics Data System (ADS)

Lu, Guoliang; Liu, Jie; Yan, Peng

2018-01-01

Detection of structural changes is critically important in operational monitoring of a rotating machine. This paper presents a novel framework for this purpose, where a graph model for data modeling is adopted to represent/capture statistical dynamics in machine operations. Meanwhile we develop a numerical method for computing temporal anomalies in the constructed graphs. The martingale-test method is employed for the change detection when making decisions on possible structural changes, where excellent performance is demonstrated outperforming exciting results such as the autoregressive-integrated-moving average (ARIMA) model. Comprehensive experimental results indicate good potentials of the proposed algorithm in various engineering applications. This work is an extension of a recent result (Lu et al., 2017).

Graph embedding and extensions: a general framework for dimensionality reduction.

PubMed

Yan, Shuicheng; Xu, Dong; Zhang, Benyu; Zhang, Hong-Jiang; Yang, Qiang; Lin, Stephen

2007-01-01

Over the past few decades, a large family of algorithms - supervised or unsupervised; stemming from statistics or geometry theory - has been designed to provide different solutions to the problem of dimensionality reduction. Despite the different motivations of these algorithms, we present in this paper a general formulation known as graph embedding to unify them within a common framework. In graph embedding, each algorithm can be considered as the direct graph embedding or its linear/kernel/tensor extension of a specific intrinsic graph that describes certain desired statistical or geometric properties of a data set, with constraints from scale normalization or a penalty graph that characterizes a statistical or geometric property that should be avoided. Furthermore, the graph embedding framework can be used as a general platform for developing new dimensionality reduction algorithms. By utilizing this framework as a tool, we propose a new supervised dimensionality reduction algorithm called Marginal Fisher Analysis in which the intrinsic graph characterizes the intraclass compactness and connects each data point with its neighboring points of the same class, while the penalty graph connects the marginal points and characterizes the interclass separability. We show that MFA effectively overcomes the limitations of the traditional Linear Discriminant Analysis algorithm due to data distribution assumptions and available projection directions. Real face recognition experiments show the superiority of our proposed MFA in comparison to LDA, also for corresponding kernel and tensor extensions.

On the degree distribution of horizontal visibility graphs associated with Markov processes and dynamical systems: diagrammatic and variational approaches

NASA Astrophysics Data System (ADS)

Lacasa, Lucas

2014-09-01

Dynamical processes can be transformed into graphs through a family of mappings called visibility algorithms, enabling the possibility of (i) making empirical time series analysis and signal processing and (ii) characterizing classes of dynamical systems and stochastic processes using the tools of graph theory. Recent works show that the degree distribution of these graphs encapsulates much information on the signals' variability, and therefore constitutes a fundamental feature for statistical learning purposes. However, exact solutions for the degree distributions are only known in a few cases, such as for uncorrelated random processes. Here we analytically explore these distributions in a list of situations. We present a diagrammatic formalism which computes for all degrees their corresponding probability as a series expansion in a coupling constant which is the number of hidden variables. We offer a constructive solution for general Markovian stochastic processes and deterministic maps. As case tests we focus on Ornstein-Uhlenbeck processes, fully chaotic and quasiperiodic maps. Whereas only for certain degree probabilities can all diagrams be summed exactly, in the general case we show that the perturbation theory converges. In a second part, we make use of a variational technique to predict the complete degree distribution for special classes of Markovian dynamics with fast-decaying correlations. In every case we compare the theory with numerical experiments.

Modification of Prim’s algorithm on complete broadcasting graph

NASA Astrophysics Data System (ADS)

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

2017-09-01

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

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.

FGRAAL: FORTRAN extended graph algorithmic language

NASA Technical Reports Server (NTRS)

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

1972-01-01

The FORTRAN version FGRAAL of the graph algorithmic language GRAAL as it has been implemented for the Univac 1108 is described. FBRAAL is an extension of FORTRAN 5 and is intended for describing and implementing graph algorithms of the type primarily arising in applications. The formal description contained in this report represents a supplement to the FORTRAN 5 manual for the Univac 1108 (UP-4060), that is, only the new features of the language are described. Several typical graph algorithms, written in FGRAAL, are included to illustrate various features of the language and to show its applicability.

A new algorithm to find fuzzy Hamilton cycle in a fuzzy network using adjacency matrix and minimum vertex degree.

PubMed

Nagoor Gani, A; Latha, S R

2016-01-01

A Hamiltonian cycle in a graph is a cycle that visits each node/vertex exactly once. A graph containing a Hamiltonian cycle is called a Hamiltonian graph. There have been several researches to find the number of Hamiltonian cycles of a Hamilton graph. As the number of vertices and edges grow, it becomes very difficult to keep track of all the different ways through which the vertices are connected. Hence, analysis of large graphs can be efficiently done with the assistance of a computer system that interprets graphs as matrices. And, of course, a good and well written algorithm will expedite the analysis even faster. The most convenient way to quickly test whether there is an edge between two vertices is to represent graphs using adjacent matrices. In this paper, a new algorithm is proposed to find fuzzy Hamiltonian cycle using adjacency matrix and the degree of the vertices of a fuzzy graph. A fuzzy graph structure is also modeled to illustrate the proposed algorithms with the selected air network of Indigo airlines.

Weighted graph cuts without eigenvectors a multilevel approach.

PubMed

Dhillon, Inderjit S; Guan, Yuqiang; Kulis, Brian

2007-11-01

A variety of clustering algorithms have recently been proposed to handle data that is not linearly separable; spectral clustering and kernel k-means are two of the main methods. In this paper, we discuss an equivalence between the objective functions used in these seemingly different methods--in particular, a general weighted kernel k-means objective is mathematically equivalent to a weighted graph clustering objective. We exploit this equivalence to develop a fast, high-quality multilevel algorithm that directly optimizes various weighted graph clustering objectives, such as the popular ratio cut, normalized cut, and ratio association criteria. This eliminates the need for any eigenvector computation for graph clustering problems, which can be prohibitive for very large graphs. Previous multilevel graph partitioning methods, such as Metis, have suffered from the restriction of equal-sized clusters; our multilevel algorithm removes this restriction by using kernel k-means to optimize weighted graph cuts. Experimental results show that our multilevel algorithm outperforms a state-of-the-art spectral clustering algorithm in terms of speed, memory usage, and quality. We demonstrate that our algorithm is applicable to large-scale clustering tasks such as image segmentation, social network analysis and gene network analysis.

Detecting community structure via the maximal sub-graphs and belonging degrees in complex networks

NASA Astrophysics Data System (ADS)

Cui, Yaozu; Wang, Xingyuan; Eustace, Justine

2014-12-01

Community structure is a common phenomenon in complex networks, and it has been shown that some communities in complex networks often overlap each other. So in this paper we propose a new algorithm to detect overlapping community structure in complex networks. To identify the overlapping community structure, our algorithm firstly extracts fully connected sub-graphs which are maximal sub-graphs from original networks. Then two maximal sub-graphs having the key pair-vertices can be merged into a new larger sub-graph using some belonging degree functions. Furthermore we extend the modularity function to evaluate the proposed algorithm. In addition, overlapping nodes between communities are founded successfully. Finally we report the comparison between the modularity and the computational complexity of the proposed algorithm with some other existing algorithms. The experimental results show that the proposed algorithm gives satisfactory results.

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

PubMed

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

2013-02-01

Bootstrap methods have recently been introduced to diffusion-weighted magnetic resonance imaging to estimate the measurement uncertainty of ensuing diffusion parameters directly from the acquired data without the necessity to assume a noise model. These methods have been previously combined with deterministic streamline tractography algorithms to allow for the assessment of connection probabilities in the human brain. Thereby, the local noise induced disturbance in the diffusion data is accumulated additively due to the incremental progression of streamline tractography algorithms. Graph based approaches have been proposed to overcome this drawback of streamline techniques. For this reason, the bootstrap method is in the present work incorporated into a graph setup to derive a new probabilistic fiber tractography method, called BootGraph. The acquired data set is thereby converted into a weighted, undirected graph by defining a vertex in each voxel and edges between adjacent vertices. By means of the cone of uncertainty, which is derived using the wild bootstrap, a weight is thereafter assigned to each edge. Two path finding algorithms are subsequently applied to derive connection probabilities. While the first algorithm is based on the shortest path approach, the second algorithm takes all existing paths between two vertices into consideration. Tracking results are compared to an established algorithm based on the bootstrap method in combination with streamline fiber tractography and to another graph based algorithm. The BootGraph shows a very good performance in crossing situations with respect to false negatives and permits incorporating additional constraints, such as a curvature threshold. By inheriting the advantages of the bootstrap method and graph theory, the BootGraph method provides a computationally efficient and flexible probabilistic tractography setup to compute connection probability maps and virtual fiber pathways without the drawbacks of streamline tractography algorithms or the assumption of a noise distribution. Moreover, the BootGraph can be applied to common DTI data sets without further modifications and shows a high repeatability. Thus, it is very well suited for longitudinal studies and meta-studies based on DTI. Copyright © 2012 Elsevier Inc. All rights reserved.

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

PubMed

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

2016-04-01

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

An auxiliary graph based dynamic traffic grooming algorithm in spatial division multiplexing enabled elastic optical networks with multi-core fibers

NASA Astrophysics Data System (ADS)

Zhao, Yongli; Tian, Rui; Yu, Xiaosong; Zhang, Jiawei; Zhang, Jie

2017-03-01

A proper traffic grooming strategy in dynamic optical networks can improve the utilization of bandwidth resources. An auxiliary graph (AG) is designed to solve the traffic grooming problem under a dynamic traffic scenario in spatial division multiplexing enabled elastic optical networks (SDM-EON) with multi-core fibers. Five traffic grooming policies achieved by adjusting the edge weights of an AG are proposed and evaluated through simulation: maximal electrical grooming (MEG), maximal optical grooming (MOG), maximal SDM grooming (MSG), minimize virtual hops (MVH), and minimize physical hops (MPH). Numeric results show that each traffic grooming policy has its own features. Among different traffic grooming policies, an MPH policy can achieve the lowest bandwidth blocking ratio, MEG can save the most transponders, and MSG can obtain the fewest cores for each request.

Exact and approximate graph matching using random walks.

PubMed

Gori, Marco; Maggini, Marco; Sarti, Lorenzo

2005-07-01

In this paper, we propose a general framework for graph matching which is suitable for different problems of pattern recognition. The pattern representation we assume is at the same time highly structured, like for classic syntactic and structural approaches, and of subsymbolic nature with real-valued features, like for connectionist and statistic approaches. We show that random walk based models, inspired by Google's PageRank, give rise to a spectral theory that nicely enhances the graph topological features at node level. As a straightforward consequence, we derive a polynomial algorithm for the classic graph isomorphism problem, under the restriction of dealing with Markovian spectrally distinguishable graphs (MSD), a class of graphs that does not seem to be easily reducible to others proposed in the literature. The experimental results that we found on different test-beds of the TC-15 graph database show that the defined MSD class "almost always" covers the database, and that the proposed algorithm is significantly more efficient than top scoring VF algorithm on the same data. Most interestingly, the proposed approach is very well-suited for dealing with partial and approximate graph matching problems, derived for instance from image retrieval tasks. We consider the objects of the COIL-100 visual collection and provide a graph-based representation, whose node's labels contain appropriate visual features. We show that the adoption of classic bipartite graph matching algorithms offers a straightforward generalization of the algorithm given for graph isomorphism and, finally, we report very promising experimental results on the COIL-100 visual collection.

Markov Dynamics as a Zooming Lens for Multiscale Community Detection: Non Clique-Like Communities and the Field-of-View Limit

PubMed Central

Schaub, Michael T.; Delvenne, Jean-Charles; Yaliraki, Sophia N.; Barahona, Mauricio

2012-01-01

In recent years, there has been a surge of interest in community detection algorithms for complex networks. A variety of computational heuristics, some with a long history, have been proposed for the identification of communities or, alternatively, of good graph partitions. In most cases, the algorithms maximize a particular objective function, thereby finding the ‘right’ split into communities. Although a thorough comparison of algorithms is still lacking, there has been an effort to design benchmarks, i.e., random graph models with known community structure against which algorithms can be evaluated. However, popular community detection methods and benchmarks normally assume an implicit notion of community based on clique-like subgraphs, a form of community structure that is not always characteristic of real networks. Specifically, networks that emerge from geometric constraints can have natural non clique-like substructures with large effective diameters, which can be interpreted as long-range communities. In this work, we show that long-range communities escape detection by popular methods, which are blinded by a restricted ‘field-of-view’ limit, an intrinsic upper scale on the communities they can detect. The field-of-view limit means that long-range communities tend to be overpartitioned. We show how by adopting a dynamical perspective towards community detection [1], [2], in which the evolution of a Markov process on the graph is used as a zooming lens over the structure of the network at all scales, one can detect both clique- or non clique-like communities without imposing an upper scale to the detection. Consequently, the performance of algorithms on inherently low-diameter, clique-like benchmarks may not always be indicative of equally good results in real networks with local, sparser connectivity. We illustrate our ideas with constructive examples and through the analysis of real-world networks from imaging, protein structures and the power grid, where a multiscale structure of non clique-like communities is revealed. PMID:22384178

Adaptive random walks on the class of Web graphs

NASA Astrophysics Data System (ADS)

Tadić, B.

2001-09-01

We study random walk with adaptive move strategies on a class of directed graphs with variable wiring diagram. The graphs are grown from the evolution rules compatible with the dynamics of the world-wide Web [B. Tadić, Physica A 293, 273 (2001)], and are characterized by a pair of power-law distributions of out- and in-degree for each value of the parameter β, which measures the degree of rewiring in the graph. The walker adapts its move strategy according to locally available information both on out-degree of the visited node and in-degree of target node. A standard random walk, on the other hand, uses the out-degree only. We compute the distribution of connected subgraphs visited by an ensemble of walkers, the average access time and survival probability of the walks. We discuss these properties of the walk dynamics relative to the changes in the global graph structure when the control parameter β is varied. For β≥ 3, corresponding to the world-wide Web, the access time of the walk to a given level of hierarchy on the graph is much shorter compared to the standard random walk on the same graph. By reducing the amount of rewiring towards rigidity limit β↦βc≲ 0.1, corresponding to the range of naturally occurring biochemical networks, the survival probability of adaptive and standard random walk become increasingly similar. The adaptive random walk can be used as an efficient message-passing algorithm on this class of graphs for large degree of rewiring.

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

PubMed

Zhang, Qin

2015-07-01

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

Path planning for persistent surveillance applications using fixed-wing unmanned aerial vehicles

NASA Astrophysics Data System (ADS)

Keller, James F.

This thesis addresses coordinated path planning for fixed-wing Unmanned Aerial Vehicles (UAVs) engaged in persistent surveillance missions. While uniquely suited to this mission, fixed wing vehicles have maneuver constraints that can limit their performance in this role. Current technology vehicles are capable of long duration flight with a minimal acoustic footprint while carrying an array of cameras and sensors. Both military tactical and civilian safety applications can benefit from this technology. We make three main contributions: C1 A sequential path planner that generates a C 2 flight plan to persistently acquire a covering set of data over a user designated area of interest. The planner features the following innovations: • A path length abstraction that embeds kino-dynamic motion constraints to estimate feasible path length. • A Traveling Salesman-type planner to generate a covering set route based on the path length abstraction. • A smooth path generator that provides C 2 routes that satisfy user specified curvature constraints. C2 A set of algorithms to coordinate multiple UAVs, including mission commencement from arbitrary locations to the start of a coordinated mission and de-confliction of paths to avoid collisions with other vehicles and fixed obstacles. C3 A numerically robust toolbox of spline-based algorithms tailored for vehicle routing validated through flight test experiments on multiple platforms. A variety of tests and platforms are discussed. The algorithms presented are based on a technical approach with approximately equal emphasis on analysis, computation, dynamic simulation, and flight test experimentation. Our planner (C1) directly takes into account vehicle maneuverability and agility constraints that could otherwise render simple solutions infeasible. This is especially important when surveillance objectives elevate the importance of optimized paths. Researchers have developed a diverse range of solutions for persistent surveillance applications but few directly address dynamic maneuver constraints. The key feature of C1 is a two stage sequential solution that discretizes the problem so that graph search techniques can be combined with parametric polynomial curve generation. A method to abstract the kino-dynamics of the aerial platforms is then presented so that a graph search solution can be adapted for this application. An A* Traveling Salesman Problem (TSP) algorithm is developed to search the discretized space using the abstract distance metric to acquire more data or avoid obstacles. Results of the graph search are then transcribed into smooth paths based on vehicle maneuver constraints. A complete solution for a single vehicle periodic tour of the area is developed using the results of the graph search algorithm. To execute the mission, we present a simultaneous arrival algorithm (C2) to coordinate execution by multiple vehicles to satisfy data refresh requirements and to ensure there are no collisions at any of the path intersections. We present a toolbox of spline-based algorithms (C3) to streamline the development of C2 continuous paths with numerical stability. These tools are applied to an aerial persistent surveillance application to illustrate their utility. Comparisons with other parametric polynomial approaches are highlighted to underscore the benefits of the B-spline framework. Performance limits with respect to feasibility constraints are documented.

Fast generation of sparse random kernel graphs

DOE PAGES

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

Discrete geometric analysis of message passing algorithm on graphs

NASA Astrophysics Data System (ADS)

Watanabe, Yusuke

2010-04-01

We often encounter probability distributions given as unnormalized products of non-negative functions. The factorization structures are represented by hypergraphs called factor graphs. Such distributions appear in various fields, including statistics, artificial intelligence, statistical physics, error correcting codes, etc. Given such a distribution, computations of marginal distributions and the normalization constant are often required. However, they are computationally intractable because of their computational costs. One successful approximation method is Loopy Belief Propagation (LBP) algorithm. The focus of this thesis is an analysis of the LBP algorithm. If the factor graph is a tree, i.e. having no cycle, the algorithm gives the exact quantities. If the factor graph has cycles, however, the LBP algorithm does not give exact results and possibly exhibits oscillatory and non-convergent behaviors. The thematic question of this thesis is "How the behaviors of the LBP algorithm are affected by the discrete geometry of the factor graph?" The primary contribution of this thesis is the discovery of a formula that establishes the relation between the LBP, the Bethe free energy and the graph zeta function. This formula provides new techniques for analysis of the LBP algorithm, connecting properties of the graph and of the LBP and the Bethe free energy. We demonstrate applications of the techniques to several problems including (non) convexity of the Bethe free energy, the uniqueness and stability of the LBP fixed point. We also discuss the loop series initiated by Chertkov and Chernyak. The loop series is a subgraph expansion of the normalization constant, or partition function, and reflects the graph geometry. We investigate theoretical natures of the series. Moreover, we show a partial connection between the loop series and the graph zeta function.

Time reversibility from visibility graphs of nonstationary processes

NASA Astrophysics Data System (ADS)

Lacasa, Lucas; Flanagan, Ryan

2015-08-01

Visibility algorithms are a family of methods to map time series into networks, with the aim of describing the structure of time series and their underlying dynamical properties in graph-theoretical terms. Here we explore some properties of both natural and horizontal visibility graphs associated to several nonstationary processes, and we pay particular attention to their capacity to assess time irreversibility. Nonstationary signals are (infinitely) irreversible by definition (independently of whether the process is Markovian or producing entropy at a positive rate), and thus the link between entropy production and time series irreversibility has only been explored in nonequilibrium stationary states. Here we show that the visibility formalism naturally induces a new working definition of time irreversibility, which allows us to quantify several degrees of irreversibility for stationary and nonstationary series, yielding finite values that can be used to efficiently assess the presence of memory and off-equilibrium dynamics in nonstationary processes without the need to differentiate or detrend them. We provide rigorous results complemented by extensive numerical simulations on several classes of stochastic processes.

Effect of wearable sensor dynamics on physical activity estimates: A comparison between SCI vs. healthy individuals.

PubMed

Jayaraman, C; Mummidisetty, C K; Jayaraman, A

2016-08-01

Accuracy of physical activity estimates predicted by activity monitoring technologies may be affected by device location, analysis algorithms, type of technology (i.e. wearable/stickable) and population demographics (disability) being studied. Consequently, the main purpose of this investigation was to study such sensor dynamics (i.e. effect of device location, type and population demographics on energy expenditure estimates) of two commercial activity monitors. It was hypothesized that device location, population studied (disability), choice of proprietary algorithm and type of technology used will significantly impact the accuracy of the predicted physical activity metrics. 10 healthy controls and eight individuals with spinal cord injury (SCI) performed structured activities in a laboratory environment. All participants wore, (i) three ActiGraph-G3TX's one each on their wrist, waist & ankle, (ii) a stickable activity monitor (Metria-IH1) on their upper-arm and (3) a Cosmed-K4B 2 metabolic unit, while performing sedentary (lying), low intensity (walk 50 steps at self-speed) and vigorous activity (a 6 minute walk test). To validate the hypothesis, the energy expenditures (EE) predicted by ActiGraph-GT3X and Metria-IH1 were benchmarked with estimated EE per Cosmed K4B 2 metabolic unit. To verify the step count accuracy predicted by ActiGraph-GT3X's and Metria-IH1, the manually calculated step count during the low intensity activity were compared to estimates from both devices. Results suggest that Metria-IH1 out-performed ActiGraph-GT3X in estimating EE during sedentary activity in both groups. The device location and population demographics, significantly affected the accuracy of predicted estimates. In conclusion, selecting activity monitor locations, analysis algorithm and choice of technology plays based on the movement threshold of population being studied can pave a better way for reliable healthcare decisions and data analytics in population with SCI.

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

PubMed

He, Tiantian; Chan, Keith C C

2018-05-01

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

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

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

2015-01-16

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

Approximate Computing Techniques for Iterative Graph Algorithms

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

Panyala, Ajay R.; Subasi, Omer; Halappanavar, Mahantesh

Approximate computing enables processing of large-scale graphs by trading off quality for performance. Approximate computing techniques have become critical not only due to the emergence of parallel architectures but also the availability of large scale datasets enabling data-driven discovery. Using two prototypical graph algorithms, PageRank and community detection, we present several approximate computing heuristics to scale the performance with minimal loss of accuracy. We present several heuristics including loop perforation, data caching, incomplete graph coloring and synchronization, and evaluate their efficiency. We demonstrate performance improvements of up to 83% for PageRank and up to 450x for community detection, with lowmore » impact of accuracy for both the algorithms. We expect the proposed approximate techniques will enable scalable graph analytics on data of importance to several applications in science and their subsequent adoption to scale similar graph algorithms.« less

Efficient enumeration of monocyclic chemical graphs with given path frequencies

PubMed Central

2014-01-01

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

Sampling from complex networks using distributed learning automata

NASA Astrophysics Data System (ADS)

Rezvanian, Alireza; Rahmati, Mohammad; Meybodi, Mohammad Reza

2014-02-01

A complex network provides a framework for modeling many real-world phenomena in the form of a network. In general, a complex network is considered as a graph of real world phenomena such as biological networks, ecological networks, technological networks, information networks and particularly social networks. Recently, major studies are reported for the characterization of social networks due to a growing trend in analysis of online social networks as dynamic complex large-scale graphs. Due to the large scale and limited access of real networks, the network model is characterized using an appropriate part of a network by sampling approaches. In this paper, a new sampling algorithm based on distributed learning automata has been proposed for sampling from complex networks. In the proposed algorithm, a set of distributed learning automata cooperate with each other in order to take appropriate samples from the given network. To investigate the performance of the proposed algorithm, several simulation experiments are conducted on well-known complex networks. Experimental results are compared with several sampling methods in terms of different measures. The experimental results demonstrate the superiority of the proposed algorithm over the others.

Learning molecular energies using localized graph kernels.

PubMed

Ferré, Grégoire; Haut, Terry; Barros, Kipton

2017-03-21

Recent machine learning methods make it possible to model potential energy of atomic configurations with chemical-level accuracy (as calculated from ab initio calculations) and at speeds suitable for molecular dynamics simulation. Best performance is achieved when the known physical constraints are encoded in the machine learning models. For example, the atomic energy is invariant under global translations and rotations; it is also invariant to permutations of same-species atoms. Although simple to state, these symmetries are complicated to encode into machine learning algorithms. In this paper, we present a machine learning approach based on graph theory that naturally incorporates translation, rotation, and permutation symmetries. Specifically, we use a random walk graph kernel to measure the similarity of two adjacency matrices, each of which represents a local atomic environment. This Graph Approximated Energy (GRAPE) approach is flexible and admits many possible extensions. We benchmark a simple version of GRAPE by predicting atomization energies on a standard dataset of organic molecules.

Learning molecular energies using localized graph kernels

NASA Astrophysics Data System (ADS)

Ferré, Grégoire; Haut, Terry; Barros, Kipton

2017-03-01

Recent machine learning methods make it possible to model potential energy of atomic configurations with chemical-level accuracy (as calculated from ab initio calculations) and at speeds suitable for molecular dynamics simulation. Best performance is achieved when the known physical constraints are encoded in the machine learning models. For example, the atomic energy is invariant under global translations and rotations; it is also invariant to permutations of same-species atoms. Although simple to state, these symmetries are complicated to encode into machine learning algorithms. In this paper, we present a machine learning approach based on graph theory that naturally incorporates translation, rotation, and permutation symmetries. Specifically, we use a random walk graph kernel to measure the similarity of two adjacency matrices, each of which represents a local atomic environment. This Graph Approximated Energy (GRAPE) approach is flexible and admits many possible extensions. We benchmark a simple version of GRAPE by predicting atomization energies on a standard dataset of organic molecules.

BFL: a node and edge betweenness based fast layout algorithm for large scale networks

PubMed Central

Hashimoto, Tatsunori B; Nagasaki, Masao; Kojima, Kaname; Miyano, Satoru

2009-01-01

Background Network visualization would serve as a useful first step for analysis. However, current graph layout algorithms for biological pathways are insensitive to biologically important information, e.g. subcellular localization, biological node and graph attributes, or/and not available for large scale networks, e.g. more than 10000 elements. Results To overcome these problems, we propose the use of a biologically important graph metric, betweenness, a measure of network flow. This metric is highly correlated with many biological phenomena such as lethality and clusters. We devise a new fast parallel algorithm calculating betweenness to minimize the preprocessing cost. Using this metric, we also invent a node and edge betweenness based fast layout algorithm (BFL). BFL places the high-betweenness nodes to optimal positions and allows the low-betweenness nodes to reach suboptimal positions. Furthermore, BFL reduces the runtime by combining a sequential insertion algorim with betweenness. For a graph with n nodes, this approach reduces the expected runtime of the algorithm to O(n2) when considering edge crossings, and to O(n log n) when considering only density and edge lengths. Conclusion Our BFL algorithm is compared against fast graph layout algorithms and approaches requiring intensive optimizations. For gene networks, we show that our algorithm is faster than all layout algorithms tested while providing readability on par with intensive optimization algorithms. We achieve a 1.4 second runtime for a graph with 4000 nodes and 12000 edges on a standard desktop computer. PMID:19146673

Auction dynamics: A volume constrained MBO scheme

NASA Astrophysics Data System (ADS)

Jacobs, Matt; Merkurjev, Ekaterina; Esedoǧlu, Selim

2018-02-01

We show how auction algorithms, originally developed for the assignment problem, can be utilized in Merriman, Bence, and Osher's threshold dynamics scheme to simulate multi-phase motion by mean curvature in the presence of equality and inequality volume constraints on the individual phases. The resulting algorithms are highly efficient and robust, and can be used in simulations ranging from minimal partition problems in Euclidean space to semi-supervised machine learning via clustering on graphs. In the case of the latter application, numerous experimental results on benchmark machine learning datasets show that our approach exceeds the performance of current state-of-the-art methods, while requiring a fraction of the computation time.

A Scheduling Algorithm for Cloud Computing System Based on the Driver of Dynamic Essential Path.

PubMed

Xie, Zhiqiang; Shao, Xia; Xin, Yu

2016-01-01

To solve the problem of task scheduling in the cloud computing system, this paper proposes a scheduling algorithm for cloud computing based on the driver of dynamic essential path (DDEP). This algorithm applies a predecessor-task layer priority strategy to solve the problem of constraint relations among task nodes. The strategy assigns different priority values to every task node based on the scheduling order of task node as affected by the constraint relations among task nodes, and the task node list is generated by the different priority value. To address the scheduling order problem in which task nodes have the same priority value, the dynamic essential long path strategy is proposed. This strategy computes the dynamic essential path of the pre-scheduling task nodes based on the actual computation cost and communication cost of task node in the scheduling process. The task node that has the longest dynamic essential path is scheduled first as the completion time of task graph is indirectly influenced by the finishing time of task nodes in the longest dynamic essential path. Finally, we demonstrate the proposed algorithm via simulation experiments using Matlab tools. The experimental results indicate that the proposed algorithm can effectively reduce the task Makespan in most cases and meet a high quality performance objective.

A Scheduling Algorithm for Cloud Computing System Based on the Driver of Dynamic Essential Path

PubMed Central

Xie, Zhiqiang; Shao, Xia; Xin, Yu

2016-01-01

To solve the problem of task scheduling in the cloud computing system, this paper proposes a scheduling algorithm for cloud computing based on the driver of dynamic essential path (DDEP). This algorithm applies a predecessor-task layer priority strategy to solve the problem of constraint relations among task nodes. The strategy assigns different priority values to every task node based on the scheduling order of task node as affected by the constraint relations among task nodes, and the task node list is generated by the different priority value. To address the scheduling order problem in which task nodes have the same priority value, the dynamic essential long path strategy is proposed. This strategy computes the dynamic essential path of the pre-scheduling task nodes based on the actual computation cost and communication cost of task node in the scheduling process. The task node that has the longest dynamic essential path is scheduled first as the completion time of task graph is indirectly influenced by the finishing time of task nodes in the longest dynamic essential path. Finally, we demonstrate the proposed algorithm via simulation experiments using Matlab tools. The experimental results indicate that the proposed algorithm can effectively reduce the task Makespan in most cases and meet a high quality performance objective. PMID:27490901

Causal discovery in the geosciences-Using synthetic data to learn how to interpret results

NASA Astrophysics Data System (ADS)

Ebert-Uphoff, Imme; Deng, Yi

2017-02-01

Causal discovery algorithms based on probabilistic graphical models have recently emerged in geoscience applications for the identification and visualization of dynamical processes. The key idea is to learn the structure of a graphical model from observed spatio-temporal data, thus finding pathways of interactions in the observed physical system. Studying those pathways allows geoscientists to learn subtle details about the underlying dynamical mechanisms governing our planet. Initial studies using this approach on real-world atmospheric data have shown great potential for scientific discovery. However, in these initial studies no ground truth was available, so that the resulting graphs have been evaluated only by whether a domain expert thinks they seemed physically plausible. The lack of ground truth is a typical problem when using causal discovery in the geosciences. Furthermore, while most of the connections found by this method match domain knowledge, we encountered one type of connection for which no explanation was found. To address both of these issues we developed a simulation framework that generates synthetic data of typical atmospheric processes (advection and diffusion). Applying the causal discovery algorithm to the synthetic data allowed us (1) to develop a better understanding of how these physical processes appear in the resulting connectivity graphs, and thus how to better interpret such connectivity graphs when obtained from real-world data; (2) to solve the mystery of the previously unexplained connections.

Study of Double-Weighted Graph Model and Optimal Path Planning for Tourist Scenic Area Oriented Intelligent Tour Guide

NASA Astrophysics Data System (ADS)

Shi, Y.; Long, Y.; Wi, X. L.

2014-04-01

When tourists visiting multiple tourist scenic spots, the travel line is usually the most effective road network according to the actual tour process, and maybe the travel line is different from planned travel line. For in the field of navigation, a proposed travel line is normally generated automatically by path planning algorithm, considering the scenic spots' positions and road networks. But when a scenic spot have a certain area and have multiple entrances or exits, the traditional described mechanism of single point coordinates is difficult to reflect these own structural features. In order to solve this problem, this paper focuses on the influence on the process of path planning caused by scenic spots' own structural features such as multiple entrances or exits, and then proposes a doubleweighted Graph Model, for the weight of both vertexes and edges of proposed Model can be selected dynamically. And then discusses the model building method, and the optimal path planning algorithm based on Dijkstra algorithm and Prim algorithm. Experimental results show that the optimal planned travel line derived from the proposed model and algorithm is more reasonable, and the travelling order and distance would be further optimized.

Exact sampling of graphs with prescribed degree correlations

NASA Astrophysics Data System (ADS)

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

2015-08-01

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

Optimal perturbations for nonlinear systems using graph-based optimal transport

NASA Astrophysics Data System (ADS)

Grover, Piyush; Elamvazhuthi, Karthik

2018-06-01

We formulate and solve a class of finite-time transport and mixing problems in the set-oriented framework. The aim is to obtain optimal discrete-time perturbations in nonlinear dynamical systems to transport a specified initial measure on the phase space to a final measure in finite time. The measure is propagated under system dynamics in between the perturbations via the associated transfer operator. Each perturbation is described by a deterministic map in the measure space that implements a version of Monge-Kantorovich optimal transport with quadratic cost. Hence, the optimal solution minimizes a sum of quadratic costs on phase space transport due to the perturbations applied at specified times. The action of the transport map is approximated by a continuous pseudo-time flow on a graph, resulting in a tractable convex optimization problem. This problem is solved via state-of-the-art solvers to global optimality. We apply this algorithm to a problem of transport between measures supported on two disjoint almost-invariant sets in a chaotic fluid system, and to a finite-time optimal mixing problem by choosing the final measure to be uniform. In both cases, the optimal perturbations are found to exploit the phase space structures, such as lobe dynamics, leading to efficient global transport. As the time-horizon of the problem is increased, the optimal perturbations become increasingly localized. Hence, by combining the transfer operator approach with ideas from the theory of optimal mass transportation, we obtain a discrete-time graph-based algorithm for optimal transport and mixing in nonlinear systems.

Optimal trajectories for an aerospace plane. Part 2: Data, tables, and graphs

NASA Technical Reports Server (NTRS)

Miele, Angelo; Lee, W. Y.; Wu, G. D.

1990-01-01

Data, tables, and graphs relative to the optimal trajectories for an aerospace plane are presented. A single-stage-to-orbit (SSTO) configuration is considered, and the transition from low supersonic speeds to orbital speeds is studied for a single aerodynamic model (GHAME) and three engine models. Four optimization problems are solved using the sequential gradient-restoration algorithm for optimal control problems: (1) minimization of the weight of fuel consumed; (2) minimization of the peak dynamic pressure; (3) minimization of the peak heating rate; and (4) minimization of the peak tangential acceleration. The above optimization studies are carried out for different combinations of constraints, specifically: initial path inclination that is either free or given; dynamic pressure that is either free or bounded; and tangential acceleration that is either free or bounded.

Using graph approach for managing connectivity in integrative landscape modelling

NASA Astrophysics Data System (ADS)

Rabotin, Michael; Fabre, Jean-Christophe; Libres, Aline; Lagacherie, Philippe; Crevoisier, David; Moussa, Roger

2013-04-01

In cultivated landscapes, a lot of landscape elements such as field boundaries, ditches or banks strongly impact water flows, mass and energy fluxes. At the watershed scale, these impacts are strongly conditionned by the connectivity of these landscape elements. An accurate representation of these elements and of their complex spatial arrangements is therefore of great importance for modelling and predicting these impacts.We developped in the framework of the OpenFLUID platform (Software Environment for Modelling Fluxes in Landscapes) a digital landscape representation that takes into account the spatial variabilities and connectivities of diverse landscape elements through the application of the graph theory concepts. The proposed landscape representation consider spatial units connected together to represent the flux exchanges or any other information exchanges. Each spatial unit of the landscape is represented as a node of a graph and relations between units as graph connections. The connections are of two types - parent-child connection and up/downstream connection - which allows OpenFLUID to handle hierarchical graphs. Connections can also carry informations and graph evolution during simulation is possible (connections or elements modifications). This graph approach allows a better genericity on landscape representation, a management of complex connections and facilitate development of new landscape representation algorithms. Graph management is fully operational in OpenFLUID for developers or modelers ; and several graph tools are available such as graph traversal algorithms or graph displays. Graph representation can be managed i) manually by the user (for example in simple catchments) through XML-based files in easily editable and readable format or ii) by using methods of the OpenFLUID-landr library which is an OpenFLUID library relying on common open-source spatial libraries (ogr vector, geos topologic vector and gdal raster libraries). OpenFLUID-landr library has been developed in order i) to be used with no GIS expert skills needed (common gis formats can be read and simplified spatial management is provided), ii) to easily develop adapted rules of landscape discretization and graph creation to follow spatialized model requirements and iii) to allow model developers to manage dynamic and complex spatial topology. Graph management in OpenFLUID are shown with i) examples of hydrological modelizations on complex farmed landscapes and ii) the new implementation of Geo-MHYDAS tool based on the OpenFLUID-landr library, which allows to discretize a landscape and create graph structure for the MHYDAS model requirements.

A Novel Graph Constructor for Semisupervised Discriminant Analysis: Combined Low-Rank and k-Nearest Neighbor Graph

PubMed Central

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

Dynamic Visualization of Co-expression in Systems Genetics Data

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

New, Joshua Ryan; Huang, Jian; Chesler, Elissa J

2008-01-01

Biologists hope to address grand scientific challenges by exploring the abundance of data made available through modern microarray technology and other high-throughput techniques. The impact of this data, however, is limited unless researchers can effectively assimilate such complex information and integrate it into their daily research; interactive visualization tools are called for to support the effort. Specifically, typical studies of gene co-expression require novel visualization tools that enable the dynamic formulation and fine-tuning of hypotheses to aid the process of evaluating sensitivity of key parameters. These tools should allow biologists to develop an intuitive understanding of the structure of biologicalmore » networks and discover genes which reside in critical positions in networks and pathways. By using a graph as a universal data representation of correlation in gene expression data, our novel visualization tool employs several techniques that when used in an integrated manner provide innovative analytical capabilities. Our tool for interacting with gene co-expression data integrates techniques such as: graph layout, qualitative subgraph extraction through a novel 2D user interface, quantitative subgraph extraction using graph-theoretic algorithms or by querying an optimized b-tree, dynamic level-of-detail graph abstraction, and template-based fuzzy classification using neural networks. We demonstrate our system using a real-world workflow from a large-scale, systems genetics study of mammalian gene co-expression.« less

Action Recommendation for Cyber Resilience

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

Choudhury, Sutanay; Rodriguez, Luke R.; Curtis, Darren S.

2015-09-01

This paper presents an unifying graph-based model for representing the infrastructure, behavior and missions of an enterprise. We describe how the model can be used to achieve resiliency against a wide class of failures and attacks. We introduce an algorithm for recommending resilience establishing actions based on dynamic updates to the models. Without loss of generality, we show the effectiveness of the algorithm for preserving latency based quality of service (QoS). Our models and the recommendation algorithms are implemented in a software framework that we seek to release as an open source framework for simulating resilient cyber systems.

Collaborative mining and transfer learning for relational data

NASA Astrophysics Data System (ADS)

Levchuk, Georgiy; Eslami, Mohammed

2015-06-01

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

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

NASA Astrophysics Data System (ADS)

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

2012-06-01

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

Thread Graphs, Linear Rank-Width and Their Algorithmic Applications

NASA Astrophysics Data System (ADS)

Ganian, Robert

The introduction of tree-width by Robertson and Seymour [7] was a breakthrough in the design of graph algorithms. A lot of research since then has focused on obtaining a width measure which would be more general and still allowed efficient algorithms for a wide range of NP-hard problems on graphs of bounded width. To this end, Oum and Seymour have proposed rank-width, which allows the solution of many such hard problems on a less restricted graph classes (see e.g. [3,4]). But what about problems which are NP-hard even on graphs of bounded tree-width or even on trees? The parameter used most often for these exceptionally hard problems is path-width, however it is extremely restrictive - for example the graphs of path-width 1 are exactly paths.

A multispin algorithm for the Kob-Andersen stochastic dynamics on regular lattices

NASA Astrophysics Data System (ADS)

Boccagna, Roberto

2017-07-01

The aim of the paper is to propose an algorithm based on the Multispin Coding technique for the Kob-Andersen glassy dynamics. We first give motivations to speed up the numerical simulation in the context of spin glass models [M. Mezard, G. Parisi, M. Virasoro, Spin Glass Theory and Beyond (World Scientific, Singapore, 1987)]; after defining the Markovian dynamics as in [W. Kob, H.C. Andersen, Phys. Rev. E 48, 4364 (1993)] as well as the related interesting observables, we extend it to the more general framework of random regular graphs, listing at the same time some known analytical results [C. Toninelli, G. Biroli, D.S. Fisher, J. Stat. Phys. 120, 167 (2005)]. The purpose of this work is a dual one; firstly, we describe how bitwise operators can be used to build up the algorithm by carefully exploiting the way data are stored on a computer. Since it was first introduced [M. Creutz, L. Jacobs, C. Rebbi, Phys. Rev. D 20, 1915 (1979); C. Rebbi, R.H. Swendsen, Phys. Rev. D 21, 4094 (1980)], this technique has been widely used to perform Monte Carlo simulations for Ising and Potts spin systems; however, it can be successfully adapted to more complex systems in which microscopic parameters may assume boolean values. Secondly, we introduce a random graph in which a characteristic parameter allows to tune the possible transition point. A consistent part is devoted to listing the numerical results obtained by running numerical simulations.

Optimal Learning Paths in Information Networks

PubMed Central

Rodi, G. C.; Loreto, V.; Servedio, V. D. P.; Tria, F.

2015-01-01

Each sphere of knowledge and information could be depicted as a complex mesh of correlated items. By properly exploiting these connections, innovative and more efficient navigation strategies could be defined, possibly leading to a faster learning process and an enduring retention of information. In this work we investigate how the topological structure embedding the items to be learned can affect the efficiency of the learning dynamics. To this end we introduce a general class of algorithms that simulate the exploration of knowledge/information networks standing on well-established findings on educational scheduling, namely the spacing and lag effects. While constructing their learning schedules, individuals move along connections, periodically revisiting some concepts, and sometimes jumping on very distant ones. In order to investigate the effect of networked information structures on the proposed learning dynamics we focused both on synthetic and real-world graphs such as subsections of Wikipedia and word-association graphs. We highlight the existence of optimal topological structures for the simulated learning dynamics whose efficiency is affected by the balance between hubs and the least connected items. Interestingly, the real-world graphs we considered lead naturally to almost optimal learning performances. PMID:26030508

Bounded-Degree Approximations of Stochastic Networks

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

Quinn, Christopher J.; Pinar, Ali; Kiyavash, Negar

2017-06-01

We propose algorithms to approximate directed information graphs. Directed information graphs are probabilistic graphical models that depict causal dependencies between stochastic processes in a network. The proposed algorithms identify optimal and near-optimal approximations in terms of Kullback-Leibler divergence. The user-chosen sparsity trades off the quality of the approximation against visual conciseness and computational tractability. One class of approximations contains graphs with speci ed in-degrees. Another class additionally requires that the graph is connected. For both classes, we propose algorithms to identify the optimal approximations and also near-optimal approximations, using a novel relaxation of submodularity. We also propose algorithms to identifymore » the r-best approximations among these classes, enabling robust decision making.« less

Automated Root Tracking with "Root System Analyzer"

NASA Astrophysics Data System (ADS)

Schnepf, Andrea; Jin, Meina; Ockert, Charlotte; Bol, Roland; Leitner, Daniel

2015-04-01

Crucial factors for plant development are water and nutrient availability in soils. Thus, root architecture is a main aspect of plant productivity and needs to be accurately considered when describing root processes. Images of root architecture contain a huge amount of information, and image analysis helps to recover parameters describing certain root architectural and morphological traits. The majority of imaging systems for root systems are designed for two-dimensional images, such as RootReader2, GiA Roots, SmartRoot, EZ-Rhizo, and Growscreen, but most of them are semi-automated and involve mouse-clicks in each root by the user. "Root System Analyzer" is a new, fully automated approach for recovering root architectural parameters from two-dimensional images of root systems. Individual roots can still be corrected manually in a user interface if required. The algorithm starts with a sequence of segmented two-dimensional images showing the dynamic development of a root system. For each image, morphological operators are used for skeletonization. Based on this, a graph representation of the root system is created. A dynamic root architecture model helps to determine which edges of the graph belong to an individual root. The algorithm elongates each root at the root tip and simulates growth confined within the already existing graph representation. The increment of root elongation is calculated assuming constant growth. For each root, the algorithm finds all possible paths and elongates the root in the direction of the optimal path. In this way, each edge of the graph is assigned to one or more coherent roots. Image sequences of root systems are handled in such a way that the previous image is used as a starting point for the current image. The algorithm is implemented in a set of Matlab m-files. Output of Root System Analyzer is a data structure that includes for each root an identification number, the branching order, the time of emergence, the parent identification number, the distance between branching point to the parent root base, the root length, the root radius and the nodes that belong to each individual root path. This information is relevant for the analysis of dynamic root system development as well as the parameterisation of root architecture models. Here, we show results of Root System Analyzer applied to analyse the root systems of wheat plants grown in rhizotrons. Different treatments with respect to soil moisture and apatite concentrations were used to test the effects of those conditions on root system development. Photographs of the root systems were taken at high spatial and temporal resolution and root systems are automatically tracked.

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

PubMed

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

2004-01-01

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

A Coherent VLSI Environment

DTIC Science & Technology

1987-03-31

processors . The symmetry-breaking algorithms give efficient ways to convert probabilistic algorithms to deterministic algorithms. Some of the...techniques have been applied to construct several efficient linear- processor algorithms for graph problems, including an O(lg* n)-time algorithm for (A + 1...On n-node graphs, the algorithm works in O(log 2 n) time using only n processors , in contrast to the previous best algorithm which used about n3

Automatic classification of protein structures relying on similarities between alignments

PubMed Central

2012-01-01

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

A Security Assessment Mechanism for Software-Defined Networking-Based Mobile Networks.

PubMed

Luo, Shibo; Dong, Mianxiong; Ota, Kaoru; Wu, Jun; Li, Jianhua

2015-12-17

Software-Defined Networking-based Mobile Networks (SDN-MNs) are considered the future of 5G mobile network architecture. With the evolving cyber-attack threat, security assessments need to be performed in the network management. Due to the distinctive features of SDN-MNs, such as their dynamic nature and complexity, traditional network security assessment methodologies cannot be applied directly to SDN-MNs, and a novel security assessment methodology is needed. In this paper, an effective security assessment mechanism based on attack graphs and an Analytic Hierarchy Process (AHP) is proposed for SDN-MNs. Firstly, this paper discusses the security assessment problem of SDN-MNs and proposes a methodology using attack graphs and AHP. Secondly, to address the diversity and complexity of SDN-MNs, a novel attack graph definition and attack graph generation algorithm are proposed. In order to quantify security levels, the Node Minimal Effort (NME) is defined to quantify attack cost and derive system security levels based on NME. Thirdly, to calculate the NME of an attack graph that takes the dynamic factors of SDN-MN into consideration, we use AHP integrated with the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) as the methodology. Finally, we offer a case study to validate the proposed methodology. The case study and evaluation show the advantages of the proposed security assessment mechanism.

A Security Assessment Mechanism for Software-Defined Networking-Based Mobile Networks

PubMed Central

Luo, Shibo; Dong, Mianxiong; Ota, Kaoru; Wu, Jun; Li, Jianhua

2015-01-01

Software-Defined Networking-based Mobile Networks (SDN-MNs) are considered the future of 5G mobile network architecture. With the evolving cyber-attack threat, security assessments need to be performed in the network management. Due to the distinctive features of SDN-MNs, such as their dynamic nature and complexity, traditional network security assessment methodologies cannot be applied directly to SDN-MNs, and a novel security assessment methodology is needed. In this paper, an effective security assessment mechanism based on attack graphs and an Analytic Hierarchy Process (AHP) is proposed for SDN-MNs. Firstly, this paper discusses the security assessment problem of SDN-MNs and proposes a methodology using attack graphs and AHP. Secondly, to address the diversity and complexity of SDN-MNs, a novel attack graph definition and attack graph generation algorithm are proposed. In order to quantify security levels, the Node Minimal Effort (NME) is defined to quantify attack cost and derive system security levels based on NME. Thirdly, to calculate the NME of an attack graph that takes the dynamic factors of SDN-MN into consideration, we use AHP integrated with the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) as the methodology. Finally, we offer a case study to validate the proposed methodology. The case study and evaluation show the advantages of the proposed security assessment mechanism. PMID:26694409

One-dimensional swarm algorithm packaging

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Dynamic Domains in Data Production Planning

NASA Technical Reports Server (NTRS)

Golden, Keith; Pang, Wanlin

2005-01-01

This paper discusses a planner-based approach to automating data production tasks, such as producing fire forecasts from satellite imagery and weather station data. Since the set of available data products is large, dynamic and mostly unknown, planning techniques developed for closed worlds are unsuitable. We discuss a number of techniques we have developed to cope with data production domains, including a novel constraint propagation algorithm based on planning graphs and a constraint-based approach to interleaved planning, sensing and execution.

Application-Specific Graph Sampling for Frequent Subgraph Mining and Community Detection

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

Purohit, Sumit; Choudhury, Sutanay; Holder, Lawrence B.

Graph mining is an important data analysis methodology, but struggles as the input graph size increases. The scalability and usability challenges posed by such large graphs make it imperative to sample the input graph and reduce its size. The critical challenge in sampling is to identify the appropriate algorithm to insure the resulting analysis does not suffer heavily from the data reduction. Predicting the expected performance degradation for a given graph and sampling algorithm is also useful. In this paper, we present different sampling approaches for graph mining applications such as Frequent Subgrpah Mining (FSM), and Community Detection (CD). Wemore » explore graph metrics such as PageRank, Triangles, and Diversity to sample a graph and conclude that for heterogeneous graphs Triangles and Diversity perform better than degree based metrics. We also present two new sampling variations for targeted graph mining applications. We present empirical results to show that knowledge of the target application, along with input graph properties can be used to select the best sampling algorithm. We also conclude that performance degradation is an abrupt, rather than gradual phenomena, as the sample size decreases. We present the empirical results to show that the performance degradation follows a logistic function.« less

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

PubMed Central

Elmetwaly, Shereef; Schlick, Tamar

2014-01-01

Graph representations have been widely used to analyze and design various economic, social, military, political, and biological networks. In systems biology, networks of cells and organs are useful for understanding disease and medical treatments and, in structural biology, structures of molecules can be described, including RNA structures. In our RNA-As-Graphs (RAG) framework, we represent RNA structures as tree graphs by translating unpaired regions into vertices and helices into edges. Here we explore the modularity of RNA structures by applying graph partitioning known in graph theory to divide an RNA graph into subgraphs. To our knowledge, this is the first application of graph partitioning to biology, and the results suggest a systematic approach for modular design in general. The graph partitioning algorithms utilize mathematical properties of the Laplacian eigenvector (µ2) corresponding to the second eigenvalues (λ2) associated with the topology matrix defining the graph: λ2 describes the overall topology, and the sum of µ2′s components is zero. The three types of algorithms, termed median, sign, and gap cuts, divide a graph by determining nodes of cut by median, zero, and largest gap of µ2′s components, respectively. We apply these algorithms to 45 graphs corresponding to all solved RNA structures up through 11 vertices (∼220 nucleotides). While we observe that the median cut divides a graph into two similar-sized subgraphs, the sign and gap cuts partition a graph into two topologically-distinct subgraphs. We find that the gap cut produces the best biologically-relevant partitioning for RNA because it divides RNAs at less stable connections while maintaining junctions intact. The iterative gap cuts suggest basic modules and assembly protocols to design large RNA structures. Our graph substructuring thus suggests a systematic approach to explore the modularity of biological networks. In our applications to RNA structures, subgraphs also suggest design strategies for novel RNA motifs. PMID:25188578

Graph Mining Meets the Semantic Web

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

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

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

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.

Exact analytical solution of irreversible binary dynamics on networks.

PubMed

Laurence, Edward; Young, Jean-Gabriel; Melnik, Sergey; Dubé, Louis J

2018-03-01

In binary cascade dynamics, the nodes of a graph are in one of two possible states (inactive, active), and nodes in the inactive state make an irreversible transition to the active state, as soon as their precursors satisfy a predetermined condition. We introduce a set of recursive equations to compute the probability of reaching any final state, given an initial state, and a specification of the transition probability function of each node. Because the naive recursive approach for solving these equations takes factorial time in the number of nodes, we also introduce an accelerated algorithm, built around a breath-first search procedure. This algorithm solves the equations as efficiently as possible in exponential time.

Exact analytical solution of irreversible binary dynamics on networks

NASA Astrophysics Data System (ADS)

Laurence, Edward; Young, Jean-Gabriel; Melnik, Sergey; Dubé, Louis J.

2018-03-01

In binary cascade dynamics, the nodes of a graph are in one of two possible states (inactive, active), and nodes in the inactive state make an irreversible transition to the active state, as soon as their precursors satisfy a predetermined condition. We introduce a set of recursive equations to compute the probability of reaching any final state, given an initial state, and a specification of the transition probability function of each node. Because the naive recursive approach for solving these equations takes factorial time in the number of nodes, we also introduce an accelerated algorithm, built around a breath-first search procedure. This algorithm solves the equations as efficiently as possible in exponential time.

Fuzzy Edge Connectivity of Graphical Fuzzy State Space Model in Multi-connected System

NASA Astrophysics Data System (ADS)

Harish, Noor Ainy; Ismail, Razidah; Ahmad, Tahir

2010-11-01

Structured networks of interacting components illustrate complex structure in a direct or intuitive way. Graph theory provides a mathematical modeling for studying interconnection among elements in natural and man-made systems. On the other hand, directed graph is useful to define and interpret the interconnection structure underlying the dynamics of the interacting subsystem. Fuzzy theory provides important tools in dealing various aspects of complexity, imprecision and fuzziness of the network structure of a multi-connected system. Initial development for systems of Fuzzy State Space Model (FSSM) and a fuzzy algorithm approach were introduced with the purpose of solving the inverse problems in multivariable system. In this paper, fuzzy algorithm is adapted in order to determine the fuzzy edge connectivity between subsystems, in particular interconnected system of Graphical Representation of FSSM. This new approach will simplify the schematic diagram of interconnection of subsystems in a multi-connected system.

Multifractal analysis of charged particle distributions using horizontal visibility graph and sandbox algorithm

NASA Astrophysics Data System (ADS)

Mali, P.; Mukhopadhyay, A.; Manna, S. K.; Haldar, P. K.; Singh, G.

2017-03-01

Horizontal visibility graphs (HVGs) and the sandbox (SB) algorithm usually applied for multifractal characterization of complex network systems that are converted from time series measurements, are used to characterize the fluctuations in pseudorapidity densities of singly charged particles produced in high-energy nucleus-nucleus collisions. Besides obtaining the degree distribution associated with event-wise pseudorapidity distributions, the common set of observables, typical of any multifractality measurement, are studied in 16O-Ag/Br and 32S-Ag/Br interactions, each at an incident laboratory energy of 200 GeV/nucleon. For a better understanding, we systematically compare the experiment with a Monte Carlo model simulation based on the Ultra-relativistic Quantum Molecular Dynamics (UrQMD). Our results suggest that the HVG-SB technique is an efficient tool that can characterize multifractality in multiparticle emission data, and in some cases, it is even superior to other methods more commonly used in this regard.

A comparison of graph- and kernel-based -omics data integration algorithms for classifying complex traits.

PubMed

Yan, Kang K; Zhao, Hongyu; Pang, Herbert

2017-12-06

High-throughput sequencing data are widely collected and analyzed in the study of complex diseases in quest of improving human health. Well-studied algorithms mostly deal with single data source, and cannot fully utilize the potential of these multi-omics data sources. In order to provide a holistic understanding of human health and diseases, it is necessary to integrate multiple data sources. Several algorithms have been proposed so far, however, a comprehensive comparison of data integration algorithms for classification of binary traits is currently lacking. In this paper, we focus on two common classes of integration algorithms, graph-based that depict relationships with subjects denoted by nodes and relationships denoted by edges, and kernel-based that can generate a classifier in feature space. Our paper provides a comprehensive comparison of their performance in terms of various measurements of classification accuracy and computation time. Seven different integration algorithms, including graph-based semi-supervised learning, graph sharpening integration, composite association network, Bayesian network, semi-definite programming-support vector machine (SDP-SVM), relevance vector machine (RVM) and Ada-boost relevance vector machine are compared and evaluated with hypertension and two cancer data sets in our study. In general, kernel-based algorithms create more complex models and require longer computation time, but they tend to perform better than graph-based algorithms. The performance of graph-based algorithms has the advantage of being faster computationally. The empirical results demonstrate that composite association network, relevance vector machine, and Ada-boost RVM are the better performers. We provide recommendations on how to choose an appropriate algorithm for integrating data from multiple sources.

Families of Graph Algorithms: SSSP Case Study

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

Kanewala Appuhamilage, Thejaka Amila Jay; Zalewski, Marcin J.; Lumsdaine, Andrew

2017-08-28

Single-Source Shortest Paths (SSSP) is a well-studied graph problem. Examples of SSSP algorithms include the original Dijkstra’s algorithm and the parallel Δ-stepping and KLA-SSSP algorithms. In this paper, we use a novel Abstract Graph Machine (AGM) model to show that all these algorithms share a common logic and differ from one another by the order in which they perform work. We use the AGM model to thoroughly analyze the family of algorithms that arises from the common logic. We start with the basic algorithm without any ordering (Chaotic), and then we derive the existing and new algorithms by methodically exploringmore » semantic and spatial ordering of work. Our experimental results show that new derived algorithms show better performance than the existing distributed memory parallel algorithms, especially at higher scales.« less

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.

Connectivity algorithm with depth first search (DFS) on simple graphs

NASA Astrophysics Data System (ADS)

Riansanti, O.; Ihsan, M.; Suhaimi, D.

2018-01-01

This paper discusses an algorithm to detect connectivity of a simple graph using Depth First Search (DFS). The DFS implementation in this paper differs than other research, that is, on counting the number of visited vertices. The algorithm obtains s from the number of vertices and visits source vertex, following by its adjacent vertices until the last vertex adjacent to the previous source vertex. Any simple graph is connected if s equals 0 and disconnected if s is greater than 0. The complexity of the algorithm is O(n2).

Reproducibility of graph metrics of human brain structural networks.

PubMed

Duda, Jeffrey T; Cook, Philip A; Gee, James C

2014-01-01

Recent interest in human brain connectivity has led to the application of graph theoretical analysis to human brain structural networks, in particular white matter connectivity inferred from diffusion imaging and fiber tractography. While these methods have been used to study a variety of patient populations, there has been less examination of the reproducibility of these methods. A number of tractography algorithms exist and many of these are known to be sensitive to user-selected parameters. The methods used to derive a connectivity matrix from fiber tractography output may also influence the resulting graph metrics. Here we examine how these algorithm and parameter choices influence the reproducibility of proposed graph metrics on a publicly available test-retest dataset consisting of 21 healthy adults. The dice coefficient is used to examine topological similarity of constant density subgraphs both within and between subjects. Seven graph metrics are examined here: mean clustering coefficient, characteristic path length, largest connected component size, assortativity, global efficiency, local efficiency, and rich club coefficient. The reproducibility of these network summary measures is examined using the intraclass correlation coefficient (ICC). Graph curves are created by treating the graph metrics as functions of a parameter such as graph density. Functional data analysis techniques are used to examine differences in graph measures that result from the choice of fiber tracking algorithm. The graph metrics consistently showed good levels of reproducibility as measured with ICC, with the exception of some instability at low graph density levels. The global and local efficiency measures were the most robust to the choice of fiber tracking algorithm.

Benchmarking the D-Wave Two

NASA Astrophysics Data System (ADS)

Job, Joshua; Wang, Zhihui; Rønnow, Troels; Troyer, Matthias; Lidar, Daniel

2014-03-01

We report on experimental work benchmarking the performance of the D-Wave Two programmable annealer on its native Ising problem, and a comparison to available classical algorithms. In this talk we will focus on the comparison with an algorithm originally proposed and implemented by Alex Selby. This algorithm uses dynamic programming to repeatedly optimize over randomly selected maximal induced trees of the problem graph starting from a random initial state. If one is looking for a quantum advantage over classical algorithms, one should compare to classical algorithms which are designed and optimized to maximally take advantage of the structure of the type of problem one is using for the comparison. In that light, this classical algorithm should serve as a good gauge for any potential quantum speedup for the D-Wave Two.

A genetic graph-based approach for partitional clustering.

PubMed

Menéndez, Héctor D; Barrero, David F; Camacho, David

2014-05-01

Clustering is one of the most versatile tools for data analysis. In the recent years, clustering that seeks the continuity of data (in opposition to classical centroid-based approaches) has attracted an increasing research interest. It is a challenging problem with a remarkable practical interest. The most popular continuity clustering method is the spectral clustering (SC) algorithm, which is based on graph cut: It initially generates a similarity graph using a distance measure and then studies its graph spectrum to find the best cut. This approach is sensitive to the parameters of the metric, and a correct parameter choice is critical to the quality of the cluster. This work proposes a new algorithm, inspired by SC, that reduces the parameter dependency while maintaining the quality of the solution. The new algorithm, named genetic graph-based clustering (GGC), takes an evolutionary approach introducing a genetic algorithm (GA) to cluster the similarity graph. The experimental validation shows that GGC increases robustness of SC and has competitive performance in comparison with classical clustering methods, at least, in the synthetic and real dataset used in the experiments.

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

PubMed

Navigli, Roberto; Lapata, Mirella

2010-04-01

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

The graph neural network model.

PubMed

Scarselli, Franco; Gori, Marco; Tsoi, Ah Chung; Hagenbuchner, Markus; Monfardini, Gabriele

2009-01-01

Many underlying relationships among data in several areas of science and engineering, e.g., computer vision, molecular chemistry, molecular biology, pattern recognition, and data mining, can be represented in terms of graphs. In this paper, we propose a new neural network model, called graph neural network (GNN) model, that extends existing neural network methods for processing the data represented in graph domains. This GNN model, which can directly process most of the practically useful types of graphs, e.g., acyclic, cyclic, directed, and undirected, implements a function tau(G,n) is an element of IR(m) that maps a graph G and one of its nodes n into an m-dimensional Euclidean space. A supervised learning algorithm is derived to estimate the parameters of the proposed GNN model. The computational cost of the proposed algorithm is also considered. Some experimental results are shown to validate the proposed learning algorithm, and to demonstrate its generalization capabilities.

Learning molecular energies using localized graph kernels

DOE PAGES

Ferré, Grégoire; Haut, Terry Scot; Barros, Kipton Marcos

2017-03-21

We report that recent machine learning methods make it possible to model potential energy of atomic configurations with chemical-level accuracy (as calculated from ab initio calculations) and at speeds suitable for molecular dynamics simulation. Best performance is achieved when the known physical constraints are encoded in the machine learning models. For example, the atomic energy is invariant under global translations and rotations; it is also invariant to permutations of same-species atoms. Although simple to state, these symmetries are complicated to encode into machine learning algorithms. In this paper, we present a machine learning approach based on graph theory that naturallymore » incorporates translation, rotation, and permutation symmetries. Specifically, we use a random walk graph kernel to measure the similarity of two adjacency matrices, each of which represents a local atomic environment. This Graph Approximated Energy (GRAPE) approach is flexible and admits many possible extensions. Finally, we benchmark a simple version of GRAPE by predicting atomization energies on a standard dataset of organic molecules.« less

Learning molecular energies using localized graph kernels

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

Ferré, Grégoire; Haut, Terry Scot; Barros, Kipton Marcos

We report that recent machine learning methods make it possible to model potential energy of atomic configurations with chemical-level accuracy (as calculated from ab initio calculations) and at speeds suitable for molecular dynamics simulation. Best performance is achieved when the known physical constraints are encoded in the machine learning models. For example, the atomic energy is invariant under global translations and rotations; it is also invariant to permutations of same-species atoms. Although simple to state, these symmetries are complicated to encode into machine learning algorithms. In this paper, we present a machine learning approach based on graph theory that naturallymore » incorporates translation, rotation, and permutation symmetries. Specifically, we use a random walk graph kernel to measure the similarity of two adjacency matrices, each of which represents a local atomic environment. This Graph Approximated Energy (GRAPE) approach is flexible and admits many possible extensions. Finally, we benchmark a simple version of GRAPE by predicting atomization energies on a standard dataset of organic molecules.« less

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

PubMed

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

2008-12-08

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

Retina verification system based on biometric graph matching.

PubMed

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

2013-09-01

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

Efficient Synthesis of Graph Methods: a Dynamically Scheduled Architecture

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

Minutoli, Marco; Castellana, Vito G.; Tumeo, Antonino

RDF databases naturally map to a graph representation and employ languages, such as SPARQL, that implements queries as graph pattern matching routines. Graph methods exhibit an irregular behavior: they present unpredictable, fine-grained data accesses, and are synchronization inten- sive. Graph data structures expose large amounts of dy- namic parallelism, but are difficult to partition without gen- erating load unbalance. In this paper, we present a novel ar- chitecture to improve the synthesis of graph methods. Our design addresses the issues of these algorithms with two com- ponents: a Dynamic Task Scheduler (DTS), which reduces load unbalance and maximize resource utilization,more » and a Hi- erarchical Memory Interface controller (HMI), which pro- vides support for concurrent memory operations on multi- ported/multi-banked shared memories. We evaluate our ap- proach by generating the accelerators for a set of SPARQL queries from the Lehigh University Benchmark (LUBM). We first analyze the load unbalance of these queries, showing that execution time among tasks can differ even of order of magnitudes. We then synthesize the queries and com- pare the performance of the resulting accelerators against the current state of the art. Experimental results show that our solution provides a speedup over the serial implementa- tion close to the theoretical maximum and a speedup up to 3.45 over a baseline parallel implementation. We conclude our study by exploring the design space to achieve maximum memory channels utilization. The best design used at least three of the four memory channels for more than 90% of the execution time.« less

Output-Sensitive Construction of Reeb Graphs.

PubMed

Doraiswamy, H; Natarajan, V

2012-01-01

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

Learning graph matching.

PubMed

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

2009-06-01

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

Fat water decomposition using globally optimal surface estimation (GOOSE) algorithm.

PubMed

Cui, Chen; Wu, Xiaodong; Newell, John D; Jacob, Mathews

2015-03-01

This article focuses on developing a novel noniterative fat water decomposition algorithm more robust to fat water swaps and related ambiguities. Field map estimation is reformulated as a constrained surface estimation problem to exploit the spatial smoothness of the field, thus minimizing the ambiguities in the recovery. Specifically, the differences in the field map-induced frequency shift between adjacent voxels are constrained to be in a finite range. The discretization of the above problem yields a graph optimization scheme, where each node of the graph is only connected with few other nodes. Thanks to the low graph connectivity, the problem is solved efficiently using a noniterative graph cut algorithm. The global minimum of the constrained optimization problem is guaranteed. The performance of the algorithm is compared with that of state-of-the-art schemes. Quantitative comparisons are also made against reference data. The proposed algorithm is observed to yield more robust fat water estimates with fewer fat water swaps and better quantitative results than other state-of-the-art algorithms in a range of challenging applications. The proposed algorithm is capable of considerably reducing the swaps in challenging fat water decomposition problems. The experiments demonstrate the benefit of using explicit smoothness constraints in field map estimation and solving the problem using a globally convergent graph-cut optimization algorithm. © 2014 Wiley Periodicals, Inc.

Efficient solution for finding Hamilton cycles in undirected graphs.

PubMed

Alhalabi, Wadee; Kitanneh, Omar; Alharbi, Amira; Balfakih, Zain; Sarirete, Akila

2016-01-01

The Hamilton cycle problem is closely related to a series of famous problems and puzzles (traveling salesman problem, Icosian game) and, due to the fact that it is NP-complete, it was extensively studied with different algorithms to solve it. The most efficient algorithm is not known. In this paper, a necessary condition for an arbitrary un-directed graph to have Hamilton cycle is proposed. Based on this condition, a mathematical solution for this problem is developed and several proofs and an algorithmic approach are introduced. The algorithm is successfully implemented on many Hamiltonian and non-Hamiltonian graphs. This provides a new effective approach to solve a problem that is fundamental in graph theory and can influence the manner in which the existing applications are used and improved.

Quantum speedup of the traveling-salesman problem for bounded-degree graphs

NASA Astrophysics Data System (ADS)

Moylett, Dominic J.; Linden, Noah; Montanaro, Ashley

2017-03-01

The traveling-salesman problem is one of the most famous problems in graph theory. However, little is currently known about the extent to which quantum computers could speed up algorithms for the problem. In this paper, we prove a quadratic quantum speedup when the degree of each vertex is at most 3 by applying a quantum backtracking algorithm to a classical algorithm by Xiao and Nagamochi. We then use similar techniques to accelerate a classical algorithm for when the degree of each vertex is at most 4, before speeding up higher-degree graphs via reductions to these instances.

Linear Algebra and Sequential Importance Sampling for Network Reliability

DTIC Science & Technology

2011-12-01

first test case is an Erdős- Renyi graph with 100 vertices and 150 edges. Figure 1 depicts the relative variance of the three Algorithms: Algorithm TOP...e va ria nc e Figure 1: Relative variance of various algorithms on Erdős Renyi graph, 100 vertices 250 edges. Key: Solid = TOP-DOWN algorithm

Nonpreemptive run-time scheduling issues on a multitasked, multiprogrammed multiprocessor with dependencies, bidimensional tasks, folding and dynamic graphs

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

Miller, Allan Ray

1987-05-01

Increases in high speed hardware have mandated studies in software techniques to exploit the parallel capabilities. This thesis examines the effects a run-time scheduler has on a multiprocessor. The model consists of directed, acyclic graphs, generated from serial FORTRAN benchmark programs by the parallel compiler Parafrase. A multitasked, multiprogrammed environment is created. Dependencies are generated by the compiler. Tasks are bidimensional, i.e., they may specify both time and processor requests. Processor requests may be folded into execution time by the scheduler. The graphs may arrive at arbitrary time intervals. The general case is NP-hard, thus, a variety of heuristics aremore » examined by a simulator. Multiprogramming demonstrates a greater need for a run-time scheduler than does monoprogramming for a variety of reasons, e.g., greater stress on the processors, a larger number of independent control paths, more variety in the task parameters, etc. The dynamic critical path series of algorithms perform well. Dynamic critical volume did not add much. Unfortunately, dynamic critical path maximizes turnaround time as well as throughput. Two schedulers are presented which balance throughput and turnaround time. The first requires classification of jobs by type; the second requires selection of a ratio value which is dependent upon system parameters. 45 refs., 19 figs., 20 tabs.« less

Dynamic multicast routing scheme in WDM optical network

NASA Astrophysics Data System (ADS)

Zhu, Yonghua; Dong, Zhiling; Yao, Hong; Yang, Jianyong; Liu, Yibin

2007-11-01

During the information era, the Internet and the service of World Wide Web develop rapidly. Therefore, the wider and wider bandwidth is required with the lower and lower cost. The demand of operation turns out to be diversified. Data, images, videos and other special transmission demands share the challenge and opportunity with the service providers. Simultaneously, the electrical equipment has approached their limit. So the optical communication based on the wavelength division multiplexing (WDM) and the optical cross-connects (OXCs) shows great potentials and brilliant future to build an optical network based on the unique technical advantage and multi-wavelength characteristic. In this paper, we propose a multi-layered graph model with inter-path between layers to solve the problem of multicast routing wavelength assignment (RWA) contemporarily by employing an efficient graph theoretic formulation. And at the same time, an efficient dynamic multicast algorithm named Distributed Message Copying Multicast (DMCM) mechanism is also proposed. The multicast tree with minimum hops can be constructed dynamically according to this proposed scheme.

Mining connected global and local dense subgraphs for bigdata

NASA Astrophysics Data System (ADS)

Wu, Bo; Shen, Haiying

2016-01-01

The problem of discovering connected dense subgraphs of natural graphs is important in data analysis. Discovering dense subgraphs that do not contain denser subgraphs or are not contained in denser subgraphs (called significant dense subgraphs) is also critical for wide-ranging applications. In spite of many works on discovering dense subgraphs, there are no algorithms that can guarantee the connectivity of the returned subgraphs or discover significant dense subgraphs. Hence, in this paper, we define two subgraph discovery problems to discover connected and significant dense subgraphs, propose polynomial-time algorithms and theoretically prove their validity. We also propose an algorithm to further improve the time and space efficiency of our basic algorithm for discovering significant dense subgraphs in big data by taking advantage of the unique features of large natural graphs. In the experiments, we use massive natural graphs to evaluate our algorithms in comparison with previous algorithms. The experimental results show the effectiveness of our algorithms for the two problems and their efficiency. This work is also the first that reveals the physical significance of significant dense subgraphs in natural graphs from different domains.

Mathematical foundations of the GraphBLAS

DOE PAGES

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

2016-12-01

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

Computing Strongly Connected Components in the Streaming Model

NASA Astrophysics Data System (ADS)

Laura, Luigi; Santaroni, Federico

In this paper we present the first algorithm to compute the Strongly Connected Components of a graph in the datastream model (W-Stream), where the graph is represented by a stream of edges and we are allowed to produce intermediate output streams. The algorithm is simple, effective, and can be implemented with few lines of code: it looks at each edge in the stream, and selects the appropriate action with respect to a tree T, representing the graph connectivity seen so far. We analyze the theoretical properties of the algorithm: correctness, memory occupation (O(n logn)), per item processing time (bounded by the current height of T), and number of passes (bounded by the maximal height of T). We conclude by presenting a brief experimental evaluation of the algorithm against massive synthetic and real graphs that confirms its effectiveness: with graphs with up to 100M nodes and 4G edges, only few passes are needed, and millions of edges per second are processed.

Contact replacement for NMR resonance assignment.

PubMed

Xiong, Fei; Pandurangan, Gopal; Bailey-Kellogg, Chris

2008-07-01

Complementing its traditional role in structural studies of proteins, nuclear magnetic resonance (NMR) spectroscopy is playing an increasingly important role in functional studies. NMR dynamics experiments characterize motions involved in target recognition, ligand binding, etc., while NMR chemical shift perturbation experiments identify and localize protein-protein and protein-ligand interactions. The key bottleneck in these studies is to determine the backbone resonance assignment, which allows spectral peaks to be mapped to specific atoms. This article develops a novel approach to address that bottleneck, exploiting an available X-ray structure or homology model to assign the entire backbone from a set of relatively fast and cheap NMR experiments. We formulate contact replacement for resonance assignment as the problem of computing correspondences between a contact graph representing the structure and an NMR graph representing the data; the NMR graph is a significantly corrupted, ambiguous version of the contact graph. We first show that by combining connectivity and amino acid type information, and exploiting the random structure of the noise, one can provably determine unique correspondences in polynomial time with high probability, even in the presence of significant noise (a constant number of noisy edges per vertex). We then detail an efficient randomized algorithm and show that, over a variety of experimental and synthetic datasets, it is robust to typical levels of structural variation (1-2 AA), noise (250-600%) and missings (10-40%). Our algorithm achieves very good overall assignment accuracy, above 80% in alpha-helices, 70% in beta-sheets and 60% in loop regions. Our contact replacement algorithm is implemented in platform-independent Python code. The software can be freely obtained for academic use by request from the authors.

Path planning of decentralized multi-quadrotor based on fuzzy-cell decomposition algorithm

NASA Astrophysics Data System (ADS)

Iswanto, Wahyunggoro, Oyas; Cahyadi, Adha Imam

2017-04-01

The paper aims to present a design algorithm for multi quadrotor lanes in order to move towards the goal quickly and avoid obstacles in an area with obstacles. There are several problems in path planning including how to get to the goal position quickly and avoid static and dynamic obstacles. To overcome the problem, therefore, the paper presents fuzzy logic algorithm and fuzzy cell decomposition algorithm. Fuzzy logic algorithm is one of the artificial intelligence algorithms which can be applied to robot path planning that is able to detect static and dynamic obstacles. Cell decomposition algorithm is an algorithm of graph theory used to make a robot path map. By using the two algorithms the robot is able to get to the goal position and avoid obstacles but it takes a considerable time because they are able to find the shortest path. Therefore, this paper describes a modification of the algorithms by adding a potential field algorithm used to provide weight values on the map applied for each quadrotor by using decentralized controlled, so that the quadrotor is able to move to the goal position quickly by finding the shortest path. The simulations conducted have shown that multi-quadrotor can avoid various obstacles and find the shortest path by using the proposed algorithms.

An algorithm for automatic reduction of complex signal flow graphs

NASA Technical Reports Server (NTRS)

Young, K. R.; Hoberock, L. L.; Thompson, J. G.

1976-01-01

A computer algorithm is developed that provides efficient means to compute transmittances directly from a signal flow graph or a block diagram. Signal flow graphs are cast as directed graphs described by adjacency matrices. Nonsearch computation, designed for compilers without symbolic capability, is used to identify all arcs that are members of simple cycles for use with Mason's gain formula. The routine does not require the visual acumen of an interpreter to reduce the topology of the graph, and it is particularly useful for analyzing control systems described for computer analyses by means of interactive graphics.

Graph 500 on OpenSHMEM: Using a Practical Survey of Past Work to Motivate Novel Algorithmic Developments

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

Grossman, Max; Pritchard Jr., Howard Porter; Budimlic, Zoran

2016-12-22

Graph500 [14] is an effort to offer a standardized benchmark across large-scale distributed platforms which captures the behavior of common communicationbound graph algorithms. Graph500 differs from other large-scale benchmarking efforts (such as HPL [6] or HPGMG [7]) primarily in the irregularity of its computation and data access patterns. The core computational kernel of Graph500 is a breadth-first search (BFS) implemented on an undirected graph. The output of Graph500 is a spanning tree of the input graph, usually represented by a predecessor mapping for every node in the graph. The Graph500 benchmark defines several pre-defined input sizes for implementers to testmore » against. This report summarizes investigation into implementing the Graph500 benchmark on OpenSHMEM, and focuses on first building a strong and practical understanding of the strengths and limitations of past work before proposing and developing novel extensions.« less

Dynamics on Networks of Manifolds

NASA Astrophysics Data System (ADS)

DeVille, Lee; Lerman, Eugene

2015-03-01

We propose a precise definition of a continuous time dynamical system made up of interacting open subsystems. The interconnections of subsystems are coded by directed graphs. We prove that the appropriate maps of graphs called graph fibrations give rise to maps of dynamical systems. Consequently surjective graph fibrations give rise to invariant subsystems and injective graph fibrations give rise to projections of dynamical systems.

Semantic Drift in Espresso-style Bootstrapping: Graph-theoretic Analysis and Evaluation in Word Sense Disambiguation

NASA Astrophysics Data System (ADS)

Komachi, Mamoru; Kudo, Taku; Shimbo, Masashi; Matsumoto, Yuji

Bootstrapping has a tendency, called semantic drift, to select instances unrelated to the seed instances as the iteration proceeds. We demonstrate the semantic drift of Espresso-style bootstrapping has the same root as the topic drift of Kleinberg's HITS, using a simplified graph-based reformulation of bootstrapping. We confirm that two graph-based algorithms, the von Neumann kernels and the regularized Laplacian, can reduce the effect of semantic drift in the task of word sense disambiguation (WSD) on Senseval-3 English Lexical Sample Task. Proposed algorithms achieve superior performance to Espresso and previous graph-based WSD methods, even though the proposed algorithms have less parameters and are easy to calibrate.

Semantic super networks: A case analysis of Wikipedia papers

NASA Astrophysics Data System (ADS)

Kostyuchenko, Evgeny; Lebedeva, Taisiya; Goritov, Alexander

2017-11-01

An algorithm for constructing super-large semantic networks has been developed in current work. Algorithm was tested using the "Cosmos" category of the Internet encyclopedia "Wikipedia" as an example. During the implementation, a parser for the syntax analysis of Wikipedia pages was developed. A graph based on list of articles and categories was formed. On the basis of the obtained graph analysis, algorithms for finding domains of high connectivity in a graph were proposed and tested. Algorithms for constructing a domain based on the number of links and the number of articles in the current subject area is considered. The shortcomings of these algorithms are shown and explained, an algorithm is developed on their joint use. The possibility of applying a combined algorithm for obtaining the final domain is shown. The problem of instability of the received domain was discovered when starting an algorithm from two neighboring vertices related to the domain.

Evolutionary dynamics on any population structure

NASA Astrophysics Data System (ADS)

Allen, Benjamin; Lippner, Gabor; Chen, Yu-Ting; Fotouhi, Babak; Momeni, Naghmeh; Yau, Shing-Tung; Nowak, Martin A.

2017-03-01

Evolution occurs in populations of reproducing individuals. The structure of a population can affect which traits evolve. Understanding evolutionary game dynamics in structured populations remains difficult. Mathematical results are known for special structures in which all individuals have the same number of neighbours. The general case, in which the number of neighbours can vary, has remained open. For arbitrary selection intensity, the problem is in a computational complexity class that suggests there is no efficient algorithm. Whether a simple solution for weak selection exists has remained unanswered. Here we provide a solution for weak selection that applies to any graph or network. Our method relies on calculating the coalescence times of random walks. We evaluate large numbers of diverse population structures for their propensity to favour cooperation. We study how small changes in population structure—graph surgery—affect evolutionary outcomes. We find that cooperation flourishes most in societies that are based on strong pairwise ties.

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

PubMed Central

2013-01-01

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

Stochastic generation of complex crystal structures combining group and graph theory with application to carbon

NASA Astrophysics Data System (ADS)

Shi, Xizhi; He, Chaoyu; Pickard, Chris J.; Tang, Chao; Zhong, Jianxin

2018-01-01

A method is introduced to stochastically generate crystal structures with defined structural characteristics. Reasonable quotient graphs for symmetric crystals are constructed using a random strategy combined with space group and graph theory. Our algorithm enables the search for large-size and complex crystal structures with a specified connectivity, such as threefold sp2 carbons, fourfold sp3 carbons, as well as mixed sp2-sp3 carbons. To demonstrate the method, we randomly construct initial structures adhering to space groups from 75 to 230 and a range of lattice constants, and we identify 281 new sp3 carbon crystals. First-principles optimization of these structures show that most of them are dynamically and mechanically stable and are energetically comparable to those previously proposed. Some of the new structures can be considered as candidates to explain the experimental cold compression of graphite.

An intelligent allocation algorithm for parallel processing

NASA Technical Reports Server (NTRS)

Carroll, Chester C.; Homaifar, Abdollah; Ananthram, Kishan G.

1988-01-01

The problem of allocating nodes of a program graph to processors in a parallel processing architecture is considered. The algorithm is based on critical path analysis, some allocation heuristics, and the execution granularity of nodes in a program graph. These factors, and the structure of interprocessor communication network, influence the allocation. To achieve realistic estimations of the executive durations of allocations, the algorithm considers the fact that nodes in a program graph have to communicate through varying numbers of tokens. Coarse and fine granularities have been implemented, with interprocessor token-communication duration, varying from zero up to values comparable to the execution durations of individual nodes. The effect on allocation of communication network structures is demonstrated by performing allocations for crossbar (non-blocking) and star (blocking) networks. The algorithm assumes the availability of as many processors as it needs for the optimal allocation of any program graph. Hence, the focus of allocation has been on varying token-communication durations rather than varying the number of processors. The algorithm always utilizes as many processors as necessary for the optimal allocation of any program graph, depending upon granularity and characteristics of the interprocessor communication network.

Efficient mapping algorithms for scheduling robot inverse dynamics computation on a multiprocessor system

NASA Technical Reports Server (NTRS)

Lee, C. S. G.; Chen, C. L.

1989-01-01

Two efficient mapping algorithms for scheduling the robot inverse dynamics computation consisting of m computational modules with precedence relationship to be executed on a multiprocessor system consisting of p identical homogeneous processors with processor and communication costs to achieve minimum computation time are presented. An objective function is defined in terms of the sum of the processor finishing time and the interprocessor communication time. The minimax optimization is performed on the objective function to obtain the best mapping. This mapping problem can be formulated as a combination of the graph partitioning and the scheduling problems; both have been known to be NP-complete. Thus, to speed up the searching for a solution, two heuristic algorithms were proposed to obtain fast but suboptimal mapping solutions. The first algorithm utilizes the level and the communication intensity of the task modules to construct an ordered priority list of ready modules and the module assignment is performed by a weighted bipartite matching algorithm. For a near-optimal mapping solution, the problem can be solved by the heuristic algorithm with simulated annealing. These proposed optimization algorithms can solve various large-scale problems within a reasonable time. Computer simulations were performed to evaluate and verify the performance and the validity of the proposed mapping algorithms. Finally, experiments for computing the inverse dynamics of a six-jointed PUMA-like manipulator based on the Newton-Euler dynamic equations were implemented on an NCUBE/ten hypercube computer to verify the proposed mapping algorithms. Computer simulation and experimental results are compared and discussed.

GoFFish: A Sub-Graph Centric Framework for Large-Scale Graph Analytics1

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

Simmhan, Yogesh; Kumbhare, Alok; Wickramaarachchi, Charith

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 themore » 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.« less

Scalable Triadic Analysis of Large-Scale Graphs: Multi-Core vs. Multi-Processor vs. Multi-Threaded Shared Memory Architectures

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

Chin, George; Marquez, Andres; Choudhury, Sutanay

2012-09-01

Triadic analysis encompasses a useful set of graph mining methods that is centered on the concept of a triad, which is a subgraph of three nodes and the configuration of directed edges across the nodes. Such methods are often applied in the social sciences as well as many other diverse fields. Triadic methods commonly operate on a triad census that counts the number of triads of every possible edge configuration in a graph. Like other graph algorithms, triadic census algorithms do not scale well when graphs reach tens of millions to billions of nodes. To enable the triadic analysis ofmore » large-scale graphs, we developed and optimized a triad census algorithm to efficiently execute on shared memory architectures. We will retrace the development and evolution of a parallel triad census algorithm. Over the course of several versions, we continually adapted the code’s data structures and program logic to expose more opportunities to exploit parallelism on shared memory that would translate into improved computational performance. We will recall the critical steps and modifications that occurred during code development and optimization. Furthermore, we will compare the performances of triad census algorithm versions on three specific systems: Cray XMT, HP Superdome, and AMD multi-core NUMA machine. These three systems have shared memory architectures but with markedly different hardware capabilities to manage parallelism.« less

Geographic Gossip: Efficient Averaging for Sensor Networks

NASA Astrophysics Data System (ADS)

Dimakis, Alexandros D. G.; Sarwate, Anand D.; Wainwright, Martin J.

Gossip algorithms for distributed computation are attractive due to their simplicity, distributed nature, and robustness in noisy and uncertain environments. However, using standard gossip algorithms can lead to a significant waste in energy by repeatedly recirculating redundant information. For realistic sensor network model topologies like grids and random geometric graphs, the inefficiency of gossip schemes is related to the slow mixing times of random walks on the communication graph. We propose and analyze an alternative gossiping scheme that exploits geographic information. By utilizing geographic routing combined with a simple resampling method, we demonstrate substantial gains over previously proposed gossip protocols. For regular graphs such as the ring or grid, our algorithm improves standard gossip by factors of $n$ and $\\sqrt{n}$ respectively. For the more challenging case of random geometric graphs, our algorithm computes the true average to accuracy $\\epsilon$ using $O(\\frac{n^{1.5}}{\\sqrt{\\log n}} \\log \\epsilon^{-1})$ radio transmissions, which yields a $\\sqrt{\\frac{n}{\\log n}}$ factor improvement over standard gossip algorithms. We illustrate these theoretical results with experimental comparisons between our algorithm and standard methods as applied to various classes of random fields.

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

PubMed

Yan, Fei; Christmas, William; Kittler, Josef

2008-10-01

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

Connectivity: Performance Portable Algorithms for graph connectivity v. 0.1

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

Slota, George; Rajamanickam, Sivasankaran; Madduri, Kamesh

Graphs occur in several places in real world from road networks, social networks and scientific simulations. Connectivity is a graph analysis software to graph connectivity in modern architectures like multicore CPUs, Xeon Phi and GPUs.

Highly Asynchronous VisitOr Queue Graph Toolkit

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

Pearce, R.

2012-10-01

HAVOQGT is a C++ framework that can be used to create highly parallel graph traversal algorithms. The framework stores the graph and algorithmic data structures on external memory that is typically mapped to high performance locally attached NAND FLASH arrays. The framework supports a vertex-centered visitor programming model. The frameworkd has been used to implement breadth first search, connected components, and single source shortest path.

Combinatorial Algorithms to Enable Computational Science and Engineering: Work from the CSCAPES Institute

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

Boman, Erik G.; Catalyurek, Umit V.; Chevalier, Cedric

2015-01-16

This final progress report summarizes the work accomplished at the Combinatorial Scientific Computing and Petascale Simulations Institute. We developed Zoltan, a parallel mesh partitioning library that made use of accurate hypergraph models to provide load balancing in mesh-based computations. We developed several graph coloring algorithms for computing Jacobian and Hessian matrices and organized them into a software package called ColPack. We developed parallel algorithms for graph coloring and graph matching problems, and also designed multi-scale graph algorithms. Three PhD students graduated, six more are continuing their PhD studies, and four postdoctoral scholars were advised. Six of these students and Fellowsmore » have joined DOE Labs (Sandia, Berkeley), as staff scientists or as postdoctoral scientists. We also organized the SIAM Workshop on Combinatorial Scientific Computing (CSC) in 2007, 2009, and 2011 to continue to foster the CSC community.« less

GraDit: graph-based data repair algorithm for multiple data edits rule violations

NASA Astrophysics Data System (ADS)

Ode Zuhayeni Madjida, Wa; Gusti Bagus Baskara Nugraha, I.

2018-03-01

Constraint-based data cleaning captures data violation to a set of rule called data quality rules. The rules consist of integrity constraint and data edits. Structurally, they are similar, where the rule contain left hand side and right hand side. Previous research proposed a data repair algorithm for integrity constraint violation. The algorithm uses undirected hypergraph as rule violation representation. Nevertheless, this algorithm can not be applied for data edits because of different rule characteristics. This study proposed GraDit, a repair algorithm for data edits rule. First, we use bipartite-directed hypergraph as model representation of overall defined rules. These representation is used for getting interaction between violation rules and clean rules. On the other hand, we proposed undirected graph as violation representation. Our experimental study showed that algorithm with undirected graph as violation representation model gave better data quality than algorithm with undirected hypergraph as representation model.

A Hybrid Shared-Memory Parallel Max-Tree Algorithm for Extreme Dynamic-Range Images.

PubMed

Moschini, Ugo; Meijster, Arnold; Wilkinson, Michael H F

2018-03-01

Max-trees, or component trees, are graph structures that represent the connected components of an image in a hierarchical way. Nowadays, many application fields rely on images with high-dynamic range or floating point values. Efficient sequential algorithms exist to build trees and compute attributes for images of any bit depth. However, we show that the current parallel algorithms perform poorly already with integers at bit depths higher than 16 bits per pixel. We propose a parallel method combining the two worlds of flooding and merging max-tree algorithms. First, a pilot max-tree of a quantized version of the image is built in parallel using a flooding method. Later, this structure is used in a parallel leaf-to-root approach to compute efficiently the final max-tree and to drive the merging of the sub-trees computed by the threads. We present an analysis of the performance both on simulated and actual 2D images and 3D volumes. Execution times are about better than the fastest sequential algorithm and speed-up goes up to on 64 threads.

Solving the Secondary Structure Matching Problem in Cryo-EM De Novo Modeling Using a Constrained K-Shortest Path Graph Algorithm.

PubMed

Al Nasr, Kamal; Ranjan, Desh; Zubair, Mohammad; Chen, Lin; He, Jing

2014-01-01

Electron cryomicroscopy is becoming a major experimental technique in solving the structures of large molecular assemblies. More and more three-dimensional images have been obtained at the medium resolutions between 5 and 10 Å. At this resolution range, major α-helices can be detected as cylindrical sticks and β-sheets can be detected as plain-like regions. A critical question in de novo modeling from cryo-EM images is to determine the match between the detected secondary structures from the image and those on the protein sequence. We formulate this matching problem into a constrained graph problem and present an O(Δ(2)N(2)2(N)) algorithm to this NP-Hard problem. The algorithm incorporates the dynamic programming approach into a constrained K-shortest path algorithm. Our method, DP-TOSS, has been tested using α-proteins with maximum 33 helices and α-β proteins up to five helices and 12 β-strands. The correct match was ranked within the top 35 for 19 of the 20 α-proteins and all nine α-β proteins tested. The results demonstrate that DP-TOSS improves accuracy, time and memory space in deriving the topologies of the secondary structure elements for proteins with a large number of secondary structures and a complex skeleton.

Reducing False Positives in Runtime Analysis of Deadlocks

NASA Technical Reports Server (NTRS)

Bensalem, Saddek; Havelund, Klaus; Clancy, Daniel (Technical Monitor)

2002-01-01

This paper presents an improvement of a standard algorithm for detecting dead-lock potentials in multi-threaded programs, in that it reduces the number of false positives. The standard algorithm works as follows. The multi-threaded program under observation is executed, while lock and unlock events are observed. A graph of locks is built, with edges between locks symbolizing locking orders. Any cycle in the graph signifies a potential for a deadlock. The typical standard example is the group of dining philosophers sharing forks. The algorithm is interesting because it can catch deadlock potentials even though no deadlocks occur in the examined trace, and at the same time it scales very well in contrast t o more formal approaches to deadlock detection. The algorithm, however, can yield false positives (as well as false negatives). The extension of the algorithm described in this paper reduces the amount of false positives for three particular cases: when a gate lock protects a cycle, when a single thread introduces a cycle, and when the code segments in different threads that cause the cycle can actually not execute in parallel. The paper formalizes a theory for dynamic deadlock detection and compares it to model checking and static analysis techniques. It furthermore describes an implementation for analyzing Java programs and its application to two case studies: a planetary rover and a space craft altitude control system.

A sampling algorithm for segregation analysis

PubMed Central

Tier, Bruce; Henshall, John

2001-01-01

Methods for detecting Quantitative Trait Loci (QTL) without markers have generally used iterative peeling algorithms for determining genotype probabilities. These algorithms have considerable shortcomings in complex pedigrees. A Monte Carlo Markov chain (MCMC) method which samples the pedigree of the whole population jointly is described. Simultaneous sampling of the pedigree was achieved by sampling descent graphs using the Metropolis-Hastings algorithm. A descent graph describes the inheritance state of each allele and provides pedigrees guaranteed to be consistent with Mendelian sampling. Sampling descent graphs overcomes most, if not all, of the limitations incurred by iterative peeling algorithms. The algorithm was able to find the QTL in most of the simulated populations. However, when the QTL was not modeled or found then its effect was ascribed to the polygenic component. No QTL were detected when they were not simulated. PMID:11742631

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…

Computing Maximum Cardinality Matchings in Parallel on Bipartite Graphs via Tree-Grafting

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

Azad, Ariful; Buluc, Aydn; Pothen, Alex

It is difficult to obtain high performance when computing matchings on parallel processors because matching algorithms explicitly or implicitly search for paths in the graph, and when these paths become long, there is little concurrency. In spite of this limitation, we present a new algorithm and its shared-memory parallelization that achieves good performance and scalability in computing maximum cardinality matchings in bipartite graphs. This algorithm searches for augmenting paths via specialized breadth-first searches (BFS) from multiple source vertices, hence creating more parallelism than single source algorithms. Algorithms that employ multiple-source searches cannot discard a search tree once no augmenting pathmore » is discovered from the tree, unlike algorithms that rely on single-source searches. We describe a novel tree-grafting method that eliminates most of the redundant edge traversals resulting from this property of multiple-source searches. We also employ the recent direction-optimizing BFS algorithm as a subroutine to discover augmenting paths faster. Our algorithm compares favorably with the current best algorithms in terms of the number of edges traversed, the average augmenting path length, and the number of iterations. Here, we provide a proof of correctness for our algorithm. Our NUMA-aware implementation is scalable to 80 threads of an Intel multiprocessor and to 240 threads on an Intel Knights Corner coprocessor. On average, our parallel algorithm runs an order of magnitude faster than the fastest algorithms available. The performance improvement is more significant on graphs with small matching number.« less

Computing Maximum Cardinality Matchings in Parallel on Bipartite Graphs via Tree-Grafting

DOE PAGES

Azad, Ariful; Buluc, Aydn; Pothen, Alex

2016-03-24

It is difficult to obtain high performance when computing matchings on parallel processors because matching algorithms explicitly or implicitly search for paths in the graph, and when these paths become long, there is little concurrency. In spite of this limitation, we present a new algorithm and its shared-memory parallelization that achieves good performance and scalability in computing maximum cardinality matchings in bipartite graphs. This algorithm searches for augmenting paths via specialized breadth-first searches (BFS) from multiple source vertices, hence creating more parallelism than single source algorithms. Algorithms that employ multiple-source searches cannot discard a search tree once no augmenting pathmore » is discovered from the tree, unlike algorithms that rely on single-source searches. We describe a novel tree-grafting method that eliminates most of the redundant edge traversals resulting from this property of multiple-source searches. We also employ the recent direction-optimizing BFS algorithm as a subroutine to discover augmenting paths faster. Our algorithm compares favorably with the current best algorithms in terms of the number of edges traversed, the average augmenting path length, and the number of iterations. Here, we provide a proof of correctness for our algorithm. Our NUMA-aware implementation is scalable to 80 threads of an Intel multiprocessor and to 240 threads on an Intel Knights Corner coprocessor. On average, our parallel algorithm runs an order of magnitude faster than the fastest algorithms available. The performance improvement is more significant on graphs with small matching number.« less

Frog: Asynchronous Graph Processing on GPU with Hybrid Coloring Model

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

Shi, Xuanhua; Luo, Xuan; Liang, Junling

GPUs have been increasingly used to accelerate graph processing for complicated computational problems regarding graph theory. Many parallel graph algorithms adopt the asynchronous computing model to accelerate the iterative convergence. Unfortunately, the consistent asynchronous computing requires locking or atomic operations, leading to significant penalties/overheads when implemented on GPUs. As such, coloring algorithm is adopted to separate the vertices with potential updating conflicts, guaranteeing the consistency/correctness of the parallel processing. Common coloring algorithms, however, may suffer from low parallelism because of a large number of colors generally required for processing a large-scale graph with billions of vertices. We propose a light-weightmore » asynchronous processing framework called Frog with a preprocessing/hybrid coloring model. The fundamental idea is based on Pareto principle (or 80-20 rule) about coloring algorithms as we observed through masses of realworld graph coloring cases. We find that a majority of vertices (about 80%) are colored with only a few colors, such that they can be read and updated in a very high degree of parallelism without violating the sequential consistency. Accordingly, our solution separates the processing of the vertices based on the distribution of colors. In this work, we mainly answer three questions: (1) how to partition the vertices in a sparse graph with maximized parallelism, (2) how to process large-scale graphs that cannot fit into GPU memory, and (3) how to reduce the overhead of data transfers on PCIe while processing each partition. We conduct experiments on real-world data (Amazon, DBLP, YouTube, RoadNet-CA, WikiTalk and Twitter) to evaluate our approach and make comparisons with well-known non-preprocessed (such as Totem, Medusa, MapGraph and Gunrock) and preprocessed (Cusha) approaches, by testing four classical algorithms (BFS, PageRank, SSSP and CC). On all the tested applications and datasets, Frog is able to significantly outperform existing GPU-based graph processing systems except Gunrock and MapGraph. MapGraph gets better performance than Frog when running BFS on RoadNet-CA. The comparison between Gunrock and Frog is inconclusive. Frog can outperform Gunrock more than 1.04X when running PageRank and SSSP, while the advantage of Frog is not obvious when running BFS and CC on some datasets especially for RoadNet-CA.« less

A novel line segment detection algorithm based on graph search

NASA Astrophysics Data System (ADS)

Zhao, Hong-dan; Liu, Guo-ying; Song, Xu

2018-02-01

To overcome the problem of extracting line segment from an image, a method of line segment detection was proposed based on the graph search algorithm. After obtaining the edge detection result of the image, the candidate straight line segments are obtained in four directions. For the candidate straight line segments, their adjacency relationships are depicted by a graph model, based on which the depth-first search algorithm is employed to determine how many adjacent line segments need to be merged. Finally we use the least squares method to fit the detected straight lines. The comparative experimental results verify that the proposed algorithm has achieved better results than the line segment detector (LSD).

Searching social networks for subgraph patterns

NASA Astrophysics Data System (ADS)

Ogaard, Kirk; Kase, Sue; Roy, Heather; Nagi, Rakesh; Sambhoos, Kedar; Sudit, Moises

2013-06-01

Software tools for Social Network Analysis (SNA) are being developed which support various types of analysis of social networks extracted from social media websites (e.g., Twitter). Once extracted and stored in a database such social networks are amenable to analysis by SNA software. This data analysis often involves searching for occurrences of various subgraph patterns (i.e., graphical representations of entities and relationships). The authors have developed the Graph Matching Toolkit (GMT) which provides an intuitive Graphical User Interface (GUI) for a heuristic graph matching algorithm called the Truncated Search Tree (TruST) algorithm. GMT is a visual interface for graph matching algorithms processing large social networks. GMT enables an analyst to draw a subgraph pattern by using a mouse to select categories and labels for nodes and links from drop-down menus. GMT then executes the TruST algorithm to find the top five occurrences of the subgraph pattern within the social network stored in the database. GMT was tested using a simulated counter-insurgency dataset consisting of cellular phone communications within a populated area of operations in Iraq. The results indicated GMT (when executing the TruST graph matching algorithm) is a time-efficient approach to searching large social networks. GMT's visual interface to a graph matching algorithm enables intelligence analysts to quickly analyze and summarize the large amounts of data necessary to produce actionable intelligence.

Statistically significant relational data mining :

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

Berry, Jonathan W.; Leung, Vitus Joseph; Phillips, Cynthia Ann

This report summarizes the work performed under the project (3z(BStatitically significant relational data mining.(3y (BThe goal of the project was to add more statistical rigor to the fairly ad hoc area of data mining on graphs. Our goal was to develop better algorithms and better ways to evaluate algorithm quality. We concetrated on algorithms for community detection, approximate pattern matching, and graph similarity measures. Approximate pattern matching involves finding an instance of a relatively small pattern, expressed with tolerance, in a large graph of data observed with uncertainty. This report gathers the abstracts and references for the eight refereed publicationsmore » that have appeared as part of this work. We then archive three pieces of research that have not yet been published. The first is theoretical and experimental evidence that a popular statistical measure for comparison of community assignments favors over-resolved communities over approximations to a ground truth. The second are statistically motivated methods for measuring the quality of an approximate match of a small pattern in a large graph. The third is a new probabilistic random graph model. Statisticians favor these models for graph analysis. The new local structure graph model overcomes some of the issues with popular models such as exponential random graph models and latent variable models.« less

Graphical Language for Data Processing

NASA Technical Reports Server (NTRS)

Alphonso, Keith

2011-01-01

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

Cooperatively surrounding control for multiple Euler-Lagrange systems subjected to uncertain dynamics and input constraints

NASA Astrophysics Data System (ADS)

Chen, Liang-Ming; Lv, Yue-Yong; Li, Chuan-Jiang; Ma, Guang-Fu

2016-12-01

In this paper, we investigate cooperatively surrounding control (CSC) of multi-agent systems modeled by Euler-Lagrange (EL) equations under a directed graph. With the consideration of the uncertain dynamics in an EL system, a backstepping CSC algorithm combined with neural-networks is proposed first such that the agents can move cooperatively to surround the stationary target. Then, a command filtered backstepping CSC algorithm is further proposed to deal with the constraints on control input and the absence of neighbors’ velocity information. Numerical examples of eight satellites surrounding one space target illustrate the effectiveness of the theoretical results. Project supported by the National Basic Research Program of China (Grant No. 2012CB720000) and the National Natural Science Foundation of China (Grant Nos. 61304005 and 61403103).

Survey of gene splicing algorithms based on reads.

PubMed

Si, Xiuhua; Wang, Qian; Zhang, Lei; Wu, Ruo; Ma, Jiquan

2017-11-02

Gene splicing is the process of assembling a large number of unordered short sequence fragments to the original genome sequence as accurately as possible. Several popular splicing algorithms based on reads are reviewed in this article, including reference genome algorithms and de novo splicing algorithms (Greedy-extension, Overlap-Layout-Consensus graph, De Bruijn graph). We also discuss a new splicing method based on the MapReduce strategy and Hadoop. By comparing these algorithms, some conclusions are drawn and some suggestions on gene splicing research are made.

Streaming data analytics via message passing with application to graph algorithms

DOE PAGES

Plimpton, Steven J.; Shead, Tim

2014-05-06

The need to process streaming data, which arrives continuously at high-volume in real-time, arises in a variety of contexts including data produced by experiments, collections of environmental or network sensors, and running simulations. Streaming data can also be formulated as queries or transactions which operate on a large dynamic data store, e.g. a distributed database. We describe a lightweight, portable framework named PHISH which enables a set of independent processes to compute on a stream of data in a distributed-memory parallel manner. Datums are routed between processes in patterns defined by the application. PHISH can run on top of eithermore » message-passing via MPI or sockets via ZMQ. The former means streaming computations can be run on any parallel machine which supports MPI; the latter allows them to run on a heterogeneous, geographically dispersed network of machines. We illustrate how PHISH can support streaming MapReduce operations, and describe streaming versions of three algorithms for large, sparse graph analytics: triangle enumeration, subgraph isomorphism matching, and connected component finding. Lastly, we also provide benchmark timings for MPI versus socket performance of several kernel operations useful in streaming algorithms.« less

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

Wylie, Brian Neil; Moreland, Kenneth D.

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 graphsmore » 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.« less

The combination of direct and paired link graphs can boost repetitive genome assembly

PubMed Central

Shi, Wenyu; Ji, Peifeng

2017-01-01

Abstract Currently, most paired link based scaffolding algorithms intrinsically mask the sequences between two linked contigs and bypass their direct link information embedded in the original de Bruijn assembly graph. Such disadvantage substantially complicates the scaffolding process and leads to the inability of resolving repetitive contig assembly. Here we present a novel algorithm, inGAP-sf, for effectively generating high-quality and continuous scaffolds. inGAP-sf achieves this by using a new strategy based on the combination of direct link and paired link graphs, in which direct link is used to increase graph connectivity and to decrease graph complexity and paired link is employed to supervise the traversing process on the direct link graph. Such advantage greatly facilitates the assembly of short-repeat enriched regions. Moreover, a new comprehensive decision model is developed to eliminate the noise routes accompanying with the introduced direct link. Through extensive evaluations on both simulated and real datasets, we demonstrated that inGAP-sf outperforms most of the genome scaffolding algorithms by generating more accurate and continuous assembly, especially for short repetitive regions. PMID:27924003

Cooperative Search by UAV Teams: A Model Predictive Approach Using Dynamic Graphs

DTIC Science & Technology

2011-10-01

decentralized processing and control architecture. SLAMEM asset models accurately represent the Unicorn UAV platforms and other standard military platforms in...IMPLEMENTATION The CGBMPS algorithm has been successfully field-tested using both Unicorn [27] and Raven [20] UAV platforms. This section describes...the hardware-software system setup and implementation used for testing with Unicorns , Toyon’s UAV test platform. We also present some results from the

Multimodal Logistics Network Design over Planning Horizon through a Hybrid Meta-Heuristic Approach

NASA Astrophysics Data System (ADS)

Shimizu, Yoshiaki; Yamazaki, Yoshihiro; Wada, Takeshi

Logistics has been acknowledged increasingly as a key issue of supply chain management to improve business efficiency under global competition and diversified customer demands. This study aims at improving a quality of strategic decision making associated with dynamic natures in logistics network optimization. Especially, noticing an importance to concern with a multimodal logistics under multiterms, we have extended a previous approach termed hybrid tabu search (HybTS). The attempt intends to deploy a strategic planning more concretely so that the strategic plan can link to an operational decision making. The idea refers to a smart extension of the HybTS to solve a dynamic mixed integer programming problem. It is a two-level iterative method composed of a sophisticated tabu search for the location problem at the upper level and a graph algorithm for the route selection at the lower level. To keep efficiency while coping with the resulting extremely large-scale problem, we invented a systematic procedure to transform the original linear program at the lower-level into a minimum cost flow problem solvable by the graph algorithm. Through numerical experiments, we verified the proposed method outperformed the commercial software. The results indicate the proposed approach can make the conventional strategic decision much more practical and is promising for real world applications.

Typical performance of approximation algorithms for NP-hard problems

NASA Astrophysics Data System (ADS)

Takabe, Satoshi; Hukushima, Koji

2016-11-01

Typical performance of approximation algorithms is studied for randomized minimum vertex cover problems. A wide class of random graph ensembles characterized by an arbitrary degree distribution is discussed with the presentation of a theoretical framework. Herein, three approximation algorithms are examined: linear-programming relaxation, loopy-belief propagation, and the leaf-removal algorithm. The former two algorithms are analyzed using a statistical-mechanical technique, whereas the average-case analysis of the last one is conducted using the generating function method. These algorithms have a threshold in the typical performance with increasing average degree of the random graph, below which they find true optimal solutions with high probability. Our study reveals that there exist only three cases, determined by the order of the typical performance thresholds. In addition, we provide some conditions for classification of the graph ensembles and demonstrate explicitly some examples for the difference in thresholds.

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

PubMed

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

2016-09-01

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

Convergence of the Graph Allen-Cahn Scheme

NASA Astrophysics Data System (ADS)

Luo, Xiyang; Bertozzi, Andrea L.

2017-05-01

The graph Laplacian and the graph cut problem are closely related to Markov random fields, and have many applications in clustering and image segmentation. The diffuse interface model is widely used for modeling in material science, and can also be used as a proxy to total variation minimization. In Bertozzi and Flenner (Multiscale Model Simul 10(3):1090-1118, 2012), an algorithm was developed to generalize the diffuse interface model to graphs to solve the graph cut problem. This work analyzes the conditions for the graph diffuse interface algorithm to converge. Using techniques from numerical PDE and convex optimization, monotonicity in function value and convergence under an a posteriori condition are shown for a class of schemes under a graph-independent stepsize condition. We also generalize our results to incorporate spectral truncation, a common technique used to save computation cost, and also to the case of multiclass classification. Various numerical experiments are done to compare theoretical results with practical performance.

Matrix product algorithm for stochastic dynamics on networks applied to nonequilibrium Glauber dynamics

NASA Astrophysics Data System (ADS)

Barthel, Thomas; De Bacco, Caterina; Franz, Silvio

2018-01-01

We introduce and apply an efficient method for the precise simulation of stochastic dynamical processes on locally treelike graphs. Networks with cycles are treated in the framework of the cavity method. Such models correspond, for example, to spin-glass systems, Boolean networks, neural networks, or other technological, biological, and social networks. Building upon ideas from quantum many-body theory, our approach is based on a matrix product approximation of the so-called edge messages—conditional probabilities of vertex variable trajectories. Computation costs and accuracy can be tuned by controlling the matrix dimensions of the matrix product edge messages (MPEM) in truncations. In contrast to Monte Carlo simulations, the algorithm has a better error scaling and works for both single instances as well as the thermodynamic limit. We employ it to examine prototypical nonequilibrium Glauber dynamics in the kinetic Ising model. Because of the absence of cancellation effects, observables with small expectation values can be evaluated accurately, allowing for the study of decay processes and temporal correlations.

DOGMA: A Disk-Oriented Graph Matching Algorithm for RDF Databases

NASA Astrophysics Data System (ADS)

Bröcheler, Matthias; Pugliese, Andrea; Subrahmanian, V. S.

RDF is an increasingly important paradigm for the representation of information on the Web. As RDF databases increase in size to approach tens of millions of triples, and as sophisticated graph matching queries expressible in languages like SPARQL become increasingly important, scalability becomes an issue. To date, there is no graph-based indexing method for RDF data where the index was designed in a way that makes it disk-resident. There is therefore a growing need for indexes that can operate efficiently when the index itself resides on disk. In this paper, we first propose the DOGMA index for fast subgraph matching on disk and then develop a basic algorithm to answer queries over this index. This algorithm is then significantly sped up via an optimized algorithm that uses efficient (but correct) pruning strategies when combined with two different extensions of the index. We have implemented a preliminary system and tested it against four existing RDF database systems developed by others. Our experiments show that our algorithm performs very well compared to these systems, with orders of magnitude improvements for complex graph queries.

Man-Made Object Extraction from Remote Sensing Imagery by Graph-Based Manifold Ranking

NASA Astrophysics Data System (ADS)

He, Y.; Wang, X.; Hu, X. Y.; Liu, S. H.

2018-04-01

The automatic extraction of man-made objects from remote sensing imagery is useful in many applications. This paper proposes an algorithm for extracting man-made objects automatically by integrating a graph model with the manifold ranking algorithm. Initially, we estimate a priori value of the man-made objects with the use of symmetric and contrast features. The graph model is established to represent the spatial relationships among pre-segmented superpixels, which are used as the graph nodes. Multiple characteristics, namely colour, texture and main direction, are used to compute the weights of the adjacent nodes. Manifold ranking effectively explores the relationships among all the nodes in the feature space as well as initial query assignment; thus, it is applied to generate a ranking map, which indicates the scores of the man-made objects. The man-made objects are then segmented on the basis of the ranking map. Two typical segmentation algorithms are compared with the proposed algorithm. Experimental results show that the proposed algorithm can extract man-made objects with high recognition rate and low omission rate.

Distributed-Memory Breadth-First Search on Massive Graphs

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

Buluc, Aydin; Beamer, Scott; Madduri, Kamesh

This chapter studies the problem of traversing large graphs using the breadth-first search order on distributed-memory supercomputers. We consider both the traditional level-synchronous top-down algorithm as well as the recently discovered direction optimizing algorithm. We analyze the performance and scalability trade-offs in using different local data structures such as CSR and DCSC, enabling in-node multithreading, and graph decompositions such as 1D and 2D decomposition.

Planning Assembly Of Large Truss Structures In Outer Space

NASA Technical Reports Server (NTRS)

De Mello, Luiz S. Homem; Desai, Rajiv S.

1992-01-01

Report dicusses developmental algorithm used in systematic planning of sequences of operations in which large truss structures assembled in outer space. Assembly sequence represented by directed graph called "assembly graph", in which each arc represents joining of two parts or subassemblies. Algorithm generates assembly graph, working backward from state of complete assembly to initial state, in which all parts disassembled. Working backward more efficient than working forward because it avoids intermediate dead ends.

Patterns and Practices for Future Architectures

DTIC Science & Technology

2014-08-01

14. SUBJECT TERMS computing architecture, graph algorithms, high-performance computing, big data , GPU 15. NUMBER OF PAGES 44 16. PRICE CODE 17...at Vertex 1 6 Figure 4: Data Structures Created by Kernel 1 of Single CPU, List Implementation Using the Graph in the Example from Section 1.2 9...Figure 5: Kernel 2 of Graph500 BFS Reference Implementation: Single CPU, List 10 Figure 6: Data Structures for Sequential CSR Algorithm 12 Figure 7

Multi-scale graph-cut algorithm for efficient water-fat separation.

PubMed

Berglund, Johan; Skorpil, Mikael

2017-09-01

To improve the accuracy and robustness to noise in water-fat separation by unifying the multiscale and graph cut based approaches to B 0 -correction. A previously proposed water-fat separation algorithm that corrects for B 0 field inhomogeneity in 3D by a single quadratic pseudo-Boolean optimization (QPBO) graph cut was incorporated into a multi-scale framework, where field map solutions are propagated from coarse to fine scales for voxels that are not resolved by the graph cut. The accuracy of the single-scale and multi-scale QPBO algorithms was evaluated against benchmark reference datasets. The robustness to noise was evaluated by adding noise to the input data prior to water-fat separation. Both algorithms achieved the highest accuracy when compared with seven previously published methods, while computation times were acceptable for implementation in clinical routine. The multi-scale algorithm was more robust to noise than the single-scale algorithm, while causing only a small increase (+10%) of the reconstruction time. The proposed 3D multi-scale QPBO algorithm offers accurate water-fat separation, robustness to noise, and fast reconstruction. The software implementation is freely available to the research community. Magn Reson Med 78:941-949, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.

Modeling and Density Estimation of an Urban Freeway Network Based on Dynamic Graph Hybrid Automata

PubMed Central

Chen, Yangzhou; Guo, Yuqi; Wang, Ying

2017-01-01

In this paper, in order to describe complex network systems, we firstly propose a general modeling framework by combining a dynamic graph with hybrid automata and thus name it Dynamic Graph Hybrid Automata (DGHA). Then we apply this framework to model traffic flow over an urban freeway network by embedding the Cell Transmission Model (CTM) into the DGHA. With a modeling procedure, we adopt a dual digraph of road network structure to describe the road topology, use linear hybrid automata to describe multi-modes of dynamic densities in road segments and transform the nonlinear expressions of the transmitted traffic flow between two road segments into piecewise linear functions in terms of multi-mode switchings. This modeling procedure is modularized and rule-based, and thus is easily-extensible with the help of a combination algorithm for the dynamics of traffic flow. It can describe the dynamics of traffic flow over an urban freeway network with arbitrary topology structures and sizes. Next we analyze mode types and number in the model of the whole freeway network, and deduce a Piecewise Affine Linear System (PWALS) model. Furthermore, based on the PWALS model, a multi-mode switched state observer is designed to estimate the traffic densities of the freeway network, where a set of observer gain matrices are computed by using the Lyapunov function approach. As an example, we utilize the PWALS model and the corresponding switched state observer to traffic flow over Beijing third ring road. In order to clearly interpret the principle of the proposed method and avoid computational complexity, we adopt a simplified version of Beijing third ring road. Practical application for a large-scale road network will be implemented by decentralized modeling approach and distributed observer designing in the future research. PMID:28353664

Modeling and Density Estimation of an Urban Freeway Network Based on Dynamic Graph Hybrid Automata.

PubMed

Chen, Yangzhou; Guo, Yuqi; Wang, Ying

2017-03-29

In this paper, in order to describe complex network systems, we firstly propose a general modeling framework by combining a dynamic graph with hybrid automata and thus name it Dynamic Graph Hybrid Automata (DGHA). Then we apply this framework to model traffic flow over an urban freeway network by embedding the Cell Transmission Model (CTM) into the DGHA. With a modeling procedure, we adopt a dual digraph of road network structure to describe the road topology, use linear hybrid automata to describe multi-modes of dynamic densities in road segments and transform the nonlinear expressions of the transmitted traffic flow between two road segments into piecewise linear functions in terms of multi-mode switchings. This modeling procedure is modularized and rule-based, and thus is easily-extensible with the help of a combination algorithm for the dynamics of traffic flow. It can describe the dynamics of traffic flow over an urban freeway network with arbitrary topology structures and sizes. Next we analyze mode types and number in the model of the whole freeway network, and deduce a Piecewise Affine Linear System (PWALS) model. Furthermore, based on the PWALS model, a multi-mode switched state observer is designed to estimate the traffic densities of the freeway network, where a set of observer gain matrices are computed by using the Lyapunov function approach. As an example, we utilize the PWALS model and the corresponding switched state observer to traffic flow over Beijing third ring road. In order to clearly interpret the principle of the proposed method and avoid computational complexity, we adopt a simplified version of Beijing third ring road. Practical application for a large-scale road network will be implemented by decentralized modeling approach and distributed observer designing in the future research.

State Tracking and Fault Diagnosis for Dynamic Systems Using Labeled Uncertainty Graph.

PubMed

Zhou, Gan; Feng, Wenquan; Zhao, Qi; Zhao, Hongbo

2015-11-05

Cyber-physical systems such as autonomous spacecraft, power plants and automotive systems become more vulnerable to unanticipated failures as their complexity increases. Accurate tracking of system dynamics and fault diagnosis are essential. This paper presents an efficient state estimation method for dynamic systems modeled as concurrent probabilistic automata. First, the Labeled Uncertainty Graph (LUG) method in the planning domain is introduced to describe the state tracking and fault diagnosis processes. Because the system model is probabilistic, the Monte Carlo technique is employed to sample the probability distribution of belief states. In addition, to address the sample impoverishment problem, an innovative look-ahead technique is proposed to recursively generate most likely belief states without exhaustively checking all possible successor modes. The overall algorithms incorporate two major steps: a roll-forward process that estimates system state and identifies faults, and a roll-backward process that analyzes possible system trajectories once the faults have been detected. We demonstrate the effectiveness of this approach by applying it to a real world domain: the power supply control unit of a spacecraft.

Modeling flow and transport in fracture networks using graphs

NASA Astrophysics Data System (ADS)

Karra, S.; O'Malley, D.; Hyman, J. D.; Viswanathan, H. S.; Srinivasan, G.

2018-03-01

Fractures form the main pathways for flow in the subsurface within low-permeability rock. For this reason, accurately predicting flow and transport in fractured systems is vital for improving the performance of subsurface applications. Fracture sizes in these systems can range from millimeters to kilometers. Although modeling flow and transport using the discrete fracture network (DFN) approach is known to be more accurate due to incorporation of the detailed fracture network structure over continuum-based methods, capturing the flow and transport in such a wide range of scales is still computationally intractable. Furthermore, if one has to quantify uncertainty, hundreds of realizations of these DFN models have to be run. To reduce the computational burden, we solve flow and transport on a graph representation of a DFN. We study the accuracy of the graph approach by comparing breakthrough times and tracer particle statistical data between the graph-based and the high-fidelity DFN approaches, for fracture networks with varying number of fractures and degree of heterogeneity. Due to our recent developments in capabilities to perform DFN high-fidelity simulations on fracture networks with large number of fractures, we are in a unique position to perform such a comparison. We show that the graph approach shows a consistent bias with up to an order of magnitude slower breakthrough when compared to the DFN approach. We show that this is due to graph algorithm's underprediction of the pressure gradients across intersections on a given fracture, leading to slower tracer particle speeds between intersections and longer travel times. We present a bias correction methodology to the graph algorithm that reduces the discrepancy between the DFN and graph predictions. We show that with this bias correction, the graph algorithm predictions significantly improve and the results are very accurate. The good accuracy and the low computational cost, with O (104) times lower times than the DFN, makes the graph algorithm an ideal technique to incorporate in uncertainty quantification methods.

Modeling flow and transport in fracture networks using graphs.

PubMed

Karra, S; O'Malley, D; Hyman, J D; Viswanathan, H S; Srinivasan, G

2018-03-01

Fractures form the main pathways for flow in the subsurface within low-permeability rock. For this reason, accurately predicting flow and transport in fractured systems is vital for improving the performance of subsurface applications. Fracture sizes in these systems can range from millimeters to kilometers. Although modeling flow and transport using the discrete fracture network (DFN) approach is known to be more accurate due to incorporation of the detailed fracture network structure over continuum-based methods, capturing the flow and transport in such a wide range of scales is still computationally intractable. Furthermore, if one has to quantify uncertainty, hundreds of realizations of these DFN models have to be run. To reduce the computational burden, we solve flow and transport on a graph representation of a DFN. We study the accuracy of the graph approach by comparing breakthrough times and tracer particle statistical data between the graph-based and the high-fidelity DFN approaches, for fracture networks with varying number of fractures and degree of heterogeneity. Due to our recent developments in capabilities to perform DFN high-fidelity simulations on fracture networks with large number of fractures, we are in a unique position to perform such a comparison. We show that the graph approach shows a consistent bias with up to an order of magnitude slower breakthrough when compared to the DFN approach. We show that this is due to graph algorithm's underprediction of the pressure gradients across intersections on a given fracture, leading to slower tracer particle speeds between intersections and longer travel times. We present a bias correction methodology to the graph algorithm that reduces the discrepancy between the DFN and graph predictions. We show that with this bias correction, the graph algorithm predictions significantly improve and the results are very accurate. The good accuracy and the low computational cost, with O(10^{4}) times lower times than the DFN, makes the graph algorithm an ideal technique to incorporate in uncertainty quantification methods.

Modeling flow and transport in fracture networks using graphs

DOE PAGES

Karra, S.; O'Malley, D.; Hyman, J. D.; ...

2018-03-09

Fractures form the main pathways for flow in the subsurface within low-permeability rock. For this reason, accurately predicting flow and transport in fractured systems is vital for improving the performance of subsurface applications. Fracture sizes in these systems can range from millimeters to kilometers. Although modeling flow and transport using the discrete fracture network (DFN) approach is known to be more accurate due to incorporation of the detailed fracture network structure over continuum-based methods, capturing the flow and transport in such a wide range of scales is still computationally intractable. Furthermore, if one has to quantify uncertainty, hundreds of realizationsmore » of these DFN models have to be run. To reduce the computational burden, we solve flow and transport on a graph representation of a DFN. We study the accuracy of the graph approach by comparing breakthrough times and tracer particle statistical data between the graph-based and the high-fidelity DFN approaches, for fracture networks with varying number of fractures and degree of heterogeneity. Due to our recent developments in capabilities to perform DFN high-fidelity simulations on fracture networks with large number of fractures, we are in a unique position to perform such a comparison. We show that the graph approach shows a consistent bias with up to an order of magnitude slower breakthrough when compared to the DFN approach. We show that this is due to graph algorithm's underprediction of the pressure gradients across intersections on a given fracture, leading to slower tracer particle speeds between intersections and longer travel times. We present a bias correction methodology to the graph algorithm that reduces the discrepancy between the DFN and graph predictions. We show that with this bias correction, the graph algorithm predictions significantly improve and the results are very accurate. In conclusion, the good accuracy and the low computational cost, with O(10 4) times lower times than the DFN, makes the graph algorithm an ideal technique to incorporate in uncertainty quantification methods.« less

Modeling flow and transport in fracture networks using graphs

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

Karra, S.; O'Malley, D.; Hyman, J. D.

Fractures form the main pathways for flow in the subsurface within low-permeability rock. For this reason, accurately predicting flow and transport in fractured systems is vital for improving the performance of subsurface applications. Fracture sizes in these systems can range from millimeters to kilometers. Although modeling flow and transport using the discrete fracture network (DFN) approach is known to be more accurate due to incorporation of the detailed fracture network structure over continuum-based methods, capturing the flow and transport in such a wide range of scales is still computationally intractable. Furthermore, if one has to quantify uncertainty, hundreds of realizationsmore » of these DFN models have to be run. To reduce the computational burden, we solve flow and transport on a graph representation of a DFN. We study the accuracy of the graph approach by comparing breakthrough times and tracer particle statistical data between the graph-based and the high-fidelity DFN approaches, for fracture networks with varying number of fractures and degree of heterogeneity. Due to our recent developments in capabilities to perform DFN high-fidelity simulations on fracture networks with large number of fractures, we are in a unique position to perform such a comparison. We show that the graph approach shows a consistent bias with up to an order of magnitude slower breakthrough when compared to the DFN approach. We show that this is due to graph algorithm's underprediction of the pressure gradients across intersections on a given fracture, leading to slower tracer particle speeds between intersections and longer travel times. We present a bias correction methodology to the graph algorithm that reduces the discrepancy between the DFN and graph predictions. We show that with this bias correction, the graph algorithm predictions significantly improve and the results are very accurate. In conclusion, the good accuracy and the low computational cost, with O(10 4) times lower times than the DFN, makes the graph algorithm an ideal technique to incorporate in uncertainty quantification methods.« less

A SAT Based Effective Algorithm for the Directed Hamiltonian Cycle Problem

NASA Astrophysics Data System (ADS)

Jäger, Gerold; Zhang, Weixiong

The Hamiltonian cycle problem (HCP) is an important combinatorial problem with applications in many areas. While thorough theoretical and experimental analyses have been made on the HCP in undirected graphs, little is known for the HCP in directed graphs (DHCP). The contribution of this work is an effective algorithm for the DHCP. Our algorithm explores and exploits the close relationship between the DHCP and the Assignment Problem (AP) and utilizes a technique based on Boolean satisfiability (SAT). By combining effective algorithms for the AP and SAT, our algorithm significantly outperforms previous exact DHCP algorithms including an algorithm based on the award-winning Concorde TSP algorithm.

Graph run-length matrices for histopathological image segmentation.

PubMed

Tosun, Akif Burak; Gunduz-Demir, Cigdem

2011-03-01

The histopathological examination of tissue specimens is essential for cancer diagnosis and grading. However, this examination is subject to a considerable amount of observer variability as it mainly relies on visual interpretation of pathologists. To alleviate this problem, it is very important to develop computational quantitative tools, for which image segmentation constitutes the core step. In this paper, we introduce an effective and robust algorithm for the segmentation of histopathological tissue images. This algorithm incorporates the background knowledge of the tissue organization into segmentation. For this purpose, it quantifies spatial relations of cytological tissue components by constructing a graph and uses this graph to define new texture features for image segmentation. This new texture definition makes use of the idea of gray-level run-length matrices. However, it considers the runs of cytological components on a graph to form a matrix, instead of considering the runs of pixel intensities. Working with colon tissue images, our experiments demonstrate that the texture features extracted from "graph run-length matrices" lead to high segmentation accuracies, also providing a reasonable number of segmented regions. Compared with four other segmentation algorithms, the results show that the proposed algorithm is more effective in histopathological image segmentation.

Minimum nonuniform graph partitioning with unrelated weights

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

On Parallel Push-Relabel based Algorithms for Bipartite Maximum Matching

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

Langguth, Johannes; Azad, Md Ariful; Halappanavar, Mahantesh

2014-07-01

We study multithreaded push-relabel based algorithms for computing maximum cardinality matching in bipartite graphs. Matching is a fundamental combinatorial (graph) problem with applications in a wide variety of problems in science and engineering. We are motivated by its use in the context of sparse linear solvers for computing maximum transversal of a matrix. We implement and test our algorithms on several multi-socket multicore systems and compare their performance to state-of-the-art augmenting path-based serial and parallel algorithms using a testset comprised of a wide range of real-world instances. Building on several heuristics for enhancing performance, we demonstrate good scaling for themore » parallel push-relabel algorithm. We show that it is comparable to the best augmenting path-based algorithms for bipartite matching. To the best of our knowledge, this is the first extensive study of multithreaded push-relabel based algorithms. In addition to a direct impact on the applications using matching, the proposed algorithmic techniques can be extended to preflow-push based algorithms for computing maximum flow in graphs.« less

Edge Pushing is Equivalent to Vertex Elimination for Computing Hessians

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

Wang, Mu; Pothen, Alex; Hovland, Paul

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

Performance of a cavity-method-based algorithm for the prize-collecting Steiner tree problem on graphs

NASA Astrophysics Data System (ADS)

Biazzo, Indaco; Braunstein, Alfredo; Zecchina, Riccardo

2012-08-01

We study the behavior of an algorithm derived from the cavity method for the prize-collecting steiner tree (PCST) problem on graphs. The algorithm is based on the zero temperature limit of the cavity equations and as such is formally simple (a fixed point equation resolved by iteration) and distributed (parallelizable). We provide a detailed comparison with state-of-the-art algorithms on a wide range of existing benchmarks, networks, and random graphs. Specifically, we consider an enhanced derivative of the Goemans-Williamson heuristics and the dhea solver, a branch and cut integer linear programming based approach. The comparison shows that the cavity algorithm outperforms the two algorithms in most large instances both in running time and quality of the solution. Finally we prove a few optimality properties of the solutions provided by our algorithm, including optimality under the two postprocessing procedures defined in the Goemans-Williamson derivative and global optimality in some limit cases.

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

PubMed

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

2017-01-01

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

Graph Drawing Aesthetics-Created by Users, Not Algorithms.

PubMed

Purchase, H C; Pilcher, C; Plimmer, B

2012-01-01

Prior empirical work on layout aesthetics for graph drawing algorithms has concentrated on the interpretation of existing graph drawings. We report on experiments which focus on the creation and layout of graph drawings: participants were asked to draw graphs based on adjacency lists, and to lay them out "nicely." Two interaction methods were used for creating the drawings: a sketch interface which allows for easy, natural hand movements, and a formal point-and-click interface similar to a typical graph editing system. We find, in common with many other studies, that removing edge crossings is the most significant aesthetic, but also discover that aligning nodes and edges to an underlying grid is important. We observe that the aesthetics favored by participants during creation of a graph drawing are often not evident in the final product and that the participants did not make a clear distinction between the processes of creation and layout. Our results suggest that graph drawing systems should integrate automatic layout with the user's manual editing process, and provide facilities to support grid-based graph creation.

Finding minimum-quotient cuts in planar graphs

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

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

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

Finding minimum-quotient cuts in planar graphs

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

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

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

Toward the optimization of normalized graph Laplacian.

PubMed

Xie, Bo; Wang, Meng; Tao, Dacheng

2011-04-01

Normalized graph Laplacian has been widely used in many practical machine learning algorithms, e.g., spectral clustering and semisupervised learning. However, all of them use the Euclidean distance to construct the graph Laplacian, which does not necessarily reflect the inherent distribution of the data. In this brief, we propose a method to directly optimize the normalized graph Laplacian by using pairwise constraints. The learned graph is consistent with equivalence and nonequivalence pairwise relationships, and thus it can better represent similarity between samples. Meanwhile, our approach, unlike metric learning, automatically determines the scale factor during the optimization. The learned normalized Laplacian matrix can be directly applied in spectral clustering and semisupervised learning algorithms. Comprehensive experiments demonstrate the effectiveness of the proposed approach.

Robust Algorithms for on Minor-Free Graphs Based on the Sherali-Adams Hierarchy

NASA Astrophysics Data System (ADS)

Magen, Avner; Moharrami, Mohammad

This work provides a Linear Programming-based Polynomial Time Approximation Scheme (PTAS) for two classical NP-hard problems on graphs when the input graph is guaranteed to be planar, or more generally Minor Free. The algorithm applies a sufficiently large number (some function of when approximation is required) of rounds of the so-called Sherali-Adams Lift-and-Project system. needed to obtain a -approximation, where f is some function that depends only on the graph that should be avoided as a minor. The problem we discuss are the well-studied problems, the and problems. An curious fact we expose is that in the world of minor-free graph, the is harder in some sense than the.

Global Binary Optimization on Graphs for Classification of High Dimensional Data

DTIC Science & Technology

2014-09-01

Buades et al . in [10] introduce a new non-local means algorithm for image denoising and compare it to some of the best methods. In [28], Grady de...scribes a random walk algorithm for image seg- mentation using the solution to a Dirichlet prob- lem. Elmoataz et al . present generalizations of the...graph Laplacian [19] for image denoising and man- ifold smoothing. Couprie et al . in [16] propose a parameterized graph-based energy function that unifies

A software tool for dataflow graph scheduling

NASA Technical Reports Server (NTRS)

Jones, Robert L., III

1994-01-01

A graph-theoretic design process and software tool is presented for selecting a multiprocessing scheduling solution for a class of computational problems. The problems of interest are those that can be described using a dataflow graph and are intended to be executed repetitively on multiple processors. The dataflow paradigm is very useful in exposing the parallelism inherent in algorithms. It provides a graphical and mathematical model which describes a partial ordering of algorithm tasks based on data precedence.

Memoryless cooperative graph search based on the simulated annealing algorithm

NASA Astrophysics Data System (ADS)

Hou, Jian; Yan, Gang-Feng; Fan, Zhen

2011-04-01

We have studied the problem of reaching a globally optimal segment for a graph-like environment with a single or a group of autonomous mobile agents. Firstly, two efficient simulated-annealing-like algorithms are given for a single agent to solve the problem in a partially known environment and an unknown environment, respectively. It shows that under both proposed control strategies, the agent will eventually converge to a globally optimal segment with probability 1. Secondly, we use multi-agent searching to simultaneously reduce the computation complexity and accelerate convergence based on the algorithms we have given for a single agent. By exploiting graph partition, a gossip-consensus method based scheme is presented to update the key parameter—radius of the graph, ensuring that the agents spend much less time finding a globally optimal segment.

The PANTHER User Experience

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

Coram, Jamie L.; Morrow, James D.; Perkins, David Nikolaus

2015-09-01

This document describes the PANTHER R&D Application, a proof-of-concept user interface application developed under the PANTHER Grand Challenge LDRD. The purpose of the application is to explore interaction models for graph analytics, drive algorithmic improvements from an end-user point of view, and support demonstration of PANTHER technologies to potential customers. The R&D Application implements a graph-centric interaction model that exposes analysts to the algorithms contained within the GeoGraphy graph analytics library. Users define geospatial-temporal semantic graph queries by constructing search templates based on nodes, edges, and the constraints among them. Users then analyze the results of the queries using bothmore » geo-spatial and temporal visualizations. Development of this application has made user experience an explicit driver for project and algorithmic level decisions that will affect how analysts one day make use of PANTHER technologies.« less

Laplacian Estrada and normalized Laplacian Estrada indices of evolving graphs.

PubMed

Shang, Yilun

2015-01-01

Large-scale time-evolving networks have been generated by many natural and technological applications, posing challenges for computation and modeling. Thus, it is of theoretical and practical significance to probe mathematical tools tailored for evolving networks. In this paper, on top of the dynamic Estrada index, we study the dynamic Laplacian Estrada index and the dynamic normalized Laplacian Estrada index of evolving graphs. Using linear algebra techniques, we established general upper and lower bounds for these graph-spectrum-based invariants through a couple of intuitive graph-theoretic measures, including the number of vertices or edges. Synthetic random evolving small-world networks are employed to show the relevance of the proposed dynamic Estrada indices. It is found that neither the static snapshot graphs nor the aggregated graph can approximate the evolving graph itself, indicating the fundamental difference between the static and dynamic Estrada indices.

An Improved Heuristic Method for Subgraph Isomorphism Problem

NASA Astrophysics Data System (ADS)

Xiang, Yingzhuo; Han, Jiesi; Xu, Haijiang; Guo, Xin

2017-09-01

This paper focus on the subgraph isomorphism (SI) problem. We present an improved genetic algorithm, a heuristic method to search the optimal solution. The contribution of this paper is that we design a dedicated crossover algorithm and a new fitness function to measure the evolution process. Experiments show our improved genetic algorithm performs better than other heuristic methods. For a large graph, such as a subgraph of 40 nodes, our algorithm outperforms the traditional tree search algorithms. We find that the performance of our improved genetic algorithm does not decrease as the number of nodes in prototype graphs.

New Graph Models and Algorithms for Detecting Salient Structures from Cluttered Images

DTIC Science & Technology

2010-02-24

Development of graph models and algorithms to detect boundaries that show certain levels of symmetry, an important geometric property of many...Bookstein. Morphometric tools for landmark data. Cambridge University Press, 1991. [8] F. L. Bookstein. Principal warps: Thin-plate splines and the

Anomaly detection in hyperspectral imagery: statistics vs. graph-based algorithms

NASA Astrophysics Data System (ADS)

Berkson, Emily E.; Messinger, David W.

2016-05-01

Anomaly detection (AD) algorithms are frequently applied to hyperspectral imagery, but different algorithms produce different outlier results depending on the image scene content and the assumed background model. This work provides the first comparison of anomaly score distributions between common statistics-based anomaly detection algorithms (RX and subspace-RX) and the graph-based Topological Anomaly Detector (TAD). Anomaly scores in statistical AD algorithms should theoretically approximate a chi-squared distribution; however, this is rarely the case with real hyperspectral imagery. The expected distribution of scores found with graph-based methods remains unclear. We also look for general trends in algorithm performance with varied scene content. Three separate scenes were extracted from the hyperspectral MegaScene image taken over downtown Rochester, NY with the VIS-NIR-SWIR ProSpecTIR instrument. In order of most to least cluttered, we study an urban, suburban, and rural scene. The three AD algorithms were applied to each scene, and the distributions of the most anomalous 5% of pixels were compared. We find that subspace-RX performs better than RX, because the data becomes more normal when the highest variance principal components are removed. We also see that compared to statistical detectors, anomalies detected by TAD are easier to separate from the background. Due to their different underlying assumptions, the statistical and graph-based algorithms highlighted different anomalies within the urban scene. These results will lead to a deeper understanding of these algorithms and their applicability across different types of imagery.

Dynamical Languages

NASA Astrophysics Data System (ADS)

Xie, Huimin

The following sections are included: * Definition of Dynamical Languages * Distinct Excluded Blocks * Definition and Properties * L and L″ in Chomsky Hierarchy * A Natural Equivalence Relation * Symbolic Flows * Symbolic Flows and Dynamical Languages * Subshifts of Finite Type * Sofic Systems * Graphs and Dynamical Languages * Graphs and Shannon-Graphs * Transitive Languages * Topological Entropy

Multiple graph regularized protein domain ranking.

PubMed

Wang, Jim Jing-Yan; Bensmail, Halima; Gao, Xin

2012-11-19

Protein domain ranking is a fundamental task in structural biology. Most protein domain ranking methods rely on the pairwise comparison of protein domains while neglecting the global manifold structure of the protein domain database. Recently, graph regularized ranking that exploits the global structure of the graph defined by the pairwise similarities has been proposed. However, the existing graph regularized ranking methods are very sensitive to the choice of the graph model and parameters, and this remains a difficult problem for most of the protein domain ranking methods. To tackle this problem, we have developed the Multiple Graph regularized Ranking algorithm, MultiG-Rank. Instead of using a single graph to regularize the ranking scores, MultiG-Rank approximates the intrinsic manifold of protein domain distribution by combining multiple initial graphs for the regularization. Graph weights are learned with ranking scores jointly and automatically, by alternately minimizing an objective function in an iterative algorithm. Experimental results on a subset of the ASTRAL SCOP protein domain database demonstrate that MultiG-Rank achieves a better ranking performance than single graph regularized ranking methods and pairwise similarity based ranking methods. The problem of graph model and parameter selection in graph regularized protein domain ranking can be solved effectively by combining multiple graphs. This aspect of generalization introduces a new frontier in applying multiple graphs to solving protein domain ranking applications.

Multiple graph regularized protein domain ranking

PubMed Central

2012-01-01

Background Protein domain ranking is a fundamental task in structural biology. Most protein domain ranking methods rely on the pairwise comparison of protein domains while neglecting the global manifold structure of the protein domain database. Recently, graph regularized ranking that exploits the global structure of the graph defined by the pairwise similarities has been proposed. However, the existing graph regularized ranking methods are very sensitive to the choice of the graph model and parameters, and this remains a difficult problem for most of the protein domain ranking methods. Results To tackle this problem, we have developed the Multiple Graph regularized Ranking algorithm, MultiG-Rank. Instead of using a single graph to regularize the ranking scores, MultiG-Rank approximates the intrinsic manifold of protein domain distribution by combining multiple initial graphs for the regularization. Graph weights are learned with ranking scores jointly and automatically, by alternately minimizing an objective function in an iterative algorithm. Experimental results on a subset of the ASTRAL SCOP protein domain database demonstrate that MultiG-Rank achieves a better ranking performance than single graph regularized ranking methods and pairwise similarity based ranking methods. Conclusion The problem of graph model and parameter selection in graph regularized protein domain ranking can be solved effectively by combining multiple graphs. This aspect of generalization introduces a new frontier in applying multiple graphs to solving protein domain ranking applications. PMID:23157331

Structure-guided Protein Transition Modeling with a Probabilistic Roadmap Algorithm.

PubMed

Maximova, Tatiana; Plaku, Erion; Shehu, Amarda

2016-07-07

Proteins are macromolecules in perpetual motion, switching between structural states to modulate their function. A detailed characterization of the precise yet complex relationship between protein structure, dynamics, and function requires elucidating transitions between functionally-relevant states. Doing so challenges both wet and dry laboratories, as protein dynamics involves disparate temporal scales. In this paper we present a novel, sampling-based algorithm to compute transition paths. The algorithm exploits two main ideas. First, it leverages known structures to initialize its search and define a reduced conformation space for rapid sampling. This is key to address the insufficient sampling issue suffered by sampling-based algorithms. Second, the algorithm embeds samples in a nearest-neighbor graph where transition paths can be efficiently computed via queries. The algorithm adapts the probabilistic roadmap framework that is popular in robot motion planning. In addition to efficiently computing lowest-cost paths between any given structures, the algorithm allows investigating hypotheses regarding the order of experimentally-known structures in a transition event. This novel contribution is likely to open up new venues of research. Detailed analysis is presented on multiple-basin proteins of relevance to human disease. Multiscaling and the AMBER ff14SB force field are used to obtain energetically-credible paths at atomistic detail.

Contact Graph Routing

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. The information carried by CGR contact plan messages is useful not only for dynamic route computation, but also for the implementation of rate control, congestion forecasting, transmission episode initiation and termination, timeout interval computation, and retransmission timer suspension and resumption.

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

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

Sengupta, Dipanjan; Song, Shuaiwen

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

Coverability graphs for a class of synchronously executed unbounded Petri net

NASA Technical Reports Server (NTRS)

Stotts, P. David; Pratt, Terrence W.

1990-01-01

After detailing a variant of the concurrent-execution rule for firing of maximal subsets, in which the simultaneous firing of conflicting transitions is prohibited, an algorithm is constructed for generating the coverability graph of a net executed under this synchronous firing rule. The omega insertion criteria in the algorithm are shown to be valid for any net on which the algorithm terminates. It is accordingly shown that the set of nets on which the algorithm terminates includes the 'conflict-free' class.

Graph Design via Convex Optimization: Online and Distributed Perspectives

NASA Astrophysics Data System (ADS)

Meng, De

Network and graph have long been natural abstraction of relations in a variety of applications, e.g. transportation, power system, social network, communication, electrical circuit, etc. As a large number of computation and optimization problems are naturally defined on graphs, graph structures not only enable important properties of these problems, but also leads to highly efficient distributed and online algorithms. For example, graph separability enables the parallelism for computation and operation as well as limits the size of local problems. More interestingly, graphs can be defined and constructed in order to take best advantage of those problem properties. This dissertation focuses on graph structure and design in newly proposed optimization problems, which establish a bridge between graph properties and optimization problem properties. We first study a new optimization problem called Geodesic Distance Maximization Problem (GDMP). Given a graph with fixed edge weights, finding the shortest path, also known as the geodesic, between two nodes is a well-studied network flow problem. We introduce the Geodesic Distance Maximization Problem (GDMP): the problem of finding the edge weights that maximize the length of the geodesic subject to convex constraints on the weights. We show that GDMP is a convex optimization problem for a wide class of flow costs, and provide a physical interpretation using the dual. We present applications of the GDMP in various fields, including optical lens design, network interdiction, and resource allocation in the control of forest fires. We develop an Alternating Direction Method of Multipliers (ADMM) by exploiting specific problem structures to solve large-scale GDMP, and demonstrate its effectiveness in numerical examples. We then turn our attention to distributed optimization on graph with only local communication. Distributed optimization arises in a variety of applications, e.g. distributed tracking and localization, estimation problems in sensor networks, multi-agent coordination. Distributed optimization aims to optimize a global objective function formed by summation of coupled local functions over a graph via only local communication and computation. We developed a weighted proximal ADMM for distributed optimization using graph structure. This fully distributed, single-loop algorithm allows simultaneous updates and can be viewed as a generalization of existing algorithms. More importantly, we achieve faster convergence by jointly designing graph weights and algorithm parameters. Finally, we propose a new problem on networks called Online Network Formation Problem: starting with a base graph and a set of candidate edges, at each round of the game, player one first chooses a candidate edge and reveals it to player two, then player two decides whether to accept it; player two can only accept limited number of edges and make online decisions with the goal to achieve the best properties of the synthesized network. The network properties considered include the number of spanning trees, algebraic connectivity and total effective resistance. These network formation games arise in a variety of cooperative multiagent systems. We propose a primal-dual algorithm framework for the general online network formation game, and analyze the algorithm performance by the competitive ratio and regret.

Visualizing Dynamic Bitcoin Transaction Patterns.

PubMed

McGinn, Dan; Birch, David; Akroyd, David; Molina-Solana, Miguel; Guo, Yike; Knottenbelt, William J

2016-06-01

This work presents a systemic top-down visualization of Bitcoin transaction activity to explore dynamically generated patterns of algorithmic behavior. Bitcoin dominates the cryptocurrency markets and presents researchers with a rich source of real-time transactional data. The pseudonymous yet public nature of the data presents opportunities for the discovery of human and algorithmic behavioral patterns of interest to many parties such as financial regulators, protocol designers, and security analysts. However, retaining visual fidelity to the underlying data to retain a fuller understanding of activity within the network remains challenging, particularly in real time. We expose an effective force-directed graph visualization employed in our large-scale data observation facility to accelerate this data exploration and derive useful insight among domain experts and the general public alike. The high-fidelity visualizations demonstrated in this article allowed for collaborative discovery of unexpected high frequency transaction patterns, including automated laundering operations, and the evolution of multiple distinct algorithmic denial of service attacks on the Bitcoin network.

Visualizing Dynamic Bitcoin Transaction Patterns

PubMed Central

McGinn, Dan; Birch, David; Akroyd, David; Molina-Solana, Miguel; Guo, Yike; Knottenbelt, William J.

2016-01-01

Abstract This work presents a systemic top-down visualization of Bitcoin transaction activity to explore dynamically generated patterns of algorithmic behavior. Bitcoin dominates the cryptocurrency markets and presents researchers with a rich source of real-time transactional data. The pseudonymous yet public nature of the data presents opportunities for the discovery of human and algorithmic behavioral patterns of interest to many parties such as financial regulators, protocol designers, and security analysts. However, retaining visual fidelity to the underlying data to retain a fuller understanding of activity within the network remains challenging, particularly in real time. We expose an effective force-directed graph visualization employed in our large-scale data observation facility to accelerate this data exploration and derive useful insight among domain experts and the general public alike. The high-fidelity visualizations demonstrated in this article allowed for collaborative discovery of unexpected high frequency transaction patterns, including automated laundering operations, and the evolution of multiple distinct algorithmic denial of service attacks on the Bitcoin network. PMID:27441715

Quantum speedup in solving the maximal-clique problem

NASA Astrophysics Data System (ADS)

Chang, Weng-Long; Yu, Qi; Li, Zhaokai; Chen, Jiahui; Peng, Xinhua; Feng, Mang

2018-03-01

The maximal-clique problem, to find the maximally sized clique in a given graph, is classically an NP-complete computational problem, which has potential applications ranging from electrical engineering, computational chemistry, and bioinformatics to social networks. Here we develop a quantum algorithm to solve the maximal-clique problem for any graph G with n vertices with quadratic speedup over its classical counterparts, where the time and spatial complexities are reduced to, respectively, O (√{2n}) and O (n2) . With respect to oracle-related quantum algorithms for the NP-complete problems, we identify our algorithm as optimal. To justify the feasibility of the proposed quantum algorithm, we successfully solve a typical clique problem for a graph G with two vertices and one edge by carrying out a nuclear magnetic resonance experiment involving four qubits.

Fitchi: haplotype genealogy graphs based on the Fitch algorithm.

PubMed

Matschiner, Michael

2016-04-15

: In population genetics and phylogeography, haplotype genealogy graphs are important tools for the visualization of population structure based on sequence data. In this type of graph, node sizes are often drawn in proportion to haplotype frequencies and edge lengths represent the minimum number of mutations separating adjacent nodes. I here present Fitchi, a new program that produces publication-ready haplotype genealogy graphs based on the Fitch algorithm. http://www.evoinformatics.eu/fitchi.htm : michaelmatschiner@mac.com Supplementary data are available at Bioinformatics online. © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

Semi-Supervised Tensor-Based Graph Embedding Learning and Its Application to Visual Discriminant Tracking.

PubMed

Hu, Weiming; Gao, Jin; Xing, Junliang; Zhang, Chao; Maybank, Stephen

2017-01-01

An appearance model adaptable to changes in object appearance is critical in visual object tracking. In this paper, we treat an image patch as a two-order tensor which preserves the original image structure. We design two graphs for characterizing the intrinsic local geometrical structure of the tensor samples of the object and the background. Graph embedding is used to reduce the dimensions of the tensors while preserving the structure of the graphs. Then, a discriminant embedding space is constructed. We prove two propositions for finding the transformation matrices which are used to map the original tensor samples to the tensor-based graph embedding space. In order to encode more discriminant information in the embedding space, we propose a transfer-learning- based semi-supervised strategy to iteratively adjust the embedding space into which discriminative information obtained from earlier times is transferred. We apply the proposed semi-supervised tensor-based graph embedding learning algorithm to visual tracking. The new tracking algorithm captures an object's appearance characteristics during tracking and uses a particle filter to estimate the optimal object state. Experimental results on the CVPR 2013 benchmark dataset demonstrate the effectiveness of the proposed tracking algorithm.

Overview and extensions of a system for routing directed graphs on SIMD architectures

NASA Technical Reports Server (NTRS)

Tomboulian, Sherryl

1988-01-01

Many problems can be described in terms of directed graphs that contain a large number of vertices where simple computations occur using data from adjacent vertices. A method is given for parallelizing such problems on an SIMD machine model that uses only nearest neighbor connections for communication, and has no facility for local indirect addressing. Each vertex of the graph will be assigned to a processor in the machine. Rules for a labeling are introduced that support the use of a simple algorithm for movement of data along the edges of the graph. Additional algorithms are defined for addition and deletion of edges. Modifying or adding a new edge takes the same time as parallel traversal. This combination of architecture and algorithms defines a system that is relatively simple to build and can do fast graph processing. All edges can be traversed in parallel in time O(T), where T is empirically proportional to the average path length in the embedding times the average degree of the graph. Additionally, researchers present an extension to the above method which allows for enhanced performance by allowing some broadcasting capabilities.

An asynchronous traversal engine for graph-based rich metadata management

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

Dai, Dong; Carns, Philip; Ross, Robert B.

Rich metadata in high-performance computing (HPC) systems contains extended information about users, jobs, data files, and their relationships. Property graphs are a promising data model to represent heterogeneous rich metadata flexibly. Specifically, a property graph can use vertices to represent different entities and edges to record the relationships between vertices with unique annotations. The high-volume HPC use case, with millions of entities and relationships, naturally requires an out-of-core distributed property graph database, which must support live updates (to ingest production information in real time), low-latency point queries (for frequent metadata operations such as permission checking), and large-scale traversals (for provenancemore » data mining). Among these needs, large-scale property graph traversals are particularly challenging for distributed graph storage systems. Most existing graph systems implement a "level synchronous" breadth-first search algorithm that relies on global synchronization in each traversal step. This performs well in many problem domains; but a rich metadata management system is characterized by imbalanced graphs, long traversal lengths, and concurrent workloads, each of which has the potential to introduce or exacerbate stragglers (i.e., abnormally slow steps or servers in a graph traversal) that lead to low overall throughput for synchronous traversal algorithms. Previous research indicated that the straggler problem can be mitigated by using asynchronous traversal algorithms, and many graph-processing frameworks have successfully demonstrated this approach. Such systems require the graph to be loaded into a separate batch-processing framework instead of being iteratively accessed, however. In this work, we investigate a general asynchronous graph traversal engine that can operate atop a rich metadata graph in its native format. We outline a traversal-aware query language and key optimizations (traversal-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

An asynchronous traversal engine for graph-based rich metadata management

DOE PAGES

Dai, Dong; Carns, Philip; Ross, Robert B.; ...

2016-06-23

Rich metadata in high-performance computing (HPC) systems contains extended information about users, jobs, data files, and their relationships. Property graphs are a promising data model to represent heterogeneous rich metadata flexibly. Specifically, a property graph can use vertices to represent different entities and edges to record the relationships between vertices with unique annotations. The high-volume HPC use case, with millions of entities and relationships, naturally requires an out-of-core distributed property graph database, which must support live updates (to ingest production information in real time), low-latency point queries (for frequent metadata operations such as permission checking), and large-scale traversals (for provenancemore » data mining). Among these needs, large-scale property graph traversals are particularly challenging for distributed graph storage systems. Most existing graph systems implement a "level synchronous" breadth-first search algorithm that relies on global synchronization in each traversal step. This performs well in many problem domains; but a rich metadata management system is characterized by imbalanced graphs, long traversal lengths, and concurrent workloads, each of which has the potential to introduce or exacerbate stragglers (i.e., abnormally slow steps or servers in a graph traversal) that lead to low overall throughput for synchronous traversal algorithms. Previous research indicated that the straggler problem can be mitigated by using asynchronous traversal algorithms, and many graph-processing frameworks have successfully demonstrated this approach. Such systems require the graph to be loaded into a separate batch-processing framework instead of being iteratively accessed, however. In this work, we investigate a general asynchronous graph traversal engine that can operate atop a rich metadata graph in its native format. We outline a traversal-aware query language and key optimizations (traversal-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

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.

A system for routing arbitrary directed graphs on SIMD architectures

NASA Technical Reports Server (NTRS)

Tomboulian, Sherryl

1987-01-01

There are many problems which can be described in terms of directed graphs that contain a large number of vertices where simple computations occur using data from connecting vertices. A method is given for parallelizing such problems on an SIMD machine model that is bit-serial and uses only nearest neighbor connections for communication. Each vertex of the graph will be assigned to a processor in the machine. Algorithms are given that will be used to implement movement of data along the arcs of the graph. This architecture and algorithms define a system that is relatively simple to build and can do graph processing. All arcs can be transversed in parallel in time O(T), where T is empirically proportional to the diameter of the interconnection network times the average degree of the graph. Modifying or adding a new arc takes the same time as parallel traversal.

Efficient and Scalable Graph Similarity Joins in MapReduce

PubMed Central

Chen, Yifan; Zhang, Weiming; Tang, Jiuyang

2014-01-01

Along with the emergence of massive graph-modeled data, it is of great importance to investigate graph similarity joins due to their wide applications for multiple purposes, including data cleaning, and near duplicate detection. This paper considers graph similarity joins with edit distance constraints, which return pairs of graphs such that their edit distances are no larger than a given threshold. Leveraging the MapReduce programming model, we propose MGSJoin, a scalable algorithm following the filtering-verification framework for efficient graph similarity joins. It relies on counting overlapping graph signatures for filtering out nonpromising candidates. With the potential issue of too many key-value pairs in the filtering phase, spectral Bloom filters are introduced to reduce the number of key-value pairs. Furthermore, we integrate the multiway join strategy to boost the verification, where a MapReduce-based method is proposed for GED calculation. The superior efficiency and scalability of the proposed algorithms are demonstrated by extensive experimental results. PMID:25121135

Efficient and scalable graph similarity joins in MapReduce.

PubMed

Chen, Yifan; Zhao, Xiang; Xiao, Chuan; Zhang, Weiming; Tang, Jiuyang

2014-01-01

Along with the emergence of massive graph-modeled data, it is of great importance to investigate graph similarity joins due to their wide applications for multiple purposes, including data cleaning, and near duplicate detection. This paper considers graph similarity joins with edit distance constraints, which return pairs of graphs such that their edit distances are no larger than a given threshold. Leveraging the MapReduce programming model, we propose MGSJoin, a scalable algorithm following the filtering-verification framework for efficient graph similarity joins. It relies on counting overlapping graph signatures for filtering out nonpromising candidates. With the potential issue of too many key-value pairs in the filtering phase, spectral Bloom filters are introduced to reduce the number of key-value pairs. Furthermore, we integrate the multiway join strategy to boost the verification, where a MapReduce-based method is proposed for GED calculation. The superior efficiency and scalability of the proposed algorithms are demonstrated by extensive experimental results.

Development of antibiotic regimens using graph based evolutionary algorithms.

PubMed

Corns, Steven M; Ashlock, Daniel A; Bryden, Kenneth M

2013-12-01

This paper examines the use of evolutionary algorithms in the development of antibiotic regimens given to production animals. A model is constructed that combines the lifespan of the animal and the bacteria living in the animal's gastro-intestinal tract from the early finishing stage until the animal reaches market weight. This model is used as the fitness evaluation for a set of graph based evolutionary algorithms to assess the impact of diversity control on the evolving antibiotic regimens. The graph based evolutionary algorithms have two objectives: to find an antibiotic treatment regimen that maintains the weight gain and health benefits of antibiotic use and to reduce the risk of spreading antibiotic resistant bacteria. This study examines different regimens of tylosin phosphate use on bacteria populations divided into Gram positive and Gram negative types, with a focus on Campylobacter spp. Treatment regimens were found that provided decreased antibiotic resistance relative to conventional methods while providing nearly the same benefits as conventional antibiotic regimes. By using a graph to control the information flow in the evolutionary algorithm, a variety of solutions along the Pareto front can be found automatically for this and other multi-objective problems. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

OpenMP Parallelization and Optimization of Graph-Based Machine Learning Algorithms

DOE PAGES

Meng, Zhaoyi; Koniges, Alice; He, Yun Helen; ...

2016-09-21

In this paper, we investigate the OpenMP parallelization and optimization of two novel data classification algorithms. The new algorithms are based on graph and PDE solution techniques and provide significant accuracy and performance advantages over traditional data classification algorithms in serial mode. The methods leverage the Nystrom extension to calculate eigenvalue/eigenvectors of the graph Laplacian and this is a self-contained module that can be used in conjunction with other graph-Laplacian based methods such as spectral clustering. We use performance tools to collect the hotspots and memory access of the serial codes and use OpenMP as the parallelization language to parallelizemore » the most time-consuming parts. Where possible, we also use library routines. We then optimize the OpenMP implementations and detail the performance on traditional supercomputer nodes (in our case a Cray XC30), and test the optimization steps on emerging testbed systems based on Intel’s Knights Corner and Landing processors. We show both performance improvement and strong scaling behavior. Finally, a large number of optimization techniques and analyses are necessary before the algorithm reaches almost ideal scaling.« less

A Multilevel Gamma-Clustering Layout Algorithm for Visualization of Biological Networks

PubMed Central

Hruz, Tomas; Lucas, Christoph; Laule, Oliver; Zimmermann, Philip

2013-01-01

Visualization of large complex networks has become an indispensable part of systems biology, where organisms need to be considered as one complex system. The visualization of the corresponding network is challenging due to the size and density of edges. In many cases, the use of standard visualization algorithms can lead to high running times and poorly readable visualizations due to many edge crossings. We suggest an approach that analyzes the structure of the graph first and then generates a new graph which contains specific semantic symbols for regular substructures like dense clusters. We propose a multilevel gamma-clustering layout visualization algorithm (MLGA) which proceeds in three subsequent steps: (i) a multilevel γ-clustering is used to identify the structure of the underlying network, (ii) the network is transformed to a tree, and (iii) finally, the resulting tree which shows the network structure is drawn using a variation of a force-directed algorithm. The algorithm has a potential to visualize very large networks because it uses modern clustering heuristics which are optimized for large graphs. Moreover, most of the edges are removed from the visual representation which allows keeping the overview over complex graphs with dense subgraphs. PMID:23864855

On the modification Highly Connected Subgraphs (HCS) algorithm in graph clustering for weighted graph

NASA Astrophysics Data System (ADS)

Albirri, E. R.; Sugeng, K. A.; Aldila, D.

2018-04-01

Nowadays, in the modern world, since technology and human civilization start to progress, all city in the world is almost connected. The various places in this world are easier to visit. It is an impact of transportation technology and highway construction. The cities which have been connected can be represented by graph. Graph clustering is one of ways which is used to answer some problems represented by graph. There are some methods in graph clustering to solve the problem spesifically. One of them is Highly Connected Subgraphs (HCS) method. HCS is used to identify cluster based on the graph connectivity k for graph G. The connectivity in graph G is denoted by k(G)> \\frac{n}{2} that n is the total of vertices in G, then it is called as HCS or the cluster. This research used literature review and completed with simulation of program in a software. We modified HCS algorithm by using weighted graph. The modification is located in the Process Phase. Process Phase is used to cut the connected graph G into two subgraphs H and \\bar{H}. We also made a program by using software Octave-401. Then we applied the data of Flight Routes Mapping of One of Airlines in Indonesia to our program.

EClerize: A customized force-directed graph drawing algorithm for biological graphs with EC attributes.

PubMed

Danaci, Hasan Fehmi; Cetin-Atalay, Rengul; Atalay, Volkan

2018-03-26

Visualizing large-scale data produced by the high throughput experiments as a biological graph leads to better understanding and analysis. This study describes a customized force-directed layout algorithm, EClerize, for biological graphs that represent pathways in which the nodes are associated with Enzyme Commission (EC) attributes. The nodes with the same EC class numbers are treated as members of the same cluster. Positions of nodes are then determined based on both the biological similarity and the connection structure. EClerize minimizes the intra-cluster distance, that is the distance between the nodes of the same EC cluster and maximizes the inter-cluster distance, that is the distance between two distinct EC clusters. EClerize is tested on a number of biological pathways and the improvement brought in is presented with respect to the original algorithm. EClerize is available as a plug-in to cytoscape ( http://apps.cytoscape.org/apps/eclerize ).

Enhancing Community Detection By Affinity-based Edge Weighting Scheme

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

Yoo, Andy; Sanders, Geoffrey; Henson, Van

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

Structural self-assembly and avalanchelike dynamics in locally adaptive networks

NASA Astrophysics Data System (ADS)

Gräwer, Johannes; Modes, Carl D.; Magnasco, Marcelo O.; Katifori, Eleni

2015-07-01

Transport networks play a key role across four realms of eukaryotic life: slime molds, fungi, plants, and animals. In addition to the developmental algorithms that build them, many also employ adaptive strategies to respond to stimuli, damage, and other environmental changes. We model these adapting network architectures using a generic dynamical system on weighted graphs and find in simulation that these networks ultimately develop a hierarchical organization of the final weighted architecture accompanied by the formation of a system-spanning backbone. In addition, we find that the long term equilibration dynamics exhibit behavior reminiscent of glassy systems characterized by long periods of slow changes punctuated by bursts of reorganization events.

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

NASA Astrophysics Data System (ADS)

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

2015-12-01

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

Distributed Sensing and Processing: A Graphical Model Approach

DTIC Science & Technology

2005-11-30

that Ramanujan graph toplogies maximize the convergence rate of distributed detection consensus algorithms, improving over three orders of...small world type network designs. 14. SUBJECT TERMS Ramanujan graphs, sensor network topology, sensor network...that Ramanujan graphs, for which there are explicit algebraic constructions, have large eigenratios, converging much faster than structured graphs

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

PubMed

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

2013-12-01

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

A path following algorithm for the graph matching problem.

PubMed

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

2009-12-01

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

X-Graphs: Language and Algorithms for Heterogeneous Graph Streams

DTIC Science & Technology

2017-09-01

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

Resource utilization model for the algorithm to architecture mapping model

NASA Technical Reports Server (NTRS)

Stoughton, John W.; Patel, Rakesh R.

1993-01-01

The analytical model for resource utilization and the variable node time and conditional node model for the enhanced ATAMM model for a real-time data flow architecture are presented in this research. The Algorithm To Architecture Mapping Model, ATAMM, is a Petri net based graph theoretic model developed at Old Dominion University, and is capable of modeling the execution of large-grained algorithms on a real-time data flow architecture. Using the resource utilization model, the resource envelope may be obtained directly from a given graph and, consequently, the maximum number of required resources may be evaluated. The node timing diagram for one iteration period may be obtained using the analytical resource envelope. The variable node time model, which describes the change in resource requirement for the execution of an algorithm under node time variation, is useful to expand the applicability of the ATAMM model to heterogeneous architectures. The model also describes a method of detecting the presence of resource limited mode and its subsequent prevention. Graphs with conditional nodes are shown to be reduced to equivalent graphs with time varying nodes and, subsequently, may be analyzed using the variable node time model to determine resource requirements. Case studies are performed on three graphs for the illustration of applicability of the analytical theories.

An effective trust-based recommendation method using a novel graph clustering algorithm

NASA Astrophysics Data System (ADS)

Moradi, Parham; Ahmadian, Sajad; Akhlaghian, Fardin

2015-10-01

Recommender systems are programs that aim to provide personalized recommendations to users for specific items (e.g. music, books) in online sharing communities or on e-commerce sites. Collaborative filtering methods are important and widely accepted types of recommender systems that generate recommendations based on the ratings of like-minded users. On the other hand, these systems confront several inherent issues such as data sparsity and cold start problems, caused by fewer ratings against the unknowns that need to be predicted. Incorporating trust information into the collaborative filtering systems is an attractive approach to resolve these problems. In this paper, we present a model-based collaborative filtering method by applying a novel graph clustering algorithm and also considering trust statements. In the proposed method first of all, the problem space is represented as a graph and then a sparsest subgraph finding algorithm is applied on the graph to find the initial cluster centers. Then, the proposed graph clustering algorithm is performed to obtain the appropriate users/items clusters. Finally, the identified clusters are used as a set of neighbors to recommend unseen items to the current active user. Experimental results based on three real-world datasets demonstrate that the proposed method outperforms several state-of-the-art recommender system methods.

Detecting independent and recurrent copy number aberrations using interval graphs.

PubMed

Wu, Hsin-Ta; Hajirasouliha, Iman; Raphael, Benjamin J

2014-06-15

Somatic copy number aberrations SCNAS: are frequent in cancer genomes, but many of these are random, passenger events. A common strategy to distinguish functional aberrations from passengers is to identify those aberrations that are recurrent across multiple samples. However, the extensive variability in the length and position of SCNA: s makes the problem of identifying recurrent aberrations notoriously difficult. We introduce a combinatorial approach to the problem of identifying independent and recurrent SCNA: s, focusing on the key challenging of separating the overlaps in aberrations across individuals into independent events. We derive independent and recurrent SCNA: s as maximal cliques in an interval graph constructed from overlaps between aberrations. We efficiently enumerate all such cliques, and derive a dynamic programming algorithm to find an optimal selection of non-overlapping cliques, resulting in a very fast algorithm, which we call RAIG (Recurrent Aberrations from Interval Graphs). We show that RAIG outperforms other methods on simulated data and also performs well on data from three cancer types from The Cancer Genome Atlas (TCGA). In contrast to existing approaches that employ various heuristics to select independent aberrations, RAIG optimizes a well-defined objective function. We show that this allows RAIG to identify rare aberrations that are likely functional, but are obscured by overlaps with larger passenger aberrations. http://compbio.cs.brown.edu/software. © The Author 2014. Published by Oxford University Press.

A note on the stability and discriminability of graph-based features for classification problems in digital pathology

NASA Astrophysics Data System (ADS)

Cruz-Roa, Angel; Xu, Jun; Madabhushi, Anant

2015-01-01

Nuclear architecture or the spatial arrangement of individual cancer nuclei on histopathology images has been shown to be associated with different grades and differential risk for a number of solid tumors such as breast, prostate, and oropharyngeal. Graph-based representations of individual nuclei (nuclei representing the graph nodes) allows for mining of quantitative metrics to describe tumor morphology. These graph features can be broadly categorized into global and local depending on the type of graph construction method. While a number of local graph (e.g. Cell Cluster Graphs) and global graph (e.g. Voronoi, Delaunay Triangulation, Minimum Spanning Tree) features have been shown to associated with cancer grade, risk, and outcome for different cancer types, the sensitivity of the preceding segmentation algorithms in identifying individual nuclei can have a significant bearing on the discriminability of the resultant features. This therefore begs the question as to which features while being discriminative of cancer grade and aggressiveness are also the most resilient to the segmentation errors. These properties are particularly desirable in the context of digital pathology images, where the method of slide preparation, staining, and type of nuclear segmentation algorithm employed can all dramatically affect the quality of the nuclear graphs and corresponding features. In this paper we evaluated the trade off between discriminability and stability of both global and local graph-based features in conjunction with a few different segmentation algorithms and in the context of two different histopathology image datasets of breast cancer from whole-slide images (WSI) and tissue microarrays (TMA). Specifically in this paper we investigate a few different performance measures including stability, discriminability and stability vs discriminability trade off, all of which are based on p-values from the Kruskal-Wallis one-way analysis of variance for local and global graph features. Apart from identifying the set of local and global features that satisfied the trade off between stability and discriminability, our most interesting finding was that a simple segmentation method was sufficient to identify the most discriminant features for invasive tumour detection in TMAs, whereas for tumour grading in WSI, the graph based features were more sensitive to the accuracy of the segmentation algorithm employed.

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

PubMed

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

2012-03-30

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

Compacting de Bruijn graphs from sequencing data quickly and in low memory.

PubMed

Chikhi, Rayan; Limasset, Antoine; Medvedev, Paul

2016-06-15

As the quantity of data per sequencing experiment increases, the challenges of fragment assembly are becoming increasingly computational. The de Bruijn graph is a widely used data structure in fragment assembly algorithms, used to represent the information from a set of reads. Compaction is an important data reduction step in most de Bruijn graph based algorithms where long simple paths are compacted into single vertices. Compaction has recently become the bottleneck in assembly pipelines, and improving its running time and memory usage is an important problem. We present an algorithm and a tool bcalm 2 for the compaction of de Bruijn graphs. bcalm 2 is a parallel algorithm that distributes the input based on a minimizer hashing technique, allowing for good balance of memory usage throughout its execution. For human sequencing data, bcalm 2 reduces the computational burden of compacting the de Bruijn graph to roughly an hour and 3 GB of memory. We also applied bcalm 2 to the 22 Gbp loblolly pine and 20 Gbp white spruce sequencing datasets. Compacted graphs were constructed from raw reads in less than 2 days and 40 GB of memory on a single machine. Hence, bcalm 2 is at least an order of magnitude more efficient than other available methods. Source code of bcalm 2 is freely available at: https://github.com/GATB/bcalm rayan.chikhi@univ-lille1.fr. © The Author 2016. Published by Oxford University Press.

Energy Minimization of Discrete Protein Titration State Models Using Graph Theory.

PubMed

Purvine, Emilie; Monson, Kyle; Jurrus, Elizabeth; Star, Keith; Baker, Nathan A

2016-08-25

There are several applications in computational biophysics that require the optimization of discrete interacting states, for example, amino acid titration states, ligand oxidation states, or discrete rotamer angles. Such optimization can be very time-consuming as it scales exponentially in the number of sites to be optimized. In this paper, we describe a new polynomial time algorithm for optimization of discrete states in macromolecular systems. This algorithm was adapted from image processing and uses techniques from discrete mathematics and graph theory to restate the optimization problem in terms of "maximum flow-minimum cut" graph analysis. The interaction energy graph, a graph in which vertices (amino acids) and edges (interactions) are weighted with their respective energies, is transformed into a flow network in which the value of the minimum cut in the network equals the minimum free energy of the protein and the cut itself encodes the state that achieves the minimum free energy. Because of its deterministic nature and polynomial time performance, this algorithm has the potential to allow for the ionization state of larger proteins to be discovered.

Energy Minimization of Discrete Protein Titration State Models Using Graph Theory

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

Purvine, Emilie AH; Monson, Kyle E.; Jurrus, Elizabeth R.

There are several applications in computational biophysics which require the optimization of discrete interacting states; e.g., amino acid titration states, ligand oxidation states, or discrete rotamer angles. Such optimization can be very time-consuming as it scales exponentially in the number of sites to be optimized. In this paper, we describe a new polynomial-time algorithm for optimization of discrete states in macromolecular systems. This algorithm was adapted from image processing and uses techniques from discrete mathematics and graph theory to restate the optimization problem in terms of maximum flow-minimum cut graph analysis. The interaction energy graph, a graph in which verticesmore » (amino acids) and edges (interactions) are weighted with their respective energies, is transformed into a flow network in which the value of the minimum cut in the network equals the minimum free energy of the protein, and the cut itself encodes the state that achieves the minimum free energy. Because of its deterministic nature and polynomial-time performance, this algorithm has the potential to allow for the ionization state of larger proteins to be discovered.« less

Energy Minimization of Discrete Protein Titration State Models Using Graph Theory

PubMed Central

Purvine, Emilie; Monson, Kyle; Jurrus, Elizabeth; Star, Keith; Baker, Nathan A.

2016-01-01

There are several applications in computational biophysics which require the optimization of discrete interacting states; e.g., amino acid titration states, ligand oxidation states, or discrete rotamer angles. Such optimization can be very time-consuming as it scales exponentially in the number of sites to be optimized. In this paper, we describe a new polynomial-time algorithm for optimization of discrete states in macromolecular systems. This algorithm was adapted from image processing and uses techniques from discrete mathematics and graph theory to restate the optimization problem in terms of “maximum flow-minimum cut” graph analysis. The interaction energy graph, a graph in which vertices (amino acids) and edges (interactions) are weighted with their respective energies, is transformed into a flow network in which the value of the minimum cut in the network equals the minimum free energy of the protein, and the cut itself encodes the state that achieves the minimum free energy. Because of its deterministic nature and polynomial-time performance, this algorithm has the potential to allow for the ionization state of larger proteins to be discovered. PMID:27089174

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

Hagberg, Aric; Swart, Pieter; S Chult, Daniel

NetworkX is a Python language package for exploration and analysis of networks and network algorithms. The core package provides data structures for representing many types of networks, or graphs, including simple graphs, directed graphs, and graphs with parallel edges and self loops. The nodes in NetworkX graphs can be any (hashable) Python object and edges can contain arbitrary data; this flexibility mades NetworkX ideal for representing networks found in many different scientific fields. In addition to the basic data structures many graph algorithms are implemented for calculating network properties and structure measures: shortest paths, betweenness centrality, clustering, and degree distributionmore » and many more. NetworkX can read and write various graph formats for eash exchange with existing data, and provides generators for many classic graphs and popular graph models, such as the Erdoes-Renyi, Small World, and Barabasi-Albert models, are included. The ease-of-use and flexibility of the Python programming language together with connection to the SciPy tools make NetworkX a powerful tool for scientific computations. We discuss some of our recent work studying synchronization of coupled oscillators to demonstrate how NetworkX enables research in the field of computational networks.« less

Comparing Algorithms for Graph Isomorphism Using Discrete- and Continuous-Time Quantum Random Walks

DOE PAGES

Rudinger, Kenneth; Gamble, John King; Bach, Eric; ...

2013-07-01

Berry and Wang [Phys. Rev. A 83, 042317 (2011)] show numerically that a discrete-time quan- tum random walk of two noninteracting particles is able to distinguish some non-isomorphic strongly regular graphs from the same family. Here we analytically demonstrate how it is possible for these walks to distinguish such graphs, while continuous-time quantum walks of two noninteracting parti- cles cannot. We show analytically and numerically that even single-particle discrete-time quantum random walks can distinguish some strongly regular graphs, though not as many as two-particle noninteracting discrete-time walks. Additionally, we demonstrate how, given the same quantum random walk, subtle di erencesmore » in the graph certi cate construction algorithm can nontrivially im- pact the walk's distinguishing power. We also show that no continuous-time walk of a xed number of particles can distinguish all strongly regular graphs when used in conjunction with any of the graph certi cates we consider. We extend this constraint to discrete-time walks of xed numbers of noninteracting particles for one kind of graph certi cate; it remains an open question as to whether or not this constraint applies to the other graph certi cates we consider.« less

Efficient Extraction of High Centrality Vertices in Distributed Graphs

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

Kumbhare, Alok; Frincu, Marc; Raghavendra, Cauligi S.

2014-09-09

Betweenness centrality (BC) is an important measure for identifying high value or critical vertices in graphs, in variety of domains such as communication networks, road networks, and social graphs. However, calculating betweenness values is prohibitively expensive and, more often, domain experts are interested only in the vertices with the highest centrality values. In this paper, we first propose a partition-centric algorithm (MS-BC) to calculate BC for a large distributed graph that optimizes resource utilization and improves overall performance. Further, we extend the notion of approximate BC by pruning the graph and removing a subset of edges and vertices that contributemore » the least to the betweenness values of other vertices (MSL-BC), which further improves the runtime performance. We evaluate the proposed algorithms using a mix of real-world and synthetic graphs on an HPC cluster and analyze its strengths and weaknesses. The experimental results show an improvement in performance of upto 12x for large sparse graphs as compared to the state-of-the-art, and at the same time highlights the need for better partitioning methods to enable a balanced workload across partitions for unbalanced graphs such as small-world or power-law graphs.« less

Tensor Spectral Clustering for Partitioning Higher-order Network Structures.

PubMed

Benson, Austin R; Gleich, David F; Leskovec, Jure

2015-01-01

Spectral graph theory-based methods represent an important class of tools for studying the structure of networks. Spectral methods are based on a first-order Markov chain derived from a random walk on the graph and thus they cannot take advantage of important higher-order network substructures such as triangles, cycles, and feed-forward loops. Here we propose a Tensor Spectral Clustering (TSC) algorithm that allows for modeling higher-order network structures in a graph partitioning framework. Our TSC algorithm allows the user to specify which higher-order network structures (cycles, feed-forward loops, etc.) should be preserved by the network clustering. Higher-order network structures of interest are represented using a tensor, which we then partition by developing a multilinear spectral method. Our framework can be applied to discovering layered flows in networks as well as graph anomaly detection, which we illustrate on synthetic networks. In directed networks, a higher-order structure of particular interest is the directed 3-cycle, which captures feedback loops in networks. We demonstrate that our TSC algorithm produces large partitions that cut fewer directed 3-cycles than standard spectral clustering algorithms.

Tensor Spectral Clustering for Partitioning Higher-order Network Structures

PubMed Central

Benson, Austin R.; Gleich, David F.; Leskovec, Jure

2016-01-01

Spectral graph theory-based methods represent an important class of tools for studying the structure of networks. Spectral methods are based on a first-order Markov chain derived from a random walk on the graph and thus they cannot take advantage of important higher-order network substructures such as triangles, cycles, and feed-forward loops. Here we propose a Tensor Spectral Clustering (TSC) algorithm that allows for modeling higher-order network structures in a graph partitioning framework. Our TSC algorithm allows the user to specify which higher-order network structures (cycles, feed-forward loops, etc.) should be preserved by the network clustering. Higher-order network structures of interest are represented using a tensor, which we then partition by developing a multilinear spectral method. Our framework can be applied to discovering layered flows in networks as well as graph anomaly detection, which we illustrate on synthetic networks. In directed networks, a higher-order structure of particular interest is the directed 3-cycle, which captures feedback loops in networks. We demonstrate that our TSC algorithm produces large partitions that cut fewer directed 3-cycles than standard spectral clustering algorithms. PMID:27812399

Exploratory Item Classification Via Spectral Graph Clustering

PubMed Central

Chen, Yunxiao; Li, Xiaoou; Liu, Jingchen; Xu, Gongjun; Ying, Zhiliang

2017-01-01

Large-scale assessments are supported by a large item pool. An important task in test development is to assign items into scales that measure different characteristics of individuals, and a popular approach is cluster analysis of items. Classical methods in cluster analysis, such as the hierarchical clustering, K-means method, and latent-class analysis, often induce a high computational overhead and have difficulty handling missing data, especially in the presence of high-dimensional responses. In this article, the authors propose a spectral clustering algorithm for exploratory item cluster analysis. The method is computationally efficient, effective for data with missing or incomplete responses, easy to implement, and often outperforms traditional clustering algorithms in the context of high dimensionality. The spectral clustering algorithm is based on graph theory, a branch of mathematics that studies the properties of graphs. The algorithm first constructs a graph of items, characterizing the similarity structure among items. It then extracts item clusters based on the graphical structure, grouping similar items together. The proposed method is evaluated through simulations and an application to the revised Eysenck Personality Questionnaire. PMID:29033476

Theory of rumour spreading in complex social networks

NASA Astrophysics Data System (ADS)

Nekovee, M.; Moreno, Y.; Bianconi, G.; Marsili, M.

2007-01-01

We introduce a general stochastic model for the spread of rumours, and derive mean-field equations that describe the dynamics of the model on complex social networks (in particular, those mediated by the Internet). We use analytical and numerical solutions of these equations to examine the threshold behaviour and dynamics of the model on several models of such networks: random graphs, uncorrelated scale-free networks and scale-free networks with assortative degree correlations. We show that in both homogeneous networks and random graphs the model exhibits a critical threshold in the rumour spreading rate below which a rumour cannot propagate in the system. In the case of scale-free networks, on the other hand, this threshold becomes vanishingly small in the limit of infinite system size. We find that the initial rate at which a rumour spreads is much higher in scale-free networks than in random graphs, and that the rate at which the spreading proceeds on scale-free networks is further increased when assortative degree correlations are introduced. The impact of degree correlations on the final fraction of nodes that ever hears a rumour, however, depends on the interplay between network topology and the rumour spreading rate. Our results show that scale-free social networks are prone to the spreading of rumours, just as they are to the spreading of infections. They are relevant to the spreading dynamics of chain emails, viral advertising and large-scale information dissemination algorithms on the Internet.

Efficient Approximation Algorithms for Weighted $b$-Matching

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

Khan, Arif; Pothen, Alex; Mostofa Ali Patwary, Md.

2016-01-01

We describe a half-approximation algorithm, b-Suitor, for computing a b-Matching of maximum weight in a graph with weights on the edges. b-Matching is a generalization of the well-known Matching problem in graphs, where the objective is to choose a subset of M edges in the graph such that at most a specified number b(v) of edges in M are incident on each vertex v. Subject to this restriction we maximize the sum of the weights of the edges in M. We prove that the b-Suitor algorithm computes the same b-Matching as the one obtained by the greedy algorithm for themore » problem. We implement the algorithm on serial and shared-memory parallel processors, and compare its performance against a collection of approximation algorithms that have been proposed for the Matching problem. Our results show that the b-Suitor algorithm outperforms the Greedy and Locally Dominant edge algorithms by one to two orders of magnitude on a serial processor. The b-Suitor algorithm has a high degree of concurrency, and it scales well up to 240 threads on a shared memory multiprocessor. The b-Suitor algorithm outperforms the Locally Dominant edge algorithm by a factor of fourteen on 16 cores of an Intel Xeon multiprocessor.« less

Coherent structure coloring: identification of coherent structures from sparse flow trajectories using graph theory

NASA Astrophysics Data System (ADS)

Schlueter, Kristy; Dabiri, John

2016-11-01

Coherent structure identification is important in many fluid dynamics applications, including transport phenomena in ocean flows and mixing and diffusion in turbulence. However, many of the techniques currently available for measuring such flows, including ocean drifter datasets and particle tracking velocimetry, only result in sparse velocity data. This is often insufficient for the use of current coherent structure detection algorithms based on analysis of the deformation gradient. Here, we present a frame-invariant method for detecting coherent structures from Lagrangian flow trajectories that can be sparse in number. The method, based on principles used in graph coloring algorithms, examines a measure of the kinematic dissimilarity of all pairs of flow trajectories, either measured experimentally, e.g. using particle tracking velocimetry; or numerically, by advecting fluid particles in the Eulerian velocity field. Coherence is assigned to groups of particles whose kinematics remain similar throughout the time interval for which trajectory data is available, regardless of their physical proximity to one another. Through the use of several analytical and experimental validation cases, this algorithm is shown to robustly detect coherent structures using significantly less flow data than is required by existing methods. This research was supported by the Department of Defense (DoD) through the National Defense Science & Engineering Graduate Fellowship (NDSEG) Program.

Transforming graph states using single-qubit operations.

PubMed

Dahlberg, Axel; Wehner, Stephanie

2018-07-13

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

Short paths in expander graphs

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

Kleinberg, J.; Rubinfeld, R.

Graph expansion has proved to be a powerful general tool for analyzing the behavior of routing algorithms and the interconnection networks on which they run. We develop new routing algorithms and structural results for bounded-degree expander graphs. Our results are unified by the fact that they are all based upon, and extend, a body of work asserting that expanders are rich in short, disjoint paths. In particular, our work has consequences for the disjoint paths problem, multicommodify flow, and graph minor containment. We show: (i) A greedy algorithm for approximating the maximum disjoint paths problem achieves a polylogarithmic approximation ratiomore » in bounded-degree expanders. Although our algorithm is both deterministic and on-line, its performance guarantee is an improvement over previous bounds in expanders. (ii) For a multicommodily flow problem with arbitrary demands on a bounded-degree expander, there is a (1 + {epsilon})-optimal solution using only flow paths of polylogarithmic length. It follows that the multicommodity flow algorithm of Awerbuch and Leighton runs in nearly linear time per commodity in expanders. Our analysis is based on establishing the following: given edge weights on an expander G, one can increase some of the weights very slightly so the resulting shortest-path metric is smooth - the min-weight path between any pair of nodes uses a polylogarithmic number of edges. (iii) Every bounded-degree expander on n nodes contains every graph with O(n/log{sup O(1)} n) nodes and edges as a minor.« less

Orbital evolution studies of planet-crossing asteroids

NASA Astrophysics Data System (ADS)

Hahn, Gerhard; Lagerkvist, Claes-Ingvar

The orbits of 26 planet-crossing Aten-Apollo-Amor asteroids are predicted on the basis of numerical integrations covering 33,000 or 100,000 yrs; the values reported supplement the preliminary findings of Hahn and Lagerkvist (1987). A solar-system dynamics model accounting for the effects of all planets from Venus to Neptune is employed, along with the 15th-order integration algorithm RADAU (Everhart, 1985). The results are presented in extensive tables and graphs and discussed in detail.

Transport in Dynamical Astronomy and Multibody Problems

NASA Astrophysics Data System (ADS)

Dellnitz, Michael; Junge, Oliver; Koon, Wang Sang; Lekien, Francois; Lo, Martin W.; Marsden, Jerrold E.; Padberg, Kathrin; Preis, Robert; Ross, Shane D.; Thiere, Bianca

We combine the techniques of almost invariant sets (using tree structured box elimination and graph partitioning algorithms) with invariant manifold and lobe dynamics techniques. The result is a new computational technique for computing key dynamical features, including almost invariant sets, resonance regions as well as transport rates and bottlenecks between regions in dynamical systems. This methodology can be applied to a variety of multibody problems, including those in molecular modeling, chemical reaction rates and dynamical astronomy. In this paper we focus on problems in dynamical astronomy to illustrate the power of the combination of these different numerical tools and their applicability. In particular, we compute transport rates between two resonance regions for the three-body system consisting of the Sun, Jupiter and a third body (such as an asteroid). These resonance regions are appropriate for certain comets and asteroids.

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

PubMed

Guturu, Parthasarathy; Dantu, Ram

2008-06-01

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

Reflections on High School Students' Graphing Skills and Their Conceptual Understanding of Drawing Chemistry Graphs

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…

Assessing dynamic brain graphs of time-varying connectivity in fMRI data: application to healthy controls and patients with schizophrenia

PubMed Central

Yu, Qingbao; Erhardt, Erik B.; Sui, Jing; Du, Yuhui; He, Hao; Hjelm, Devon; Cetin, Mustafa S.; Rachakonda, Srinivas; Miller, Robyn L.; Pearlson, Godfrey; Calhoun, Vince D.

2014-01-01

Graph theory-based analysis has been widely employed in brain imaging studies, and altered topological properties of brain connectivity have emerged as important features of mental diseases such as schizophrenia. However, most previous studies have focused on graph metrics of stationary brain graphs, ignoring that brain connectivity exhibits fluctuations over time. Here we develop a new framework for accessing dynamic graph properties of time-varying functional brain connectivity in resting state fMRI data and apply it to healthy controls (HCs) and patients with schizophrenia (SZs). Specifically, nodes of brain graphs are defined by intrinsic connectivity networks (ICNs) identified by group independent component analysis (ICA). Dynamic graph metrics of the time-varying brain connectivity estimated by the correlation of sliding time-windowed ICA time courses of ICNs are calculated. First- and second-level connectivity states are detected based on the correlation of nodal connectivity strength between time-varying brain graphs. Our results indicate that SZs show decreased variance in the dynamic graph metrics. Consistent with prior stationary functional brain connectivity works, graph measures of identified first-level connectivity states show lower values in SZs. In addition, more first-level connectivity states are disassociated with the second-level connectivity state which resembles the stationary connectivity pattern computed by the entire scan. Collectively, the findings provide new evidence about altered dynamic brain graphs in schizophrenia which may underscore the abnormal brain performance in this mental illness. PMID:25514514

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

PubMed

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

2017-11-29

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

The number comb for a soil physical properties dynamic measurement

NASA Astrophysics Data System (ADS)

Olechko, K.; Patiño, P.; Tarquis, A. M.

2012-04-01

We propose the prime numbers distribution extracted from the soil digital multiscale images and some physical properties time series as the precise indicator of the spatial and temporal dynamics under soil management changes. With this new indicator the soil dynamics can be studied as a critical phenomenon where each phase transition is estimated and modeled by the graph partitioning induced phase transition. The critical point of prime numbers distribution was correlated with the beginning of Andosols, Vertisols and saline soils physical degradation under the unsustainable soil management in Michoacan, Guanajuato and Veracruz States of Mexico. The data banks corresponding to the long time periods (between 10 and 28 years) were statistically compared by RISK 5.0 software and our own algorithms. Our approach makes us able to distill free-form natural laws of soils physical properties dynamics directly from the experimental data. The Richter (1987) and Schmidt and Lipson (2009) original approaches were very useful to design the algorithms to identify Hamiltonians, Lagrangians and other laws of geometric and momentum conservation especially for erosion case.

MO-FG-CAMPUS-TeP2-01: A Graph Form ADMM Algorithm for Constrained Quadratic Radiation Treatment Planning

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

Liu, X; Belcher, AH; Wiersma, R

Purpose: In radiation therapy optimization the constraints can be either hard constraints which must be satisfied or soft constraints which are included but do not need to be satisfied exactly. Currently the voxel dose constraints are viewed as soft constraints and included as a part of the objective function and approximated as an unconstrained problem. However in some treatment planning cases the constraints should be specified as hard constraints and solved by constrained optimization. The goal of this work is to present a computation efficiency graph form alternating direction method of multipliers (ADMM) algorithm for constrained quadratic treatment planning optimizationmore » and compare it with several commonly used algorithms/toolbox. Method: ADMM can be viewed as an attempt to blend the benefits of dual decomposition and augmented Lagrangian methods for constrained optimization. Various proximal operators were first constructed as applicable to quadratic IMRT constrained optimization and the problem was formulated in a graph form of ADMM. A pre-iteration operation for the projection of a point to a graph was also proposed to further accelerate the computation. Result: The graph form ADMM algorithm was tested by the Common Optimization for Radiation Therapy (CORT) dataset including TG119, prostate, liver, and head & neck cases. Both unconstrained and constrained optimization problems were formulated for comparison purposes. All optimizations were solved by LBFGS, IPOPT, Matlab built-in toolbox, CVX (implementing SeDuMi) and Mosek solvers. For unconstrained optimization, it was found that LBFGS performs the best, and it was 3–5 times faster than graph form ADMM. However, for constrained optimization, graph form ADMM was 8 – 100 times faster than the other solvers. Conclusion: A graph form ADMM can be applied to constrained quadratic IMRT optimization. It is more computationally efficient than several other commercial and noncommercial optimizers and it also used significantly less computer memory.« less

Random graph models for dynamic networks

NASA Astrophysics Data System (ADS)

Zhang, Xiao; Moore, Cristopher; Newman, Mark E. J.

2017-10-01

Recent theoretical work on the modeling of network structure has focused primarily on networks that are static and unchanging, but many real-world networks change their structure over time. There exist natural generalizations to the dynamic case of many static network models, including the classic random graph, the configuration model, and the stochastic block model, where one assumes that the appearance and disappearance of edges are governed by continuous-time Markov processes with rate parameters that can depend on properties of the nodes. Here we give an introduction to this class of models, showing for instance how one can compute their equilibrium properties. We also demonstrate their use in data analysis and statistical inference, giving efficient algorithms for fitting them to observed network data using the method of maximum likelihood. This allows us, for example, to estimate the time constants of network evolution or infer community structure from temporal network data using cues embedded both in the probabilities over time that node pairs are connected by edges and in the characteristic dynamics of edge appearance and disappearance. We illustrate these methods with a selection of applications, both to computer-generated test networks and real-world examples.

Maximal clique enumeration with data-parallel primitives

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

Lessley, Brenton; Perciano, Talita; Mathai, Manish

The enumeration of all maximal cliques in an undirected graph is a fundamental problem arising in several research areas. We consider maximal clique enumeration on shared-memory, multi-core architectures and introduce an approach consisting entirely of data-parallel operations, in an effort to achieve efficient and portable performance across different architectures. We study the performance of the algorithm via experiments varying over benchmark graphs and architectures. Overall, we observe that our algorithm achieves up to a 33-time speedup and 9-time speedup over state-of-the-art distributed and serial algorithms, respectively, for graphs with higher ratios of maximal cliques to total cliques. Further, we attainmore » additional speedups on a GPU architecture, demonstrating the portable performance of our data-parallel design.« less

Dynamic path planning for mobile robot based on particle swarm optimization

NASA Astrophysics Data System (ADS)

Wang, Yong; Cai, Feng; Wang, Ying

2017-08-01

In the contemporary, robots are used in many fields, such as cleaning, medical treatment, space exploration, disaster relief and so on. The dynamic path planning of robot without collision is becoming more and more the focus of people's attention. A new method of path planning is proposed in this paper. Firstly, the motion space model of the robot is established by using the MAKLINK graph method. Then the A* algorithm is used to get the shortest path from the start point to the end point. Secondly, this paper proposes an effective method to detect and avoid obstacles. When an obstacle is detected on the shortest path, the robot will choose the nearest safety point to move. Moreover, calculate the next point which is nearest to the target. Finally, the particle swarm optimization algorithm is used to optimize the path. The experimental results can prove that the proposed method is more effective.

Emerging hierarchies in dynamically adapting webs

NASA Astrophysics Data System (ADS)

Katifori, Eleni; Graewer, Johannes; Magnasco, Marcelo; Modes, Carl

Transport networks play a key role across four realms of eukaryotic life: slime molds, fungi, plants, and animals. In addition to the developmental algorithms that build them, many also employ adaptive strategies to respond to stimuli, damage, and other environmental changes. We model these adapting network architectures using a generic dynamical system on weighted graphs and find in simulation that these networks ultimately develop a hierarchical organization of the final weighted architecture accompanied by the formation of a system-spanning backbone. We quantify the hierarchical organization of the networks by developing an algorithm that decomposes the architecture to multiple scales and analyzes how the organization in each scale relates to that of the scale above and below it. The methodologies developed in this work are applicable to a wide range of systems including the slime mold physarum polycephalum, human microvasculature, and force chains in granular media.

Ring system-based chemical graph generation for de novo molecular design

NASA Astrophysics Data System (ADS)

Miyao, Tomoyuki; Kaneko, Hiromasa; Funatsu, Kimito

2016-05-01

Generating chemical graphs in silico by combining building blocks is important and fundamental in virtual combinatorial chemistry. A premise in this area is that generated structures should be irredundant as well as exhaustive. In this study, we develop structure generation algorithms regarding combining ring systems as well as atom fragments. The proposed algorithms consist of three parts. First, chemical structures are generated through a canonical construction path. During structure generation, ring systems can be treated as reduced graphs having fewer vertices than those in the original ones. Second, diversified structures are generated by a simple rule-based generation algorithm. Third, the number of structures to be generated can be estimated with adequate accuracy without actual exhaustive generation. The proposed algorithms were implemented in structure generator Molgilla. As a practical application, Molgilla generated chemical structures mimicking rosiglitazone in terms of a two dimensional pharmacophore pattern. The strength of the algorithms lies in simplicity and flexibility. Therefore, they may be applied to various computer programs regarding structure generation by combining building blocks.

A Partitioning Algorithm for Block-Diagonal Matrices With Overlap

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

Guy Antoine Atenekeng Kahou; Laura Grigori; Masha Sosonkina

2008-02-02

We present a graph partitioning algorithm that aims at partitioning a sparse matrix into a block-diagonal form, such that any two consecutive blocks overlap. We denote this form of the matrix as the overlapped block-diagonal matrix. The partitioned matrix is suitable for applying the explicit formulation of Multiplicative Schwarz preconditioner (EFMS) described in [3]. The graph partitioning algorithm partitions the graph of the input matrix into K partitions, such that every partition {Omega}{sub i} has at most two neighbors {Omega}{sub i-1} and {Omega}{sub i+1}. First, an ordering algorithm, such as the reverse Cuthill-McKee algorithm, that reduces the matrix profile ismore » performed. An initial overlapped block-diagonal partition is obtained from the profile of the matrix. An iterative strategy is then used to further refine the partitioning by allowing nodes to be transferred between neighboring partitions. Experiments are performed on matrices arising from real-world applications to show the feasibility and usefulness of this approach.« less

Enhanced Contact Graph Routing (ECGR) MACHETE Simulation Model

NASA Technical Reports Server (NTRS)

Segui, John S.; Jennings, Esther H.; Clare, Loren P.

2013-01-01

Contact Graph Routing (CGR) for Delay/Disruption Tolerant Networking (DTN) space-based networks makes use of the predictable nature of node contacts to make real-time routing decisions given unpredictable traffic patterns. The contact graph will have been disseminated to all nodes before the start of route computation. CGR was designed for space-based networking environments where future contact plans are known or are independently computable (e.g., using known orbital dynamics). For each data item (known as a bundle in DTN), a node independently performs route selection by examining possible paths to the destination. Route computation could conceivably run thousands of times a second, so computational load is important. This work refers to the simulation software model of Enhanced Contact Graph Routing (ECGR) for DTN Bundle Protocol in JPL's MACHETE simulation tool. The simulation model was used for performance analysis of CGR and led to several performance enhancements. The simulation model was used to demonstrate the improvements of ECGR over CGR as well as other routing methods in space network scenarios. ECGR moved to using earliest arrival time because it is a global monotonically increasing metric that guarantees the safety properties needed for the solution's correctness since route re-computation occurs at each node to accommodate unpredicted changes (e.g., traffic pattern, link quality). Furthermore, using earliest arrival time enabled the use of the standard Dijkstra algorithm for path selection. The Dijkstra algorithm for path selection has a well-known inexpensive computational cost. These enhancements have been integrated into the open source CGR implementation. The ECGR model is also useful for route metric experimentation and comparisons with other DTN routing protocols particularly when combined with MACHETE's space networking models and Delay Tolerant Link State Routing (DTLSR) model.

Extracting Knowledge from Graph Data in Adversarial Settings

NASA Astrophysics Data System (ADS)

Skillicorn, David

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

Temporal networks

NASA Astrophysics Data System (ADS)

Holme, Petter; Saramäki, Jari

2012-10-01

A great variety of systems in nature, society and technology-from the web of sexual contacts to the Internet, from the nervous system to power grids-can be modeled as graphs of vertices coupled by edges. The network structure, describing how the graph is wired, helps us understand, predict and optimize the behavior of dynamical systems. In many cases, however, the edges are not continuously active. As an example, in networks of communication via e-mail, text messages, or phone calls, edges represent sequences of instantaneous or practically instantaneous contacts. In some cases, edges are active for non-negligible periods of time: e.g., the proximity patterns of inpatients at hospitals can be represented by a graph where an edge between two individuals is on throughout the time they are at the same ward. Like network topology, the temporal structure of edge activations can affect dynamics of systems interacting through the network, from disease contagion on the network of patients to information diffusion over an e-mail network. In this review, we present the emergent field of temporal networks, and discuss methods for analyzing topological and temporal structure and models for elucidating their relation to the behavior of dynamical systems. In the light of traditional network theory, one can see this framework as moving the information of when things happen from the dynamical system on the network, to the network itself. Since fundamental properties, such as the transitivity of edges, do not necessarily hold in temporal networks, many of these methods need to be quite different from those for static networks. The study of temporal networks is very interdisciplinary in nature. Reflecting this, even the object of study has many names-temporal graphs, evolving graphs, time-varying graphs, time-aggregated graphs, time-stamped graphs, dynamic networks, dynamic graphs, dynamical graphs, and so on. This review covers different fields where temporal graphs are considered, but does not attempt to unify related terminology-rather, we want to make papers readable across disciplines.

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.

Multiple sclerosis lesion segmentation using an automatic multimodal graph cuts.

PubMed

García-Lorenzo, Daniel; Lecoeur, Jeremy; Arnold, Douglas L; Collins, D Louis; Barillot, Christian

2009-01-01

Graph Cuts have been shown as a powerful interactive segmentation technique in several medical domains. We propose to automate the Graph Cuts in order to automatically segment Multiple Sclerosis (MS) lesions in MRI. We replace the manual interaction with a robust EM-based approach in order to discriminate between MS lesions and the Normal Appearing Brain Tissues (NABT). Evaluation is performed in synthetic and real images showing good agreement between the automatic segmentation and the target segmentation. We compare our algorithm with the state of the art techniques and with several manual segmentations. An advantage of our algorithm over previously published ones is the possibility to semi-automatically improve the segmentation due to the Graph Cuts interactive feature.

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

NASA Astrophysics Data System (ADS)

Kumar, Manoj; Kumar, Ravinder; Weigel, Martin; Banerjee, Varsha; Janke, Wolfhard; Puri, Sanjay

2018-05-01

While the ground-state problem for the random-field Ising model is polynomial, and can be solved using a number of well-known algorithms for maximum flow or graph cut, the analog random-field Potts model corresponds to a multiterminal flow problem that is known to be NP-hard. Hence an efficient exact algorithm is very unlikely to exist. As we show here, it is nevertheless possible to use an embedding of binary degrees of freedom into the Potts spins in combination with graph-cut methods to solve the corresponding ground-state problem approximately in polynomial time. We benchmark this heuristic algorithm using a set of quasiexact ground states found for small systems from long parallel tempering runs. For a not-too-large number q of Potts states, the method based on graph cuts finds the same solutions in a fraction of the time. We employ the new technique to analyze the breakup length of the random-field Potts model in two dimensions.

A Novel Strategy Using Factor Graphs and the Sum-Product Algorithm for Satellite Broadcast Scheduling Problems

NASA Astrophysics Data System (ADS)

Chen, Jung-Chieh

This paper presents a low complexity algorithmic framework for finding a broadcasting schedule in a low-altitude satellite system, i. e., the satellite broadcast scheduling (SBS) problem, based on the recent modeling and computational methodology of factor graphs. Inspired by the huge success of the low density parity check (LDPC) codes in the field of error control coding, in this paper, we transform the SBS problem into an LDPC-like problem through a factor graph instead of using the conventional neural network approaches to solve the SBS problem. Based on a factor graph framework, the soft-information, describing the probability that each satellite will broadcast information to a terminal at a specific time slot, is exchanged among the local processing in the proposed framework via the sum-product algorithm to iteratively optimize the satellite broadcasting schedule. Numerical results show that the proposed approach not only can obtain optimal solution but also enjoys the low complexity suitable for integral-circuit implementation.

Adaptive fuzzy wavelet network control of second order multi-agent systems with unknown nonlinear dynamics.

PubMed

Taheri, Mehdi; Sheikholeslam, Farid; Najafi, Majddedin; Zekri, Maryam

2017-07-01

In this paper, consensus problem is considered for second order multi-agent systems with unknown nonlinear dynamics under undirected graphs. A novel distributed control strategy is suggested for leaderless systems based on adaptive fuzzy wavelet networks. Adaptive fuzzy wavelet networks are employed to compensate for the effect of unknown nonlinear dynamics. Moreover, the proposed method is developed for leader following systems and leader following systems with state time delays. Lyapunov functions are applied to prove uniformly ultimately bounded stability of closed loop systems and to obtain adaptive laws. Three simulation examples are presented to illustrate the effectiveness of the proposed control algorithms. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Applied Graph-Mining Algorithms to Study Biomolecular Interaction Networks

PubMed Central

2014-01-01

Protein-protein interaction (PPI) networks carry vital information on the organization of molecular interactions in cellular systems. The identification of functionally relevant modules in PPI networks is one of the most important applications of biological network analysis. Computational analysis is becoming an indispensable tool to understand large-scale biomolecular interaction networks. Several types of computational methods have been developed and employed for the analysis of PPI networks. Of these computational methods, graph comparison and module detection are the two most commonly used strategies. This review summarizes current literature on graph kernel and graph alignment methods for graph comparison strategies, as well as module detection approaches including seed-and-extend, hierarchical clustering, optimization-based, probabilistic, and frequent subgraph methods. Herein, we provide a comprehensive review of the major algorithms employed under each theme, including our recently published frequent subgraph method, for detecting functional modules commonly shared across multiple cancer PPI networks. PMID:24800226

Projected power iteration for network alignment

NASA Astrophysics Data System (ADS)

Onaran, Efe; Villar, Soledad

2017-08-01

The network alignment problem asks for the best correspondence between two given graphs, so that the largest possible number of edges are matched. This problem appears in many scientific problems (like the study of protein-protein interactions) and it is very closely related to the quadratic assignment problem which has graph isomorphism, traveling salesman and minimum bisection problems as particular cases. The graph matching problem is NP-hard in general. However, under some restrictive models for the graphs, algorithms can approximate the alignment efficiently. In that spirit the recent work by Feizi and collaborators introduce EigenAlign, a fast spectral method with convergence guarantees for Erd-s-Renyí graphs. In this work we propose the algorithm Projected Power Alignment, which is a projected power iteration version of EigenAlign. We numerically show it improves the recovery rates of EigenAlign and we describe the theory that may be used to provide performance guarantees for Projected Power Alignment.

Percolator: Scalable Pattern Discovery in Dynamic Graphs

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

Choudhury, Sutanay; Purohit, Sumit; Lin, Peng

We demonstrate Percolator, a distributed system for graph pattern discovery in dynamic graphs. In contrast to conventional mining systems, Percolator advocates efficient pattern mining schemes that (1) support pattern detection with keywords; (2) integrate incremental and parallel pattern mining; and (3) support analytical queries such as trend analysis. The core idea of Percolator is to dynamically decide and verify a small fraction of patterns and their in- stances that must be inspected in response to buffered updates in dynamic graphs, with a total mining cost independent of graph size. We demonstrate a) the feasibility of incremental pattern mining by walkingmore » through each component of Percolator, b) the efficiency and scalability of Percolator over the sheer size of real-world dynamic graphs, and c) how the user-friendly GUI of Percolator inter- acts with users to support keyword-based queries that detect, browse and inspect trending patterns. We also demonstrate two user cases of Percolator, in social media trend analysis and academic collaboration analysis, respectively.« less

Graph-drawing algorithms geometries versus molecular mechanics in fullereness

NASA Astrophysics Data System (ADS)

Kaufman, M.; Pisanski, T.; Lukman, D.; Borštnik, B.; Graovac, A.

1996-09-01

The algorithms of Kamada-Kawai (KK) and Fruchterman-Reingold (FR) have been recently generalized (Pisanski et al., Croat. Chem. Acta 68 (1995) 283) in order to draw molecular graphs in three-dimensional space. The quality of KK and FR geometries is studied here by comparing them with the molecular mechanics (MM) and the adjacency matrix eigenvectors (AME) algorithm geometries. In order to compare different layouts of the same molecule, an appropriate method has been developed. Its application to a series of experimentally detected fullerenes indicates that the KK, FR and AME algorithms are able to reproduce plausible molecular geometries.

Finding Maximum Cliques on the D-Wave Quantum Annealer

DOE PAGES

Chapuis, Guillaume; Djidjev, Hristo; Hahn, Georg; ...

2018-05-03

This work assesses the performance of the D-Wave 2X (DW) quantum annealer for finding a maximum clique in a graph, one of the most fundamental and important NP-hard problems. Because the size of the largest graphs DW can directly solve is quite small (usually around 45 vertices), we also consider decomposition algorithms intended for larger graphs and analyze their performance. For smaller graphs that fit DW, we provide formulations of the maximum clique problem as a quadratic unconstrained binary optimization (QUBO) problem, which is one of the two input types (together with the Ising model) acceptable by the machine, andmore » compare several quantum implementations to current classical algorithms such as simulated annealing, Gurobi, and third-party clique finding heuristics. We further estimate the contributions of the quantum phase of the quantum annealer and the classical post-processing phase typically used to enhance each solution returned by DW. We demonstrate that on random graphs that fit DW, no quantum speedup can be observed compared with the classical algorithms. On the other hand, for instances specifically designed to fit well the DW qubit interconnection network, we observe substantial speed-ups in computing time over classical approaches.« less

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

PubMed

Zhao, Dongfang; Yang, Li

2009-01-01

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

Finding Maximum Cliques on the D-Wave Quantum Annealer

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

Chapuis, Guillaume; Djidjev, Hristo; Hahn, Georg

This work assesses the performance of the D-Wave 2X (DW) quantum annealer for finding a maximum clique in a graph, one of the most fundamental and important NP-hard problems. Because the size of the largest graphs DW can directly solve is quite small (usually around 45 vertices), we also consider decomposition algorithms intended for larger graphs and analyze their performance. For smaller graphs that fit DW, we provide formulations of the maximum clique problem as a quadratic unconstrained binary optimization (QUBO) problem, which is one of the two input types (together with the Ising model) acceptable by the machine, andmore » compare several quantum implementations to current classical algorithms such as simulated annealing, Gurobi, and third-party clique finding heuristics. We further estimate the contributions of the quantum phase of the quantum annealer and the classical post-processing phase typically used to enhance each solution returned by DW. We demonstrate that on random graphs that fit DW, no quantum speedup can be observed compared with the classical algorithms. On the other hand, for instances specifically designed to fit well the DW qubit interconnection network, we observe substantial speed-ups in computing time over classical approaches.« less

Coloring geographical threshold graphs

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

Bradonjic, Milan; Percus, Allon; Muller, Tobias

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 analyzemore » 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.« less

Claw-Free Maximal Planar Graphs

DTIC Science & Technology

1989-01-01

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

Can SNOMED CT be squeezed without losing its shape?

PubMed

López-García, Pablo; Schulz, Stefan

2016-09-21

In biomedical applications where the size and complexity of SNOMED CT become problematic, using a smaller subset that can act as a reasonable substitute is usually preferred. In a special class of use cases-like ontology-based quality assurance, or when performing scaling experiments for real-time performance-it is essential that modules show a similar shape than SNOMED CT in terms of concept distribution per sub-hierarchy. Exactly how to extract such balanced modules remains unclear, as most previous work on ontology modularization has focused on other problems. In this study, we investigate to what extent extracting balanced modules that preserve the original shape of SNOMED CT is possible, by presenting and evaluating an iterative algorithm. We used a graph-traversal modularization approach based on an input signature. To conform to our definition of a balanced module, we implemented an iterative algorithm that carefully bootstraped and dynamically adjusted the signature at each step. We measured the error for each sub-hierarchy and defined convergence as a residual sum of squares <1. Using 2000 concepts as an initial signature, our algorithm converged after seven iterations and extracted a module 4.7 % the size of SNOMED CT. Seven sub-hierarhies were either over or under-represented within a range of 1-8 %. Our study shows that balanced modules from large terminologies can be extracted using ontology graph-traversal modularization techniques under certain conditions: that the process is repeated a number of times, the input signature is dynamically adjusted in each iteration, and a moderate under/over-representation of some hierarchies is tolerated. In the case of SNOMED CT, our results conclusively show that it can be squeezed to less than 5 % of its size without any sub-hierarchy losing its shape more than 8 %, which is likely sufficient in most use cases.

Rapid Onboard Trajectory Design for Autonomous Spacecraft in Multibody Systems

NASA Astrophysics Data System (ADS)

Trumbauer, Eric Michael

This research develops automated, on-board trajectory planning algorithms in order to support current and new mission concepts. These include orbiter missions to Phobos or Deimos, Outer Planet Moon orbiters, and robotic and crewed missions to small bodies. The challenges stem from the limited on-board computing resources which restrict full trajectory optimization with guaranteed convergence in complex dynamical environments. The approach taken consists of leveraging pre-mission computations to create a large database of pre-computed orbits and arcs. Such a database is used to generate a discrete representation of the dynamics in the form of a directed graph, which acts to index these arcs. This allows the use of graph search algorithms on-board in order to provide good approximate solutions to the path planning problem. Coupled with robust differential correction and optimization techniques, this enables the determination of an efficient path between any boundary conditions with very little time and computing effort. Furthermore, the optimization methods developed here based on sequential convex programming are shown to have provable convergence properties, as well as generating feasible major iterates in case of a system interrupt -- a key requirement for on-board application. The outcome of this project is thus the development of an algorithmic framework which allows the deployment of this approach in a variety of specific mission contexts. Test cases related to missions of interest to NASA and JPL such as a Phobos orbiter and a Near Earth Asteroid interceptor are demonstrated, including the results of an implementation on the RAD750 flight processor. This method fills a gap in the toolbox being developed to create fully autonomous space exploration systems.

Interferometric synthetic aperture radar phase unwrapping based on sparse Markov random fields by graph cuts

NASA Astrophysics Data System (ADS)

Zhou, Lifan; Chai, Dengfeng; Xia, Yu; Ma, Peifeng; Lin, Hui

2018-01-01

Phase unwrapping (PU) is one of the key processes in reconstructing the digital elevation model of a scene from its interferometric synthetic aperture radar (InSAR) data. It is known that two-dimensional (2-D) PU problems can be formulated as maximum a posteriori estimation of Markov random fields (MRFs). However, considering that the traditional MRF algorithm is usually defined on a rectangular grid, it fails easily if large parts of the wrapped data are dominated by noise caused by large low-coherence area or rapid-topography variation. A PU solution based on sparse MRF is presented to extend the traditional MRF algorithm to deal with sparse data, which allows the unwrapping of InSAR data dominated by high phase noise. To speed up the graph cuts algorithm for sparse MRF, we designed dual elementary graphs and merged them to obtain the Delaunay triangle graph, which is used to minimize the energy function efficiently. The experiments on simulated and real data, compared with other existing algorithms, both confirm the effectiveness of the proposed MRF approach, which suffers less from decorrelation effects caused by large low-coherence area or rapid-topography variation.

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

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

Sengupta, Dipanjan; Song, Shuaiwen; Agarwal, Kapil

2015-11-15

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

The many faces of graph dynamics

NASA Astrophysics Data System (ADS)

Pignolet, Yvonne Anne; Roy, Matthieu; Schmid, Stefan; Tredan, Gilles

2017-06-01

The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is known today about the network dynamics: indeed, complex networks in reality are not static, but rather dynamically evolve over time. Our paper is motivated by the empirical observation that network evolution patterns seem far from random, but exhibit structure. Moreover, the specific patterns appear to depend on the network type, contradicting the existence of a ‘one fits it all’ model. However, we still lack observables to quantify these intuitions, as well as metrics to compare graph evolutions. Such observables and metrics are needed for extrapolating or predicting evolutions, as well as for interpolating graph evolutions. To explore the many faces of graph dynamics and to quantify temporal changes, this paper suggests to build upon the concept of centrality, a measure of node importance in a network. In particular, we introduce the notion of centrality distance, a natural similarity measure for two graphs which depends on a given centrality, characterizing the graph type. Intuitively, centrality distances reflect the extent to which (non-anonymous) node roles are different or, in case of dynamic graphs, have changed over time, between two graphs. We evaluate the centrality distance approach for five evolutionary models and seven real-world social and physical networks. Our results empirically show the usefulness of centrality distances for characterizing graph dynamics compared to a null-model of random evolution, and highlight the differences between the considered scenarios. Interestingly, our approach allows us to compare the dynamics of very different networks, in terms of scale and evolution speed.

Fast Decentralized Averaging via Multi-scale Gossip

NASA Astrophysics Data System (ADS)

Tsianos, Konstantinos I.; Rabbat, Michael G.

We are interested in the problem of computing the average consensus in a distributed fashion on random geometric graphs. We describe a new algorithm called Multi-scale Gossip which employs a hierarchical decomposition of the graph to partition the computation into tractable sub-problems. Using only pairwise messages of fixed size that travel at most O(n^{1/3}) hops, our algorithm is robust and has communication cost of O(n loglogn logɛ - 1) transmissions, which is order-optimal up to the logarithmic factor in n. Simulated experiments verify the good expected performance on graphs of many thousands of nodes.

Iterative cross section sequence graph for handwritten character segmentation.

PubMed

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 graph-Laplacian-based feature extraction algorithm for neural spike sorting.

PubMed

Ghanbari, Yasser; Spence, Larry; Papamichalis, Panos

2009-01-01

Analysis of extracellular neural spike recordings is highly dependent upon the accuracy of neural waveform classification, commonly referred to as spike sorting. Feature extraction is an important stage of this process because it can limit the quality of clustering which is performed in the feature space. This paper proposes a new feature extraction method (which we call Graph Laplacian Features, GLF) based on minimizing the graph Laplacian and maximizing the weighted variance. The algorithm is compared with Principal Components Analysis (PCA, the most commonly-used feature extraction method) using simulated neural data. The results show that the proposed algorithm produces more compact and well-separated clusters compared to PCA. As an added benefit, tentative cluster centers are output which can be used to initialize a subsequent clustering stage.

Visibility graph analysis on heartbeat dynamics of meditation training

NASA Astrophysics Data System (ADS)

Jiang, Sen; Bian, Chunhua; Ning, Xinbao; Ma, Qianli D. Y.

2013-06-01

We apply the visibility graph analysis to human heartbeat dynamics by constructing the complex networks of heartbeat interval time series and investigating the statistical properties of the network before and during chi and yoga meditation. The experiment results show that visibility graph analysis can reveal the dynamical changes caused by meditation training manifested as regular heartbeat, which is closely related to the adjustment of autonomous neural system, and visibility graph analysis is effective to evaluate the effect of meditation.

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

DTIC Science & Technology

2012-06-01

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

Diagnostic and Remedial Learning Strategy Based on Conceptual Graphs

ERIC Educational Resources Information Center

Jong, BinShyan; Lin, TsongWuu; Wu, YuLung; Chan, Teyi

2004-01-01

Numerous scholars have applied conceptual graphs for explanatory purposes. This study devised the Remedial-Instruction Decisive path (RID path) algorithm for diagnosing individual student learning situation. This study focuses on conceptual graphs. According to the concepts learned by students and the weight values of relations among these…

SDIA: A dynamic situation driven information fusion algorithm for cloud environment

NASA Astrophysics Data System (ADS)

Guo, Shuhang; Wang, Tong; Wang, Jian

2017-09-01

Information fusion is an important issue in information integration domain. In order to form an extensive information fusion technology under the complex and diverse situations, a new information fusion algorithm is proposed. Firstly, a fuzzy evaluation model of tag utility was proposed that can be used to count the tag entropy. Secondly, a ubiquitous situation tag tree model is proposed to define multidimensional structure of information situation. Thirdly, the similarity matching between the situation models is classified into three types: the tree inclusion, the tree embedding, and the tree compatibility. Next, in order to reduce the time complexity of the tree compatible matching algorithm, a fast and ordered tree matching algorithm is proposed based on the node entropy, which is used to support the information fusion by ubiquitous situation. Since the algorithm revolve from the graph theory of disordered tree matching algorithm, it can improve the information fusion present recall rate and precision rate in the situation. The information fusion algorithm is compared with the star and the random tree matching algorithm, and the difference between the three algorithms is analyzed in the view of isomorphism, which proves the innovation and applicability of the algorithm.

An Integrated Approach to Locality-Conscious Processor Allocation and Scheduling of Mixed-Parallel Applications

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

Vydyanathan, Naga; Krishnamoorthy, Sriram; Sabin, Gerald M.

2009-08-01

Complex parallel applications can often be modeled as directed acyclic graphs of coarse-grained application-tasks with dependences. These applications exhibit both task- and data-parallelism, and combining these two (also called mixedparallelism), has been shown to be an effective model for their execution. In this paper, we present an algorithm to compute the appropriate mix of task- and data-parallelism required to minimize the parallel completion time (makespan) of these applications. In other words, our algorithm determines the set of tasks that should be run concurrently and the number of processors to be allocated to each task. The processor allocation and scheduling decisionsmore » are made in an integrated manner and are based on several factors such as the structure of the taskgraph, the runtime estimates and scalability characteristics of the tasks and the inter-task data communication volumes. A locality conscious scheduling strategy is used to improve inter-task data reuse. Evaluation through simulations and actual executions of task graphs derived from real applications as well as synthetic graphs shows that our algorithm consistently generates schedules with lower makespan as compared to CPR and CPA, two previously proposed scheduling algorithms. Our algorithm also produces schedules that have lower makespan than pure taskand data-parallel schedules. For task graphs with known optimal schedules or lower bounds on the makespan, our algorithm generates schedules that are closer to the optima than other scheduling approaches.« less

Feasibility of using the linac real-time log data for VMAT treatment verification

NASA Astrophysics Data System (ADS)

Midi, N. S.; Zin, Hafiz M.

2017-05-01

This study investigates the feasibility of using the real-time log data from a linac to verify Volumetric Modulated Arc Therapy (VMAT) treatment. The treatment log data for an Elekta Synergy linac can be recorded at a sampling rate of 4 Hz using the service graphing tool on the linac control computer. A treatment plan that simulates a VMAT treatment was delivered from the linac and all the dynamic treatment parameters including monitor unit (MU), Multileaf Collimator (MLC) position, jaw position, gantry angle and collimator angle were recorded in real-time using the service graphing tool. The recorded raw data were extracted and analysed using algorithms written in Matlab (MathWorks, Natick, MA). The actual treatment parameters logged using the service graphing tool was compared to the prescription and the deviations were analysed. The MLC position errors travelling at the speed range from -3.25 to 5.92 cm/s were between -1.7 mm to 2.5 mm, well within the 3.5 mm tolerance value (AAPM TG-142). The discrepancies of other delivery parameters were also within the tolerance. The real-time linac parameters logged using the service graphing tool can be used as a supplementary data for patient specific VMAT pre-treatment quality assurance.

Quantum snake walk on graphs

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

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, whichmore » 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.« less

Simulator for heterogeneous dataflow architectures

NASA Technical Reports Server (NTRS)

Malekpour, Mahyar R.

1993-01-01

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

The Roadmaker's algorithm for the discrete pulse transform.

PubMed

Laurie, Dirk P

2011-02-01

The discrete pulse transform (DPT) is a decomposition of an observed signal into a sum of pulses, i.e., signals that are constant on a connected set and zero elsewhere. Originally developed for 1-D signal processing, the DPT has recently been generalized to more dimensions. Applications in image processing are currently being investigated. The time required to compute the DPT as originally defined via the successive application of LULU operators (members of a class of minimax filters studied by Rohwer) has been a severe drawback to its applicability. This paper introduces a fast method for obtaining such a decomposition, called the Roadmaker's algorithm because it involves filling pits and razing bumps. It acts selectively only on those features actually present in the signal, flattening them in order of increasing size by subtracing an appropriate positive or negative pulse, which is then appended to the decomposition. The implementation described here covers 1-D signal as well as two and 3-D image processing in a single framework. This is achieved by considering the signal or image as a function defined on a graph, with the geometry specified by the edges of the graph. Whenever a feature is flattened, nodes in the graph are merged, until eventually only one node remains. At that stage, a new set of edges for the same nodes as the graph, forming a tree structure, defines the obtained decomposition. The Roadmaker's algorithm is shown to be equivalent to the DPT in the sense of obtaining the same decomposition. However, its simpler operators are not in general equivalent to the LULU operators in situations where those operators are not applied successively. A by-product of the Roadmaker's algorithm is that it yields a proof of the so-called Highlight Conjecture, stated as an open problem in 2006. We pay particular attention to algorithmic details and complexity, including a demonstration that in the 1-D case, and also in the case of a complete graph, the Roadmaker's algorithm has optimal complexity: it runs in time O(m), where m is the number of arcs in the graph.

The Edge-Disjoint Path Problem on Random Graphs by Message-Passing.

PubMed

Altarelli, Fabrizio; Braunstein, Alfredo; Dall'Asta, Luca; De Bacco, Caterina; Franz, Silvio

2015-01-01

We present a message-passing algorithm to solve a series of edge-disjoint path problems on graphs based on the zero-temperature cavity equations. Edge-disjoint paths problems are important in the general context of routing, that can be defined by incorporating under a unique framework both traffic optimization and total path length minimization. The computation of the cavity equations can be performed efficiently by exploiting a mapping of a generalized edge-disjoint path problem on a star graph onto a weighted maximum matching problem. We perform extensive numerical simulations on random graphs of various types to test the performance both in terms of path length minimization and maximization of the number of accommodated paths. In addition, we test the performance on benchmark instances on various graphs by comparison with state-of-the-art algorithms and results found in the literature. Our message-passing algorithm always outperforms the others in terms of the number of accommodated paths when considering non trivial instances (otherwise it gives the same trivial results). Remarkably, the largest improvement in performance with respect to the other methods employed is found in the case of benchmarks with meshes, where the validity hypothesis behind message-passing is expected to worsen. In these cases, even though the exact message-passing equations do not converge, by introducing a reinforcement parameter to force convergence towards a sub optimal solution, we were able to always outperform the other algorithms with a peak of 27% performance improvement in terms of accommodated paths. On random graphs, we numerically observe two separated regimes: one in which all paths can be accommodated and one in which this is not possible. We also investigate the behavior of both the number of paths to be accommodated and their minimum total length.

A critical analysis of computational protein design with sparse residue interaction graphs

PubMed Central

Georgiev, Ivelin S.

2017-01-01

Protein design algorithms enumerate a combinatorial number of candidate structures to compute the Global Minimum Energy Conformation (GMEC). To efficiently find the GMEC, protein design algorithms must methodically reduce the conformational search space. By applying distance and energy cutoffs, the protein system to be designed can thus be represented using a sparse residue interaction graph, where the number of interacting residue pairs is less than all pairs of mutable residues, and the corresponding GMEC is called the sparse GMEC. However, ignoring some pairwise residue interactions can lead to a change in the energy, conformation, or sequence of the sparse GMEC vs. the original or the full GMEC. Despite the widespread use of sparse residue interaction graphs in protein design, the above mentioned effects of their use have not been previously analyzed. To analyze the costs and benefits of designing with sparse residue interaction graphs, we computed the GMECs for 136 different protein design problems both with and without distance and energy cutoffs, and compared their energies, conformations, and sequences. Our analysis shows that the differences between the GMECs depend critically on whether or not the design includes core, boundary, or surface residues. Moreover, neglecting long-range interactions can alter local interactions and introduce large sequence differences, both of which can result in significant structural and functional changes. Designs on proteins with experimentally measured thermostability show it is beneficial to compute both the full and the sparse GMEC accurately and efficiently. To this end, we show that a provable, ensemble-based algorithm can efficiently compute both GMECs by enumerating a small number of conformations, usually fewer than 1000. This provides a novel way to combine sparse residue interaction graphs with provable, ensemble-based algorithms to reap the benefits of sparse residue interaction graphs while avoiding their potential inaccuracies. PMID:28358804

Eigenvector synchronization, graph rigidity and the molecule problemR

PubMed Central

Cucuringu, Mihai; Singer, Amit; Cowburn, David

2013-01-01

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 ℝ3, 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 ℝ3, 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. PMID:24432187

The Edge-Disjoint Path Problem on Random Graphs by Message-Passing

PubMed Central

2015-01-01

We present a message-passing algorithm to solve a series of edge-disjoint path problems on graphs based on the zero-temperature cavity equations. Edge-disjoint paths problems are important in the general context of routing, that can be defined by incorporating under a unique framework both traffic optimization and total path length minimization. The computation of the cavity equations can be performed efficiently by exploiting a mapping of a generalized edge-disjoint path problem on a star graph onto a weighted maximum matching problem. We perform extensive numerical simulations on random graphs of various types to test the performance both in terms of path length minimization and maximization of the number of accommodated paths. In addition, we test the performance on benchmark instances on various graphs by comparison with state-of-the-art algorithms and results found in the literature. Our message-passing algorithm always outperforms the others in terms of the number of accommodated paths when considering non trivial instances (otherwise it gives the same trivial results). Remarkably, the largest improvement in performance with respect to the other methods employed is found in the case of benchmarks with meshes, where the validity hypothesis behind message-passing is expected to worsen. In these cases, even though the exact message-passing equations do not converge, by introducing a reinforcement parameter to force convergence towards a sub optimal solution, we were able to always outperform the other algorithms with a peak of 27% performance improvement in terms of accommodated paths. On random graphs, we numerically observe two separated regimes: one in which all paths can be accommodated and one in which this is not possible. We also investigate the behavior of both the number of paths to be accommodated and their minimum total length. PMID:26710102

Multiclass Data Segmentation Using Diffuse Interface Methods on Graphs

DTIC Science & Technology

2014-01-01

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

Spatial Search by Quantum Walk is Optimal for Almost all Graphs.

PubMed

Chakraborty, Shantanav; Novo, Leonardo; Ambainis, Andris; Omar, Yasser

2016-03-11

The problem of finding a marked node in a graph can be solved by the spatial search algorithm based on continuous-time quantum walks (CTQW). However, this algorithm is known to run in optimal time only for a handful of graphs. In this work, we prove that for Erdös-Renyi random graphs, i.e., graphs of n vertices where each edge exists with probability p, search by CTQW is almost surely optimal as long as p≥log^{3/2}(n)/n. Consequently, we show that quantum spatial search is in fact optimal for almost all graphs, meaning that the fraction of graphs of n vertices for which this optimality holds tends to one in the asymptotic limit. We obtain this result by proving that search is optimal on graphs where the ratio between the second largest and the largest eigenvalue is bounded by a constant smaller than 1. Finally, we show that we can extend our results on search to establish high fidelity quantum communication between two arbitrary nodes of a random network of interacting qubits, namely, to perform quantum state transfer, as well as entanglement generation. Our work shows that quantum information tasks typically designed for structured systems retain performance in very disordered structures.

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

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

Sengupta, Dipanjan; Agarwal, Kapil; Song, Shuaiwen

2015-09-30

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

Attributed relational graphs for cell nucleus segmentation in fluorescence microscopy images.

PubMed

Arslan, Salim; Ersahin, Tulin; Cetin-Atalay, Rengul; Gunduz-Demir, Cigdem

2013-06-01

More rapid and accurate high-throughput screening in molecular cellular biology research has become possible with the development of automated microscopy imaging, for which cell nucleus segmentation commonly constitutes the core step. Although several promising methods exist for segmenting the nuclei of monolayer isolated and less-confluent cells, it still remains an open problem to segment the nuclei of more-confluent cells, which tend to grow in overlayers. To address this problem, we propose a new model-based nucleus segmentation algorithm. This algorithm models how a human locates a nucleus by identifying the nucleus boundaries and piecing them together. In this algorithm, we define four types of primitives to represent nucleus boundaries at different orientations and construct an attributed relational graph on the primitives to represent their spatial relations. Then, we reduce the nucleus identification problem to finding predefined structural patterns in the constructed graph and also use the primitives in region growing to delineate the nucleus borders. Working with fluorescence microscopy images, our experiments demonstrate that the proposed algorithm identifies nuclei better than previous nucleus segmentation algorithms.

Finding Hierarchical and Overlapping Dense Subgraphs using Nucleus Decompositions

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

Seshadhri, Comandur; Pinar, Ali; Sariyuce, Ahmet Erdem

Finding dense substructures in a graph is a fundamental graph mining operation, with applications in bioinformatics, social networks, and visualization to name a few. Yet most standard formulations of this problem (like clique, quasiclique, k-densest subgraph) are NP-hard. Furthermore, the goal is rarely to nd the \\true optimum", but to identify many (if not all) dense substructures, understand their distribution in the graph, and ideally determine a hierarchical structure among them. Current dense subgraph nding algorithms usually optimize some objective, and only nd a few such subgraphs without providing any hierarchy. It is also not clear how to account formore » overlaps in dense substructures. We de ne the nucleus decomposition of a graph, which represents the graph as a forest of nuclei. Each nucleus is a subgraph where smaller cliques are present in many larger cliques. The forest of nuclei is a hierarchy by containment, where the edge density increases as we proceed towards leaf nuclei. Sibling nuclei can have limited intersections, which allows for discovery of overlapping dense subgraphs. With the right parameters, the nuclear decomposition generalizes the classic notions of k-cores and k-trusses. We give provable e cient algorithms for nuclear decompositions, and empirically evaluate their behavior in a variety of real graphs. The tree of nuclei consistently gives a global, hierarchical snapshot of dense substructures, and outputs dense subgraphs of higher quality than other state-of-theart solutions. Our algorithm can process graphs with tens of millions of edges in less than an hour.« less

Attribute-based Decision Graphs: A framework for multiclass data classification.

PubMed

Bertini, João Roberto; Nicoletti, Maria do Carmo; Zhao, Liang

2017-01-01

Graph-based algorithms have been successfully applied in machine learning and data mining tasks. A simple but, widely used, approach to build graphs from vector-based data is to consider each data instance as a vertex and connecting pairs of it using a similarity measure. Although this abstraction presents some advantages, such as arbitrary shape representation of the original data, it is still tied to some drawbacks, for example, it is dependent on the choice of a pre-defined distance metric and is biased by the local information among data instances. Aiming at exploring alternative ways to build graphs from data, this paper proposes an algorithm for constructing a new type of graph, called Attribute-based Decision Graph-AbDG. Given a vector-based data set, an AbDG is built by partitioning each data attribute range into disjoint intervals and representing each interval as a vertex. The edges are then established between vertices from different attributes according to a pre-defined pattern. Classification is performed through a matching process among the attribute values of the new instance and AbDG. Moreover, AbDG provides an inner mechanism to handle missing attribute values, which contributes for expanding its applicability. Results of classification tasks have shown that AbDG is a competitive approach when compared to well-known multiclass algorithms. The main contribution of the proposed framework is the combination of the advantages of attribute-based and graph-based techniques to perform robust pattern matching data classification, while permitting the analysis the input data considering only a subset of its attributes. Copyright © 2016 Elsevier Ltd. All rights reserved.

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

PubMed

Pang, Jiahao; Cheung, Gene

2017-04-01

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

A heuristic for efficient data distribution management in distributed simulation

NASA Astrophysics Data System (ADS)

Gupta, Pankaj; Guha, Ratan K.

2005-05-01

In this paper, we propose an algorithm for reducing the complexity of region matching and efficient multicasting in data distribution management component of High Level Architecture (HLA) Run Time Infrastructure (RTI). The current data distribution management (DDM) techniques rely on computing the intersection between the subscription and update regions. When a subscription region and an update region of different federates overlap, RTI establishes communication between the publisher and the subscriber. It subsequently routes the updates from the publisher to the subscriber. The proposed algorithm computes the update/subscription regions matching for dynamic allocation of multicast group. It provides new multicast routines that exploit the connectivity of federation by communicating updates regarding interactions and routes information only to those federates that require them. The region-matching problem in DDM reduces to clique-covering problem using the connections graph abstraction where the federations represent the vertices and the update/subscribe relations represent the edges. We develop an abstract model based on connection graph for data distribution management. Using this abstract model, we propose a heuristic for solving the region-matching problem of DDM. We also provide complexity analysis of the proposed heuristics.

Basin Hopping Graph: a computational framework to characterize RNA folding landscapes

PubMed Central

Kucharík, Marcel; Hofacker, Ivo L.; Stadler, Peter F.; Qin, Jing

2014-01-01

Motivation: RNA folding is a complicated kinetic process. The minimum free energy structure provides only a static view of the most stable conformational state of the system. It is insufficient to give detailed insights into the dynamic behavior of RNAs. A sufficiently sophisticated analysis of the folding free energy landscape, however, can provide the relevant information. Results: We introduce the Basin Hopping Graph (BHG) as a novel coarse-grained model of folding landscapes. Each vertex of the BHG is a local minimum, which represents the corresponding basin in the landscape. Its edges connect basins when the direct transitions between them are ‘energetically favorable’. Edge weights endcode the corresponding saddle heights and thus measure the difficulties of these favorable transitions. BHGs can be approximated accurately and efficiently for RNA molecules well beyond the length range accessible to enumerative algorithms. Availability and implementation: The algorithms described here are implemented in C++ as standalone programs. Its source code and supplemental material can be freely downloaded from http://www.tbi.univie.ac.at/bhg.html. Contact: qin@bioinf.uni-leipzig.de Supplementary information: Supplementary data are available at Bioinformatics online. PMID:24648041

Automated intraretinal layer segmentation of optical coherence tomography images using graph-theoretical methods

NASA Astrophysics Data System (ADS)

Roy, Priyanka; Gholami, Peyman; Kuppuswamy Parthasarathy, Mohana; Zelek, John; Lakshminarayanan, Vasudevan

2018-02-01

Segmentation of spectral-domain Optical Coherence Tomography (SD-OCT) images facilitates visualization and quantification of sub-retinal layers for diagnosis of retinal pathologies. However, manual segmentation is subjective, expertise dependent, and time-consuming, which limits applicability of SD-OCT. Efforts are therefore being made to implement active-contours, artificial intelligence, and graph-search to automatically segment retinal layers with accuracy comparable to that of manual segmentation, to ease clinical decision-making. Although, low optical contrast, heavy speckle noise, and pathologies pose challenges to automated segmentation. Graph-based image segmentation approach stands out from the rest because of its ability to minimize the cost function while maximising the flow. This study has developed and implemented a shortest-path based graph-search algorithm for automated intraretinal layer segmentation of SD-OCT images. The algorithm estimates the minimal-weight path between two graph-nodes based on their gradients. Boundary position indices (BPI) are computed from the transition between pixel intensities. The mean difference between BPIs of two consecutive layers quantify individual layer thicknesses, which shows statistically insignificant differences when compared to a previous study [for overall retina: p = 0.17, for individual layers: p > 0.05 (except one layer: p = 0.04)]. These results substantiate the accurate delineation of seven intraretinal boundaries in SD-OCT images by this algorithm, with a mean computation time of 0.93 seconds (64-bit Windows10, core i5, 8GB RAM). Besides being self-reliant for denoising, the algorithm is further computationally optimized to restrict segmentation within the user defined region-of-interest. The efficiency and reliability of this algorithm, even in noisy image conditions, makes it clinically applicable.

GraphStore: A Distributed Graph Storage System for Big Data Networks

ERIC Educational Resources Information Center

Martha, VenkataSwamy

2013-01-01

Networks, such as social networks, are a universal solution for modeling complex problems in real time, especially in the Big Data community. While previous studies have attempted to enhance network processing algorithms, none have paved a path for the development of a persistent storage system. The proposed solution, GraphStore, provides an…

Graph rigidity, cyclic belief propagation, and point pattern matching.

PubMed

McAuley, Julian J; Caetano, Tibério S; Barbosa, Marconi S

2008-11-01

A recent paper [1] proposed a provably optimal polynomial time method for performing near-isometric point pattern matching by means of exact probabilistic inference in a chordal graphical model. Its fundamental result is that the chordal graph in question is shown to be globally rigid, implying that exact inference provides the same matching solution as exact inference in a complete graphical model. This implies that the algorithm is optimal when there is no noise in the point patterns. In this paper, we present a new graph that is also globally rigid but has an advantage over the graph proposed in [1]: Its maximal clique size is smaller, rendering inference significantly more efficient. However, this graph is not chordal, and thus, standard Junction Tree algorithms cannot be directly applied. Nevertheless, we show that loopy belief propagation in such a graph converges to the optimal solution. This allows us to retain the optimality guarantee in the noiseless case, while substantially reducing both memory requirements and processing time. Our experimental results show that the accuracy of the proposed solution is indistinguishable from that in [1] when there is noise in the point patterns.

Listing triangles in expected linear time on a class of power law graphs.

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

Nordman, Daniel J.; Wilson, Alyson G.; Phillips, Cynthia Ann

Enumerating triangles (3-cycles) in graphs is a kernel operation for social network analysis. For example, many community detection methods depend upon finding common neighbors of two related entities. We consider Cohen's simple and elegant solution for listing triangles: give each node a 'bucket.' Place each edge into the bucket of its endpoint of lowest degree, breaking ties consistently. Each node then checks each pair of edges in its bucket, testing for the adjacency that would complete that triangle. Cohen presents an informal argument that his algorithm should run well on real graphs. We formalize this argument by providing an analysismore » for the expected running time on a class of random graphs, including power law graphs. We consider a rigorously defined method for generating a random simple graph, the erased configuration model (ECM). In the ECM each node draws a degree independently from a marginal degree distribution, endpoints pair randomly, and we erase self loops and multiedges. If the marginal degree distribution has a finite second moment, it follows immediately that Cohen's algorithm runs in expected linear time. Furthermore, it can still run in expected linear time even when the degree distribution has such a heavy tail that the second moment is not finite. We prove that Cohen's algorithm runs in expected linear time when the marginal degree distribution has finite 4/3 moment and no vertex has degree larger than {radical}n. In fact we give the precise asymptotic value of the expected number of edge pairs per bucket. A finite 4/3 moment is required; if it is unbounded, then so is the number of pairs. The marginal degree distribution of a power law graph has bounded 4/3 moment when its exponent {alpha} is more than 7/3. Thus for this class of power law graphs, with degree at most {radical}n, Cohen's algorithm runs in expected linear time. This is precisely the value of {alpha} for which the clustering coefficient tends to zero asymptotically, and it is in the range that is relevant for the degree distribution of the World-Wide Web.« less

Distributed Optimal Consensus Over Resource Allocation Network and Its Application to Dynamical Economic Dispatch.

PubMed

Li, Chaojie; Yu, Xinghuo; Huang, Tingwen; He, Xing; Chaojie Li; Xinghuo Yu; Tingwen Huang; Xing He; Li, Chaojie; Huang, Tingwen; He, Xing; Yu, Xinghuo

2018-06-01

The resource allocation problem is studied and reformulated by a distributed interior point method via a -logarithmic barrier. By the facilitation of the graph Laplacian, a fully distributed continuous-time multiagent system is developed for solving the problem. Specifically, to avoid high singularity of the -logarithmic barrier at boundary, an adaptive parameter switching strategy is introduced into this dynamical multiagent system. The convergence rate of the distributed algorithm is obtained. Moreover, a novel distributed primal-dual dynamical multiagent system is designed in a smart grid scenario to seek the saddle point of dynamical economic dispatch, which coincides with the optimal solution. The dual decomposition technique is applied to transform the optimization problem into easily solvable resource allocation subproblems with local inequality constraints. The good performance of the new dynamical systems is, respectively, verified by a numerical example and the IEEE six-bus test system-based simulations.

Bayesian Analysis for Exponential Random Graph Models Using the Adaptive Exchange Sampler.

PubMed

Jin, Ick Hoon; Yuan, Ying; Liang, Faming

2013-10-01

Exponential random graph models have been widely used in social network analysis. However, these models are extremely difficult to handle from a statistical viewpoint, because of the intractable normalizing constant and model degeneracy. In this paper, we consider a fully Bayesian analysis for exponential random graph models using the adaptive exchange sampler, which solves the intractable normalizing constant and model degeneracy issues encountered in Markov chain Monte Carlo (MCMC) simulations. The adaptive exchange sampler can be viewed as a MCMC extension of the exchange algorithm, and it generates auxiliary networks via an importance sampling procedure from an auxiliary Markov chain running in parallel. The convergence of this algorithm is established under mild conditions. The adaptive exchange sampler is illustrated using a few social networks, including the Florentine business network, molecule synthetic network, and dolphins network. The results indicate that the adaptive exchange algorithm can produce more accurate estimates than approximate exchange algorithms, while maintaining the same computational efficiency.

Graph determined symbolic dynamics and hybrid systems

NASA Astrophysics Data System (ADS)

Ayers, Kimberly Danielle

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

A formation control strategy with coupling weights for the multi-robot system

NASA Astrophysics Data System (ADS)

Liang, Xudong; Wang, Siming; Li, Weijie

2017-12-01

The distributed formation problem of the multi-robot system with general linear dynamic characteristics and directed communication topology is discussed. In order to avoid that the multi-robot system can not maintain the desired formation in the complex communication environment, the distributed cooperative algorithm with coupling weights based on zipf distribution is designed. The asymptotic stability condition for the formation of the multi-robot system is given, and the theory of the graph and the Lyapunov theory are used to prove that the formation can converge to the desired geometry formation and the desired motion rules of the virtual leader under this condition. Nontrivial simulations are performed to validate the effectiveness of the distributed cooperative algorithm with coupling weights.

Design tool for multiprocessor scheduling and evaluation of iterative dataflow algorithms

NASA Technical Reports Server (NTRS)

Jones, Robert L., III

1995-01-01

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

Efficient dynamic graph construction for inductive semi-supervised learning.

PubMed

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

2017-10-01

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

Phase unwrapping with graph cuts optimization and dual decomposition acceleration for 3D high-resolution MRI data.

PubMed

Dong, Jianwu; Chen, Feng; Zhou, Dong; Liu, Tian; Yu, Zhaofei; Wang, Yi

2017-03-01

Existence of low SNR regions and rapid-phase variations pose challenges to spatial phase unwrapping algorithms. Global optimization-based phase unwrapping methods are widely used, but are significantly slower than greedy methods. In this paper, dual decomposition acceleration is introduced to speed up a three-dimensional graph cut-based phase unwrapping algorithm. The phase unwrapping problem is formulated as a global discrete energy minimization problem, whereas the technique of dual decomposition is used to increase the computational efficiency by splitting the full problem into overlapping subproblems and enforcing the congruence of overlapping variables. Using three dimensional (3D) multiecho gradient echo images from an agarose phantom and five brain hemorrhage patients, we compared this proposed method with an unaccelerated graph cut-based method. Experimental results show up to 18-fold acceleration in computation time. Dual decomposition significantly improves the computational efficiency of 3D graph cut-based phase unwrapping algorithms. Magn Reson Med 77:1353-1358, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.

A Graph-Centric Approach for Metagenome-Guided Peptide and Protein Identification in Metaproteomics

PubMed Central

Tang, Haixu; Li, Sujun; Ye, Yuzhen

2016-01-01

Metaproteomic studies adopt the common bottom-up proteomics approach to investigate the protein composition and the dynamics of protein expression in microbial communities. When matched metagenomic and/or metatranscriptomic data of the microbial communities are available, metaproteomic data analyses often employ a metagenome-guided approach, in which complete or fragmental protein-coding genes are first directly predicted from metagenomic (and/or metatranscriptomic) sequences or from their assemblies, and the resulting protein sequences are then used as the reference database for peptide/protein identification from MS/MS spectra. This approach is often limited because protein coding genes predicted from metagenomes are incomplete and fragmental. In this paper, we present a graph-centric approach to improving metagenome-guided peptide and protein identification in metaproteomics. Our method exploits the de Bruijn graph structure reported by metagenome assembly algorithms to generate a comprehensive database of protein sequences encoded in the community. We tested our method using several public metaproteomic datasets with matched metagenomic and metatranscriptomic sequencing data acquired from complex microbial communities in a biological wastewater treatment plant. The results showed that many more peptides and proteins can be identified when assembly graphs were utilized, improving the characterization of the proteins expressed in the microbial communities. The additional proteins we identified contribute to the characterization of important pathways such as those involved in degradation of chemical hazards. Our tools are released as open-source software on github at https://github.com/COL-IU/Graph2Pro. PMID:27918579

Classification of Domain Movements in Proteins Using Dynamic Contact Graphs

PubMed Central

Taylor, Daniel; Cawley, Gavin; Hayward, Steven

2013-01-01

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

Task scheduling in dataflow computer architectures

NASA Technical Reports Server (NTRS)

Katsinis, Constantine

1994-01-01

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

Terminal Sliding Mode-Based Consensus Tracking Control for Networked Uncertain Mechanical Systems on Digraphs.

PubMed

Chen, Gang; Song, Yongduan; Guan, Yanfeng

2018-03-01

This brief investigates the finite-time consensus tracking control problem for networked uncertain mechanical systems on digraphs. A new terminal sliding-mode-based cooperative control scheme is developed to guarantee that the tracking errors converge to an arbitrarily small bound around zero in finite time. All the networked systems can have different dynamics and all the dynamics are unknown. A neural network is used at each node to approximate the local unknown dynamics. The control schemes are implemented in a fully distributed manner. The proposed control method eliminates some limitations in the existing terminal sliding-mode-based consensus control methods and extends the existing analysis methods to the case of directed graphs. Simulation results on networked robot manipulators are provided to show the effectiveness of the proposed control algorithms.

Graph theory applied to the analysis of motor activity in patients with schizophrenia and depression

PubMed Central

Fasmer, Erlend Eindride; Berle, Jan Øystein; Oedegaard, Ketil J.; Hauge, Erik R.

2018-01-01

Depression and schizophrenia are defined only by their clinical features, and diagnostic separation between them can be difficult. Disturbances in motor activity pattern are central features of both types of disorders. We introduce a new method to analyze time series, called the similarity graph algorithm. Time series of motor activity, obtained from actigraph registrations over 12 days in depressed and schizophrenic patients, were mapped into a graph and we then applied techniques from graph theory to characterize these time series, primarily looking for changes in complexity. The most marked finding was that depressed patients were found to be significantly different from both controls and schizophrenic patients, with evidence of less regularity of the time series, when analyzing the recordings with one hour intervals. These findings support the contention that there are important differences in control systems regulating motor behavior in patients with depression and schizophrenia. The similarity graph algorithm we have described can easily be applied to the study of other types of time series. PMID:29668743

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

NASA Astrophysics Data System (ADS)

Jiang, Minghui

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

A graph-based network-vulnerability analysis system

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

Swiler, L.P.; Phillips, C.; Gaylor, T.

1998-05-03

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

A graph-based network-vulnerability analysis system

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

Swiler, L.P.; Phillips, C.; Gaylor, T.

1998-01-01

This report presents a graph-based approach to network vulnerability analysis. The method is flexible, allowing analysis of attacks from both outside and inside the network. It can analyze risks to a specific network asset, or examine the universe of possible consequences following a successful attack. The analysis system requires as input a database of common attacks, broken into atomic steps, specific network configuration and topology information, and an attacker profile. The attack information is matched with the network configuration information and an attacker profile to create a superset attack graph. Nodes identify a stage of attack, for example the classmore » of machines the attacker has accessed and the user privilege level he or she has compromised. The arcs in the attack graph represent attacks or stages of attacks. By assigning probabilities of success on the arcs or costs representing level-of-effort for the attacker, various graph algorithms such as shortest-path algorithms can identify the attack paths with the highest probability of success.« less

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

PubMed

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

2017-05-01

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

Multi-View Multi-Instance Learning Based on Joint Sparse Representation and Multi-View Dictionary Learning.

PubMed

Li, Bing; Yuan, Chunfeng; Xiong, Weihua; Hu, Weiming; Peng, Houwen; Ding, Xinmiao; Maybank, Steve

2017-12-01

In multi-instance learning (MIL), the relations among instances in a bag convey important contextual information in many applications. Previous studies on MIL either ignore such relations or simply model them with a fixed graph structure so that the overall performance inevitably degrades in complex environments. To address this problem, this paper proposes a novel multi-view multi-instance learning algorithm (MIL) that combines multiple context structures in a bag into a unified framework. The novel aspects are: (i) we propose a sparse -graph model that can generate different graphs with different parameters to represent various context relations in a bag, (ii) we propose a multi-view joint sparse representation that integrates these graphs into a unified framework for bag classification, and (iii) we propose a multi-view dictionary learning algorithm to obtain a multi-view graph dictionary that considers cues from all views simultaneously to improve the discrimination of the MIL. Experiments and analyses in many practical applications prove the effectiveness of the M IL.

Graph theory applied to the analysis of motor activity in patients with schizophrenia and depression.

PubMed

Fasmer, Erlend Eindride; Fasmer, Ole Bernt; Berle, Jan Øystein; Oedegaard, Ketil J; Hauge, Erik R

2018-01-01

Depression and schizophrenia are defined only by their clinical features, and diagnostic separation between them can be difficult. Disturbances in motor activity pattern are central features of both types of disorders. We introduce a new method to analyze time series, called the similarity graph algorithm. Time series of motor activity, obtained from actigraph registrations over 12 days in depressed and schizophrenic patients, were mapped into a graph and we then applied techniques from graph theory to characterize these time series, primarily looking for changes in complexity. The most marked finding was that depressed patients were found to be significantly different from both controls and schizophrenic patients, with evidence of less regularity of the time series, when analyzing the recordings with one hour intervals. These findings support the contention that there are important differences in control systems regulating motor behavior in patients with depression and schizophrenia. The similarity graph algorithm we have described can easily be applied to the study of other types of time series.

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

PubMed

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

2016-11-01

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

A learning approach to the bandwidth multicolouring problem

NASA Astrophysics Data System (ADS)

Akbari Torkestani, Javad

2016-05-01

In this article, a generalisation of the vertex colouring problem known as bandwidth multicolouring problem (BMCP), in which a set of colours is assigned to each vertex such that the difference between the colours, assigned to each vertex and its neighbours, is by no means less than a predefined threshold, is considered. It is shown that the proposed method can be applied to solve the bandwidth colouring problem (BCP) as well. BMCP is known to be NP-hard in graph theory, and so a large number of approximation solutions, as well as exact algorithms, have been proposed to solve it. In this article, two learning automata-based approximation algorithms are proposed for estimating a near-optimal solution to the BMCP. We show, for the first proposed algorithm, that by choosing a proper learning rate, the algorithm finds the optimal solution with a probability close enough to unity. Moreover, we compute the worst-case time complexity of the first algorithm for finding a 1/(1-ɛ) optimal solution to the given problem. The main advantage of this method is that a trade-off between the running time of algorithm and the colour set size (colouring optimality) can be made, by a proper choice of the learning rate also. Finally, it is shown that the running time of the proposed algorithm is independent of the graph size, and so it is a scalable algorithm for large graphs. The second proposed algorithm is compared with some well-known colouring algorithms and the results show the efficiency of the proposed algorithm in terms of the colour set size and running time of algorithm.

On the Control of Consensus Networks: Theory and Applications

NASA Astrophysics Data System (ADS)

Hudoba de Badyn, Mathias

Signed networks allow the study of positive and negative interactions between agents. In this thesis, three papers are presented that address controllability of networked dynamics. First, controllability of signed consensus networks is approached from a symmetry perspective, for both linear and nonlinear consensus protocols. It is shown that the graph-theoretic property of signed networks known as structural balance renders the consensus protocol uncontrollable when coupled with a certain type of symmetry. Stabilizability and output controllability of signed linear consensus is also examined, as well as a data-driven approach to finding bipartite consensus stemming from structural balance for signed nonlinear consensus. Second, an algorithm is constructed that allows one to grow a network while preserving controllability, and some generalizations of this algorithm are presented. Submodular optimization is used to analyze a second algorithm that adds nodes to a network to maximize the network connectivity.

An efficient, large-scale, non-lattice-detection algorithm for exhaustive structural auditing of biomedical ontologies.

PubMed

Zhang, Guo-Qiang; Xing, Guangming; Cui, Licong

2018-04-01

One of the basic challenges in developing structural methods for systematic audition on the quality of biomedical ontologies is the computational cost usually involved in exhaustive sub-graph analysis. We introduce ANT-LCA, a new algorithm for computing all non-trivial lowest common ancestors (LCA) of each pair of concepts in the hierarchical order induced by an ontology. The computation of LCA is a fundamental step for non-lattice approach for ontology quality assurance. Distinct from existing approaches, ANT-LCA only computes LCAs for non-trivial pairs, those having at least one common ancestor. To skip all trivial pairs that may be of no practical interest, ANT-LCA employs a simple but innovative algorithmic strategy combining topological order and dynamic programming to keep track of non-trivial pairs. We provide correctness proofs and demonstrate a substantial reduction in computational time for two largest biomedical ontologies: SNOMED CT and Gene Ontology (GO). ANT-LCA achieved an average computation time of 30 and 3 sec per version for SNOMED CT and GO, respectively, about 2 orders of magnitude faster than the best known approaches. Our algorithm overcomes a fundamental computational barrier in sub-graph based structural analysis of large ontological systems. It enables the implementation of a new breed of structural auditing methods that not only identifies potential problematic areas, but also automatically suggests changes to fix the issues. Such structural auditing methods can lead to more effective tools supporting ontology quality assurance work. Copyright © 2018 Elsevier Inc. All rights reserved.

A cooperative game framework for detecting overlapping communities in social networks

NASA Astrophysics Data System (ADS)

Jonnalagadda, Annapurna; Kuppusamy, Lakshmanan

2018-02-01

Community detection in social networks is a challenging and complex task, which received much attention from researchers of multiple domains in recent years. The evolution of communities in social networks happens merely due to the self-interest of the nodes. The interesting feature of community structure in social networks is the multi membership of the nodes resulting in overlapping communities. Assuming the nodes of the social network as self-interested players, the dynamics of community formation can be captured in the form of a game. In this paper, we propose a greedy algorithm, namely, Weighted Graph Community Game (WGCG), in order to model the interactions among the self-interested nodes of the social network. The proposed algorithm employs the Shapley value mechanism to discover the inherent communities of the underlying social network. The experimental evaluation on the real-world and synthetic benchmark networks demonstrates that the performance of the proposed algorithm is superior to the state-of-the-art overlapping community detection algorithms.

Several classes of graphs and their r-dynamic chromatic numbers

NASA Astrophysics Data System (ADS)

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

2017-06-01

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

A model for dynamic allocation of human attention among multiple tasks

NASA Technical Reports Server (NTRS)

Sheridan, T. B.; Tulga, M. K.

1978-01-01

The problem of multi-task attention allocation with special reference to aircraft piloting is discussed with the experimental paradigm used to characterize this situation and the experimental results obtained in the first phase of the research. A qualitative description of an approach to mathematical modeling, and some results obtained with it are also presented to indicate what aspects of the model are most promising. Two appendices are given which (1) discuss the model in relation to graph theory and optimization and (2) specify the optimization algorithm of the model.

Bipartite graphs as models of population structures in evolutionary multiplayer games.

PubMed

Peña, Jorge; Rochat, Yannick

2012-01-01

By combining evolutionary game theory and graph theory, "games on graphs" study the evolutionary dynamics of frequency-dependent selection in population structures modeled as geographical or social networks. Networks are usually represented by means of unipartite graphs, and social interactions by two-person games such as the famous prisoner's dilemma. Unipartite graphs have also been used for modeling interactions going beyond pairwise interactions. In this paper, we argue that bipartite graphs are a better alternative to unipartite graphs for describing population structures in evolutionary multiplayer games. To illustrate this point, we make use of bipartite graphs to investigate, by means of computer simulations, the evolution of cooperation under the conventional and the distributed N-person prisoner's dilemma. We show that several implicit assumptions arising from the standard approach based on unipartite graphs (such as the definition of replacement neighborhoods, the intertwining of individual and group diversity, and the large overlap of interaction neighborhoods) can have a large impact on the resulting evolutionary dynamics. Our work provides a clear example of the importance of construction procedures in games on graphs, of the suitability of bigraphs and hypergraphs for computational modeling, and of the importance of concepts from social network analysis such as centrality, centralization and bipartite clustering for the understanding of dynamical processes occurring on networked population structures.

Random Walk Graph Laplacian-Based Smoothness Prior for Soft Decoding of JPEG Images.

PubMed

Liu, Xianming; Cheung, Gene; Wu, Xiaolin; Zhao, Debin

2017-02-01

Given the prevalence of joint photographic experts group (JPEG) compressed images, optimizing image reconstruction from the compressed format remains an important problem. Instead of simply reconstructing a pixel block from the centers of indexed discrete cosine transform (DCT) coefficient quantization bins (hard decoding), soft decoding reconstructs a block by selecting appropriate coefficient values within the indexed bins with the help of signal priors. The challenge thus lies in how to define suitable priors and apply them effectively. In this paper, we combine three image priors-Laplacian prior for DCT coefficients, sparsity prior, and graph-signal smoothness prior for image patches-to construct an efficient JPEG soft decoding algorithm. Specifically, we first use the Laplacian prior to compute a minimum mean square error initial solution for each code block. Next, we show that while the sparsity prior can reduce block artifacts, limiting the size of the overcomplete dictionary (to lower computation) would lead to poor recovery of high DCT frequencies. To alleviate this problem, we design a new graph-signal smoothness prior (desired signal has mainly low graph frequencies) based on the left eigenvectors of the random walk graph Laplacian matrix (LERaG). Compared with the previous graph-signal smoothness priors, LERaG has desirable image filtering properties with low computation overhead. We demonstrate how LERaG can facilitate recovery of high DCT frequencies of a piecewise smooth signal via an interpretation of low graph frequency components as relaxed solutions to normalized cut in spectral clustering. Finally, we construct a soft decoding algorithm using the three signal priors with appropriate prior weights. Experimental results show that our proposal outperforms the state-of-the-art soft decoding algorithms in both objective and subjective evaluations noticeably.

A Constant-Factor Approximation Algorithm for the Link Building Problem

NASA Astrophysics Data System (ADS)

Olsen, Martin; Viglas, Anastasios; Zvedeniouk, Ilia

In this work we consider the problem of maximizing the PageRank of a given target node in a graph by adding k new links. We consider the case that the new links must point to the given target node (backlinks). Previous work [7] shows that this problem has no fully polynomial time approximation schemes unless P = NP. We present a polynomial time algorithm yielding a PageRank value within a constant factor from the optimal. We also consider the naive algorithm where we choose backlinks from nodes with high PageRank values compared to the outdegree and show that the naive algorithm performs much worse on certain graphs compared to the constant factor approximation scheme.

Local Higher-Order Graph Clustering

PubMed Central

Yin, Hao; Benson, Austin R.; Leskovec, Jure; Gleich, David F.

2018-01-01

Local graph clustering methods aim to find a cluster of nodes by exploring a small region of the graph. These methods are attractive because they enable targeted clustering around a given seed node and are faster than traditional global graph clustering methods because their runtime does not depend on the size of the input graph. However, current local graph partitioning methods are not designed to account for the higher-order structures crucial to the network, nor can they effectively handle directed networks. Here we introduce a new class of local graph clustering methods that address these issues by incorporating higher-order network information captured by small subgraphs, also called network motifs. We develop the Motif-based Approximate Personalized PageRank (MAPPR) algorithm that finds clusters containing a seed node with minimal motif conductance, a generalization of the conductance metric for network motifs. We generalize existing theory to prove the fast running time (independent of the size of the graph) and obtain theoretical guarantees on the cluster quality (in terms of motif conductance). We also develop a theory of node neighborhoods for finding sets that have small motif conductance, and apply these results to the case of finding good seed nodes to use as input to the MAPPR algorithm. Experimental validation on community detection tasks in both synthetic and real-world networks, shows that our new framework MAPPR outperforms the current edge-based personalized PageRank methodology. PMID:29770258

Decentralized Control of Scheduling in Distributed Systems.

DTIC Science & Technology

1983-03-18

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

Graph Based Models for Unsupervised High Dimensional Data Clustering and Network Analysis

DTIC Science & Technology

2015-01-01

ApprovedOMB No. 0704-0188 Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for...algorithms we proposed improve the time e ciency signi cantly for large scale datasets. In the last chapter, we also propose an incremental reseeding...plume detection in hyper-spectral video data. These graph based clustering algorithms we proposed improve the time efficiency significantly for large

Salient object detection: manifold-based similarity adaptation approach

NASA Astrophysics Data System (ADS)

Zhou, Jingbo; Ren, Yongfeng; Yan, Yunyang; Gao, Shangbing

2014-11-01

A saliency detection algorithm based on manifold-based similarity adaptation is proposed. The proposed algorithm is divided into three steps. First, we segment an input image into superpixels, which are represented as the nodes in a graph. Second, a new similarity measurement is used in the proposed algorithm. The weight matrix of the graph, which indicates the similarities between the nodes, uses a similarity-based method. It also captures the manifold structure of the image patches, in which the graph edges are determined in a data adaptive manner in terms of both similarity and manifold structure. Then, we use local reconstruction method as a diffusion method to obtain the saliency maps. The objective function in the proposed method is based on local reconstruction, with which estimated weights capture the manifold structure. Experiments on four bench-mark databases demonstrate the accuracy and robustness of the proposed method.

Graph Kernels for Molecular Similarity.

PubMed

Rupp, Matthias; Schneider, Gisbert

2010-04-12

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

Fully Decomposable Split Graphs

NASA Astrophysics Data System (ADS)

Broersma, Hajo; Kratsch, Dieter; Woeginger, Gerhard J.

We discuss various questions around partitioning a split graph into connected parts. Our main result is a polynomial time algorithm that decides whether a given split graph is fully decomposable, i.e., whether it can be partitioned into connected parts of order α 1,α 2,...,α k for every α 1,α 2,...,α k summing up to the order of the graph. In contrast, we show that the decision problem whether a given split graph can be partitioned into connected parts of order α 1,α 2,...,α k for a given partition α 1,α 2,...,α k of the order of the graph, is NP-hard.

A Constraint-Based Planner for Data Production

NASA Technical Reports Server (NTRS)

Pang, Wanlin; Golden, Keith

2005-01-01

This paper presents a graph-based backtracking algorithm designed to support constrain-tbased planning in data production domains. This algorithm performs backtracking at two nested levels: the outer- backtracking following the structure of the planning graph to select planner subgoals and actions to achieve them and the inner-backtracking inside a subproblem associated with a selected action to find action parameter values. We show this algorithm works well in a planner applied to automating data production in an ecological forecasting system. We also discuss how the idea of multi-level backtracking may improve efficiency of solving semi-structured constraint problems.

On the r-dynamic chromatic number of the corronation by complete graph

NASA Astrophysics Data System (ADS)

Indah Kristiana, Arika; Imam Utoyo, M.; Dafik

2018-04-01

In this paper we will study the r-dynamic chromatic number of the coronation by complete graph. A proper k-coloring of graph G such that the neighbors of any vertex v receive at least min{r, d(v)} different colors. The r-dynamic chromatic number, χ r (G) is the minimum k such that graph G has an r-dynamic k-coloring. We will obtain lower bound of the r-dynamic chromatic number of {χ }r({K}nȯ H), and {χ }r(Hȯ {K}m) We also study the exact value of the r-dynamic chromatic number of {χ }r({K}nȯ {S}m),{χ }r({K}nȯ {F}m),{χ }r({S}nȯ {K}m),{χ }r({F}nȯ {K}m) and {χ }r({K}nȯ {K}m) for m, n > 3.

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.

Tree decomposition based fast search of RNA structures including pseudoknots in genomes.

PubMed

Song, Yinglei; Liu, Chunmei; Malmberg, Russell; Pan, Fangfang; Cai, Liming

2005-01-01

Searching genomes for RNA secondary structure with computational methods has become an important approach to the annotation of non-coding RNAs. However, due to the lack of efficient algorithms for accurate RNA structure-sequence alignment, computer programs capable of fast and effectively searching genomes for RNA secondary structures have not been available. In this paper, a novel RNA structure profiling model is introduced based on the notion of a conformational graph to specify the consensus structure of an RNA family. Tree decomposition yields a small tree width t for such conformation graphs (e.g., t = 2 for stem loops and only a slight increase for pseudo-knots). Within this modelling framework, the optimal alignment of a sequence to the structure model corresponds to finding a maximum valued isomorphic subgraph and consequently can be accomplished through dynamic programming on the tree decomposition of the conformational graph in time O(k(t)N(2)), where k is a small parameter; and N is the size of the projiled RNA structure. Experiments show that the application of the alignment algorithm to search in genomes yields the same search accuracy as methods based on a Covariance model with a significant reduction in computation time. In particular; very accurate searches of tmRNAs in bacteria genomes and of telomerase RNAs in yeast genomes can be accomplished in days, as opposed to months required by other methods. The tree decomposition based searching tool is free upon request and can be downloaded at our site h t t p ://w.uga.edu/RNA-informatics/software/index.php.

Directional Agglomeration Multigrid Techniques for High Reynolds Number Viscous Flow Solvers

NASA Technical Reports Server (NTRS)

1998-01-01

A preconditioned directional-implicit agglomeration algorithm is developed for solving two- and three-dimensional viscous flows on highly anisotropic unstructured meshes of mixed-element types. The multigrid smoother consists of a pre-conditioned point- or line-implicit solver which operates on lines constructed in the unstructured mesh using a weighted graph algorithm. Directional coarsening or agglomeration is achieved using a similar weighted graph algorithm. A tight coupling of the line construction and directional agglomeration algorithms enables the use of aggressive coarsening ratios in the multigrid algorithm, which in turn reduces the cost of a multigrid cycle. Convergence rates which are independent of the degree of grid stretching are demonstrated in both two and three dimensions. Further improvement of the three-dimensional convergence rates through a GMRES technique is also demonstrated.

Directional Agglomeration Multigrid Techniques for High-Reynolds Number Viscous Flows

NASA Technical Reports Server (NTRS)

Mavriplis, Dimitri J.

1998-01-01

A preconditioned directional-implicit agglomeration algorithm is developed for solving two- and three-dimensional viscous flows on highly anisotropic unstructured meshes of mixed-element types. The multigrid smoother consists of a pre-conditioned point- or line-implicit solver which operates on lines constructed in the unstructured mesh using a weighted graph algorithm. Directional coarsening or agglomeration is achieved using a similar weighted graph algorithm. A tight coupling of the line construction and directional agglomeration algorithms enables the use of aggressive coarsening ratios in the multigrid algorithm, which in turn reduces the cost of a multigrid cycle. Convergence rates which are independent of the degree of grid stretching are demonstrated in both two and three dimensions. Further improvement of the three-dimensional convergence rates through a GMRES technique is also demonstrated.

Semantic Health Knowledge Graph: Semantic Integration of Heterogeneous Medical Knowledge and Services.

PubMed

Shi, Longxiang; Li, Shijian; Yang, Xiaoran; Qi, Jiaheng; Pan, Gang; Zhou, Binbin

2017-01-01

With the explosion of healthcare information, there has been a tremendous amount of heterogeneous textual medical knowledge (TMK), which plays an essential role in healthcare information systems. Existing works for integrating and utilizing the TMK mainly focus on straightforward connections establishment and pay less attention to make computers interpret and retrieve knowledge correctly and quickly. In this paper, we explore a novel model to organize and integrate the TMK into conceptual graphs. We then employ a framework to automatically retrieve knowledge in knowledge graphs with a high precision. In order to perform reasonable inference on knowledge graphs, we propose a contextual inference pruning algorithm to achieve efficient chain inference. Our algorithm achieves a better inference result with precision and recall of 92% and 96%, respectively, which can avoid most of the meaningless inferences. In addition, we implement two prototypes and provide services, and the results show our approach is practical and effective.

Semantic Health Knowledge Graph: Semantic Integration of Heterogeneous Medical Knowledge and Services

PubMed Central

Yang, Xiaoran; Qi, Jiaheng; Pan, Gang; Zhou, Binbin

2017-01-01

With the explosion of healthcare information, there has been a tremendous amount of heterogeneous textual medical knowledge (TMK), which plays an essential role in healthcare information systems. Existing works for integrating and utilizing the TMK mainly focus on straightforward connections establishment and pay less attention to make computers interpret and retrieve knowledge correctly and quickly. In this paper, we explore a novel model to organize and integrate the TMK into conceptual graphs. We then employ a framework to automatically retrieve knowledge in knowledge graphs with a high precision. In order to perform reasonable inference on knowledge graphs, we propose a contextual inference pruning algorithm to achieve efficient chain inference. Our algorithm achieves a better inference result with precision and recall of 92% and 96%, respectively, which can avoid most of the meaningless inferences. In addition, we implement two prototypes and provide services, and the results show our approach is practical and effective. PMID:28299322

Using Betweenness Centrality to Identify Manifold Shortcuts

PubMed Central

Cukierski, William J.; Foran, David J.

2010-01-01

High-dimensional data presents a challenge to tasks of pattern recognition and machine learning. Dimensionality reduction (DR) methods remove the unwanted variance and make these tasks tractable. Several nonlinear DR methods, such as the well known ISOMAP algorithm, rely on a neighborhood graph to compute geodesic distances between data points. These graphs can contain unwanted edges which connect disparate regions of one or more manifolds. This topological sensitivity is well known [1], [2], [3], yet handling high-dimensional, noisy data in the absence of a priori manifold knowledge, remains an open and difficult problem. This work introduces a divisive, edge-removal method based on graph betweenness centrality which can robustly identify manifold-shorting edges. The problem of graph construction in high dimension is discussed and the proposed algorithm is fit into the ISOMAP workflow. ROC analysis is performed and the performance is tested on synthetic and real datasets. PMID:20607142

GrouseFlocks: steerable exploration of graph hierarchy space.

PubMed

Archambault, Daniel; Munzner, Tamara; Auber, David

2008-01-01

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

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

PubMed Central

2014-01-01

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

Learning In networks

NASA Technical Reports Server (NTRS)

Buntine, Wray L.

1995-01-01

Intelligent systems require software incorporating probabilistic reasoning, and often times learning. Networks provide a framework and methodology for creating this kind of software. This paper introduces network models based on chain graphs with deterministic nodes. Chain graphs are defined as a hierarchical combination of Bayesian and Markov networks. To model learning, plates on chain graphs are introduced to model independent samples. The paper concludes by discussing various operations that can be performed on chain graphs with plates as a simplification process or to generate learning algorithms.

PuReD-MCL: a graph-based PubMed document clustering methodology.

PubMed

Theodosiou, T; Darzentas, N; Angelis, L; Ouzounis, C A

2008-09-01

Biomedical literature is the principal repository of biomedical knowledge, with PubMed being the most complete database collecting, organizing and analyzing such textual knowledge. There are numerous efforts that attempt to exploit this information by using text mining and machine learning techniques. We developed a novel approach, called PuReD-MCL (Pubmed Related Documents-MCL), which is based on the graph clustering algorithm MCL and relevant resources from PubMed. PuReD-MCL avoids using natural language processing (NLP) techniques directly; instead, it takes advantage of existing resources, available from PubMed. PuReD-MCL then clusters documents efficiently using the MCL graph clustering algorithm, which is based on graph flow simulation. This process allows users to analyse the results by highlighting important clues, and finally to visualize the clusters and all relevant information using an interactive graph layout algorithm, for instance BioLayout Express 3D. The methodology was applied to two different datasets, previously used for the validation of the document clustering tool TextQuest. The first dataset involves the organisms Escherichia coli and yeast, whereas the second is related to Drosophila development. PuReD-MCL successfully reproduces the annotated results obtained from TextQuest, while at the same time provides additional insights into the clusters and the corresponding documents. Source code in perl and R are available from http://tartara.csd.auth.gr/~theodos/

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

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

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

1996-12-31

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

Nonschematic drawing recognition: a new approach based on attributed graph grammar with flexible embedding

NASA Astrophysics Data System (ADS)

Lee, Kyu J.; Kunii, T. L.; Noma, T.

1993-01-01

In this paper, we propose a syntactic pattern recognition method for non-schematic drawings, based on a new attributed graph grammar with flexible embedding. In our graph grammar, the embedding rule permits the nodes of a guest graph to be arbitrarily connected with the nodes of a host graph. The ambiguity caused by this flexible embedding is controlled with the evaluation of synthesized attributes and the check of context sensitivity. To integrate parsing with the synthesized attribute evaluation and the context sensitivity check, we also develop a bottom up parsing algorithm.

JavaGenes and Condor: Cycle-Scavenging Genetic Algorithms

NASA Technical Reports Server (NTRS)

Globus, Al; Langhirt, Eric; Livny, Miron; Ramamurthy, Ravishankar; Soloman, Marvin; Traugott, Steve

2000-01-01

A genetic algorithm code, JavaGenes, was written in Java and used to evolve pharmaceutical drug molecules and digital circuits. JavaGenes was run under the Condor cycle-scavenging batch system managing 100-170 desktop SGI workstations. Genetic algorithms mimic biological evolution by evolving solutions to problems using crossover and mutation. While most genetic algorithms evolve strings or trees, JavaGenes evolves graphs representing (currently) molecules and circuits. Java was chosen as the implementation language because the genetic algorithm requires random splitting and recombining of graphs, a complex data structure manipulation with ample opportunities for memory leaks, loose pointers, out-of-bound indices, and other hard to find bugs. Java garbage-collection memory management, lack of pointer arithmetic, and array-bounds index checking prevents these bugs from occurring, substantially reducing development time. While a run-time performance penalty must be paid, the only unacceptable performance we encountered was using standard Java serialization to checkpoint and restart the code. This was fixed by a two-day implementation of custom checkpointing. JavaGenes is minimally integrated with Condor; in other words, JavaGenes must do its own checkpointing and I/O redirection. A prototype Java-aware version of Condor was developed using standard Java serialization for checkpointing. For the prototype to be useful, standard Java serialization must be significantly optimized. JavaGenes is approximately 8700 lines of code and a few thousand JavaGenes jobs have been run. Most jobs ran for a few days. Results include proof that genetic algorithms can evolve directed and undirected graphs, development of a novel crossover operator for graphs, a paper in the journal Nanotechnology, and another paper in preparation.

A greedy, graph-based algorithm for the alignment of multiple homologous gene lists.

PubMed

Fostier, Jan; Proost, Sebastian; Dhoedt, Bart; Saeys, Yvan; Demeester, Piet; Van de Peer, Yves; Vandepoele, Klaas

2011-03-15

Many comparative genomics studies rely on the correct identification of homologous genomic regions using accurate alignment tools. In such case, the alphabet of the input sequences consists of complete genes, rather than nucleotides or amino acids. As optimal multiple sequence alignment is computationally impractical, a progressive alignment strategy is often employed. However, such an approach is susceptible to the propagation of alignment errors in early pairwise alignment steps, especially when dealing with strongly diverged genomic regions. In this article, we present a novel accurate and efficient greedy, graph-based algorithm for the alignment of multiple homologous genomic segments, represented as ordered gene lists. Based on provable properties of the graph structure, several heuristics are developed to resolve local alignment conflicts that occur due to gene duplication and/or rearrangement events on the different genomic segments. The performance of the algorithm is assessed by comparing the alignment results of homologous genomic segments in Arabidopsis thaliana to those obtained by using both a progressive alignment method and an earlier graph-based implementation. Especially for datasets that contain strongly diverged segments, the proposed method achieves a substantially higher alignment accuracy, and proves to be sufficiently fast for large datasets including a few dozens of eukaryotic genomes. http://bioinformatics.psb.ugent.be/software. The algorithm is implemented as a part of the i-ADHoRe 3.0 package.

RGB-D SLAM Combining Visual Odometry and Extended Information Filter

PubMed Central

Zhang, Heng; Liu, Yanli; Tan, Jindong; Xiong, Naixue

2015-01-01

In this paper, we present a novel RGB-D SLAM system based on visual odometry and an extended information filter, which does not require any other sensors or odometry. In contrast to the graph optimization approaches, this is more suitable for online applications. A visual dead reckoning algorithm based on visual residuals is devised, which is used to estimate motion control input. In addition, we use a novel descriptor called binary robust appearance and normals descriptor (BRAND) to extract features from the RGB-D frame and use them as landmarks. Furthermore, considering both the 3D positions and the BRAND descriptors of the landmarks, our observation model avoids explicit data association between the observations and the map by marginalizing the observation likelihood over all possible associations. Experimental validation is provided, which compares the proposed RGB-D SLAM algorithm with just RGB-D visual odometry and a graph-based RGB-D SLAM algorithm using the publicly-available RGB-D dataset. The results of the experiments demonstrate that our system is quicker than the graph-based RGB-D SLAM algorithm. PMID:26263990

Differentially Private Frequent Subgraph Mining

PubMed Central

Xu, Shengzhi; Xiong, Li; Cheng, Xiang; Xiao, Ke

2016-01-01

Mining frequent subgraphs from a collection of input graphs is an important topic in data mining research. However, if the input graphs contain sensitive information, releasing frequent subgraphs may pose considerable threats to individual's privacy. In this paper, we study the problem of frequent subgraph mining (FGM) under the rigorous differential privacy model. We introduce a novel differentially private FGM algorithm, which is referred to as DFG. In this algorithm, we first privately identify frequent subgraphs from input graphs, and then compute the noisy support of each identified frequent subgraph. In particular, to privately identify frequent subgraphs, we present a frequent subgraph identification approach which can improve the utility of frequent subgraph identifications through candidates pruning. Moreover, to compute the noisy support of each identified frequent subgraph, we devise a lattice-based noisy support derivation approach, where a series of methods has been proposed to improve the accuracy of the noisy supports. Through formal privacy analysis, we prove that our DFG algorithm satisfies ε-differential privacy. Extensive experimental results on real datasets show that the DFG algorithm can privately find frequent subgraphs with high data utility. PMID:27616876

Improving graph-based OCT segmentation for severe pathology in retinitis pigmentosa patients

NASA Astrophysics Data System (ADS)

Lang, Andrew; Carass, Aaron; Bittner, Ava K.; Ying, Howard S.; Prince, Jerry L.

2017-03-01

Three dimensional segmentation of macular optical coherence tomography (OCT) data of subjects with retinitis pigmentosa (RP) is a challenging problem due to the disappearance of the photoreceptor layers, which causes algorithms developed for segmentation of healthy data to perform poorly on RP patients. In this work, we present enhancements to a previously developed graph-based OCT segmentation pipeline to enable processing of RP data. The algorithm segments eight retinal layers in RP data by relaxing constraints on the thickness and smoothness of each layer learned from healthy data. Following from prior work, a random forest classifier is first trained on the RP data to estimate boundary probabilities, which are used by a graph search algorithm to find the optimal set of nine surfaces that fit the data. Due to the intensity disparity between normal layers of healthy controls and layers in various stages of degeneration in RP patients, an additional intensity normalization step is introduced. Leave-one-out validation on data acquired from nine subjects showed an average overall boundary error of 4.22 μm as compared to 6.02 μm using the original algorithm.

Efficient FPT Algorithms for (Strict) Compatibility of Unrooted Phylogenetic Trees.

PubMed

Baste, Julien; Paul, Christophe; Sau, Ignasi; Scornavacca, Celine

2017-04-01

In phylogenetics, a central problem is to infer the evolutionary relationships between a set of species X; these relationships are often depicted via a phylogenetic tree-a tree having its leaves labeled bijectively by elements of X and without degree-2 nodes-called the "species tree." One common approach for reconstructing a species tree consists in first constructing several phylogenetic trees from primary data (e.g., DNA sequences originating from some species in X), and then constructing a single phylogenetic tree maximizing the "concordance" with the input trees. The obtained tree is our estimation of the species tree and, when the input trees are defined on overlapping-but not identical-sets of labels, is called "supertree." In this paper, we focus on two problems that are central when combining phylogenetic trees into a supertree: the compatibility and the strict compatibility problems for unrooted phylogenetic trees. These problems are strongly related, respectively, to the notions of "containing as a minor" and "containing as a topological minor" in the graph community. Both problems are known to be fixed parameter tractable in the number of input trees k, by using their expressibility in monadic second-order logic and a reduction to graphs of bounded treewidth. Motivated by the fact that the dependency on k of these algorithms is prohibitively large, we give the first explicit dynamic programming algorithms for solving these problems, both running in time [Formula: see text], where n is the total size of the input.

Application of the PageRank Algorithm to Alarm Graphs

NASA Astrophysics Data System (ADS)

Treinen, James J.; Thurimella, Ramakrishna

The task of separating genuine attacks from false alarms in large intrusion detection infrastructures is extremely difficult. The number of alarms received in such environments can easily enter into the millions of alerts per day. The overwhelming noise created by these alarms can cause genuine attacks to go unnoticed. As means of highlighting these attacks, we introduce a host ranking technique utilizing Alarm Graphs. Rather than enumerate all potential attack paths as in Attack Graphs, we build and analyze graphs based on the alarms generated by the intrusion detection sensors installed on a network. Given that the alarms are predominantly false positives, the challenge is to identify, separate, and ideally predict future attacks. In this paper, we propose a novel approach to tackle this problem based on the PageRank algorithm. By elevating the rank of known attackers and victims we are able to observe the effect that these hosts have on the other nodes in the Alarm Graph. Using this information we are able to discover previously overlooked attacks, as well as defend against future intrusions.

Efficient Algorithmic Frameworks via Structural Graph Theory

DTIC Science & Technology

2016-10-28

centrally planned solution. Policy recommendation: Given a socioeconomic game among multiple parties (countries, armies, political parties, terrorist...etc.). 2 Graph Structure of Network Creation Games We completed the final versions of two of our papers about the graph structure inherent in...network creation games ”, which appeared in the following venues: Erik D. Demaine, MohammadTaghi Hajiaghayi, Hamid Mahini, and Morteza Zadi- moghaddam, “The

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

PubMed

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

2017-07-01

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

Proximity Networks and Epidemics

NASA Astrophysics Data System (ADS)

Guclu, Hasan; Toroczkai, Zoltán

2007-03-01

We presented the basis of a framework to account for the dynamics of contacts in epidemic processes, through the notion of dynamic proximity graphs. By varying the integration time-parameter T, which is the period of infectivity one can give a simple account for some of the differences in the observed contact networks for different diseases, such as smallpox, or AIDS. Our simplistic model also seems to shed some light on the shape of the degree distribution of the measured people-people contact network from the EPISIM data. We certainly do not claim that the simplistic graph integration model above is a good model for dynamic contact graphs. It only contains the essential ingredients for such processes to produce a qualitative agreement with some observations. We expect that further refinements and extensions to this picture, in particular deriving the link-probabilities in the dynamic proximity graph from more realistic contact dynamics should improve the agreement between models and data.

Global dynamics for switching systems and their extensions by linear differential equations

NASA Astrophysics Data System (ADS)

Huttinga, Zane; Cummins, Bree; Gedeon, Tomáš; Mischaikow, Konstantin

2018-03-01

Switching systems use piecewise constant nonlinearities to model gene regulatory networks. This choice provides advantages in the analysis of behavior and allows the global description of dynamics in terms of Morse graphs associated to nodes of a parameter graph. The parameter graph captures spatial characteristics of a decomposition of parameter space into domains with identical Morse graphs. However, there are many cellular processes that do not exhibit threshold-like behavior and thus are not well described by a switching system. We consider a class of extensions of switching systems formed by a mixture of switching interactions and chains of variables governed by linear differential equations. We show that the parameter graphs associated to the switching system and any of its extensions are identical. For each parameter graph node, there is an order-preserving map from the Morse graph of the switching system to the Morse graph of any of its extensions. We provide counterexamples that show why possible stronger relationships between the Morse graphs are not valid.

Global dynamics for switching systems and their extensions by linear differential equations.

PubMed

Huttinga, Zane; Cummins, Bree; Gedeon, Tomáš; Mischaikow, Konstantin

2018-03-15

Switching systems use piecewise constant nonlinearities to model gene regulatory networks. This choice provides advantages in the analysis of behavior and allows the global description of dynamics in terms of Morse graphs associated to nodes of a parameter graph. The parameter graph captures spatial characteristics of a decomposition of parameter space into domains with identical Morse graphs. However, there are many cellular processes that do not exhibit threshold-like behavior and thus are not well described by a switching system. We consider a class of extensions of switching systems formed by a mixture of switching interactions and chains of variables governed by linear differential equations. We show that the parameter graphs associated to the switching system and any of its extensions are identical. For each parameter graph node, there is an order-preserving map from the Morse graph of the switching system to the Morse graph of any of its extensions. We provide counterexamples that show why possible stronger relationships between the Morse graphs are not valid.

Finding Statistically Significant Communities in Networks

PubMed Central

Lancichinetti, Andrea; Radicchi, Filippo; Ramasco, José J.; Fortunato, Santo

2011-01-01

Community structure is one of the main structural features of networks, revealing both their internal organization and the similarity of their elementary units. Despite the large variety of methods proposed to detect communities in graphs, there is a big need for multi-purpose techniques, able to handle different types of datasets and the subtleties of community structure. In this paper we present OSLOM (Order Statistics Local Optimization Method), the first method capable to detect clusters in networks accounting for edge directions, edge weights, overlapping communities, hierarchies and community dynamics. It is based on the local optimization of a fitness function expressing the statistical significance of clusters with respect to random fluctuations, which is estimated with tools of Extreme and Order Statistics. OSLOM can be used alone or as a refinement procedure of partitions/covers delivered by other techniques. We have also implemented sequential algorithms combining OSLOM with other fast techniques, so that the community structure of very large networks can be uncovered. Our method has a comparable performance as the best existing algorithms on artificial benchmark graphs. Several applications on real networks are shown as well. OSLOM is implemented in a freely available software (http://www.oslom.org), and we believe it will be a valuable tool in the analysis of networks. PMID:21559480

Heuristic-driven graph wavelet modeling of complex terrain

NASA Astrophysics Data System (ADS)

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

2015-03-01

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

Identifying Vulnerabilities and Hardening Attack Graphs for Networked Systems

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

Saha, Sudip; Vullinati, Anil K.; Halappanavar, Mahantesh

We investigate efficient security control methods for protecting against vulnerabilities in networked systems. A large number of interdependent vulnerabilities typically exist in the computing nodes of a cyber-system; as vulnerabilities get exploited, starting from low level ones, they open up the doors to more critical vulnerabilities. These cannot be understood just by a topological analysis of the network, and we use the attack graph abstraction of Dewri et al. to study these problems. In contrast to earlier approaches based on heuristics and evolutionary algorithms, we study rigorous methods for quantifying the inherent vulnerability and hardening cost for the system. Wemore » develop algorithms with provable approximation guarantees, and evaluate them for real and synthetic attack graphs.« less

Figure-ground segmentation based on class-independent shape priors

NASA Astrophysics Data System (ADS)

Li, Yang; Liu, Yang; Liu, Guojun; Guo, Maozu

2018-01-01

We propose a method to generate figure-ground segmentation by incorporating shape priors into the graph-cuts algorithm. Given an image, we first obtain a linear representation of an image and then apply directional chamfer matching to generate class-independent, nonparametric shape priors, which provide shape clues for the graph-cuts algorithm. We then enforce shape priors in a graph-cuts energy function to produce object segmentation. In contrast to previous segmentation methods, the proposed method shares shape knowledge for different semantic classes and does not require class-specific model training. Therefore, the approach obtains high-quality segmentation for objects. We experimentally validate that the proposed method outperforms previous approaches using the challenging PASCAL VOC 2010/2012 and Berkeley (BSD300) segmentation datasets.

Quantum walks of two interacting particles on percolation graphs

NASA Astrophysics Data System (ADS)

Siloi, Ilaria; Benedetti, Claudia; Piccinini, Enrico; Paris, Matteo G. A.; Bordone, Paolo

2017-10-01

We address the dynamics of two indistinguishable interacting particles moving on a dynamical percolation graph, i.e., a graph where the edges are independent random telegraph processes whose values jump between 0 and 1, thus mimicking percolation. The interplay between the particle interaction strength, initial state and the percolation rate determine different dynamical regimes for the walkers. We show that, whenever the walkers are initially localised within the interaction range, fast noise enhances the particle spread compared to the noiseless case.

Comparing Internet Probing Methodologies Through an Analysis of Large Dynamic Graphs

DTIC Science & Technology

2014-06-01

comparable Internet topologies in less time. We compare these by modeling union of traceroute outputs as graphs, and using standard graph theoretical...topologies in less time. We compare these by modeling union of traceroute outputs as graphs, and using standard graph theoretical measurements as well...We compare these by modeling union of traceroute outputs as graphs, and study the graphs by using vertex and edge count, average vertex degree

Analysis of Community Detection Algorithms for Large Scale Cyber Networks

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

Mane, Prachita; Shanbhag, Sunanda; Kamath, Tanmayee

The aim of this project is to use existing community detection algorithms on an IP network dataset to create supernodes within the network. This study compares the performance of different algorithms on the network in terms of running time. The paper begins with an introduction to the concept of clustering and community detection followed by the research question that the team aimed to address. Further the paper describes the graph metrics that were considered in order to shortlist algorithms followed by a brief explanation of each algorithm with respect to the graph metric on which it is based. The nextmore » section in the paper describes the methodology used by the team in order to run the algorithms and determine which algorithm is most efficient with respect to running time. Finally, the last section of the paper includes the results obtained by the team and a conclusion based on those results as well as future work.« less

A scalable approach to solving dense linear algebra problems on hybrid CPU-GPU systems

DOE PAGES

Song, Fengguang; Dongarra, Jack

2014-10-01

Aiming to fully exploit the computing power of all CPUs and all graphics processing units (GPUs) on hybrid CPU-GPU systems to solve dense linear algebra problems, in this paper we design a class of heterogeneous tile algorithms to maximize the degree of parallelism, to minimize the communication volume, and to accommodate the heterogeneity between CPUs and GPUs. The new heterogeneous tile algorithms are executed upon our decentralized dynamic scheduling runtime system, which schedules a task graph dynamically and transfers data between compute nodes automatically. The runtime system uses a new distributed task assignment protocol to solve data dependencies between tasksmore » without any coordination between processing units. By overlapping computation and communication through dynamic scheduling, we are able to attain scalable performance for the double-precision Cholesky factorization and QR factorization. Finally, our approach demonstrates a performance comparable to Intel MKL on shared-memory multicore systems and better performance than both vendor (e.g., Intel MKL) and open source libraries (e.g., StarPU) in the following three environments: heterogeneous clusters with GPUs, conventional clusters without GPUs, and shared-memory systems with multiple GPUs.« less

A scalable approach to solving dense linear algebra problems on hybrid CPU-GPU systems

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

Song, Fengguang; Dongarra, Jack

Aiming to fully exploit the computing power of all CPUs and all graphics processing units (GPUs) on hybrid CPU-GPU systems to solve dense linear algebra problems, in this paper we design a class of heterogeneous tile algorithms to maximize the degree of parallelism, to minimize the communication volume, and to accommodate the heterogeneity between CPUs and GPUs. The new heterogeneous tile algorithms are executed upon our decentralized dynamic scheduling runtime system, which schedules a task graph dynamically and transfers data between compute nodes automatically. The runtime system uses a new distributed task assignment protocol to solve data dependencies between tasksmore » without any coordination between processing units. By overlapping computation and communication through dynamic scheduling, we are able to attain scalable performance for the double-precision Cholesky factorization and QR factorization. Finally, our approach demonstrates a performance comparable to Intel MKL on shared-memory multicore systems and better performance than both vendor (e.g., Intel MKL) and open source libraries (e.g., StarPU) in the following three environments: heterogeneous clusters with GPUs, conventional clusters without GPUs, and shared-memory systems with multiple GPUs.« less

Tractable Algorithms for Proximity Search on Large Graphs

DTIC Science & Technology

2010-07-01

development in information retrieval, 2005. 5.1 164 A. K. Chandra, P. Raghavan, W. L. Ruzzo, and R. Smolensky. The electrical resistance of a graph captures...2007] show how to use hitting times for designing provably manipulation resistant reputation systems. Harmonic func- tions have been used for...commute times with electrical net- works (Doyle and Snell [1984]). Consider an undirected graph. Now think of each edge as a resistor with conductance

A graph-based system for network-vulnerability analysis

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

Swiler, L.P.; Phillips, C.

1998-06-01

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

TreeNetViz: revealing patterns of networks over tree structures.

PubMed

Gou, Liang; Zhang, Xiaolong Luke

2011-12-01

Network data often contain important attributes from various dimensions such as social affiliations and areas of expertise in a social network. If such attributes exhibit a tree structure, visualizing a compound graph consisting of tree and network structures becomes complicated. How to visually reveal patterns of a network over a tree has not been fully studied. In this paper, we propose a compound graph model, TreeNet, to support visualization and analysis of a network at multiple levels of aggregation over a tree. We also present a visualization design, TreeNetViz, to offer the multiscale and cross-scale exploration and interaction of a TreeNet graph. TreeNetViz uses a Radial, Space-Filling (RSF) visualization to represent the tree structure, a circle layout with novel optimization to show aggregated networks derived from TreeNet, and an edge bundling technique to reduce visual complexity. Our circular layout algorithm reduces both total edge-crossings and edge length and also considers hierarchical structure constraints and edge weight in a TreeNet graph. These experiments illustrate that the algorithm can reduce visual cluttering in TreeNet graphs. Our case study also shows that TreeNetViz has the potential to support the analysis of a compound graph by revealing multiscale and cross-scale network patterns. © 2011 IEEE

GreedyMAX-type Algorithms for the Maximum Independent Set Problem

NASA Astrophysics Data System (ADS)

Borowiecki, Piotr; Göring, Frank

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

Information Retrieval and Graph Analysis Approaches for Book Recommendation.

PubMed

Benkoussas, Chahinez; Bellot, Patrice

2015-01-01

A combination of multiple information retrieval approaches is proposed for the purpose of book recommendation. In this paper, book recommendation is based on complex user's query. We used different theoretical retrieval models: probabilistic as InL2 (Divergence from Randomness model) and language model and tested their interpolated combination. Graph analysis algorithms such as PageRank have been successful in Web environments. We consider the application of this algorithm in a new retrieval approach to related document network comprised of social links. We called Directed Graph of Documents (DGD) a network constructed with documents and social information provided from each one of them. Specifically, this work tackles the problem of book recommendation in the context of INEX (Initiative for the Evaluation of XML retrieval) Social Book Search track. A series of reranking experiments demonstrate that combining retrieval models yields significant improvements in terms of standard ranked retrieval metrics. These results extend the applicability of link analysis algorithms to different environments.

Information Retrieval and Graph Analysis Approaches for Book Recommendation

PubMed Central

Benkoussas, Chahinez; Bellot, Patrice

2015-01-01

A combination of multiple information retrieval approaches is proposed for the purpose of book recommendation. In this paper, book recommendation is based on complex user's query. We used different theoretical retrieval models: probabilistic as InL2 (Divergence from Randomness model) and language model and tested their interpolated combination. Graph analysis algorithms such as PageRank have been successful in Web environments. We consider the application of this algorithm in a new retrieval approach to related document network comprised of social links. We called Directed Graph of Documents (DGD) a network constructed with documents and social information provided from each one of them. Specifically, this work tackles the problem of book recommendation in the context of INEX (Initiative for the Evaluation of XML retrieval) Social Book Search track. A series of reranking experiments demonstrate that combining retrieval models yields significant improvements in terms of standard ranked retrieval metrics. These results extend the applicability of link analysis algorithms to different environments. PMID:26504899

Reaction factoring and bipartite update graphs accelerate the Gillespie Algorithm for large-scale biochemical systems.

PubMed

Indurkhya, Sagar; Beal, Jacob

2010-01-06

ODE simulations of chemical systems perform poorly when some of the species have extremely low concentrations. Stochastic simulation methods, which can handle this case, have been impractical for large systems due to computational complexity. We observe, however, that when modeling complex biological systems: (1) a small number of reactions tend to occur a disproportionately large percentage of the time, and (2) a small number of species tend to participate in a disproportionately large percentage of reactions. We exploit these properties in LOLCAT Method, a new implementation of the Gillespie Algorithm. First, factoring reaction propensities allows many propensities dependent on a single species to be updated in a single operation. Second, representing dependencies between reactions with a bipartite graph of reactions and species requires only storage for reactions, rather than the required for a graph that includes only reactions. Together, these improvements allow our implementation of LOLCAT Method to execute orders of magnitude faster than currently existing Gillespie Algorithm variants when simulating several yeast MAPK cascade models.

Reaction Factoring and Bipartite Update Graphs Accelerate the Gillespie Algorithm for Large-Scale Biochemical Systems

PubMed Central

Indurkhya, Sagar; Beal, Jacob

2010-01-01

ODE simulations of chemical systems perform poorly when some of the species have extremely low concentrations. Stochastic simulation methods, which can handle this case, have been impractical for large systems due to computational complexity. We observe, however, that when modeling complex biological systems: (1) a small number of reactions tend to occur a disproportionately large percentage of the time, and (2) a small number of species tend to participate in a disproportionately large percentage of reactions. We exploit these properties in LOLCAT Method, a new implementation of the Gillespie Algorithm. First, factoring reaction propensities allows many propensities dependent on a single species to be updated in a single operation. Second, representing dependencies between reactions with a bipartite graph of reactions and species requires only storage for reactions, rather than the required for a graph that includes only reactions. Together, these improvements allow our implementation of LOLCAT Method to execute orders of magnitude faster than currently existing Gillespie Algorithm variants when simulating several yeast MAPK cascade models. PMID:20066048

A hierarchical graph neuron scheme for real-time pattern recognition.

PubMed

Nasution, B B; Khan, A I

2008-02-01

The hierarchical graph neuron (HGN) implements a single cycle memorization and recall operation through a novel algorithmic design. The HGN is an improvement on the already published original graph neuron (GN) algorithm. In this improved approach, it recognizes incomplete/noisy patterns. It also resolves the crosstalk problem, which is identified in the previous publications, within closely matched patterns. To accomplish this, the HGN links multiple GN networks for filtering noise and crosstalk out of pattern data inputs. Intrinsically, the HGN is a lightweight in-network processing algorithm which does not require expensive floating point computations; hence, it is very suitable for real-time applications and tiny devices such as the wireless sensor networks. This paper describes that the HGN's pattern matching capability and the small response time remain insensitive to the increases in the number of stored patterns. Moreover, the HGN does not require definition of rules or setting of thresholds by the operator to achieve the desired results nor does it require heuristics entailing iterative operations for memorization and recall of patterns.

Bipartite Graphs as Models of Population Structures in Evolutionary Multiplayer Games

PubMed Central

Peña, Jorge; Rochat, Yannick

2012-01-01

By combining evolutionary game theory and graph theory, “games on graphs” study the evolutionary dynamics of frequency-dependent selection in population structures modeled as geographical or social networks. Networks are usually represented by means of unipartite graphs, and social interactions by two-person games such as the famous prisoner’s dilemma. Unipartite graphs have also been used for modeling interactions going beyond pairwise interactions. In this paper, we argue that bipartite graphs are a better alternative to unipartite graphs for describing population structures in evolutionary multiplayer games. To illustrate this point, we make use of bipartite graphs to investigate, by means of computer simulations, the evolution of cooperation under the conventional and the distributed N-person prisoner’s dilemma. We show that several implicit assumptions arising from the standard approach based on unipartite graphs (such as the definition of replacement neighborhoods, the intertwining of individual and group diversity, and the large overlap of interaction neighborhoods) can have a large impact on the resulting evolutionary dynamics. Our work provides a clear example of the importance of construction procedures in games on graphs, of the suitability of bigraphs and hypergraphs for computational modeling, and of the importance of concepts from social network analysis such as centrality, centralization and bipartite clustering for the understanding of dynamical processes occurring on networked population structures. PMID:22970237

A Clustering Graph Generator

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

Winlaw, Manda; De Sterck, Hans; Sanders, Geoffrey

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 tomore » 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.« less

An Expert System toward Buiding An Earth Science Knowledge Graph

NASA Astrophysics Data System (ADS)

Zhang, J.; Duan, X.; Ramachandran, R.; Lee, T. J.; Bao, Q.; Gatlin, P. N.; Maskey, M.

2017-12-01

In this ongoing work, we aim to build foundations of Cognitive Computing for Earth Science research. The goal of our project is to develop an end-to-end automated methodology for incrementally constructing Knowledge Graphs for Earth Science (KG4ES). These knowledge graphs can then serve as the foundational components for building cognitive systems in Earth science, enabling researchers to uncover new patterns and hypotheses that are virtually impossible to identify today. In addition, this research focuses on developing mining algorithms needed to exploit these constructed knowledge graphs. As such, these graphs will free knowledge from publications that are generated in a very linear, deterministic manner, and structure knowledge in a way that users can both interact and connect with relevant pieces of information. Our major contributions are two-fold. First, we have developed an end-to-end methodology for constructing Knowledge Graphs for Earth Science (KG4ES) using existing corpus of journal papers and reports. One of the key challenges in any machine learning, especially deep learning applications, is the need for robust and large training datasets. We have developed techniques capable of automatically retraining models and incrementally building and updating KG4ES, based on ever evolving training data. We also adopt the evaluation instrument based on common research methodologies used in Earth science research, especially in Atmospheric Science. Second, we have developed an algorithm to infer new knowledge that can exploit the constructed KG4ES. In more detail, we have developed a network prediction algorithm aiming to explore and predict possible new connections in the KG4ES and aid in new knowledge discovery.

LSG: An External-Memory Tool to Compute String Graphs for Next-Generation Sequencing Data Assembly.

PubMed

Bonizzoni, Paola; Vedova, Gianluca Della; Pirola, Yuri; Previtali, Marco; Rizzi, Raffaella

2016-03-01

The large amount of short read data that has to be assembled in future applications, such as in metagenomics or cancer genomics, strongly motivates the investigation of disk-based approaches to index next-generation sequencing (NGS) data. Positive results in this direction stimulate the investigation of efficient external memory algorithms for de novo assembly from NGS data. Our article is also motivated by the open problem of designing a space-efficient algorithm to compute a string graph using an indexing procedure based on the Burrows-Wheeler transform (BWT). We have developed a disk-based algorithm for computing string graphs in external memory: the light string graph (LSG). LSG relies on a new representation of the FM-index that is exploited to use an amount of main memory requirement that is independent from the size of the data set. Moreover, we have developed a pipeline for genome assembly from NGS data that integrates LSG with the assembly step of SGA (Simpson and Durbin, 2012 ), a state-of-the-art string graph-based assembler, and uses BEETL for indexing the input data. LSG is open source software and is available online. We have analyzed our implementation on a 875-million read whole-genome dataset, on which LSG has built the string graph using only 1GB of main memory (reducing the memory occupation by a factor of 50 with respect to SGA), while requiring slightly more than twice the time than SGA. The analysis of the entire pipeline shows an important decrease in memory usage, while managing to have only a moderate increase in the running time.

Decomposition Algorithm for Global Reachability on a Time-Varying Graph

NASA Technical Reports Server (NTRS)

Kuwata, Yoshiaki

2010-01-01

A decomposition algorithm has been developed for global reachability analysis on a space-time grid. By exploiting the upper block-triangular structure, the planning problem is decomposed into smaller subproblems, which is much more scalable than the original approach. Recent studies have proposed the use of a hot-air (Montgolfier) balloon for possible exploration of Titan and Venus because these bodies have thick haze or cloud layers that limit the science return from an orbiter, and the atmospheres would provide enough buoyancy for balloons. One of the important questions that needs to be addressed is what surface locations the balloon can reach from an initial location, and how long it would take. This is referred to as the global reachability problem, where the paths from starting locations to all possible target locations must be computed. The balloon could be driven with its own actuation, but its actuation capability is fairly limited. It would be more efficient to take advantage of the wind field and ride the wind that is much stronger than what the actuator could produce. It is possible to pose the path planning problem as a graph search problem on a directed graph by discretizing the spacetime world and the vehicle actuation. The decomposition algorithm provides reachability analysis of a time-varying graph. Because the balloon only moves in the positive direction in time, the adjacency matrix of the graph can be represented with an upper block-triangular matrix, and this upper block-triangular structure can be exploited to decompose a large graph search problem. The new approach consumes a much smaller amount of memory, which also helps speed up the overall computation when the computing resource has a limited physical memory compared to the problem size.

Graph processing platforms at scale: practices and experiences

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

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

2015-01-01

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

Stability and dynamical properties of material flow systems on random networks

NASA Astrophysics Data System (ADS)

Anand, K.; Galla, T.

2009-04-01

The theory of complex networks and of disordered systems is used to study the stability and dynamical properties of a simple model of material flow networks defined on random graphs. In particular we address instabilities that are characteristic of flow networks in economic, ecological and biological systems. Based on results from random matrix theory, we work out the phase diagram of such systems defined on extensively connected random graphs, and study in detail how the choice of control policies and the network structure affects stability. We also present results for more complex topologies of the underlying graph, focussing on finitely connected Erdös-Réyni graphs, Small-World Networks and Barabási-Albert scale-free networks. Results indicate that variability of input-output matrix elements, and random structures of the underlying graph tend to make the system less stable, while fast price dynamics or strong responsiveness to stock accumulation promote stability.

Normalized Cut Algorithm for Automated Assignment of Protein Domains

NASA Technical Reports Server (NTRS)

Samanta, M. P.; Liang, S.; Zha, H.; Biegel, Bryan A. (Technical Monitor)

2002-01-01

We present a novel computational method for automatic assignment of protein domains from structural data. At the core of our algorithm lies a recently proposed clustering technique that has been very successful for image-partitioning applications. This grap.,l-theory based clustering method uses the notion of a normalized cut to partition. an undirected graph into its strongly-connected components. Computer implementation of our method tested on the standard comparison set of proteins from the literature shows a high success rate (84%), better than most existing alternative In addition, several other features of our algorithm, such as reliance on few adjustable parameters, linear run-time with respect to the size of the protein and reduced complexity compared to other graph-theory based algorithms, would make it an attractive tool for structural biologists.

Loops in hierarchical channel networks

NASA Astrophysics Data System (ADS)

Katifori, Eleni; Magnasco, Marcelo

2012-02-01

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

Graph Matching: Relax at Your Own Risk.

PubMed

Lyzinski, Vince; Fishkind, Donniell E; Fiori, Marcelo; Vogelstein, Joshua T; Priebe, Carey E; Sapiro, Guillermo

2016-01-01

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.

On transitions in the behaviour of tabu search algorithm TabuCol for graph colouring

NASA Astrophysics Data System (ADS)

Chalupa, D.

2018-01-01

Even though tabu search is one of the most popular metaheuristic search strategies, its understanding in terms of behavioural transitions and parameter tuning is still very limited. In this paper, we present a theoretical and experimental study of a popular tabu search algorithm TabuCol for graph colouring. We show that for some instances, there are sharp transitions in the behaviour of TabuCol, depending on the value of tabu tenure parameter. The location of this transition depends on graph structure and may also depend on its size. This is further supported by an experimental study of success rate profiles, which we define as an empirical measure of these transitions. We study the success rate profiles for a range of graph colouring instances, from 2-colouring of trees and forests to several instances from the DIMACS benchmark. These reveal that TabuCol may exhibit a spectrum of different behaviours ranging from simple transitions to highly complex probabilistic behaviour.

Constructing a Graph Database for Semantic Literature-Based Discovery.

PubMed

Hristovski, Dimitar; Kastrin, Andrej; Dinevski, Dejan; Rindflesch, Thomas C

2015-01-01

Literature-based discovery (LBD) generates discoveries, or hypotheses, by combining what is already known in the literature. Potential discoveries have the form of relations between biomedical concepts; for example, a drug may be determined to treat a disease other than the one for which it was intended. LBD views the knowledge in a domain as a network; a set of concepts along with the relations between them. As a starting point, we used SemMedDB, a database of semantic relations between biomedical concepts extracted with SemRep from Medline. SemMedDB is distributed as a MySQL relational database, which has some problems when dealing with network data. We transformed and uploaded SemMedDB into the Neo4j graph database, and implemented the basic LBD discovery algorithms with the Cypher query language. We conclude that storing the data needed for semantic LBD is more natural in a graph database. Also, implementing LBD discovery algorithms is conceptually simpler with a graph query language when compared with standard SQL.

MorphoGraphX: A platform for quantifying morphogenesis in 4D.

PubMed

Barbier de Reuille, Pierre; Routier-Kierzkowska, Anne-Lise; Kierzkowski, Daniel; Bassel, George W; Schüpbach, Thierry; Tauriello, Gerardo; Bajpai, Namrata; Strauss, Sören; Weber, Alain; Kiss, Annamaria; Burian, Agata; Hofhuis, Hugo; Sapala, Aleksandra; Lipowczan, Marcin; Heimlicher, Maria B; Robinson, Sarah; Bayer, Emmanuelle M; Basler, Konrad; Koumoutsakos, Petros; Roeder, Adrienne H K; Aegerter-Wilmsen, Tinri; Nakayama, Naomi; Tsiantis, Miltos; Hay, Angela; Kwiatkowska, Dorota; Xenarios, Ioannis; Kuhlemeier, Cris; Smith, Richard S

2015-05-06

Morphogenesis emerges from complex multiscale interactions between genetic and mechanical processes. To understand these processes, the evolution of cell shape, proliferation and gene expression must be quantified. This quantification is usually performed either in full 3D, which is computationally expensive and technically challenging, or on 2D planar projections, which introduces geometrical artifacts on highly curved organs. Here we present MorphoGraphX ( www.MorphoGraphX.org), a software that bridges this gap by working directly with curved surface images extracted from 3D data. In addition to traditional 3D image analysis, we have developed algorithms to operate on curved surfaces, such as cell segmentation, lineage tracking and fluorescence signal quantification. The software's modular design makes it easy to include existing libraries, or to implement new algorithms. Cell geometries extracted with MorphoGraphX can be exported and used as templates for simulation models, providing a powerful platform to investigate the interactions between shape, genes and growth.

Evolutionary dynamics on graphs: Efficient method for weak selection

NASA Astrophysics Data System (ADS)

Fu, Feng; Wang, Long; Nowak, Martin A.; Hauert, Christoph

2009-04-01

Investigating the evolutionary dynamics of game theoretical interactions in populations where individuals are arranged on a graph can be challenging in terms of computation time. Here, we propose an efficient method to study any type of game on arbitrary graph structures for weak selection. In this limit, evolutionary game dynamics represents a first-order correction to neutral evolution. Spatial correlations can be empirically determined under neutral evolution and provide the basis for formulating the game dynamics as a discrete Markov process by incorporating a detailed description of the microscopic dynamics based on the neutral correlations. This framework is then applied to one of the most intriguing questions in evolutionary biology: the evolution of cooperation. We demonstrate that the degree heterogeneity of a graph impedes cooperation and that the success of tit for tat depends not only on the number of rounds but also on the degree of the graph. Moreover, considering the mutation-selection equilibrium shows that the symmetry of the stationary distribution of states under weak selection is skewed in favor of defectors for larger selection strengths. In particular, degree heterogeneity—a prominent feature of scale-free networks—generally results in a more pronounced increase in the critical benefit-to-cost ratio required for evolution to favor cooperation as compared to regular graphs. This conclusion is corroborated by an analysis of the effects of population structures on the fixation probabilities of strategies in general 2×2 games for different types of graphs. Computer simulations confirm the predictive power of our method and illustrate the improved accuracy as compared to previous studies.

Restarting and recentering genetic algorithm variations for DNA fragment assembly: The necessity of a multi-strategy approach.

PubMed

Hughes, James Alexander; Houghten, Sheridan; Ashlock, Daniel

2016-12-01

DNA Fragment assembly - an NP-Hard problem - is one of the major steps in of DNA sequencing. Multiple strategies have been used for this problem, including greedy graph-based algorithms, deBruijn graphs, and the overlap-layout-consensus approach. This study focuses on the overlap-layout-consensus approach. Heuristics and computational intelligence methods are combined to exploit their respective benefits. These algorithm combinations were able to produce high quality results surpassing the best results obtained by a number of competitive algorithms specially designed and tuned for this problem on thirteen of sixteen popular benchmarks. This work also reinforces the necessity of using multiple search strategies as it is clearly observed that algorithm performance is dependent on problem instance; without a deeper look into many searches, top solutions could be missed entirely. Copyright © 2016. Published by Elsevier Ireland Ltd.

A parallel computing engine for a class of time critical processes.

PubMed

Nabhan, T M; Zomaya, A Y

1997-01-01

This paper focuses on the efficient parallel implementation of systems of numerically intensive nature over loosely coupled multiprocessor architectures. These analytical models are of significant importance to many real-time systems that have to meet severe time constants. A parallel computing engine (PCE) has been developed in this work for the efficient simplification and the near optimal scheduling of numerical models over the different cooperating processors of the parallel computer. First, the analytical system is efficiently coded in its general form. The model is then simplified by using any available information (e.g., constant parameters). A task graph representing the interconnections among the different components (or equations) is generated. The graph can then be compressed to control the computation/communication requirements. The task scheduler employs a graph-based iterative scheme, based on the simulated annealing algorithm, to map the vertices of the task graph onto a Multiple-Instruction-stream Multiple-Data-stream (MIMD) type of architecture. The algorithm uses a nonanalytical cost function that properly considers the computation capability of the processors, the network topology, the communication time, and congestion possibilities. Moreover, the proposed technique is simple, flexible, and computationally viable. The efficiency of the algorithm is demonstrated by two case studies with good results.

Object recognition in images via a factor graph model

NASA Astrophysics Data System (ADS)

He, Yong; Wang, Long; Wu, Zhaolin; Zhang, Haisu

2018-04-01

Object recognition in images suffered from huge search space and uncertain object profile. Recently, the Bag-of- Words methods are utilized to solve these problems, especially the 2-dimension CRF(Conditional Random Field) model. In this paper we suggest the method based on a general and flexible fact graph model, which can catch the long-range correlation in Bag-of-Words by constructing a network learning framework contrasted from lattice in CRF. Furthermore, we explore a parameter learning algorithm based on the gradient descent and Loopy Sum-Product algorithms for the factor graph model. Experimental results on Graz 02 dataset show that, the recognition performance of our method in precision and recall is better than a state-of-art method and the original CRF model, demonstrating the effectiveness of the proposed method.

Evolutionary dynamics on graphs

NASA Astrophysics Data System (ADS)

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

2005-01-01

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

Automated boundary detection of the optic disc and layer segmentation of the peripapillary retina in volumetric structural and angiographic optical coherence tomography.

PubMed

Zang, Pengxiao; Gao, Simon S; Hwang, Thomas S; Flaxel, Christina J; Wilson, David J; Morrison, John C; Huang, David; Li, Dengwang; Jia, Yali

2017-03-01

To improve optic disc boundary detection and peripapillary retinal layer segmentation, we propose an automated approach for structural and angiographic optical coherence tomography. The algorithm was performed on radial cross-sectional B-scans. The disc boundary was detected by searching for the position of Bruch's membrane opening, and retinal layer boundaries were detected using a dynamic programming-based graph search algorithm on each B-scan without the disc region. A comparison of the disc boundary using our method with that determined by manual delineation showed good accuracy, with an average Dice similarity coefficient ≥0.90 in healthy eyes and eyes with diabetic retinopathy and glaucoma. The layer segmentation accuracy in the same cases was on average less than one pixel (3.13 μm).

Automated boundary detection of the optic disc and layer segmentation of the peripapillary retina in volumetric structural and angiographic optical coherence tomography

PubMed Central

Zang, Pengxiao; Gao, Simon S.; Hwang, Thomas S.; Flaxel, Christina J.; Wilson, David J.; Morrison, John C.; Huang, David; Li, Dengwang; Jia, Yali

2017-01-01

To improve optic disc boundary detection and peripapillary retinal layer segmentation, we propose an automated approach for structural and angiographic optical coherence tomography. The algorithm was performed on radial cross-sectional B-scans. The disc boundary was detected by searching for the position of Bruch’s membrane opening, and retinal layer boundaries were detected using a dynamic programming-based graph search algorithm on each B-scan without the disc region. A comparison of the disc boundary using our method with that determined by manual delineation showed good accuracy, with an average Dice similarity coefficient ≥0.90 in healthy eyes and eyes with diabetic retinopathy and glaucoma. The layer segmentation accuracy in the same cases was on average less than one pixel (3.13 μm). PMID:28663830

Graph-based sensor fusion for classification of transient acoustic signals.

PubMed

Srinivas, Umamahesh; Nasrabadi, Nasser M; Monga, Vishal

2015-03-01

Advances in acoustic sensing have enabled the simultaneous acquisition of multiple measurements of the same physical event via co-located acoustic sensors. We exploit the inherent correlation among such multiple measurements for acoustic signal classification, to identify the launch/impact of munition (i.e., rockets, mortars). Specifically, we propose a probabilistic graphical model framework that can explicitly learn the class conditional correlations between the cepstral features extracted from these different measurements. Additionally, we employ symbolic dynamic filtering-based features, which offer improvements over the traditional cepstral features in terms of robustness to signal distortions. Experiments on real acoustic data sets show that our proposed algorithm outperforms conventional classifiers as well as the recently proposed joint sparsity models for multisensor acoustic classification. Additionally our proposed algorithm is less sensitive to insufficiency in training samples compared to competing approaches.

Properties of the numerical algorithms for problems of quantum information technologies: Benefits of deep analysis

NASA Astrophysics Data System (ADS)

Chernyavskiy, Andrey; Khamitov, Kamil; Teplov, Alexey; Voevodin, Vadim; Voevodin, Vladimir

2016-10-01

In recent years, quantum information technologies (QIT) showed great development, although, the way of the implementation of QIT faces the serious difficulties, some of which are challenging computational tasks. This work is devoted to the deep and broad analysis of the parallel algorithmic properties of such tasks. As an example we take one- and two-qubit transformations of a many-qubit quantum state, which are the most critical kernels of many important QIT applications. The analysis of the algorithms uses the methodology of the AlgoWiki project (algowiki-project.org) and consists of two parts: theoretical and experimental. Theoretical part includes features like sequential and parallel complexity, macro structure, and visual information graph. Experimental part was made by using the petascale Lomonosov supercomputer (Moscow State University, Russia) and includes the analysis of locality and memory access, scalability and the set of more specific dynamic characteristics of realization. This approach allowed us to obtain bottlenecks and generate ideas of efficiency improvement.

Method for Identification of Results of Dynamic Overloads in Assessment of Safety Use of the Mine Auxiliary Transportation System

NASA Astrophysics Data System (ADS)

Tokarczyk, Jarosław

2016-12-01

Method for identification the effects of dynamic overload affecting the people, which may occur in the emergency state of suspended monorail is presented in the paper. The braking curve using MBS (Multi-Body System) simulation was determined. For this purpose a computational model (MBS) of suspended monorail was developed and two different variants of numerical calculations were carried out. An algorithm of conducting numerical simulations to assess the effects of dynamic overload acting on the suspended monorails' users is also posted in the paper. An example of computational model FEM (Finite Element Method) composed of technical mean and the anthropometrical model ATB (Articulated Total Body) is shown. The simulation results are presented: graph of HIC (Head Injury Criterion) parameter and successive phases of dislocation of ATB model. Generator of computational models for safety criterion, which enables preparation of input data and remote starting the simulation, is proposed.

A graph-based approach for designing extensible pipelines

PubMed Central

2012-01-01

Background In bioinformatics, it is important to build extensible and low-maintenance systems that are able to deal with the new tools and data formats that are constantly being developed. The traditional and simplest implementation of pipelines involves hardcoding the execution steps into programs or scripts. This approach can lead to problems when a pipeline is expanding because the incorporation of new tools is often error prone and time consuming. Current approaches to pipeline development such as workflow management systems focus on analysis tasks that are systematically repeated without significant changes in their course of execution, such as genome annotation. However, more dynamism on the pipeline composition is necessary when each execution requires a different combination of steps. Results We propose a graph-based approach to implement extensible and low-maintenance pipelines that is suitable for pipeline applications with multiple functionalities that require different combinations of steps in each execution. Here pipelines are composed automatically by compiling a specialised set of tools on demand, depending on the functionality required, instead of specifying every sequence of tools in advance. We represent the connectivity of pipeline components with a directed graph in which components are the graph edges, their inputs and outputs are the graph nodes, and the paths through the graph are pipelines. To that end, we developed special data structures and a pipeline system algorithm. We demonstrate the applicability of our approach by implementing a format conversion pipeline for the fields of population genetics and genetic epidemiology, but our approach is also helpful in other fields where the use of multiple software is necessary to perform comprehensive analyses, such as gene expression and proteomics analyses. The project code, documentation and the Java executables are available under an open source license at http://code.google.com/p/dynamic-pipeline. The system has been tested on Linux and Windows platforms. Conclusions Our graph-based approach enables the automatic creation of pipelines by compiling a specialised set of tools on demand, depending on the functionality required. It also allows the implementation of extensible and low-maintenance pipelines and contributes towards consolidating openness and collaboration in bioinformatics systems. It is targeted at pipeline developers and is suited for implementing applications with sequential execution steps and combined functionalities. In the format conversion application, the automatic combination of conversion tools increased both the number of possible conversions available to the user and the extensibility of the system to allow for future updates with new file formats. PMID:22788675

Integrating atlas and graph cut methods for right ventricle blood-pool segmentation from cardiac cine MRI

NASA Astrophysics Data System (ADS)

Dangi, Shusil; Linte, Cristian A.

2017-03-01

Segmentation of right ventricle from cardiac MRI images can be used to build pre-operative anatomical heart models to precisely identify regions of interest during minimally invasive therapy. Furthermore, many functional parameters of right heart such as right ventricular volume, ejection fraction, myocardial mass and thickness can also be assessed from the segmented images. To obtain an accurate and computationally efficient segmentation of right ventricle from cardiac cine MRI, we propose a segmentation algorithm formulated as an energy minimization problem in a graph. Shape prior obtained by propagating label from an average atlas using affine registration is incorporated into the graph framework to overcome problems in ill-defined image regions. The optimal segmentation corresponding to the labeling with minimum energy configuration of the graph is obtained via graph-cuts and is iteratively refined to produce the final right ventricle blood pool segmentation. We quantitatively compare the segmentation results obtained from our algorithm to the provided gold-standard expert manual segmentation for 16 cine-MRI datasets available through the MICCAI 2012 Cardiac MR Right Ventricle Segmentation Challenge according to several similarity metrics, including Dice coefficient, Jaccard coefficient, Hausdorff distance, and Mean absolute distance error.

Iterative-cuts: longitudinal and scale-invariant segmentation via user-defined templates for rectosigmoid colon in gynecological brachytherapy.

PubMed

Lüddemann, Tobias; Egger, Jan

2016-04-01

Among all types of cancer, gynecological malignancies belong to the fourth most frequent type of cancer among women. In addition to chemotherapy and external beam radiation, brachytherapy is the standard procedure for the treatment of these malignancies. In the progress of treatment planning, localization of the tumor as the target volume and adjacent organs of risks by segmentation is crucial to accomplish an optimal radiation distribution to the tumor while simultaneously preserving healthy tissue. Segmentation is performed manually and represents a time-consuming task in clinical daily routine. This study focuses on the segmentation of the rectum/sigmoid colon as an organ-at-risk in gynecological brachytherapy. The proposed segmentation method uses an interactive, graph-based segmentation scheme with a user-defined template. The scheme creates a directed two-dimensional graph, followed by the minimal cost closed set computation on the graph, resulting in an outlining of the rectum. The graph's outline is dynamically adapted to the last calculated cut. Evaluation was performed by comparing manual segmentations of the rectum/sigmoid colon to results achieved with the proposed method. The comparison of the algorithmic to manual result yielded a dice similarity coefficient value of [Formula: see text], in comparison to [Formula: see text] for the comparison of two manual segmentations by the same physician. Utilizing the proposed methodology resulted in a median time of [Formula: see text], compared to 300 s needed for pure manual segmentation.

Interactive and scale invariant segmentation of the rectum/sigmoid via user-defined templates

NASA Astrophysics Data System (ADS)

Lüddemann, Tobias; Egger, Jan

2016-03-01

Among all types of cancer, gynecological malignancies belong to the 4th most frequent type of cancer among women. Besides chemotherapy and external beam radiation, brachytherapy is the standard procedure for the treatment of these malignancies. In the progress of treatment planning, localization of the tumor as the target volume and adjacent organs of risks by segmentation is crucial to accomplish an optimal radiation distribution to the tumor while simultaneously preserving healthy tissue. Segmentation is performed manually and represents a time-consuming task in clinical daily routine. This study focuses on the segmentation of the rectum/sigmoid colon as an Organ-At-Risk in gynecological brachytherapy. The proposed segmentation method uses an interactive, graph-based segmentation scheme with a user-defined template. The scheme creates a directed two dimensional graph, followed by the minimal cost closed set computation on the graph, resulting in an outlining of the rectum. The graphs outline is dynamically adapted to the last calculated cut. Evaluation was performed by comparing manual segmentations of the rectum/sigmoid colon to results achieved with the proposed method. The comparison of the algorithmic to manual results yielded to a Dice Similarity Coefficient value of 83.85+/-4.08%, in comparison to 83.97+/-8.08% for the comparison of two manual segmentations of the same physician. Utilizing the proposed methodology resulted in a median time of 128 seconds per dataset, compared to 300 seconds needed for pure manual segmentation.

Graph partitions and cluster synchronization in networks of oscillators

PubMed Central

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

Modeling and optimum time performance for concurrent processing

NASA Technical Reports Server (NTRS)

Mielke, Roland R.; Stoughton, John W.; Som, Sukhamoy

1988-01-01

The development of a new graph theoretic model for describing the relation between a decomposed algorithm and its execution in a data flow environment is presented. Called ATAMM, the model consists of a set of Petri net marked graphs useful for representing decision-free algorithms having large-grained, computationally complex primitive operations. Performance time measures which determine computing speed and throughput capacity are defined, and the ATAMM model is used to develop lower bounds for these times. A concurrent processing operating strategy for achieving optimum time performance is presented and illustrated by example.

Modeling heterogeneous processor scheduling for real time systems

NASA Technical Reports Server (NTRS)

Leathrum, J. F.; Mielke, R. R.; Stoughton, J. W.

1994-01-01

A new model is presented to describe dataflow algorithms implemented in a multiprocessing system. Called the resource/data flow graph (RDFG), the model explicitly represents cyclo-static processor schedules as circuits of processor arcs which reflect the order that processors execute graph nodes. The model also allows the guarantee of meeting hard real-time deadlines. When unfolded, the model identifies statically the processor schedule. The model therefore is useful for determining the throughput and latency of systems with heterogeneous processors. The applicability of the model is demonstrated using a space surveillance algorithm.

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

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

The dynamics and control of large flexible space structures-V

NASA Technical Reports Server (NTRS)

Bainum, P. M.; Reddy, A. S. S. R.; Diarra, C. M.; Kumar, V. K.

1982-01-01

A general survey of the progress made in the areas of mathematical modelling of the system dynamics, structural analysis, development of control algorithms, and simulation of environmental disturbances is presented. The use of graph theory techniques is employed to examine the effects of inherent damping associated with LSST systems on the number and locations of the required control actuators. A mathematical model of the forces and moments induced on a flexible orbiting beam due to solar radiation pressure is developed and typical steady state open loop responses obtained for the case when rotations and vibrations are limited to occur within the orbit plane. A preliminary controls analysis based on a truncated (13 mode) finite element model of the 122m. Hoop/Column antenna indicates that a minimum of six appropriately placed actuators is required for controllability. An algorithm to evaluate the coefficients which describe coupling between the rigid rotational and flexible modes and also intramodal coupling was developed and numerical evaluation based on the finite element model of Hoop/Column system is currently in progress.

Sensor selection cost optimisation for tracking structurally cyclic systems: a P-order solution

NASA Astrophysics Data System (ADS)

Doostmohammadian, M.; Zarrabi, H.; Rabiee, H. R.

2017-08-01

Measurements and sensing implementations impose certain cost in sensor networks. The sensor selection cost optimisation is the problem of minimising the sensing cost of monitoring a physical (or cyber-physical) system. Consider a given set of sensors tracking states of a dynamical system for estimation purposes. For each sensor assume different costs to measure different (realisable) states. The idea is to assign sensors to measure states such that the global cost is minimised. The number and selection of sensor measurements need to ensure the observability to track the dynamic state of the system with bounded estimation error. The main question we address is how to select the state measurements to minimise the cost while satisfying the observability conditions. Relaxing the observability condition for structurally cyclic systems, the main contribution is to propose a graph theoretic approach to solve the problem in polynomial time. Note that polynomial time algorithms are suitable for large-scale systems as their running time is upper-bounded by a polynomial expression in the size of input for the algorithm. We frame the problem as a linear sum assignment with solution complexity of ?.

Integrating multiple data sources for malware classification

DOEpatents

Anderson, Blake Harrell; Storlie, Curtis B; Lane, Terran

2015-04-28

Disclosed herein are representative embodiments of tools and techniques for classifying programs. According to one exemplary technique, at least one graph representation of at least one dynamic data source of at least one program is generated. Also, at least one graph representation of at least one static data source of the at least one program is generated. Additionally, at least using the at least one graph representation of the at least one dynamic data source and the at least one graph representation of the at least one static data source, the at least one program is classified.

Distributed-Memory Fast Maximal Independent Set

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

Kanewala Appuhamilage, Thejaka Amila J.; Zalewski, Marcin J.; Lumsdaine, Andrew

The Maximal Independent Set (MIS) graph problem arises in many applications such as computer vision, information theory, molecular biology, and process scheduling. The growing scale of MIS problems suggests the use of distributed-memory hardware as a cost-effective approach to providing necessary compute and memory resources. Luby proposed four randomized algorithms to solve the MIS problem. All those algorithms are designed focusing on shared-memory machines and are analyzed using the PRAM model. These algorithms do not have direct efficient distributed-memory implementations. In this paper, we extend two of Luby’s seminal MIS algorithms, “Luby(A)” and “Luby(B),” to distributed-memory execution, and we evaluatemore » their performance. We compare our results with the “Filtered MIS” implementation in the Combinatorial BLAS library for two types of synthetic graph inputs.« less

Dynamical graph theory networks techniques for the analysis of sparse connectivity networks in dementia

NASA Astrophysics Data System (ADS)

Tahmassebi, Amirhessam; Pinker-Domenig, Katja; Wengert, Georg; Lobbes, Marc; Stadlbauer, Andreas; Romero, Francisco J.; Morales, Diego P.; Castillo, Encarnacion; Garcia, Antonio; Botella, Guillermo; Meyer-Bäse, Anke

2017-05-01

Graph network models in dementia have become an important computational technique in neuroscience to study fundamental organizational principles of brain structure and function of neurodegenerative diseases such as dementia. The graph connectivity is reflected in the connectome, the complete set of structural and functional connections of the graph network, which is mostly based on simple Pearson correlation links. In contrast to simple Pearson correlation networks, the partial correlations (PC) only identify direct correlations while indirect associations are eliminated. In addition to this, the state-of-the-art techniques in brain research are based on static graph theory, which is unable to capture the dynamic behavior of the brain connectivity, as it alters with disease evolution. We propose a new research avenue in neuroimaging connectomics based on combining dynamic graph network theory and modeling strategies at different time scales. We present the theoretical framework for area aggregation and time-scale modeling in brain networks as they pertain to disease evolution in dementia. This novel paradigm is extremely powerful, since we can derive both static parameters pertaining to node and area parameters, as well as dynamic parameters, such as system's eigenvalues. By implementing and analyzing dynamically both disease driven PC-networks and regular concentration networks, we reveal differences in the structure of these network that play an important role in the temporal evolution of this disease. The described research is key to advance biomedical research on novel disease prediction trajectories and dementia therapies.

Graph Theory and Ion and Molecular Aggregation in Aqueous Solutions.

PubMed

Choi, Jun-Ho; Lee, Hochan; Choi, Hyung Ran; Cho, Minhaeng

2018-04-20

In molecular and cellular biology, dissolved ions and molecules have decisive effects on chemical and biological reactions, conformational stabilities, and functions of small to large biomolecules. Despite major efforts, the current state of understanding of the effects of specific ions, osmolytes, and bioprotecting sugars on the structure and dynamics of water H-bonding networks and proteins is not yet satisfactory. Recently, to gain deeper insight into this subject, we studied various aggregation processes of ions and molecules in high-concentration salt, osmolyte, and sugar solutions with time-resolved vibrational spectroscopy and molecular dynamics simulation methods. It turns out that ions (or solute molecules) have a strong propensity to self-assemble into large and polydisperse aggregates that affect both local and long-range water H-bonding structures. In particular, we have shown that graph-theoretical approaches can be used to elucidate morphological characteristics of large aggregates in various aqueous salt, osmolyte, and sugar solutions. When ion and molecular aggregates in such aqueous solutions are treated as graphs, a variety of graph-theoretical properties, such as graph spectrum, degree distribution, clustering coefficient, minimum path length, and graph entropy, can be directly calculated by considering an ensemble of configurations taken from molecular dynamics trajectories. Here we show percolating behavior exhibited by ion and molecular aggregates upon increase in solute concentration in high solute concentrations and discuss compelling evidence of the isomorphic relation between percolation transitions of ion and molecular aggregates and water H-bonding networks. We anticipate that the combination of graph theory and molecular dynamics simulation methods will be of exceptional use in achieving a deeper understanding of the fundamental physical chemistry of dissolution and in describing the interplay between the self-aggregation of solute molecules and the structure and dynamics of water.