Chao, T.T.; Sanzolone, R.F.
1992-01-01
Sample decomposition is a fundamental and integral step in the procedure of geochemical analysis. It is often the limiting factor to sample throughput, especially with the recent application of the fast and modern multi-element measurement instrumentation. The complexity of geological materials makes it necessary to choose the sample decomposition technique that is compatible with the specific objective of the analysis. When selecting a decomposition technique, consideration should be given to the chemical and mineralogical characteristics of the sample, elements to be determined, precision and accuracy requirements, sample throughput, technical capability of personnel, and time constraints. This paper addresses these concerns and discusses the attributes and limitations of many techniques of sample decomposition along with examples of their application to geochemical analysis. The chemical properties of reagents as to their function as decomposition agents are also reviewed. The section on acid dissolution techniques addresses the various inorganic acids that are used individually or in combination in both open and closed systems. Fluxes used in sample fusion are discussed. The promising microwave-oven technology and the emerging field of automation are also examined. A section on applications highlights the use of decomposition techniques for the determination of Au, platinum group elements (PGEs), Hg, U, hydride-forming elements, rare earth elements (REEs), and multi-elements in geological materials. Partial dissolution techniques used for geochemical exploration which have been treated in detail elsewhere are not discussed here; nor are fire-assaying for noble metals and decomposition techniques for X-ray fluorescence or nuclear methods be discussed. ?? 1992.
Parallel Algorithms for Graph Optimization using Tree Decompositions
Sullivan, Blair D [ORNL; Weerapurage, Dinesh P [ORNL; Groer, Christopher S [ORNL
2012-06-01
Although many $\\cal{NP}$-hard graph optimization problems can be solved in polynomial time on graphs of bounded tree-width, the adoption of these techniques into mainstream scientific computation has been limited due to the high memory requirements of the necessary dynamic programming tables and excessive runtimes of sequential implementations. This work addresses both challenges by proposing a set of new parallel algorithms for all steps of a tree decomposition-based approach to solve the maximum weighted independent set problem. A hybrid OpenMP/MPI implementation includes a highly scalable parallel dynamic programming algorithm leveraging the MADNESS task-based runtime, and computational results demonstrate scaling. This work enables a significant expansion of the scale of graphs on which exact solutions to maximum weighted independent set can be obtained, and forms a framework for solving additional graph optimization problems with similar techniques.
INDDGO: Integrated Network Decomposition & Dynamic programming for Graph Optimization
Groer, Christopher S [ORNL; Sullivan, Blair D [ORNL; Weerapurage, Dinesh P [ORNL
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 we 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.
C7-Decompositions of the Tensor Product of Complete Graphs
Manikandan R.S.
2017-08-01
Full Text Available In this paper we consider a decomposition of Km × Kn, where × denotes the tensor product of graphs, into cycles of length seven. We prove that for m, n ≥ 3, cycles of length seven decompose the graph Km × Kn if and only if (1 either m or n is odd and (2 14 | m(m − 1n(n − 1. The results of this paper together with the results of [Cp-Decompositions of some regular graphs, Discrete Math. 306 (2006 429–451] and [C5-Decompositions of the tensor product of complete graphs, Australasian J. Combinatorics 37 (2007 285–293], give necessary and sufficient conditions for the existence of a p-cycle decomposition, where p ≥ 5 is a prime number, of the graph Km × Kn.
Central limit theorems for large graphs: Method of quantum decomposition
Hashimoto, Yukihiro; Hora, Akihito; Obata, Nobuaki
2003-01-01
A new method is proposed for investigating spectral distribution of the combinatorial Laplacian (adjacency matrix) of a large regular graph on the basis of quantum decomposition and quantum central limit theorem. General results are proved for Cayley graphs of discrete groups and for distance-regular graphs. The Coxeter groups and the Johnson graphs are discussed in detail by way of illustration. In particular, the limit distributions obtained from the Johnson graphs are characterized by the Meixner polynomials which form a one-parameter deformation of the Laguerre polynomials
Edge compression techniques for visualization of dense directed graphs.
Dwyer, Tim; Henry Riche, Nathalie; Marriott, Kim; Mears, Christopher
2013-12-01
We explore the effectiveness of visualizing dense directed graphs by replacing individual edges with edges connected to 'modules'-or groups of nodes-such that the new edges imply aggregate connectivity. We only consider techniques that offer a lossless compression: that is, where the entire graph can still be read from the compressed version. The techniques considered are: a simple grouping of nodes with identical neighbor sets; Modular Decomposition which permits internal structure in modules and allows them to be nested; and Power Graph Analysis which further allows edges to cross module boundaries. These techniques all have the same goal--to compress the set of edges that need to be rendered to fully convey connectivity--but each successive relaxation of the module definition permits fewer edges to be drawn in the rendered graph. Each successive technique also, we hypothesize, requires a higher degree of mental effort to interpret. We test this hypothetical trade-off with two studies involving human participants. For Power Graph Analysis we propose a novel optimal technique based on constraint programming. This enables us to explore the parameter space for the technique more precisely than could be achieved with a heuristic. Although applicable to many domains, we are motivated by--and discuss in particular--the application to software dependency analysis.
Approximate Computing Techniques for Iterative Graph Algorithms
Panyala, Ajay R.; Subasi, Omer; Halappanavar, Mahantesh; Kalyanaraman, Anantharaman; Chavarria Miranda, Daniel G.; Krishnamoorthy, Sriram
2017-12-18
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 low 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.
Graph based techniques for tag cloud generation
Leginus, Martin; Dolog, Peter; Lage, Ricardo Gomes
2013-01-01
Tag cloud is one of the navigation aids for exploring documents. Tag cloud also link documents through the user defined terms. We explore various graph based techniques to improve the tag cloud generation. Moreover, we introduce relevance measures based on underlying data such as ratings...... or citation counts for improved measurement of relevance of tag clouds. We show, that on the given data sets, our approach outperforms the state of the art baseline methods with respect to such relevance by 41 % on Movielens dataset and by 11 % on Bibsonomy data set....
Scaling Techniques for Massive Scale-Free Graphs in Distributed (External) Memory
Pearce, Roger
2013-05-01
We present techniques to process large scale-free graphs in distributed memory. Our aim is to scale to trillions of edges, and our research is targeted at leadership class supercomputers and clusters with local non-volatile memory, e.g., NAND Flash. We apply an edge list partitioning technique, designed to accommodate high-degree vertices (hubs) that create scaling challenges when processing scale-free graphs. In addition to partitioning hubs, we use ghost vertices to represent the hubs to reduce communication hotspots. We present a scaling study with three important graph algorithms: Breadth-First Search (BFS), K-Core decomposition, and Triangle Counting. We also demonstrate scalability on BG/P Intrepid by comparing to best known Graph500 results. We show results on two clusters with local NVRAM storage that are capable of traversing trillion-edge scale-free graphs. By leveraging node-local NAND Flash, our approach can process thirty-two times larger datasets with only a 39% performance degradation in Traversed Edges Per Second (TEPS). © 2013 IEEE.
Aggregation by Provenance Types: A Technique for Summarising Provenance Graphs
Luc Moreau
2015-04-01
Full Text Available As users become confronted with a deluge of provenance data, dedicated techniques are required to make sense of this kind of information. We present Aggregation by Provenance Types, a provenance graph analysis that is capable of generating provenance graph summaries. It proceeds by converting provenance paths up to some length k to attributes, referred to as provenance types, and by grouping nodes that have the same provenance types. The summary also includes numeric values representing the frequency of nodes and edges in the original graph. A quantitative evaluation and a complexity analysis show that this technique is tractable; with small values of k, it can produce useful summaries and can help detect outliers. We illustrate how the generated summaries can further be used for conformance checking and visualization.
Decomposition Technique for Remaining Useful Life Prediction
Saha, Bhaskar (Inventor); Goebel, Kai F. (Inventor); Saxena, Abhinav (Inventor); Celaya, Jose R. (Inventor)
2014-01-01
The prognostic tool disclosed here decomposes the problem of estimating the remaining useful life (RUL) of a component or sub-system into two separate regression problems: the feature-to-damage mapping and the operational conditions-to-damage-rate mapping. These maps are initially generated in off-line mode. One or more regression algorithms are used to generate each of these maps from measurements (and features derived from these), operational conditions, and ground truth information. This decomposition technique allows for the explicit quantification and management of different sources of uncertainty present in the process. Next, the maps are used in an on-line mode where run-time data (sensor measurements and operational conditions) are used in conjunction with the maps generated in off-line mode to estimate both current damage state as well as future damage accumulation. Remaining life is computed by subtracting the instance when the extrapolated damage reaches the failure threshold from the instance when the prediction is made.
Applications of Graph Spectral Techniques to Water Distribution Network Management
Armando di Nardo
2018-01-01
Full Text Available Cities depend on multiple heterogeneous, interconnected infrastructures to provide safe water to consumers. Given this complexity, efficient numerical techniques are needed to support optimal control and management of a water distribution network (WDN. This paper introduces a holistic analysis framework to support water utilities on the decision making process for an efficient supply management. The proposal is based on graph spectral techniques that take advantage of eigenvalues and eigenvectors properties of matrices that are associated with graphs. Instances of these matrices are the adjacency matrix and the Laplacian, among others. The interest for this application is to work on a graph that specifically represents a WDN. This is a complex network that is made by nodes corresponding to water sources and consumption points and links corresponding to pipes and valves. The aim is to face new challenges on urban water supply, ranging from computing approximations for network performance assessment to setting device positioning for efficient and automatic WDN division into district metered areas. It is consequently created a novel tool-set of graph spectral techniques adapted to improve main water management tasks and to simplify the identification of water losses through the definition of an optimal network partitioning. Two WDNs are used to analyze the proposed methodology. Firstly, the well-known network of C-Town is investigated for benchmarking of the proposed graph spectral framework. This allows for comparing the obtained results with others coming from previously proposed approaches in literature. The second case-study corresponds to an operational network. It shows the usefulness and optimality of the proposal to effectively manage a WDN.
Weighted graph based ordering techniques for preconditioned conjugate gradient methods
Clift, Simon S.; Tang, Wei-Pai
1994-01-01
We describe the basis of a matrix ordering heuristic for improving the incomplete factorization used in preconditioned conjugate gradient techniques applied to anisotropic PDE's. Several new matrix ordering techniques, derived from well-known algorithms in combinatorial graph theory, which attempt to implement this heuristic, are described. These ordering techniques are tested against a number of matrices arising from linear anisotropic PDE's, and compared with other matrix ordering techniques. A variation of RCM is shown to generally improve the quality of incomplete factorization preconditioners.
Factors and factorizations of graphs proof techniques in factor theory
Akiyama, Jin
2011-01-01
This book chronicles the development of graph factors and factorizations. It pursues a comprehensive approach, addressing most of the important results from hundreds of findings over the last century. One of the main themes is the observation that many theorems can be proved using only a few standard proof techniques. This stands in marked contrast to the seemingly countless, complex proof techniques offered by the extant body of papers and books. In addition to covering the history and development of this area, the book offers conjectures and discusses open problems. It also includes numerous explanatory figures that enable readers to progressively and intuitively understand the most important notions and proofs in the area of factors and factorization.
Graph-theoretic techniques for web content mining
Schenker, Adam; Bunke, Horst; Last, Mark
2005-01-01
This book describes exciting new opportunities for utilizing robust graph representations of data with common machine learning algorithms. Graphs can model additional information which is often not present in commonly used data representations, such as vectors.
Faenza, Y.; Oriolo, G.; Stauffer, G.
2011-01-01
We propose an algorithm for solving the maximum weighted stable set problem on claw-free graphs that runs in O(n^3)-time, drastically improving the previous best known complexity bound. This algorithm is based on a novel decomposition theorem for claw-free graphs, which is also intioduced in the present paper. Despite being weaker than the well-known structure result for claw-free graphs given by Chudnovsky and Seymour, our decomposition theorem is, on the other hand, algorithmic, i.e. it is ...
Enumeration for spanning trees and forests of join graphs based on the combinatorial decomposition
Sung Sik U
2016-10-01
Full Text Available This paper discusses the enumeration for rooted spanning trees and forests of the labelled join graphs $K_m+H_n$ and $K_m+K_{n,p}$, where $H_n$ is a graph with $n$ isolated vertices.
Decomposition techniques in mathematical programming engineering and science applications
Conejo, Antonio J; Minguez, Roberto; Garcia-Bertrand, Raquel
2006-01-01
Optimization plainly dominates the design, planning, operation, and c- trol of engineering systems. This is a book on optimization that considers particular cases of optimization problems, those with a decomposable str- ture that can be advantageously exploited. Those decomposable optimization problems are ubiquitous in engineering and science applications. The book considers problems with both complicating constraints and complicating va- ables, and analyzes linear and nonlinear problems, with and without in- ger variables. The decomposition techniques analyzed include Dantzig-Wolfe, Benders, Lagrangian relaxation, Augmented Lagrangian decomposition, and others. Heuristic techniques are also considered. Additionally, a comprehensive sensitivity analysis for characterizing the solution of optimization problems is carried out. This material is particularly novel and of high practical interest. This book is built based on many clarifying, illustrative, and compu- tional examples, which facilitate the learning p...
Lubna Moin
2009-04-01
Full Text Available This research paper basically explores and compares the different modeling and analysis techniques and than it also explores the model order reduction approach and significance. The traditional modeling and simulation techniques for dynamic systems are generally adequate for single-domain systems only, but the Bond Graph technique provides new strategies for reliable solutions of multi-domain system. They are also used for analyzing linear and non linear dynamic production system, artificial intelligence, image processing, robotics and industrial automation. This paper describes a unique technique of generating the Genetic design from the tree structured transfer function obtained from Bond Graph. This research work combines bond graphs for model representation with Genetic programming for exploring different ideas on design space tree structured transfer function result from replacing typical bond graph element with their impedance equivalent specifying impedance lows for Bond Graph multiport. This tree structured form thus obtained from Bond Graph is applied for generating the Genetic Tree. Application studies will identify key issues and importance for advancing this approach towards becoming on effective and efficient design tool for synthesizing design for Electrical system. In the first phase, the system is modeled using Bond Graph technique. Its system response and transfer function with conventional and Bond Graph method is analyzed and then a approach towards model order reduction is observed. The suggested algorithm and other known modern model order reduction techniques are applied to a 11th order high pass filter [1], with different approach. The model order reduction technique developed in this paper has least reduction errors and secondly the final model retains structural information. The system response and the stability analysis of the system transfer function taken by conventional and by Bond Graph method is compared and
Parallel pic plasma simulation through particle decomposition techniques
Briguglio, S.; Vlad, G.; Di Martino, B.; Naples, Univ. 'Federico II'
1998-02-01
Particle-in-cell (PIC) codes are among the major candidates to yield a satisfactory description of the detail of kinetic effects, such as the resonant wave-particle interaction, relevant in determining the transport mechanism in magnetically confined plasmas. A significant improvement of the simulation performance of such codes con be expected from parallelization, e.g., by distributing the particle population among several parallel processors. Parallelization of a hybrid magnetohydrodynamic-gyrokinetic code has been accomplished within the High Performance Fortran (HPF) framework, and tested on the IBM SP2 parallel system, using a 'particle decomposition' technique. The adopted technique requires a moderate effort in porting the code in parallel form and results in intrinsic load balancing and modest inter processor communication. The performance tests obtained confirm the hypothesis of high effectiveness of the strategy, if targeted towards moderately parallel architectures. Optimal use of resources is also discussed with reference to a specific physics problem [it
Graph-based Techniques for Topic Classification of Tweets in Spanish
Hector Cordobés
2014-03-01
Full Text Available Topic classification of texts is one of the most interesting challenges in Natural Language Processing (NLP. Topic classifiers commonly use a bag-of-words approach, in which the classifier uses (and is trained with selected terms from the input texts. In this work we present techniques based on graph similarity to classify short texts by topic. In our classifier we build graphs from the input texts, and then use properties of these graphs to classify them. We have tested the resulting algorithm by classifying Twitter messages in Spanish among a predefined set of topics, achieving more than 70% accuracy.
Theoretical Bound of CRLB for Energy Efficient Technique of RSS-Based Factor Graph Geolocation
Kahar Aziz, Muhammad Reza; Heriansyah; Saputra, EfaMaydhona; Musa, Ardiansyah
2018-03-01
To support the increase of wireless geolocation development as the key of the technology in the future, this paper proposes theoretical bound derivation, i.e., Cramer Rao lower bound (CRLB) for energy efficient of received signal strength (RSS)-based factor graph wireless geolocation technique. The theoretical bound derivation is crucially important to evaluate whether the energy efficient technique of RSS-based factor graph wireless geolocation is effective as well as to open the opportunity to further innovation of the technique. The CRLB is derived in this paper by using the Fisher information matrix (FIM) of the main formula of the RSS-based factor graph geolocation technique, which is lied on the Jacobian matrix. The simulation result shows that the derived CRLB has the highest accuracy as a bound shown by its lowest root mean squared error (RMSE) curve compared to the RMSE curve of the RSS-based factor graph geolocation technique. Hence, the derived CRLB becomes the lower bound for the efficient technique of RSS-based factor graph wireless geolocation.
Accelerated decomposition techniques for large discounted Markov decision processes
Larach, Abdelhadi; Chafik, S.; Daoui, C.
2017-12-01
Many hierarchical techniques to solve large Markov decision processes (MDPs) are based on the partition of the state space into strongly connected components (SCCs) that can be classified into some levels. In each level, smaller problems named restricted MDPs are solved, and then these partial solutions are combined to obtain the global solution. In this paper, we first propose a novel algorithm, which is a variant of Tarjan's algorithm that simultaneously finds the SCCs and their belonging levels. Second, a new definition of the restricted MDPs is presented to ameliorate some hierarchical solutions in discounted MDPs using value iteration (VI) algorithm based on a list of state-action successors. Finally, a robotic motion-planning example and the experiment results are presented to illustrate the benefit of the proposed decomposition algorithms.
Guimarães Katia S
2006-04-01
Full Text Available Abstract Background Most cellular processes are carried out by multi-protein complexes, groups of proteins that bind together to perform a specific task. Some proteins form stable complexes, while other proteins form transient associations and are part of several complexes at different stages of a cellular process. A better understanding of this higher-order organization of proteins into overlapping complexes is an important step towards unveiling functional and evolutionary mechanisms behind biological networks. Results We propose a new method for identifying and representing overlapping protein complexes (or larger units called functional groups within a protein interaction network. We develop a graph-theoretical framework that enables automatic construction of such representation. We illustrate the effectiveness of our method by applying it to TNFα/NF-κB and pheromone signaling pathways. Conclusion The proposed representation helps in understanding the transitions between functional groups and allows for tracking a protein's path through a cascade of functional groups. Therefore, depending on the nature of the network, our representation is capable of elucidating temporal relations between functional groups. Our results show that the proposed method opens a new avenue for the analysis of protein interaction networks.
Energy Efficiency Tracking in Thai Manufacturing Sector by Decomposition Technique
Wongsapai Wongkot
2016-01-01
Full Text Available This paper presents an analysis of energy saving and changes in energy intensities in Thai manufacturing sector by Logarithmic Mean Divisia Index decomposition technique. This method includes three effects consists of the energy intensity effect, the structural effect and the effect of the economic growth on the energy consumption in Thailand by using the 25-year annual data from 1990 to 2014, carried out in four phases; (i before National Energy Conservation law, (ii during the effect of the law, (iii Transition period of the law from first to second version, and (iv during the effect of the law (No.2. We found that the most effective intensity effect is in the third phase due to the effect of the implementation of new energy efficient equipment from the second phase by enforcement of the law, especially in non-metallic sector, while the first phase illustrates the lowest intensity effect due to the energy conservation law had not been occurred. However, due to the highest economic growth of the country and change from agricultural to industrial development direction, the first phase presents the most effective structural effect, then this effect continuously decreased by time. We also conclude that the energy conservation law have direct effect to energy efficiency of the country however, strictly individual regulation which have target to enforce to energy intensive industries is still required for sustainable energy efficiency improvement.
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.
Scaling Techniques for Massive Scale-Free Graphs in Distributed (External) Memory
Pearce, Roger; Gokhale, Maya; Amato, Nancy M.
2013-01-01
We present techniques to process large scale-free graphs in distributed memory. Our aim is to scale to trillions of edges, and our research is targeted at leadership class supercomputers and clusters with local non-volatile memory, e.g., NAND Flash
Partitioned Alternating Least Squares Technique for Canonical Polyadic Tensor Decomposition
Tichavský, Petr; Phan, A. H.; Cichocki, A.
2016-01-01
Roč. 23, č. 7 (2016), s. 993-997 ISSN 1070-9908 R&D Projects: GA ČR(CZ) GA14-13713S Institutional support: RVO:67985556 Keywords : canonical polyadic decomposition * PARAFAC * tensor decomposition Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 2.528, year: 2016 http://library.utia.cas.cz/separaty/2016/SI/tichavsky-0460710.pdf
Modeling, Control and Analyze of Multi-Machine Drive Systems using Bond Graph Technique
J. Belhadj
2006-03-01
Full Text Available In this paper, a system viewpoint method has been investigated to study and analyze complex systems using Bond Graph technique. These systems are multimachine multi-inverter based on Induction Machine (IM, well used in industries like rolling mills, textile, and railway traction. These systems are multi-domains, multi-scales time and present very strong internal and external couplings, with non-linearity characterized by a high model order. The classical study with analytic model is difficult to manipulate and it is limited to some performances. In this study, a “systemic approach” is presented to design these kinds of systems, using an energetic representation based on Bond Graph formalism. Three types of multimachine are studied with their control strategies. The modeling is carried out by Bond Graph and results are discussed to show the performances of this methodology
Decomposition based parallel processing technique for efficient collaborative optimization
Park, Hyung Wook; Kim, Sung Chan; Kim, Min Soo; Choi, Dong Hoon
2000-01-01
In practical design studies, most of designers solve multidisciplinary problems with complex design structure. These multidisciplinary problems have hundreds of analysis and thousands of variables. The sequence of process to solve these problems affects the speed of total design cycle. Thus it is very important for designer to reorder original design processes to minimize total cost and time. This is accomplished by decomposing large multidisciplinary problem into several MultiDisciplinary Analysis SubSystem (MDASS) and processing it in parallel. This paper proposes new strategy for parallel decomposition of multidisciplinary problem to raise design efficiency by using genetic algorithm and shows the relationship between decomposition and Multidisciplinary Design Optimization(MDO) methodology
Optimization Problems on Threshold Graphs
Elena Nechita
2010-06-01
Full Text Available During the last three decades, different types of decompositions have been processed in the field of graph theory. Among these we mention: decompositions based on the additivity of some characteristics of the graph, decompositions where the adjacency law between the subsets of the partition is known, decompositions where the subgraph induced by every subset of the partition must have predeterminate properties, as well as combinations of such decompositions. In this paper we characterize threshold graphs using the weakly decomposition, determine: density and stability number, Wiener index and Wiener polynomial for threshold graphs.
Parallel processing based decomposition technique for efficient collaborative optimization
Park, Hyung Wook; Kim, Sung Chan; Kim, Min Soo; Choi, Dong Hoon
2001-01-01
In practical design studies, most of designers solve multidisciplinary problems with large sized and complex design system. These multidisciplinary problems have hundreds of analysis and thousands of variables. The sequence of process to solve these problems affects the speed of total design cycle. Thus it is very important for designer to reorder the original design processes to minimize total computational cost. This is accomplished by decomposing large multidisciplinary problem into several MultiDisciplinary Analysis SubSystem (MDASS) and processing it in parallel. This paper proposes new strategy for parallel decomposition of multidisciplinary problem to raise design efficiency by using genetic algorithm and shows the relationship between decomposition and Multidisciplinary Design Optimization(MDO) methodology
Intelligent transportation systems data compression using wavelet decomposition technique.
2009-12-01
Intelligent Transportation Systems (ITS) generates massive amounts of traffic data, which posts : challenges for data storage, transmission and retrieval. Data compression and reconstruction technique plays an : important role in ITS data procession....
Domain decomposition techniques for boundary elements application to fluid flow
Brebbia, C A; Skerget, L
2007-01-01
The sub-domain techniques in the BEM are nowadays finding its place in the toolbox of numerical modellers, especially when dealing with complex 3D problems. We see their main application in conjunction with the classical BEM approach, which is based on a single domain, when part of the domain needs to be solved using a single domain approach, the classical BEM, and part needs to be solved using a domain approach, BEM subdomain technique. This has usually been done in the past by coupling the BEM with the FEM, however, it is much more efficient to use a combination of the BEM and a BEM sub-domain technique. The advantage arises from the simplicity of coupling the single domain and multi-domain solutions, and from the fact that only one formulation needs to be developed, rather than two separate formulations based on different techniques. There are still possibilities for improving the BEM sub-domain techniques. However, considering the increased interest and research in this approach we believe that BEM sub-do...
Fast Discrete Fourier Transform Computations Using the Reduced Adder Graph Technique
Andrew G. Dempster
2007-01-01
Full Text Available It has recently been shown that the n-dimensional reduced adder graph (RAG-n technique is beneficial for many DSP applications such as for FIR and IIR filters, where multipliers can be grouped in multiplier blocks. This paper highlights the importance of DFT and FFT as DSP objects and also explores how the RAG-n technique can be applied to these algorithms. This RAG-n DFT will be shown to be of low complexity and possess an attractively regular VLSI data flow when implemented with the Rader DFT algorithm or the Bluestein chirp-z algorithm. ASIC synthesis data are provided and demonstrate the low complexity and high speed of the design when compared to other alternatives.
Fast Discrete Fourier Transform Computations Using the Reduced Adder Graph Technique
Dempster Andrew G
2007-01-01
Full Text Available It has recently been shown that the -dimensional reduced adder graph (RAG- technique is beneficial for many DSP applications such as for FIR and IIR filters, where multipliers can be grouped in multiplier blocks. This paper highlights the importance of DFT and FFT as DSP objects and also explores how the RAG- technique can be applied to these algorithms. This RAG- DFT will be shown to be of low complexity and possess an attractively regular VLSI data flow when implemented with the Rader DFT algorithm or the Bluestein chirp- algorithm. ASIC synthesis data are provided and demonstrate the low complexity and high speed of the design when compared to other alternatives.
Multiscale analysis of damage using dual and primal domain decomposition techniques
Lloberas-Valls, O.; Everdij, F.P.X.; Rixen, D.J.; Simone, A.; Sluys, L.J.
2014-01-01
In this contribution, dual and primal domain decomposition techniques are studied for the multiscale analysis of failure in quasi-brittle materials. The multiscale strategy essentially consists in decomposing the structure into a number of nonoverlapping domains and considering a refined spatial
Hydrothermal decomposition of TBP and fixation of its decomposed residue by HHP technique
Yamasaki, N.; Fujiki, M.; Nishioka, M.; Ioku, K.; Yanagisawa, K.; Kozai, N.; Muraoka, S.
1991-01-01
The tributyl phosphate (TBP) used for the fuel reprocessing by Purex process is discharged as spent solvent because of the chemical decomposition and the damage due to radiation. Alkaline hydrothermal treatment in oxygen which is the reaction in a closed system is effective for the decomposition of TBP as it can transform organic materials to stable inorganic ions. Hydrothermal hot pressing technique has been applied to the immobilization of various radioactive wastes. This work deals with the continuous treatment process for the decomposition of TBP waste and the immobilization of its decomposed residue under hydrothermal condition. These processes are outlined. The experiment and the results are reported. TBP was completely decomposed above 200degC, and COD value showed the maximum at 250degC. The reaction process consists of two steps of the hydrolysis of TBP and the oxidation of the formed organic material. (K.I.)
A leakage-free resonance sparse decomposition technique for bearing fault detection in gearboxes
Osman, Shazali; Wang, Wilson
2018-03-01
Most of rotating machinery deficiencies are related to defects in rolling element bearings. Reliable bearing fault detection still remains a challenging task, especially for bearings in gearboxes as bearing-defect-related features are nonstationary and modulated by gear mesh vibration. A new leakage-free resonance sparse decomposition (LRSD) technique is proposed in this paper for early bearing fault detection of gearboxes. In the proposed LRSD technique, a leakage-free filter is suggested to remove strong gear mesh and shaft running signatures. A kurtosis and cosine distance measure is suggested to select appropriate redundancy r and quality factor Q. The signal residual is processed by signal sparse decomposition for highpass and lowpass resonance analysis to extract representative features for bearing fault detection. The effectiveness of the proposed technique is verified by a succession of experimental tests corresponding to different gearbox and bearing conditions.
Jha, Mayank Shekhar; Chatti, Nizar; Declerck, Philippe
2017-09-01
This paper addresses the fault diagnosis problem of uncertain systems in the context of Bond Graph modelling technique. The main objective is to enhance the fault detection step based on Interval valued Analytical Redundancy Relations (named I-ARR) in order to overcome the problems related to false alarms, missed alarms and robustness issues. These I-ARRs are a set of fault indicators that generate the interval bounds called thresholds. A fault is detected once the nominal residuals (point valued part of I-ARRs) exceed the thresholds. However, the existing fault detection method is limited to parametric faults and it presents various limitations with regards to estimation of measurement signal derivatives, to which I-ARRs are sensitive. The novelties and scientific interest of the proposed methodology are: (1) to improve the accuracy of the measurements derivatives estimation by using a dedicated sliding mode differentiator proposed in this work, (2) to suitably integrate the Fourier-Motzkin Elimination (FME) technique within the I-ARRs based diagnosis so that measurements faults can be detected successfully. The latter provides interval bounds over the derivatives which are included in the thresholds. The proposed methodology is studied under various scenarios (parametric and measurement faults) via simulations over a mechatronic torsion bar system.
Probabilistic Decision Graphs - Combining Verification and AI Techniques for Probabilistic Inference
Jaeger, Manfred
2004-01-01
We adopt probabilistic decision graphs developed in the field of automated verification as a tool for probabilistic model representation and inference. We show that probabilistic inference has linear time complexity in the size of the probabilistic decision graph, that the smallest probabilistic ...
Previti, Alberto; Furfaro, Roberto; Picca, Paolo; Ganapol, Barry D.; Mostacci, Domiziano
2011-01-01
This paper deals with finding accurate solutions for photon transport problems in highly heterogeneous media fastly, efficiently and with modest memory resources. We propose an extended version of the analytical discrete ordinates method, coupled with domain decomposition-derived algorithms and non-linear convergence acceleration techniques. Numerical performances are evaluated using a challenging case study available in the literature. A study of accuracy versus computational time and memory requirements is reported for transport calculations that are relevant for remote sensing applications.
Analysis and Prediction of Sea Ice Evolution using Koopman Mode Decomposition Techniques
2018-04-30
Resources: N/A TOTAL: $18,687 2 TECHNICAL STATUS REPORT Abstract The program goal is analysis of sea ice dynamical behavior using Koopman Mode Decompo...Title: Analysis and Prediction of Sea Ice Evolution using Koopman Mode Decomposition Techniques Subject: Monthly Progress Report Period of...Attn: Code 5596 4555 Overlook Avenue, SW Washington, D.C. 20375-5320 E-mail: reports@library.nrl.navy.mil Defense Technical Information Center
A novel decomposition technique of friable asbestos by CHClF2-decomposed acidic gas
Yanagisawa, Kazumichi; Kozawa, Takahiro; Onda, Ayumu; Kanazawa, Masazumi; Shinohara, Junichi; Takanami, Tetsuro; Shiraishi, Masatsugu
2009-01-01
Asbestos was widely used in numerous materials and building products due to their desirable properties. It is, however, well known that asbestos inhalation causes health damage and its inexpensive decomposition technique is necessary to be developed for pollution prevention. We report here an innovative decomposition technique of friable asbestos by acidic gas (HF and HCl) generated from the decomposition of CHClF 2 by the reaction with superheated steam at 800 deg. C. Chrysotile-asbestos fibers were completely decomposed to sellaite and magnesium silicofluoride hexahydrate by the reaction with CHClF 2 -decomposed acidic gas at 150 deg. C for 30 min. At high temperatures beyond 400 deg. C, sellaite and hematite were detected in the decomposed product. In addition, crocidolite containing wastes and amosite containing wastes were decomposed at 500 deg. C and 600 deg. C for 30 min, respectively, by CHClF 2 -decomposed acidic gas. The observation of the reaction products by phase-contrast microscopy (PCM) and scanning electron microscopy (SEM) confirmed that the resulting products did not contain any asbestos
Girardi, E.; Ruggieri, J.M. [CEA Cadarache (DER/SPRC/LEPH), 13 - Saint-Paul-lez-Durance (France). Dept. d' Etudes des Reacteurs; Santandrea, S. [CEA Saclay, Dept. Modelisation de Systemes et Structures DM2S/SERMA/LENR, 91 - Gif sur Yvette (France)
2005-07-01
This paper describes a recently-developed extension of our 'Multi-methods,multi-domains' (MM-MD) method for the solution of the multigroup transport equation. Based on a domain decomposition technique, our approach allows us to treat the one-group equation by cooperatively employing several numerical methods together. In this work, we describe the coupling between the Method of Characteristics (integro-differential equation, unstructured meshes) with the Variational Nodal Method (even parity equation, cartesian meshes). Then, the coupling method is applied to the benchmark model of the Phebus experimental facility (Cea Cadarache). Our domain decomposition method give us the capability to employ a very fine mesh in describing a particular fuel bundle with an appropriate numerical method (MOC), while using a much large mesh size in the rest of the core, in conjunction with a coarse-mesh method (VNM). This application shows the benefits of our MM-MD approach, in terms of accuracy and computing time: the domain decomposition method allows us to reduce the Cpu time, while preserving a good accuracy of the neutronic indicators: reactivity, core-to-bundle power coupling coefficient and flux error. (authors)
Girardi, E.; Ruggieri, J.M.
2005-01-01
This paper describes a recently-developed extension of our 'Multi-methods,multi-domains' (MM-MD) method for the solution of the multigroup transport equation. Based on a domain decomposition technique, our approach allows us to treat the one-group equation by cooperatively employing several numerical methods together. In this work, we describe the coupling between the Method of Characteristics (integro-differential equation, unstructured meshes) with the Variational Nodal Method (even parity equation, cartesian meshes). Then, the coupling method is applied to the benchmark model of the Phebus experimental facility (Cea Cadarache). Our domain decomposition method give us the capability to employ a very fine mesh in describing a particular fuel bundle with an appropriate numerical method (MOC), while using a much large mesh size in the rest of the core, in conjunction with a coarse-mesh method (VNM). This application shows the benefits of our MM-MD approach, in terms of accuracy and computing time: the domain decomposition method allows us to reduce the Cpu time, while preserving a good accuracy of the neutronic indicators: reactivity, core-to-bundle power coupling coefficient and flux error. (authors)
Quantitative graph theory mathematical foundations and applications
Dehmer, Matthias
2014-01-01
The first book devoted exclusively to quantitative graph theory, Quantitative Graph Theory: Mathematical Foundations and Applications presents and demonstrates existing and novel methods for analyzing graphs quantitatively. Incorporating interdisciplinary knowledge from graph theory, information theory, measurement theory, and statistical techniques, this book covers a wide range of quantitative-graph theoretical concepts and methods, including those pertaining to real and random graphs such as:Comparative approaches (graph similarity or distance)Graph measures to characterize graphs quantitat
Jacobsen, Niels-Jørgen; Andersen, Palle; Brincker, Rune
2006-01-01
The presence of harmonic components in the measured responses is unavoidable in many applications of Operational Modal Analysis. This is especially true when measuring on mechanical structures containing rotating or reciprocating parts. This paper describes a new method based on the popular...... agreement is found and the method is proven to be an easy-to-use and robust tool for handling responses with deterministic and stochastic content....... Enhanced Frequency Domain Decomposition technique for eliminating the influence of these harmonic components in the modal parameter extraction process. For various experiments, the quality of the method is assessed and compared to the results obtained using broadband stochastic excitation forces. Good...
Bapat, Ravindra B
2014-01-01
This new edition illustrates the power of linear algebra in the study of graphs. The emphasis on matrix techniques is greater than in other texts on algebraic graph theory. Important matrices associated with graphs (for example, incidence, adjacency and Laplacian matrices) are treated in detail. Presenting a useful overview of selected topics in algebraic graph theory, early chapters of the text focus on regular graphs, algebraic connectivity, the distance matrix of a tree, and its generalized version for arbitrary graphs, known as the resistance matrix. Coverage of later topics include Laplacian eigenvalues of threshold graphs, the positive definite completion problem and matrix games based on a graph. Such an extensive coverage of the subject area provides a welcome prompt for further exploration. The inclusion of exercises enables practical learning throughout the book. In the new edition, a new chapter is added on the line graph of a tree, while some results in Chapter 6 on Perron-Frobenius theory are reo...
Mixed Volume and Distance Geometry Techniques for Counting Euclidean Embeddings of Rigid Graphs
I.Z. Emiris; E.P. Tsigaridas; A. Varvitsiotis (Antonios); A. Mucherino (Antonio); C. Lavor; L. Liberti; N. Maculan
2013-01-01
htmlabstractA graph G is called generically minimally rigid in Rd if, for any choice of sufficiently generic edge lengths, it can be embedded in Rd in a finite number of distinct ways, modulo rigid transformations. Here, we deal with the problem of determining tight bounds on the number of such
Electrocardiogram signal denoising based on empirical mode decomposition technique: an overview
Han, G.; Lin, B.; Xu, Z.
2017-01-01
Electrocardiogram (ECG) signal is nonlinear and non-stationary weak signal which reflects whether the heart is functioning normally or abnormally. ECG signal is susceptible to various kinds of noises such as high/low frequency noises, powerline interference and baseline wander. Hence, the removal of noises from ECG signal becomes a vital link in the ECG signal processing and plays a significant role in the detection and diagnosis of heart diseases. The review will describe the recent developments of ECG signal denoising based on Empirical Mode Decomposition (EMD) technique including high frequency noise removal, powerline interference separation, baseline wander correction, the combining of EMD and Other Methods, EEMD technique. EMD technique is a quite potential and prospective but not perfect method in the application of processing nonlinear and non-stationary signal like ECG signal. The EMD combined with other algorithms is a good solution to improve the performance of noise cancellation. The pros and cons of EMD technique in ECG signal denoising are discussed in detail. Finally, the future work and challenges in ECG signal denoising based on EMD technique are clarified.
Electrocardiogram signal denoising based on empirical mode decomposition technique: an overview
Han, G.; Lin, B.; Xu, Z.
2017-03-01
Electrocardiogram (ECG) signal is nonlinear and non-stationary weak signal which reflects whether the heart is functioning normally or abnormally. ECG signal is susceptible to various kinds of noises such as high/low frequency noises, powerline interference and baseline wander. Hence, the removal of noises from ECG signal becomes a vital link in the ECG signal processing and plays a significant role in the detection and diagnosis of heart diseases. The review will describe the recent developments of ECG signal denoising based on Empirical Mode Decomposition (EMD) technique including high frequency noise removal, powerline interference separation, baseline wander correction, the combining of EMD and Other Methods, EEMD technique. EMD technique is a quite potential and prospective but not perfect method in the application of processing nonlinear and non-stationary signal like ECG signal. The EMD combined with other algorithms is a good solution to improve the performance of noise cancellation. The pros and cons of EMD technique in ECG signal denoising are discussed in detail. Finally, the future work and challenges in ECG signal denoising based on EMD technique are clarified.
An acceleration technique for 2D MOC based on Krylov subspace and domain decomposition methods
Zhang Hongbo; Wu Hongchun; Cao Liangzhi
2011-01-01
Highlights: → We convert MOC into linear system solved by GMRES as an acceleration method. → We use domain decomposition method to overcome the inefficiency on large matrices. → Parallel technology is applied and a matched ray tracing system is developed. → Results show good efficiency even in large-scale and strong scattering problems. → The emphasis is that the technique is geometry-flexible. - Abstract: The method of characteristics (MOC) has great geometrical flexibility but poor computational efficiency in neutron transport calculations. The generalized minimal residual (GMRES) method, a type of Krylov subspace method, is utilized to accelerate a 2D generalized geometry characteristics solver AutoMOC. In this technique, a form of linear algebraic equation system for angular flux moments and boundary fluxes is derived to replace the conventional characteristics sweep (i.e. inner iteration) scheme, and then the GMRES method is implemented as an efficient linear system solver. This acceleration method is proved to be reliable in theory and simple for implementation. Furthermore, as introducing no restriction in geometry treatment, it is suitable for acceleration of an arbitrary geometry MOC solver. However, it is observed that the speedup decreases when the matrix becomes larger. The spatial domain decomposition method and multiprocessing parallel technology are then employed to overcome the problem. The calculation domain is partitioned into several sub-domains. For each of them, a smaller matrix is established and solved by GMRES; and the adjacent sub-domains are coupled by 'inner-edges', where the trajectory mismatches are considered adequately. Moreover, a matched ray tracing system is developed on the basis of AutoCAD, which allows a user to define the sub-domains on demand conveniently. Numerical results demonstrate that the acceleration techniques are efficient without loss of accuracy, even in the case of large-scale and strong scattering
Lajmert Paweł
2018-01-01
Full Text Available In the paper a cutting stability in the milling process of nickel based alloy Inconel 625 is analysed. This problem is often considered theoretically, but the theoretical finding do not always agree with experimental results. For this reason, the paper presents different methods for instability identification during real machining process. A stability lobe diagram is created based on data obtained in impact test of an end mill. Next, the cutting tests were conducted in which the axial cutting depth of cut was gradually increased in order to find a stability limit. Finally, based on the cutting force measurements the stability estimation problem is investigated using the recurrence plot technique and Hilbert vibration decomposition method.
Decomposition and (importance) sampling techniques for multi-stage stochastic linear programs
Infanger, G.
1993-11-01
The difficulty of solving large-scale multi-stage stochastic linear programs arises from the sheer number of scenarios associated with numerous stochastic parameters. The number of scenarios grows exponentially with the number of stages and problems get easily out of hand even for very moderate numbers of stochastic parameters per stage. Our method combines dual (Benders) decomposition with Monte Carlo sampling techniques. We employ importance sampling to efficiently obtain accurate estimates of both expected future costs and gradients and right-hand sides of cuts. The method enables us to solve practical large-scale problems with many stages and numerous stochastic parameters per stage. We discuss the theory of sharing and adjusting cuts between different scenarios in a stage. We derive probabilistic lower and upper bounds, where we use importance path sampling for the upper bound estimation. Initial numerical results turned out to be promising.
Mondal, Ashok; Bhattacharya, P S; Saha, Goutam
2011-01-01
During the recording time of lung sound (LS) signals from the chest wall of a subject, there is always heart sound (HS) signal interfering with it. This obscures the features of lung sound signals and creates confusion on pathological states, if any, of the lungs. A novel method based on empirical mode decomposition (EMD) technique is proposed in this paper for reducing the undesired heart sound interference from the desired lung sound signals. In this, the mixed signal is split into several components. Some of these components contain larger proportions of interfering signals like heart sound, environmental noise etc. and are filtered out. Experiments have been conducted on simulated and real-time recorded mixed signals of heart sound and lung sound. The proposed method is found to be superior in terms of time domain, frequency domain, and time-frequency domain representations and also in listening test performed by pulmonologist.
Gould, Ronald
2012-01-01
This introduction to graph theory focuses on well-established topics, covering primary techniques and including both algorithmic and theoretical problems. The algorithms are presented with a minimum of advanced data structures and programming details. This thoroughly corrected 1988 edition provides insights to computer scientists as well as advanced undergraduates and graduate students of topology, algebra, and matrix theory. Fundamental concepts and notation and elementary properties and operations are the first subjects, followed by examinations of paths and searching, trees, and networks. S
Cicone, A.; Zhou, H.; Piersanti, M.; Materassi, M.; Spogli, L.
2017-12-01
Nonlinear and nonstationary signals are ubiquitous in real life. Their decomposition and analysis is of crucial importance in many research fields. Traditional techniques, like Fourier and wavelet Transform have been proved to be limited in this context. In the last two decades new kind of nonlinear methods have been developed which are able to unravel hidden features of these kinds of signals. In this poster we present a new method, called Adaptive Local Iterative Filtering (ALIF). This technique, originally developed to study mono-dimensional signals, unlike any other algorithm proposed so far, can be easily generalized to study two or higher dimensional signals. Furthermore, unlike most of the similar methods, it does not require any a priori assumption on the signal itself, so that the technique can be applied as it is to any kind of signals. Applications of ALIF algorithm to real life signals analysis will be presented. Like, for instance, the behavior of the water level near the coastline in presence of a Tsunami, length of the day signal, pressure measured at ground level on a global grid, radio power scintillation from GNSS signals,
Liang, Bin; Li, Yongbao; Wei, Ran; Guo, Bin; Xu, Xuang; Liu, Bo; Li, Jiafeng; Wu, Qiuwen; Zhou, Fugen
2018-01-01
With robot-controlled linac positioning, robotic radiotherapy systems such as CyberKnife significantly increase freedom of radiation beam placement, but also impose more challenges on treatment plan optimization. The resampling mechanism in the vendor-supplied treatment planning system (MultiPlan) cannot fully explore the increased beam direction search space. Besides, a sparse treatment plan (using fewer beams) is desired to improve treatment efficiency. This study proposes a singular value decomposition linear programming (SVDLP) optimization technique for circular collimator based robotic radiotherapy. The SVDLP approach initializes the input beams by simulating the process of covering the entire target volume with equivalent beam tapers. The requirements on dosimetry distribution are modeled as hard and soft constraints, and the sparsity of the treatment plan is achieved by compressive sensing. The proposed linear programming (LP) model optimizes beam weights by minimizing the deviation of soft constraints subject to hard constraints, with a constraint on the l 1 norm of the beam weight. A singular value decomposition (SVD) based acceleration technique was developed for the LP model. Based on the degeneracy of the influence matrix, the model is first compressed into lower dimension for optimization, and then back-projected to reconstruct the beam weight. After beam weight optimization, the number of beams is reduced by removing the beams with low weight, and optimizing the weights of the remaining beams using the same model. This beam reduction technique is further validated by a mixed integer programming (MIP) model. The SVDLP approach was tested on a lung case. The results demonstrate that the SVD acceleration technique speeds up the optimization by a factor of 4.8. Furthermore, the beam reduction achieves a similar plan quality to the globally optimal plan obtained by the MIP model, but is one to two orders of magnitude faster. Furthermore, the SVDLP
Liang, Bin; Li, Yongbao; Wei, Ran; Guo, Bin; Xu, Xuang; Liu, Bo; Li, Jiafeng; Wu, Qiuwen; Zhou, Fugen
2018-01-05
With robot-controlled linac positioning, robotic radiotherapy systems such as CyberKnife significantly increase freedom of radiation beam placement, but also impose more challenges on treatment plan optimization. The resampling mechanism in the vendor-supplied treatment planning system (MultiPlan) cannot fully explore the increased beam direction search space. Besides, a sparse treatment plan (using fewer beams) is desired to improve treatment efficiency. This study proposes a singular value decomposition linear programming (SVDLP) optimization technique for circular collimator based robotic radiotherapy. The SVDLP approach initializes the input beams by simulating the process of covering the entire target volume with equivalent beam tapers. The requirements on dosimetry distribution are modeled as hard and soft constraints, and the sparsity of the treatment plan is achieved by compressive sensing. The proposed linear programming (LP) model optimizes beam weights by minimizing the deviation of soft constraints subject to hard constraints, with a constraint on the l 1 norm of the beam weight. A singular value decomposition (SVD) based acceleration technique was developed for the LP model. Based on the degeneracy of the influence matrix, the model is first compressed into lower dimension for optimization, and then back-projected to reconstruct the beam weight. After beam weight optimization, the number of beams is reduced by removing the beams with low weight, and optimizing the weights of the remaining beams using the same model. This beam reduction technique is further validated by a mixed integer programming (MIP) model. The SVDLP approach was tested on a lung case. The results demonstrate that the SVD acceleration technique speeds up the optimization by a factor of 4.8. Furthermore, the beam reduction achieves a similar plan quality to the globally optimal plan obtained by the MIP model, but is one to two orders of magnitude faster. Furthermore, the SVDLP
Endriss, U.; Grandi, U.
Graph aggregation is the process of computing a single output graph that constitutes a good compromise between several input graphs, each provided by a different source. One needs to perform graph aggregation in a wide variety of situations, e.g., when applying a voting rule (graphs as preference
FAN Hong-Yi; FAN Yue
2002-01-01
By virtue of the technique of integration within an ordered product of operators and the Schmidt decomposition of the entangled state |η〉, we reduce the general projection calculation in the theory of quantum teleportation to a as simple as possible form and present a general formalism for teleportating quantum states of continuous variable.
Solving Graph Laplacian Systems Through Recursive Bisections and Two-Grid Preconditioning
Ponce, Colin [Cornell Univ., Ithaca, NY (United States); Vassilevski, Panayot S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2016-02-18
We present a parallelizable direct method for computing the solution to graph Laplacian-based linear systems derived from graphs that can be hierarchically bipartitioned with small edge cuts. For a graph of size n with constant-size edge cuts, our method decomposes a graph Laplacian in time O(n log n), and then uses that decomposition to perform a linear solve in time O(n log n). We then use the developed technique to design a preconditioner for graph Laplacians that do not have this property. Finally, we augment this preconditioner with a two-grid method that accounts for much of the preconditioner's weaknesses. We present an analysis of this method, as well as a general theorem for the condition number of a general class of two-grid support graph-based preconditioners. Numerical experiments illustrate the performance of the studied methods.
Introduction to quantum graphs
Berkolaiko, Gregory
2012-01-01
A "quantum graph" is a graph considered as a one-dimensional complex and equipped with a differential operator ("Hamiltonian"). Quantum graphs arise naturally as simplified models in mathematics, physics, chemistry, and engineering when one considers propagation of waves of various nature through a quasi-one-dimensional (e.g., "meso-" or "nano-scale") system that looks like a thin neighborhood of a graph. Works that currently would be classified as discussing quantum graphs have been appearing since at least the 1930s, and since then, quantum graphs techniques have been applied successfully in various areas of mathematical physics, mathematics in general and its applications. One can mention, for instance, dynamical systems theory, control theory, quantum chaos, Anderson localization, microelectronics, photonic crystals, physical chemistry, nano-sciences, superconductivity theory, etc. Quantum graphs present many non-trivial mathematical challenges, which makes them dear to a mathematician's heart. Work on qu...
Vatutin Eduard
2017-12-01
Full Text Available The article deals with the problem of analysis of effectiveness of the heuristic methods with limited depth-first search techniques of decision obtaining in the test problem of getting the shortest path in graph. The article briefly describes the group of methods based on the limit of branches number of the combinatorial search tree and limit of analyzed subtree depth used to solve the problem. The methodology of comparing experimental data for the estimation of the quality of solutions based on the performing of computational experiments with samples of graphs with pseudo-random structure and selected vertices and arcs number using the BOINC platform is considered. It also shows description of obtained experimental results which allow to identify the areas of the preferable usage of selected subset of heuristic methods depending on the size of the problem and power of constraints. It is shown that the considered pair of methods is ineffective in the selected problem and significantly inferior to the quality of solutions that are provided by ant colony optimization method and its modification with combinatorial returns.
Vatutin, Eduard
2017-12-01
The article deals with the problem of analysis of effectiveness of the heuristic methods with limited depth-first search techniques of decision obtaining in the test problem of getting the shortest path in graph. The article briefly describes the group of methods based on the limit of branches number of the combinatorial search tree and limit of analyzed subtree depth used to solve the problem. The methodology of comparing experimental data for the estimation of the quality of solutions based on the performing of computational experiments with samples of graphs with pseudo-random structure and selected vertices and arcs number using the BOINC platform is considered. It also shows description of obtained experimental results which allow to identify the areas of the preferable usage of selected subset of heuristic methods depending on the size of the problem and power of constraints. It is shown that the considered pair of methods is ineffective in the selected problem and significantly inferior to the quality of solutions that are provided by ant colony optimization method and its modification with combinatorial returns.
Singular value decomposition based feature extraction technique for physiological signal analysis.
Chang, Cheng-Ding; Wang, Chien-Chih; Jiang, Bernard C
2012-06-01
Multiscale entropy (MSE) is one of the popular techniques to calculate and describe the complexity of the physiological signal. Many studies use this approach to detect changes in the physiological conditions in the human body. However, MSE results are easily affected by noise and trends, leading to incorrect estimation of MSE values. In this paper, singular value decomposition (SVD) is adopted to replace MSE to extract the features of physiological signals, and adopt the support vector machine (SVM) to classify the different physiological states. A test data set based on the PhysioNet website was used, and the classification results showed that using SVD to extract features of the physiological signal could attain a classification accuracy rate of 89.157%, which is higher than that using the MSE value (71.084%). The results show the proposed analysis procedure is effective and appropriate for distinguishing different physiological states. This promising result could be used as a reference for doctors in diagnosis of congestive heart failure (CHF) disease.
Chartrand, Gary
1984-01-01
Graph theory is used today in the physical sciences, social sciences, computer science, and other areas. Introductory Graph Theory presents a nontechnical introduction to this exciting field in a clear, lively, and informative style. Author Gary Chartrand covers the important elementary topics of graph theory and its applications. In addition, he presents a large variety of proofs designed to strengthen mathematical techniques and offers challenging opportunities to have fun with mathematics. Ten major topics - profusely illustrated - include: Mathematical Models, Elementary Concepts of Grap
Zhang, L.-C.; Patone, M.
2017-01-01
We synthesise the existing theory of graph sampling. We propose a formal definition of sampling in finite graphs, and provide a classification of potential graph parameters. We develop a general approach of Horvitz–Thompson estimation to T-stage snowball sampling, and present various reformulations of some common network sampling methods in the literature in terms of the outlined graph sampling theory.
Creating more effective graphs
Robbins, Naomi B
2012-01-01
A succinct and highly readable guide to creating effective graphs The right graph can be a powerful tool for communicating information, improving a presentation, or conveying your point in print. If your professional endeavors call for you to present data graphically, here's a book that can help you do it more effectively. Creating More Effective Graphs gives you the basic knowledge and techniques required to choose and create appropriate graphs for a broad range of applications. Using real-world examples everyone can relate to, the author draws on her years of experience in gr
Stevanovic, Dragan
2015-01-01
Spectral Radius of Graphs provides a thorough overview of important results on the spectral radius of adjacency matrix of graphs that have appeared in the literature in the preceding ten years, most of them with proofs, and including some previously unpublished results of the author. The primer begins with a brief classical review, in order to provide the reader with a foundation for the subsequent chapters. Topics covered include spectral decomposition, the Perron-Frobenius theorem, the Rayleigh quotient, the Weyl inequalities, and the Interlacing theorem. From this introduction, the
Proxy Graph: Visual Quality Metrics of Big Graph Sampling.
Nguyen, Quan Hoang; Hong, Seok-Hee; Eades, Peter; Meidiana, Amyra
2017-06-01
Data sampling has been extensively studied for large scale graph mining. Many analyses and tasks become more efficient when performed on graph samples of much smaller size. The use of proxy objects is common in software engineering for analysis and interaction with heavy objects or systems. In this paper, we coin the term 'proxy graph' and empirically investigate how well a proxy graph visualization can represent a big graph. Our investigation focuses on proxy graphs obtained by sampling; this is one of the most common proxy approaches. Despite the plethora of data sampling studies, this is the first evaluation of sampling in the context of graph visualization. For an objective evaluation, we propose a new family of quality metrics for visual quality of proxy graphs. Our experiments cover popular sampling techniques. Our experimental results lead to guidelines for using sampling-based proxy graphs in visualization.
Mohn, Joachim; Gutjahr, Wilhelm; Toyoda, Sakae; Harris, Eliza; Ibraim, Erkan; Geilmann, Heike; Schleppi, Patrick; Kuhn, Thomas; Lehmann, Moritz F; Decock, Charlotte; Werner, Roland A; Yoshida, Naohiro; Brand, Willi A
2016-09-08
In the last few years, the study of N 2 O site-specific nitrogen isotope composition has been established as a powerful technique to disentangle N 2 O emission pathways. This trend has been accelerated by significant analytical progress in the field of isotope-ratio mass-spectrometry (IRMS) and more recently quantum cascade laser absorption spectroscopy (QCLAS). Methods The ammonium nitrate (NH 4 NO 3 ) decomposition technique provides a strategy to scale the 15 N site-specific (SP ≡ δ 15 N α - δ 15 N β ) and bulk (δ 15 N bulk = (δ 15 N α + δ 15 N β )/2) isotopic composition of N 2 O against the international standard for the 15 N/ 14 N isotope ratio (AIR-N 2 ). Within the current project 15 N fractionation effects during thermal decomposition of NH 4 NO 3 on the N 2 O site preference were studied using static and dynamic decomposition techniques. The validity of the NH 4 NO 3 decomposition technique to link NH 4 + and NO 3 - moiety-specific δ 15 N analysis by IRMS to the site-specific nitrogen isotopic composition of N 2 O was confirmed. However, the accuracy of this approach for the calibration of δ 15 N α and δ 15 N β values was found to be limited by non-quantitative NH 4 NO 3 decomposition in combination with substantially different isotope enrichment factors for the conversion of the NO 3 - or NH 4 + nitrogen atom into the α or β position of the N 2 O molecule. The study reveals that the completeness and reproducibility of the NH 4 NO 3 decomposition reaction currently confine the anchoring of N 2 O site-specific isotopic composition to the international isotope ratio scale AIR-N 2 . The authors suggest establishing a set of N 2 O isotope reference materials with appropriate site-specific isotopic composition, as community standards, to improve inter-laboratory compatibility. This article is protected by copyright. All rights reserved.
A NOVEL TECHNIQUE TO IMPROVE PHOTOMETRY IN CONFUSED IMAGES USING GRAPHS AND BAYESIAN PRIORS
Safarzadeh, Mohammadtaher; Ferguson, Henry C.; Lu, Yu; Inami, Hanae; Somerville, Rachel S.
2015-01-01
We present a new technique for overcoming confusion noise in deep far-infrared Herschel space telescope images making use of prior information from shorter λ < 2 μm wavelengths. For the deepest images obtained by Herschel, the flux limit due to source confusion is about a factor of three brighter than the flux limit due to instrumental noise and (smooth) sky background. We have investigated the possibility of de-confusing simulated Herschel PACS 160 μm images by using strong Bayesian priors on the positions and weak priors on the flux of sources. We find the blended sources and group them together and simultaneously fit their fluxes. We derive the posterior probability distribution function of fluxes subject to these priors through Monte Carlo Markov Chain (MCMC) sampling by fitting the image. Assuming we can predict the FIR flux of sources based on the ultraviolet-optical part of their SEDs to within an order of magnitude, the simulations show that we can obtain reliable fluxes and uncertainties at least a factor of three fainter than the confusion noise limit of 3σ c = 2.7 mJy in our simulated PACS-160 image. This technique could in principle be used to mitigate the effects of source confusion in any situation where one has prior information of positions and plausible fluxes of blended sources. For Herschel, application of this technique will improve our ability to constrain the dust content in normal galaxies at high redshift
Fundamentals of algebraic graph transformation
Ehrig, Hartmut; Prange, Ulrike; Taentzer, Gabriele
2006-01-01
Graphs are widely used to represent structural information in the form of objects and connections between them. Graph transformation is the rule-based manipulation of graphs, an increasingly important concept in computer science and related fields. This is the first textbook treatment of the algebraic approach to graph transformation, based on algebraic structures and category theory. Part I is an introduction to the classical case of graph and typed graph transformation. In Part II basic and advanced results are first shown for an abstract form of replacement systems, so-called adhesive high-level replacement systems based on category theory, and are then instantiated to several forms of graph and Petri net transformation systems. Part III develops typed attributed graph transformation, a technique of key relevance in the modeling of visual languages and in model transformation. Part IV contains a practical case study on model transformation and a presentation of the AGG (attributed graph grammar) tool envir...
Brouwer, A.E.; Haemers, W.H.; Brouwer, A.E.; Haemers, W.H.
2012-01-01
This chapter presents some simple results on graph spectra.We assume the reader is familiar with elementary linear algebra and graph theory. Throughout, J will denote the all-1 matrix, and 1 is the all-1 vector.
Daily water level forecasting using wavelet decomposition and artificial intelligence techniques
Seo, Youngmin; Kim, Sungwon; Kisi, Ozgur; Singh, Vijay P.
2015-01-01
Reliable water level forecasting for reservoir inflow is essential for reservoir operation. The objective of this paper is to develop and apply two hybrid models for daily water level forecasting and investigate their accuracy. These two hybrid models are wavelet-based artificial neural network (WANN) and wavelet-based adaptive neuro-fuzzy inference system (WANFIS). Wavelet decomposition is employed to decompose an input time series into approximation and detail components. The decomposed time series are used as inputs to artificial neural networks (ANN) and adaptive neuro-fuzzy inference system (ANFIS) for WANN and WANFIS models, respectively. Based on statistical performance indexes, the WANN and WANFIS models are found to produce better efficiency than the ANN and ANFIS models. WANFIS7-sym10 yields the best performance among all other models. It is found that wavelet decomposition improves the accuracy of ANN and ANFIS. This study evaluates the accuracy of the WANN and WANFIS models for different mother wavelets, including Daubechies, Symmlet and Coiflet wavelets. It is found that the model performance is dependent on input sets and mother wavelets, and the wavelet decomposition using mother wavelet, db10, can further improve the efficiency of ANN and ANFIS models. Results obtained from this study indicate that the conjunction of wavelet decomposition and artificial intelligence models can be a useful tool for accurate forecasting daily water level and can yield better efficiency than the conventional forecasting models.
Abdel-Halim Hassan, I.H.
2008-01-01
In this paper, we will compare the differential transformation method DTM and Adomian decomposition method ADM to solve partial differential equations (PDEs). The definition and operations of differential transform method was introduced by Zhou [Zhou JK. Differential transformation and its application for electrical circuits. Wuuhahn, China: Huarjung University Press; 1986 [in Chinese
Wang, Hang; Felder, Stefan; Chanson, Hubert
2014-07-01
Intense turbulence develops in the two-phase flow region of hydraulic jump, with a broad range of turbulent length and time scales. Detailed air-water flow measurements using intrusive phase-detection probes enabled turbulence characterisation of the bubbly flow, although the phenomenon is not a truly random process because of the existence of low-frequency, pseudo-periodic fluctuating motion in the jump roller. This paper presents new measurements of turbulent properties in hydraulic jumps, including turbulence intensity, longitudinal and transverse integral length and time scales. The results characterised very high turbulent levels and reflected a combination of both fast and slow turbulent components. The respective contributions of the fast and slow motions were quantified using a triple decomposition technique. The decomposition of air-water detection signal revealed "true" turbulent characteristics linked with the fast, microscopic velocity turbulence of hydraulic jumps. The high-frequency turbulence intensities were between 0.5 and 1.5 close to the jump toe, and maximum integral turbulent length scales were found next to the bottom. Both decreased in the flow direction with longitudinal turbulence dissipation. The results highlighted the considerable influence of hydrodynamic instabilities of the flow on the turbulence characterisation. The successful application of triple decomposition technique provided the means for the true turbulence properties of hydraulic jumps.
A New Efficient Algorithm for the 2D WLP-FDTD Method Based on Domain Decomposition Technique
Bo-Ao Xu
2016-01-01
Full Text Available This letter introduces a new efficient algorithm for the two-dimensional weighted Laguerre polynomials finite difference time-domain (WLP-FDTD method based on domain decomposition scheme. By using the domain decomposition finite difference technique, the whole computational domain is decomposed into several subdomains. The conventional WLP-FDTD and the efficient WLP-FDTD methods are, respectively, used to eliminate the splitting error and speed up the calculation in different subdomains. A joint calculation scheme is presented to reduce the amount of calculation. Through our work, the iteration is not essential to obtain the accurate results. Numerical example indicates that the efficiency and accuracy are improved compared with the efficient WLP-FDTD method.
Girardi, E.; Ruggieri, J.M.
2003-01-01
The aim of this paper is to present the last developments made on a domain decomposition method applied to reactor core calculations. In this method, two kind of balance equation with two different numerical methods dealing with two different unknowns are coupled. In the first part the two balance transport equations (first order and second order one) are presented with the corresponding following numerical methods: Variational Nodal Method and Discrete Ordinate Nodal Method. In the second part, the Multi-Method/Multi-Domain algorithm is introduced by applying the Schwarz domain decomposition to the multigroup eigenvalue problem of the transport equation. The resulting algorithm is then provided. The projection operators used to coupled the two methods are detailed in the last part of the paper. Finally some preliminary numerical applications on benchmarks are given showing encouraging results. (authors)
Syed, M.; Khan, A.M.; Khan, R.A.
2016-01-01
This study investigates the decomposition of clofibric acid (CLF) by different advanced oxidation processes (AOPs), such as UV (254 nm), VUV (185 nm), UV / TiO/sub 2/ and VUV / TiO/sub 2/. The removal efficiencies of applied AOPs were compared in the presence and absence of dissolved oxygen. The removal efficiency of the studied AOPs towards degradation of CLF were found in the order of VUV / TiO/sub 2/ + O/sub 2/ > VUV/TiO/sub 2/ + N/sub 2/ > VUV alone > UV / TiO/sub 2/ + O/sub 2/ > UV / TiO/sub 2/ +N/sub 2/ > UV alone. The decomposition kinetics of CLF was found to follow pseudo-first order rate law. VUV / TiO2 process was found to be most cheap and effective one for decomposition of CLF as compared to other applied AOPs in terms of electrical energy per order. Degradation products resulting from the degradation processes were also investigated using UPLC-MS /MS, accordingly degradation pathway was proposed. (author)
Generalized connectivity of graphs
Li, Xueliang
2016-01-01
Noteworthy results, proof techniques, open problems and conjectures in generalized (edge-) connectivity are discussed in this book. Both theoretical and practical analyses for generalized (edge-) connectivity of graphs are provided. Topics covered in this book include: generalized (edge-) connectivity of graph classes, algorithms, computational complexity, sharp bounds, Nordhaus-Gaddum-type results, maximum generalized local connectivity, extremal problems, random graphs, multigraphs, relations with the Steiner tree packing problem and generalizations of connectivity. This book enables graduate students to understand and master a segment of graph theory and combinatorial optimization. Researchers in graph theory, combinatorics, combinatorial optimization, probability, computer science, discrete algorithms, complexity analysis, network design, and the information transferring models will find this book useful in their studies.
Zabiniako Vitaly
2014-12-01
Full Text Available In this article, the authors perform an analysis in order to assess adaptation of magnetic force-directed algorithms for context-based information extraction from multi-attributed graphs during visualization sessions. Theoretic standings behind magnetic force-directed approach are stated together with review on how particular features of respective algorithms in combination with appropriate visual techniques are especially suitable for improved processing and presenting of knowledge that is captured in form of graphs. The complexity of retrieving multi-attributed information within the proposed approach is handled with dedicated tools, such as selective attraction of nodes to MFE (Magnetic Force Emitter based on search criteria, localization of POI (Point of Interest regions, graph node anchoring, etc. Implicit compatibility of aforementioned tools with interactive nature of data exploration is distinguished. Description of case study, based on bibliometric network analysis is given, which is followed by the review of existing related works in this field. Conclusions are made and further studies in the field of visualization of multi-attributed graphs are defined.
Hendrix, William; Jenkins, John; Padmanabhan, Kanchana; Chakraborty, Arpan
2014-01-01
Practical Graph Mining with R presents a "do-it-yourself" approach to extracting interesting patterns from graph data. It covers many basic and advanced techniques for the identification of anomalous or frequently recurring patterns in a graph, the discovery of groups or clusters of nodes that share common patterns of attributes and relationships, the extraction of patterns that distinguish one category of graphs from another, and the use of those patterns to predict the category of new graphs. Hands-On Application of Graph Data Mining Each chapter in the book focuses on a graph mining task, such as link analysis, cluster analysis, and classification. Through applications using real data sets, the book demonstrates how computational techniques can help solve real-world problems. The applications covered include network intrusion detection, tumor cell diagnostics, face recognition, predictive toxicology, mining metabolic and protein-protein interaction networks, and community detection in social networks. De...
Bedini, Andrea; Jacobsen, Jesper Lykke
2010-01-01
Combining tree decomposition and transfer matrix techniques provides a very general algorithm for computing exact partition functions of statistical models defined on arbitrary graphs. The algorithm is particularly efficient in the case of planar graphs. We illustrate it by computing the Potts model partition functions and chromatic polynomials (the number of proper vertex colourings using Q colours) for large samples of random planar graphs with up to N = 100 vertices. In the latter case, our algorithm yields a sub-exponential average running time of ∼ exp(1.516√N), a substantial improvement over the exponential running time ∼exp (0.245N) provided by the hitherto best-known algorithm. We study the statistics of chromatic roots of random planar graphs in some detail, comparing the findings with results for finite pieces of a regular lattice.
Vestergaard, Preben Dahl; Hartnell, Bert L.
2006-01-01
There are many results dealing with the problem of decomposing a fixed graph into isomorphic subgraphs. There has also been work on characterizing graphs with the property that one can delete the edges of a number of edge disjoint copies of the subgraph and, regardless of how that is done, the gr...
Orientations of infinite graphs with prescribed edge-connectivity
Thomassen, Carsten
2016-01-01
We prove a decomposition result for locally finite graphs which can be used to extend results on edge-connectivity from finite to infinite graphs. It implies that every 4k-edge-connected graph G contains an immersion of some finite 2k-edge-connected Eulerian graph containing any prescribed vertex...... set (while planar graphs show that G need not containa subdivision of a simple finite graph of large edge-connectivity). Also, every 8k-edge connected infinite graph has a k-arc-connected orientation, as conjectured in 1989....
Characterizing graphs of maximum matching width at most 2
Jeong, Jisu; Ok, Seongmin; Suh, Geewon
2017-01-01
The maximum matching width is a width-parameter that is de ned on a branch-decomposition over the vertex set of a graph. The size of a maximum matching in the bipartite graph is used as a cut-function. In this paper, we characterize the graphs of maximum matching width at most 2 using the minor o...
Bounding spectral gaps of Markov chains: a novel exact multi-decomposition technique
Destainville, N
2003-01-01
We propose an exact technique to calculate lower bounds of spectral gaps of discrete time reversible Markov chains on finite state sets. Spectral gaps are a common tool for evaluating convergence rates of Markov chains. As an illustration, we successfully use this technique to evaluate the 'absorption time' of the 'Backgammon model', a paradigmatic model for glassy dynamics. We also discuss the application of this technique to the 'contingency table problem', a notoriously difficult problem from probability theory. The interest of this technique is that it connects spectral gaps, which are quantities related to dynamics, with static quantities, calculated at equilibrium
Bounding spectral gaps of Markov chains: a novel exact multi-decomposition technique
Destainville, N [Laboratoire de Physique Theorique - IRSAMC, CNRS/Universite Paul Sabatier, 118, route de Narbonne, 31062 Toulouse Cedex 04 (France)
2003-04-04
We propose an exact technique to calculate lower bounds of spectral gaps of discrete time reversible Markov chains on finite state sets. Spectral gaps are a common tool for evaluating convergence rates of Markov chains. As an illustration, we successfully use this technique to evaluate the 'absorption time' of the 'Backgammon model', a paradigmatic model for glassy dynamics. We also discuss the application of this technique to the 'contingency table problem', a notoriously difficult problem from probability theory. The interest of this technique is that it connects spectral gaps, which are quantities related to dynamics, with static quantities, calculated at equilibrium.
A medium term bulk production cost model based on decomposition techniques
Ramos, A.; Munoz, L. [Univ. Pontificia Comillas, Madrid (Spain). Inst. de Investigacion Tecnologica; Martinez-Corcoles, F.; Martin-Corrochano, V. [IBERDROLA, Madrid (Spain)
1995-11-01
This model provides the minimum variable cost subject to operating constraints (generation, transmission and fuel constraints). Generation constraints include power reserve margin with respect to the system peak load, first Kirchhoff`s law at each node, hydro energy scheduling, maintenance scheduling, and generation limitations. Transmission constraints cover the second Kirchhoff`s law and transmission limitations. The generation and transmission economic dispatch is approximated by the linearized (also called DC) load flow. Network losses are included as a non linear approximation. Fuel constraints include minimum consumption quotas and fuel scheduling for domestic coal thermal plants. This production costing problem is formulated as a large-scale non linear optimization problem solved by generalized Benders decomposition method. Master problem determines the inter-period decisions, i.e., maintenance, fuel and hydro scheduling, and each subproblem solves the intra-period decisions, i.e., generation and transmission economic dispatch for one period. The model has been implemented in GAMS, a mathematical programming language. An application to the large-scale Spanish electric power system is presented. 11 refs
Spectral Decomposition Algorithm (SDA)
National Aeronautics and Space Administration — Spectral Decomposition Algorithm (SDA) is an unsupervised feature extraction technique similar to PCA that was developed to better distinguish spectral features in...
Efficient morse decompositions of vector fields.
Chen, Guoning; Mischaikow, Konstantin; Laramee, Robert S; Zhang, Eugene
2008-01-01
Existing topology-based vector field analysis techniques rely on the ability to extract the individual trajectories such as fixed points, periodic orbits, and separatrices that are sensitive to noise and errors introduced by simulation and interpolation. This can make such vector field analysis unsuitable for rigorous interpretations. We advocate the use of Morse decompositions, which are robust with respect to perturbations, to encode the topological structures of a vector field in the form of a directed graph, called a Morse connection graph (MCG). While an MCG exists for every vector field, it need not be unique. Previous techniques for computing MCG's, while fast, are overly conservative and usually results in MCG's that are too coarse to be useful for the applications. To address this issue, we present a new technique for performing Morse decomposition based on the concept of tau-maps, which typically provides finer MCG's than existing techniques. Furthermore, the choice of tau provides a natural tradeoff between the fineness of the MCG's and the computational costs. We provide efficient implementations of Morse decomposition based on tau-maps, which include the use of forward and backward mapping techniques and an adaptive approach in constructing better approximations of the images of the triangles in the meshes used for simulation.. Furthermore, we propose the use of spatial tau-maps in addition to the original temporal tau-maps. These techniques provide additional trade-offs between the quality of the MCGs and the speed of computation. We demonstrate the utility of our technique with various examples in the plane and on surfaces including engine simulation data sets.
X-Graphs: Language and Algorithms for Heterogeneous Graph Streams
2017-09-01
are widely used by academia and industry. 15. SUBJECT TERMS Data Analytics, Graph Analytics, High-Performance Computing 16. SECURITY CLASSIFICATION...form the core of the DeepDive Knowledge Construction System. 2 INTRODUCTION The goal of the X-Graphs project was to develop computational techniques...memory multicore machine. Ringo is based on Snap.py and SNAP, and uses Python . Ringo now allows the integration of Delite DSL Framework Graph
Benhammouda, Brahim
2016-01-01
Since 1980, the Adomian decomposition method (ADM) has been extensively used as a simple powerful tool that applies directly to solve different kinds of nonlinear equations including functional, differential, integro-differential and algebraic equations. However, for differential-algebraic equations (DAEs) the ADM is applied only in four earlier works. There, the DAEs are first pre-processed by some transformations like index reductions before applying the ADM. The drawback of such transformations is that they can involve complex algorithms, can be computationally expensive and may lead to non-physical solutions. The purpose of this paper is to propose a novel technique that applies the ADM directly to solve a class of nonlinear higher-index Hessenberg DAEs systems efficiently. The main advantage of this technique is that; firstly it avoids complex transformations like index reductions and leads to a simple general algorithm. Secondly, it reduces the computational work by solving only linear algebraic systems with a constant coefficient matrix at each iteration, except for the first iteration where the algebraic system is nonlinear (if the DAE is nonlinear with respect to the algebraic variable). To demonstrate the effectiveness of the proposed technique, we apply it to a nonlinear index-three Hessenberg DAEs system with nonlinear algebraic constraints. This technique is straightforward and can be programmed in Maple or Mathematica to simulate real application problems.
Konar, Partha; Kong, Kyoungchul; Matchev, Konstantin T.; Park, Myeonghun
2010-07-01
We propose a new model-independent technique for mass measurements in missing energy events at hadron colliders. We illustrate our method with the most challenging case of a single-step decay chain. We consider inclusive same-sign chargino pair production in supersymmetry, followed by leptonic decays to sneutrinos χ+χ+→ℓ+ℓ'+ν˜ℓν˜ℓ' and invisible decays ν˜ℓ→νℓχ˜10. We introduce two one-dimensional decompositions of the Cambridge MT2 variable: MT2∥ and MT2⊥, on the direction of the upstream transverse momentum P→T and the direction orthogonal to it, respectively. We show that the sneutrino mass Mc can be measured directly by minimizing the number of events N(M˜c) in which MT2 exceeds a certain threshold, conveniently measured from the end point MT2⊥max(M˜c).
Xu, Shenzhi; Ai, Xiaomeng; Fang, Jiakun
2017-01-01
Photovoltaic (PV) power generation has made considerable developments in recent years. But its intermittent and volatility of its output has seriously affected the security operation of the power system. In order to better understand the PV generation and provide sufficient data support...... for analysis the impacts, a novel generation method for PV power time series combining decomposition technique and Markov chain theory is presented in this paper. It digs important factors from historical data from existing PV plants and then reproduce new data with similar patterns. In detail, the proposed...... method first decomposes the PV power time series into ideal output curve, amplitude parameter series and random fluctuating component three parts. Then generating daily ideal output curve by the extraction of typical daily data, amplitude parameter series based on the Markov chain Monte Carlo (MCMC...
Murphy, P.D.; Gerstein, B.C.
1979-02-01
A report is presented which describes a digital filtering technique using both a bandpass filter and an exponential filter. The properties of Lorentzian and Gaussian lineshapes are discussed. A procedure for decomposing NMR absorption spectra with overlapping lines into Lorentzian and Gaussian components is also described. Finally, two FORTRAN computer programs which implement concepts developed in this report are presented
Faster Parallel Traversal of Scale Free Graphs at Extreme Scale with Vertex Delegates
Pearce, Roger
2014-11-01
© 2014 IEEE. At extreme scale, irregularities in the structure of scale-free graphs such as social network graphs limit our ability to analyze these important and growing datasets. A key challenge is the presence of high-degree vertices (hubs), that leads to parallel workload and storage imbalances. The imbalances occur because existing partitioning techniques are not able to effectively partition high-degree vertices. We present techniques to distribute storage, computation, and communication of hubs for extreme scale graphs in distributed memory supercomputers. To balance the hub processing workload, we distribute hub data structures and related computation among a set of delegates. The delegates coordinate using highly optimized, yet portable, asynchronous broadcast and reduction operations. We demonstrate scalability of our new algorithmic technique using Breadth-First Search (BFS), Single Source Shortest Path (SSSP), K-Core Decomposition, and Page-Rank on synthetically generated scale-free graphs. Our results show excellent scalability on large scale-free graphs up to 131K cores of the IBM BG/P, and outperform the best known Graph500 performance on BG/P Intrepid by 15%
Faster Parallel Traversal of Scale Free Graphs at Extreme Scale with Vertex Delegates
Pearce, Roger; Gokhale, Maya; Amato, Nancy M.
2014-01-01
© 2014 IEEE. At extreme scale, irregularities in the structure of scale-free graphs such as social network graphs limit our ability to analyze these important and growing datasets. A key challenge is the presence of high-degree vertices (hubs), that leads to parallel workload and storage imbalances. The imbalances occur because existing partitioning techniques are not able to effectively partition high-degree vertices. We present techniques to distribute storage, computation, and communication of hubs for extreme scale graphs in distributed memory supercomputers. To balance the hub processing workload, we distribute hub data structures and related computation among a set of delegates. The delegates coordinate using highly optimized, yet portable, asynchronous broadcast and reduction operations. We demonstrate scalability of our new algorithmic technique using Breadth-First Search (BFS), Single Source Shortest Path (SSSP), K-Core Decomposition, and Page-Rank on synthetically generated scale-free graphs. Our results show excellent scalability on large scale-free graphs up to 131K cores of the IBM BG/P, and outperform the best known Graph500 performance on BG/P Intrepid by 15%
Multiresolution signal decomposition schemes
J. Goutsias (John); H.J.A.M. Heijmans (Henk)
1998-01-01
textabstract[PNA-R9810] Interest in multiresolution techniques for signal processing and analysis is increasing steadily. An important instance of such a technique is the so-called pyramid decomposition scheme. This report proposes a general axiomatic pyramid decomposition scheme for signal analysis
Seiller, Thomas
2016-01-01
Interaction graphs were introduced as a general, uniform, construction of dynamic models of linear logic, encompassing all Geometry of Interaction (GoI) constructions introduced so far. This series of work was inspired from Girard's hyperfinite GoI, and develops a quantitative approach that should...... be understood as a dynamic version of weighted relational models. Until now, the interaction graphs framework has been shown to deal with exponentials for the constrained system ELL (Elementary Linear Logic) while keeping its quantitative aspect. Adapting older constructions by Girard, one can clearly define...... "full" exponentials, but at the cost of these quantitative features. We show here that allowing interpretations of proofs to use continuous (yet finite in a measure-theoretic sense) sets of states, as opposed to earlier Interaction Graphs constructions were these sets of states were discrete (and finite...
Trudeau, Richard J
1994-01-01
Preface1. Pure Mathematics Introduction; Euclidean Geometry as Pure Mathematics; Games; Why Study Pure Mathematics?; What's Coming; Suggested Reading2. Graphs Introduction; Sets; Paradox; Graphs; Graph diagrams; Cautions; Common Graphs; Discovery; Complements and Subgraphs; Isomorphism; Recognizing Isomorphic Graphs; Semantics The Number of Graphs Having a Given nu; Exercises; Suggested Reading3. Planar Graphs Introduction; UG, K subscript 5, and the Jordan Curve Theorem; Are there More Nonplanar Graphs?; Expansions; Kuratowski's Theorem; Determining Whether a Graph is Planar or
Decomposing a graph into bistars
Thomassen, Carsten
2013-01-01
Bárat and the present author conjectured that, for each tree T, there exists a natural number kT such that the following holds: If G is a kT-edge-connected graph such that |E(T)| divides |E(G)|, then G has a T-decomposition, that is, a decomposition of the edge set into trees each of which...... is isomorphic to T. The conjecture has been verified for infinitely many paths and for each star. In this paper we verify the conjecture for an infinite family of trees that are neither paths nor stars, namely all the bistars S(k,k+1)....
Diestel, Reinhard
2017-01-01
This standard textbook of modern graph theory, now in its fifth edition, combines the authority of a classic with the engaging freshness of style that is the hallmark of active mathematics. It covers the core material of the subject with concise yet reliably complete proofs, while offering glimpses of more advanced methods in each field by one or two deeper results, again with proofs given in full detail. The book can be used as a reliable text for an introductory course, as a graduate text, and for self-study. From the reviews: “This outstanding book cannot be substituted with any other book on the present textbook market. It has every chance of becoming the standard textbook for graph theory.”Acta Scientiarum Mathematiciarum “Deep, clear, wonderful. This is a serious book about the heart of graph theory. It has depth and integrity. ”Persi Diaconis & Ron Graham, SIAM Review “The book has received a very enthusiastic reception, which it amply deserves. A masterly elucidation of modern graph theo...
Smooth Bundling of Large Streaming and Sequence Graphs
Hurter, C.; Ersoy, O.; Telea, A.
2013-01-01
Dynamic graphs are increasingly pervasive in modern information systems. However, understanding how a graph changes in time is difficult. We present here two techniques for simplified visualization of dynamic graphs using edge bundles. The first technique uses a recent image-based graph bundling
Nash-Williams’ cycle-decomposition theorem
Thomassen, Carsten
2016-01-01
We give an elementary proof of the theorem of Nash-Williams that a graph has an edge-decomposition into cycles if and only if it does not contain an odd cut. We also prove that every bridgeless graph has a collection of cycles covering each edge at least once and at most 7 times. The two results...
A Type Graph Model for Java Programs
Rensink, Arend; Zambon, Eduardo
2009-01-01
In this report we present a type graph that models all executable constructs of the Java programming language. Such a model is useful for any graph-based technique that relies on a representation of Java programs as graphs. The model can be regarded as a common representation to which all Java
A Type Graph Model for Java Programs
Rensink, Arend; Zambon, Eduardo; Lee, D.; Lopes, A.; Poetzsch-Heffter, A.
2009-01-01
In this work we present a type graph that models all executable constructs of the Java programming language. Such a model is useful for any graph-based technique that relies on a representation of Java programs as graphs. The model can be regarded as a common representation to which all Java syntax
Deep Learning with Dynamic Computation Graphs
Looks, Moshe; Herreshoff, Marcello; Hutchins, DeLesley; Norvig, Peter
2017-01-01
Neural networks that compute over graph structures are a natural fit for problems in a variety of domains, including natural language (parse trees) and cheminformatics (molecular graphs). However, since the computation graph has a different shape and size for every input, such networks do not directly support batched training or inference. They are also difficult to implement in popular deep learning libraries, which are based on static data-flow graphs. We introduce a technique called dynami...
Wang, Deyun; Wei, Shuai; Luo, Hongyuan; Yue, Chenqiang; Grunder, Olivier
2017-02-15
The randomness, non-stationarity and irregularity of air quality index (AQI) series bring the difficulty of AQI forecasting. To enhance forecast accuracy, a novel hybrid forecasting model combining two-phase decomposition technique and extreme learning machine (ELM) optimized by differential evolution (DE) algorithm is developed for AQI forecasting in this paper. In phase I, the complementary ensemble empirical mode decomposition (CEEMD) is utilized to decompose the AQI series into a set of intrinsic mode functions (IMFs) with different frequencies; in phase II, in order to further handle the high frequency IMFs which will increase the forecast difficulty, variational mode decomposition (VMD) is employed to decompose the high frequency IMFs into a number of variational modes (VMs). Then, the ELM model optimized by DE algorithm is applied to forecast all the IMFs and VMs. Finally, the forecast value of each high frequency IMF is obtained through adding up the forecast results of all corresponding VMs, and the forecast series of AQI is obtained by aggregating the forecast results of all IMFs. To verify and validate the proposed model, two daily AQI series from July 1, 2014 to June 30, 2016 collected from Beijing and Shanghai located in China are taken as the test cases to conduct the empirical study. The experimental results show that the proposed hybrid model based on two-phase decomposition technique is remarkably superior to all other considered models for its higher forecast accuracy. Copyright © 2016 Elsevier B.V. All rights reserved.
Hu, Yijia; Zhong, Zhong; Zhu, Yimin; Ha, Yao
2018-04-01
In this paper, a statistical forecast model using the time-scale decomposition method is established to do the seasonal prediction of the rainfall during flood period (FPR) over the middle and lower reaches of the Yangtze River Valley (MLYRV). This method decomposites the rainfall over the MLYRV into three time-scale components, namely, the interannual component with the period less than 8 years, the interdecadal component with the period from 8 to 30 years, and the interdecadal component with the period larger than 30 years. Then, the predictors are selected for the three time-scale components of FPR through the correlation analysis. At last, a statistical forecast model is established using the multiple linear regression technique to predict the three time-scale components of the FPR, respectively. The results show that this forecast model can capture the interannual and interdecadal variation of FPR. The hindcast of FPR during 14 years from 2001 to 2014 shows that the FPR can be predicted successfully in 11 out of the 14 years. This forecast model performs better than the model using traditional scheme without time-scale decomposition. Therefore, the statistical forecast model using the time-scale decomposition technique has good skills and application value in the operational prediction of FPR over the MLYRV.
Chartrand, Gary; Zhang, Ping
2010-01-01
Gary Chartrand has influenced the world of Graph Theory for almost half a century. He has supervised more than a score of Ph.D. dissertations and written several books on the subject. The most widely known of these texts, Graphs and Digraphs, … has much to recommend it, with clear exposition, and numerous challenging examples [that] make it an ideal textbook for the advanced undergraduate or beginning graduate course. The authors have updated their notation to reflect the current practice in this still-growing area of study. By the authors' estimation, the 5th edition is approximately 50% longer than the 4th edition. … the legendary Frank Harary, author of the second graph theory text ever produced, is one of the figures profiled. His book was the standard in the discipline for several decades. Chartrand, Lesniak and Zhang have produced a worthy successor.-John T. Saccoman, MAA Reviews, June 2012 (This book is in the MAA's basic library list.)As with the earlier editions, the current text emphasizes clear...
Planar graphs theory and algorithms
Nishizeki, T
1988-01-01
Collected in this volume are most of the important theorems and algorithms currently known for planar graphs, together with constructive proofs for the theorems. Many of the algorithms are written in Pidgin PASCAL, and are the best-known ones; the complexities are linear or 0(nlogn). The first two chapters provide the foundations of graph theoretic notions and algorithmic techniques. The remaining chapters discuss the topics of planarity testing, embedding, drawing, vertex- or edge-coloring, maximum independence set, subgraph listing, planar separator theorem, Hamiltonian cycles, and single- or multicommodity flows. Suitable for a course on algorithms, graph theory, or planar graphs, the volume will also be useful for computer scientists and graph theorists at the research level. An extensive reference section is included.
RJSplot: Interactive Graphs with R.
Barrios, David; Prieto, Carlos
2018-03-01
Data visualization techniques provide new methods for the generation of interactive graphs. These graphs allow a better exploration and interpretation of data but their creation requires advanced knowledge of graphical libraries. Recent packages have enabled the integration of interactive graphs in R. However, R provides limited graphical packages that allow the generation of interactive graphs for computational biology applications. The present project has joined the analytical power of R with the interactive graphical features of JavaScript in a new R package (RJSplot). It enables the easy generation of interactive graphs in R, provides new visualization capabilities, and contributes to the advance of computational biology analytical methods. At present, 16 interactive graphics are available in RJSplot, such as the genome viewer, Manhattan plots, 3D plots, heatmaps, dendrograms, networks, and so on. The RJSplot package is freely available online at http://rjsplot.net. © 2018 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.
Towards a theory of geometric graphs
Pach, Janos
2004-01-01
The early development of graph theory was heavily motivated and influenced by topological and geometric themes, such as the Konigsberg Bridge Problem, Euler's Polyhedral Formula, or Kuratowski's characterization of planar graphs. In 1936, when Denes Konig published his classical Theory of Finite and Infinite Graphs, the first book ever written on the subject, he stressed this connection by adding the subtitle Combinatorial Topology of Systems of Segments. He wanted to emphasize that the subject of his investigations was very concrete: planar figures consisting of points connected by straight-line segments. However, in the second half of the twentieth century, graph theoretical research took an interesting turn. In the most popular and most rapidly growing areas (the theory of random graphs, Ramsey theory, extremal graph theory, algebraic graph theory, etc.), graphs were considered as abstract binary relations rather than geometric objects. Many of the powerful techniques developed in these fields have been su...
Automorphism group of the modified bubble-sort graph
Ganesan, Ashwin
2014-01-01
The modified bubble-sort graph of dimension $n$ is the Cayley graph of $S_n$ generated by $n$ cyclically adjacent transpositions. In the present paper, it is shown that the automorphism group of the modified bubble sort graph of dimension $n$ is $S_n \\times D_{2n}$, for all $n \\ge 5$. Thus, a complete structural description of the automorphism group of the modified bubble-sort graph is obtained. A similar direct product decomposition is seen to hold for arbitrary normal Cayley graphs generate...
Query Optimizations over Decentralized RDF Graphs
Abdelaziz, Ibrahim
2017-05-18
Applications in life sciences, decentralized social networks, Internet of Things, and statistical linked dataspaces integrate data from multiple decentralized RDF graphs via SPARQL queries. Several approaches have been proposed to optimize query processing over a small number of heterogeneous data sources by utilizing schema information. In the case of schema similarity and interlinks among sources, these approaches cause unnecessary data retrieval and communication, leading to poor scalability and response time. This paper addresses these limitations and presents Lusail, a system for scalable and efficient SPARQL query processing over decentralized graphs. Lusail achieves scalability and low query response time through various optimizations at compile and run times. At compile time, we use a novel locality-aware query decomposition technique that maximizes the number of query triple patterns sent together to a source based on the actual location of the instances satisfying these triple patterns. At run time, we use selectivity-awareness and parallel query execution to reduce network latency and to increase parallelism by delaying the execution of subqueries expected to return large results. We evaluate Lusail using real and synthetic benchmarks, with data sizes up to billions of triples on an in-house cluster and a public cloud. We show that Lusail outperforms state-of-the-art systems by orders of magnitude in terms of scalability and response time.
Distributed-Memory Breadth-First Search on Massive Graphs
Buluc, Aydin [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division; Beamer, Scott [Univ. of California, Berkeley, CA (United States). Dept. of Electrical Engineering and Computer Sciences; Madduri, Kamesh [Pennsylvania State Univ., University Park, PA (United States). Computer Science & Engineering Dept.; Asanovic, Krste [Univ. of California, Berkeley, CA (United States). Dept. of Electrical Engineering and Computer Sciences; Patterson, David [Univ. of California, Berkeley, CA (United States). Dept. of Electrical Engineering and Computer Sciences
2017-09-26
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.
Yu, C. W.; Hodges, B. R.; Liu, F.
2017-12-01
Development of continental-scale river network models creates challenges where the massive amount of boundary condition data encounters the sensitivity of a dynamic nu- merical model. The topographic data sets used to define the river channel characteristics may include either corrupt data or complex configurations that cause instabilities in a numerical solution of the Saint-Venant equations. For local-scale river models (e.g. HEC- RAS), modelers typically rely on past experience to make ad hoc boundary condition adjustments that ensure a stable solution - the proof of the adjustment is merely the sta- bility of the solution. To date, there do not exist any formal methodologies or automated procedures for a priori detecting/fixing boundary conditions that cause instabilities in a dynamic model. Formal methodologies for data screening and adjustment are a critical need for simulations with a large number of river reaches that draw their boundary con- dition data from a wide variety of sources. At the continental scale, we simply cannot assume that we will have access to river-channel cross-section data that has been ade- quately analyzed and processed. Herein, we argue that problematic boundary condition data for unsteady dynamic modeling can be identified through numerical modeling with the steady-state Saint-Venant equations. The fragility of numerical stability increases with the complexity of branching in river network system and instabilities (even in an unsteady solution) are typically triggered by the nonlinear advection term in Saint-Venant equations. It follows that the behavior of the simpler steady-state equations (which retain the nonlin- ear term) can be used to screen the boundary condition data for problematic regions. In this research, we propose a graph-theory based method to isolate the location of corrupted boundary condition data in a continental-scale river network and demonstrate its utility with a network of O(10^4) elements. Acknowledgement
Optimal Embeddings of Distance Regular Graphs into Euclidean Spaces
F. Vallentin (Frank)
2008-01-01
htmlabstractIn this paper we give a lower bound for the least distortion embedding of a distance regular graph into Euclidean space. We use the lower bound for finding the least distortion for Hamming graphs, Johnson graphs, and all strongly regular graphs. Our technique involves semidefinite
On cyclic orthogonal double covers of circulant graphs by special infinite graphs
R. El-Shanawany
2017-12-01
Full Text Available In this article, a technique to construct cyclic orthogonal double covers (CODCs of regular circulant graphs by certain infinite graph classes such as complete bipartite and tripartite graphs and disjoint union of butterfly and K1,2n−10 is introduced.
Solving network design problems via decomposition, aggregation and approximation
Bärmann, Andreas
2016-01-01
Andreas Bärmann develops novel approaches for the solution of network design problems as they arise in various contexts of applied optimization. At the example of an optimal expansion of the German railway network until 2030, the author derives a tailor-made decomposition technique for multi-period network design problems. Next, he develops a general framework for the solution of network design problems via aggregation of the underlying graph structure. This approach is shown to save much computation time as compared to standard techniques. Finally, the author devises a modelling framework for the approximation of the robust counterpart under ellipsoidal uncertainty, an often-studied case in the literature. Each of these three approaches opens up a fascinating branch of research which promises a better theoretical understanding of the problem and an increasing range of solvable application settings at the same time. Contents Decomposition for Multi-Period Network Design Solving Network Design Problems via Ag...
Winlaw, Manda [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); De Sterck, Hans [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Sanders, Geoffrey [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2015-10-26
In very simple terms a network can be de ned as a collection of points joined together by lines. Thus, networks can be used to represent connections between entities in a wide variety of elds including engi- neering, science, medicine, and sociology. Many large real-world networks share a surprising number of properties, leading to a strong interest in model development research and techniques for building synthetic networks have been developed, that capture these similarities and replicate real-world graphs. Modeling these real-world networks serves two purposes. First, building models that mimic the patterns and prop- erties of real networks helps to understand the implications of these patterns and helps determine which patterns are important. If we develop a generative process to synthesize real networks we can also examine which growth processes are plausible and which are not. Secondly, high-quality, large-scale network data is often not available, because of economic, legal, technological, or other obstacles [7]. Thus, there are many instances where the systems of interest cannot be represented by a single exemplar network. As one example, consider the eld of cybersecurity, where systems require testing across diverse threat scenarios and validation across diverse network structures. In these cases, where there is no single exemplar network, the systems must instead be modeled as a collection of networks in which the variation among them may be just as important as their common features. By developing processes to build synthetic models, so-called graph generators, we can build synthetic networks that capture both the essential features of a system and realistic variability. Then we can use such synthetic graphs to perform tasks such as simulations, analysis, and decision making. We can also use synthetic graphs to performance test graph analysis algorithms, including clustering algorithms and anomaly detection algorithms.
*Artur Bobrowski
2018-03-01
Full Text Available This paper presents results of thermoanalytical and structural research on phenolic binder used in foundry for the preparation of moulding sand. The binder has been prepared based on resole type phenolic resin with the addition of ester hardener. The aim of the study was to determine the structural changes taking place in the phenolic binder under the influence of temperature. Results show that in the investigated range of temperatures,phenolic binder exhibits three exothermic thermal effects accompanying the decomposition process. The test results using the Diffuse Reflectance Infrared Fourier Transform Spectroscopy (DRIFTS technique show that the addition of a hardener stabilizes the binder structure within methylene bridges. The reduction in the reaction rate observed in the DTA curve at about 330 癈 can be associated with the formation of gaseous products by decomposition of the binder or, as suggested by the literature data, the formation of triple bonds and CN-HCN groups.
Semantic graphs and associative memories
Pomi, Andrés; Mizraji, Eduardo
2004-12-01
Graphs have been increasingly utilized in the characterization of complex networks from diverse origins, including different kinds of semantic networks. Human memories are associative and are known to support complex semantic nets; these nets are represented by graphs. However, it is not known how the brain can sustain these semantic graphs. The vision of cognitive brain activities, shown by modern functional imaging techniques, assigns renewed value to classical distributed associative memory models. Here we show that these neural network models, also known as correlation matrix memories, naturally support a graph representation of the stored semantic structure. We demonstrate that the adjacency matrix of this graph of associations is just the memory coded with the standard basis of the concept vector space, and that the spectrum of the graph is a code invariant of the memory. As long as the assumptions of the model remain valid this result provides a practical method to predict and modify the evolution of the cognitive dynamics. Also, it could provide us with a way to comprehend how individual brains that map the external reality, almost surely with different particular vector representations, are nevertheless able to communicate and share a common knowledge of the world. We finish presenting adaptive association graphs, an extension of the model that makes use of the tensor product, which provides a solution to the known problem of branching in semantic nets.
Darbar, Devendrasinh [School of Mechanical and Building Science, Vellore Institute of Technology (VIT), Vellore 632014, Tamil Nadu (India); Department of Mechanical Engineering, National University of Singapore, 117576 (Singapore); Department of Physics, National University of Singapore, 117542 (Singapore); Reddy, M.V., E-mail: phymvvr@nus.edu.sg [Department of Physics, National University of Singapore, 117542 (Singapore); Department of Materials Science and Engineering, National University of Singapore, 117546 (Singapore); Sundarrajan, S. [Department of Mechanical Engineering, National University of Singapore, 117576 (Singapore); Pattabiraman, R. [School of Mechanical and Building Science, Vellore Institute of Technology (VIT), Vellore 632014, Tamil Nadu (India); Ramakrishna, S. [Department of Mechanical Engineering, National University of Singapore, 117576 (Singapore); Chowdari, B.V.R. [Department of Physics, National University of Singapore, 117542 (Singapore)
2016-01-15
Highlights: • MgCo{sub 2}O{sub 4} was prepared by oxalate decomposition method and electrospinning technique. • Electrospun MgCo{sub 2}O{sub 4} shows the reversible capacity of 795 and 227 mAh g{sup −1} oxalate decomposition MgCo{sub 2}O{sub 4} after 50 cycle. • Electrospun MgCo{sub 2}O{sub 4} show good cycling stability and electrochemical performance. - Abstract: Magnesium cobalt oxide, MgCo{sub 2}O{sub 4} was synthesized by oxalate decomposition method and electrospinning technique. The electrochemical performances, structures, phase formation and morphology of MgCo{sub 2}O{sub 4} synthesized by both the methods are compared. Scanning electron microscope (SEM) studies show spherical and fiber type morphology, respectively for the oxalate decomposition and electrospinning method. The electrospun nanofibers of MgCo{sub 2}O{sub 4} calcined at 650 °C, showed a very good reversible capacity of 795 mAh g{sup −1} after 50 cycles when compared to bulk material capacity of 227 mAh g{sup −1} at current rate of 60 mA g{sup −1}. MgCo{sub 2}O{sub 4} nanofiber showed a reversible capacity of 411 mAh g{sup −1} (at cycle) at current density of 240 mA g{sup −1}. Improved performance was due to improved conductivity of MgO, which may act as buffer layer leading to improved cycling stability. The cyclic voltammetry studies at scan rate of 0.058 mV/s show main cathodic at around 1.0 V and anodic peaks at 2.1 V vs. Li.
Chartrand, Gary; Rosen, Kenneth H
2008-01-01
Beginning with the origin of the four color problem in 1852, the field of graph colorings has developed into one of the most popular areas of graph theory. Introducing graph theory with a coloring theme, Chromatic Graph Theory explores connections between major topics in graph theory and graph colorings as well as emerging topics. This self-contained book first presents various fundamentals of graph theory that lie outside of graph colorings, including basic terminology and results, trees and connectivity, Eulerian and Hamiltonian graphs, matchings and factorizations, and graph embeddings. The remainder of the text deals exclusively with graph colorings. It covers vertex colorings and bounds for the chromatic number, vertex colorings of graphs embedded on surfaces, and a variety of restricted vertex colorings. The authors also describe edge colorings, monochromatic and rainbow edge colorings, complete vertex colorings, several distinguishing vertex and edge colorings, and many distance-related vertex coloring...
Properly colored connectivity of graphs
Li, Xueliang; Qin, Zhongmei
2018-01-01
A comprehensive survey of proper connection of graphs is discussed in this book with real world applications in computer science and network security. Beginning with a brief introduction, comprising relevant definitions and preliminary results, this book moves on to consider a variety of properties of graphs that imply bounds on the proper connection number. Detailed proofs of significant advancements toward open problems and conjectures are presented with complete references. Researchers and graduate students with an interest in graph connectivity and colorings will find this book useful as it builds upon fundamental definitions towards modern innovations, strategies, and techniques. The detailed presentation lends to use as an introduction to proper connection of graphs for new and advanced researchers, a solid book for a graduate level topics course, or as a reference for those interested in expanding and further developing research in the area.
Generating random networks and graphs
Coolen, Ton; Roberts, Ekaterina
2017-01-01
This book supports researchers who need to generate random networks, or who are interested in the theoretical study of random graphs. The coverage includes exponential random graphs (where the targeted probability of each network appearing in the ensemble is specified), growth algorithms (i.e. preferential attachment and the stub-joining configuration model), special constructions (e.g. geometric graphs and Watts Strogatz models) and graphs on structured spaces (e.g. multiplex networks). The presentation aims to be a complete starting point, including details of both theory and implementation, as well as discussions of the main strengths and weaknesses of each approach. It includes extensive references for readers wishing to go further. The material is carefully structured to be accessible to researchers from all disciplines while also containing rigorous mathematical analysis (largely based on the techniques of statistical mechanics) to support those wishing to further develop or implement the theory of rand...
Attack Graph Construction for Security Events Analysis
Andrey Alexeevich Chechulin
2014-09-01
Full Text Available The paper is devoted to investigation of the attack graphs construction and analysis task for a network security evaluation and real-time security event processing. Main object of this research is the attack modeling process. The paper contains the description of attack graphs building, modifying and analysis technique as well as overview of implemented prototype for network security analysis based on attack graph approach.
Graph visualization (Invited talk)
Wijk, van J.J.; Kreveld, van M.J.; Speckmann, B.
2012-01-01
Black and white node link diagrams are the classic method to depict graphs, but these often fall short to give insight in large graphs or when attributes of nodes and edges play an important role. Graph visualization aims obtaining insight in such graphs using interactive graphical representations.
Incremental Frequent Subgraph Mining on Large Evolving Graphs
Abdelhamid, Ehab; Canim, Mustafa; Sadoghi, Mohammad; Bhatta, Bishwaranjan; Chang, Yuan-Chi; Kalnis, Panos
2017-01-01
, such as social networks, utilize large evolving graphs. Mining these graphs using existing techniques is infeasible, due to the high computational cost. In this paper, we propose IncGM+, a fast incremental approach for continuous frequent subgraph mining problem
Atallah, Therese
2014-05-01
Organic amendments, green manure and plant residues incorporation are the main sources of nutrients in organic farming, their decomposition rate is crucial for the accumulation and long-term storage of organic matter in soils. In this study the decomposition of compost from olive mill waste (N: 29.3 g kg-1; total dissolved nitrogen or TDN: 3.82 g kg-1), goat manure (N: 31.5 g kg-1; TDN: 0.94 g kg-1), the shoots (N: 33.6 g kg-1; TDN: 17.57 g kg-1) and roots (N: 22.12 g kg-1; TDN: 8.87 g kg-1) of Medicago sativa was followed in three Lebanese soils. The nitrogen, phosphorus and potassium released were followed over one year, starting in early winter (December-January). The mild sub-humid Mediterranean conditions allowed a rapid mass loss in alfalfa shoots 30 days after incorporation. Manure and compost were more persistent. Between 80 and 90% of TDN were released, after 30 days of in-situ incubation for compost, the release was over 90% for alfalfa shoots. The movement of P was slower, as the compost (6.99 g kg-1 of P) and manure (9.81 g kg-1 of P) lost 33% and 22%, respectively, during 30 days of incubation. After one year, 15 to 35% of P remained in the soils. The manure was the richest in potassium (19.66 g kg-1) followed by the alfalfa shoots (15.56 g kg-1), the compost (8.19 g kg-1) and the roots (5.96 g kg-1). The loss of potassium was important, as over 88% had disappeared over the year. All decomposition curves followed an exponential model. The calculated coefficients of decomposition for total nitrogen (lnfinal - lninitial/days) were significantly higher for alfalfa shoots (0.00547 day-1) and similar for the compost (0.00184 day-1) and the manure (0.00175 day-1). The ANOVA test showed a difference between two of the sites (Site A: 521 g kg-1 of clay and 42 g kg-1 of calcium carbonate; Site S: 260 g kg-1 of clay and 269 g kg-1 of CaCO3) and the third one (Site L: 315 g kg-1 of clay and 591 g kg-1 of CaCO3). The relationships between the soil calcium
Pragmatic Graph Rewriting Modifications
Rodgers, Peter; Vidal, Natalia
1999-01-01
We present new pragmatic constructs for easing programming in visual graph rewriting programming languages. The first is a modification to the rewriting process for nodes the host graph, where nodes specified as 'Once Only' in the LHS of a rewrite match at most once with a corresponding node in the host graph. This reduces the previously common use of tags to indicate the progress of matching in the graph. The second modification controls the application of LHS graphs, where those specified a...
Choudhary, Alok Nidhi; Leung, Mun K.; Huang, Thomas S.; Patel, Janak H.
1989-01-01
Computer vision systems employ a sequence of vision algorithms in which the output of an algorithm is the input of the next algorithm in the sequence. Algorithms that constitute such systems exhibit vastly different computational characteristics, and therefore, require different data decomposition techniques and efficient load balancing techniques for parallel implementation. However, since the input data for a task is produced as the output data of the previous task, this information can be exploited to perform knowledge based data decomposition and load balancing. Presented here are algorithms for a motion estimation system. The motion estimation is based on the point correspondence between the involved images which are a sequence of stereo image pairs. Researchers propose algorithms to obtain point correspondences by matching feature points among stereo image pairs at any two consecutive time instants. Furthermore, the proposed algorithms employ non-iterative procedures, which results in saving considerable amounts of computation time. The system consists of the following steps: (1) extraction of features; (2) stereo match of images in one time instant; (3) time match of images from consecutive time instants; (4) stereo match to compute final unambiguous points; and (5) computation of motion parameters.
Umegaki, Kikuo; Miki, Kazuyoshi
1990-01-01
A numerical method is developed to solve three-dimensional incompressible viscous flow in complicated geometry using curvilinear coordinate transformation and domain decomposition technique. In this approach, a complicated flow domain is decomposed into several subdomains, each of which has an overlapping region with neighboring subdomains. Curvilinear coordinates are numerically generated in each subdomain using the boundary-fitted coordinate transformation technique. The modified SMAC scheme is developed to solve Navier-Stokes equations in which the convective terms are discretized by the QUICK method. A fully vectorized computer program is developed on the basis of the proposed method. The program is applied to flow analysis in a semicircular curved, 90deg elbow and T-shape branched pipes. Computational time with the vector processor of the HITAC S-810/20 supercomputer system, is reduced to 1/10∼1/20 of that with a scalar processor. (author)
Generalized graph manifolds and their effective recognition
Matveev, S V
1998-01-01
A generalized graph manifold is a three-dimensional manifold obtained by gluing together elementary blocks, each of which is either a Seifert manifold or contains no essential tori or annuli. By a well-known result on torus decomposition each compact three-dimensional manifold with boundary that is either empty or consists of tori has a canonical representation as a generalized graph manifold. A short simple proof of the existence of a canonical representation is presented and a (partial) algorithm for its construction is described. A simple hyperbolicity test for blocks that are not Seifert manifolds is also presented
Proving termination of graph transformation systems using weighted type graphs over semirings
Bruggink, H.J.S.; König, B.; Nolte, D.; Zantema, H.; Parisi-Presicce, F.; Westfechtel, B.
2015-01-01
We introduce techniques for proving uniform termination of graph transformation systems, based on matrix interpretations for string rewriting. We generalize this technique by adapting it to graph rewriting instead of string rewriting and by generalizing to ordered semirings. In this way we obtain a
Crockett, R. G. M.; Gillmore, G. K.
2009-04-01
During the second half of 2002, the University of Northampton Radon Research Group operated two continuous hourly-sampling radon detectors 2.25 km apart in Northampton, in the (English) East Midlands. This period included the Dudley earthquake (22/09/2002) which was widely noticed by members of the public in the Northampton area. Also, at various periods during 2008 the Group has operated another pair of continuous hourly-sampling radon detectors similar distances apart in Northampton. One such period included the Market Rasen earthquake (27/02/2008) which was also widely noticed by members of the public in the Northampton area. During each period of monitoring, two time-series of radon readings were obtained, one from each detector. These have been analysed for evidence of simultaneous similar anomalies: the premise being that big disturbances occurring at big distances (in relation to the detector separation) should produce simultaneous similar anomalies but that simultaneous anomalies occurring by chance will be dissimilar. As previously reported, cross-correlating the two 2002 time-series over periods of 1-30 days duration, rolled forwards through the time-series at one-hour intervals produced two periods of significant correlation, i.e. two periods of simultaneous similar behaviour in the radon concentrations. One of these periods corresponded in time to the Dudley earthquake, the other corresponded in time to a smaller earthquake which occurred in the English Channel (26/08/2002). We here report subsequent investigation of the 2002 time-series and the 2008 time-series using spectral-decomposition techniques. These techniques have revealed additional simultaneous similar behaviour in the two radon concentrations, not revealed by the rolling correlation on the raw data. These correspond in time to the Manchester earthquake swarm of October 2002 and the Market Rasen earthquake of February 2008. The spectral-decomposition techniques effectively ‘de-noise' the
Adaptive Graph Convolutional Neural Networks
Li, Ruoyu; Wang, Sheng; Zhu, Feiyun; Huang, Junzhou
2018-01-01
Graph Convolutional Neural Networks (Graph CNNs) are generalizations of classical CNNs to handle graph data such as molecular data, point could and social networks. Current filters in graph CNNs are built for fixed and shared graph structure. However, for most real data, the graph structures varies in both size and connectivity. The paper proposes a generalized and flexible graph CNN taking data of arbitrary graph structure as input. In that way a task-driven adaptive graph is learned for eac...
C. Dalfo
2015-10-01
Full Text Available We study a family of graphs related to the $n$-cube. The middle cube graph of parameter k is the subgraph of $Q_{2k-1}$ induced by the set of vertices whose binary representation has either $k-1$ or $k$ number of ones. The middle cube graphs can be obtained from the well-known odd graphs by doubling their vertex set. Here we study some of the properties of the middle cube graphs in the light of the theory of distance-regular graphs. In particular, we completely determine their spectra (eigenvalues and their multiplicities, and associated eigenvectors.
Batakliev Todor
2014-06-01
Full Text Available Catalytic ozone decomposition is of great significance because ozone is a toxic substance commonly found or generated in human environments (aircraft cabins, offices with photocopiers, laser printers, sterilizers. Considerable work has been done on ozone decomposition reported in the literature. This review provides a comprehensive summary of the literature, concentrating on analysis of the physico-chemical properties, synthesis and catalytic decomposition of ozone. This is supplemented by a review on kinetics and catalyst characterization which ties together the previously reported results. Noble metals and oxides of transition metals have been found to be the most active substances for ozone decomposition. The high price of precious metals stimulated the use of metal oxide catalysts and particularly the catalysts based on manganese oxide. It has been determined that the kinetics of ozone decomposition is of first order importance. A mechanism of the reaction of catalytic ozone decomposition is discussed, based on detailed spectroscopic investigations of the catalytic surface, showing the existence of peroxide and superoxide surface intermediates
Ghebali, Sacha; Garicano-Mena, Jesús; Ferrer, Esteban; Valero, Eusebio
2018-04-01
A Dynamic Mode Decomposition (DMD) of Direct Numerical Simulations (DNS) of fully developed channel flows is undertaken in order to study the main differences in flow features between a plane-channel flow and a passively “controlled” flow wherein the mean friction was reduced relative to the baseline by modifying the geometry in order to generate a streamwise-periodic spanwise pressure gradient, as is the case for an oblique wavy wall. The present analysis reports POD and DMD modes for the plane channel, jointly with the application of a sparsity-promoting method, as well as a reconstruction of the Reynolds shear stress with the dynamic modes. Additionally, a dynamic link between the streamwise velocity fluctuations and the friction on the wall is sought by means of a composite approach both in the plane and wavy cases. One of the DMD modes associated with the wavy-wall friction exhibits a meandering motion which was hardly identifiable on the instantaneous friction fluctuations.
Hierarchical organisation of causal graphs
Dziopa, P.
1993-01-01
This paper deals with the design of a supervision system using a hierarchy of models formed by graphs, in which the variables are the nodes and the causal relations between the variables of the arcs. To obtain a representation of the variables evolutions which contains only the relevant features of their real evolutions, the causal relations are completed with qualitative transfer functions (QTFs) which produce roughly the behaviour of the classical transfer functions. Major improvements have been made in the building of the hierarchical organization. First, the basic variables of the uppermost level and the causal relations between them are chosen. The next graph is built by adding intermediary variables to the upper graph. When the undermost graph has been built, the transfer functions parameters corresponding to its causal relations are identified. The second task consists in the upwelling of the information from the undermost graph to the uppermost one. A fusion procedure of the causal relations has been designed to compute the QFTs relevant for each level. This procedure aims to reduce the number of parameters needed to represent an evolution at a high level of abstraction. These techniques have been applied to the hierarchical modelling of nuclear process. (authors). 8 refs., 12 figs
Mechatronic modeling and simulation using bond graphs
Das, Shuvra
2009-01-01
Introduction to Mechatronics and System ModelingWhat Is Mechatronics?What Is a System and Why Model Systems?Mathematical Modeling Techniques Used in PracticeSoftwareBond Graphs: What Are They?Engineering SystemsPortsGeneralized VariablesBond GraphsBasic Components in SystemsA Brief Note about Bond Graph Power DirectionsSummary of Bond Direction RulesDrawing Bond Graphs for Simple Systems: Electrical and MechanicalSimplification Rules for Junction StructureDrawing Bond Graphs for Electrical SystemsDrawing Bond Graphs for Mechanical SystemsCausalityDrawing Bond Graphs for Hydraulic and Electronic Components and SystemsSome Basic Properties and Concepts for FluidsBond Graph Model of Hydraulic SystemsElectronic SystemsDeriving System Equations from Bond GraphsSystem VariablesDeriving System EquationsTackling Differential CausalityAlgebraic LoopsSolution of Model Equations and Their InterpretationZeroth Order SystemsFirst Order SystemsSecond Order SystemTransfer Functions and Frequency ResponsesNumerical Solution ...
Huaishuo Xiao
2017-11-01
Full Text Available In order to identify various kinds of combined power quality disturbances, the singular value decomposition (SVD and the improved total least squares-estimation of signal parameters via rotational invariance techniques (TLS-ESPRIT are combined as the basis of disturbance identification in this paper. SVD is applied to identify the catastrophe points of disturbance intervals, based on which the disturbance intervals are segmented. Then the improved TLS-ESPRIT optimized by singular value norm method is used to analyze each data segment, and extract the amplitude, frequency, attenuation coefficient and initial phase of various kinds of disturbances. Multi-group combined disturbance test signals are constructed by MATLAB and the proposed method is also tested by the measured data of IEEE Power and Energy Society (PES Database. The test results show that the new method proposed has a relatively higher accuracy than conventional TLS-ESPRIT, which could be used in the identification of measured data.
Soetevent, A.R.
2010-01-01
This paper extends Hotelling's model of price competition with quadratic transportation costs from a line to graphs. I propose an algorithm to calculate firm-level demand for any given graph, conditional on prices and firm locations. One feature of graph models of price competition is that spatial
Graphing Inequalities, Connecting Meaning
Switzer, J. Matt
2014-01-01
Students often have difficulty with graphing inequalities (see Filloy, Rojano, and Rubio 2002; Drijvers 2002), and J. Matt Switzer's students were no exception. Although students can produce graphs for simple inequalities, they often struggle when the format of the inequality is unfamiliar. Even when producing a correct graph of an…
Amine Labriji
2017-07-01
Full Text Available The topic of identifying the similarity of graphs was considered as highly recommended research field in the Web semantic, artificial intelligence, the shape recognition and information research. One of the fundamental problems of graph databases is finding similar graphs to a graph query. Existing approaches dealing with this problem are usually based on the nodes and arcs of the two graphs, regardless of parental semantic links. For instance, a common connection is not identified as being part of the similarity of two graphs in cases like two graphs without common concepts, the measure of similarity based on the union of two graphs, or the one based on the notion of maximum common sub-graph (SCM, or the distance of edition of graphs. This leads to an inadequate situation in the context of information research. To overcome this problem, we suggest a new measure of similarity between graphs, based on the similarity measure of Wu and Palmer. We have shown that this new measure satisfies the properties of a measure of similarities and we applied this new measure on examples. The results show that our measure provides a run time with a gain of time compared to existing approaches. In addition, we compared the relevance of the similarity values obtained, it appears that this new graphs measure is advantageous and offers a contribution to solving the problem mentioned above.
van Dam, Edwin R.; Koolen, Jack H.; Tanaka, Hajime
2016-01-01
This is a survey of distance-regular graphs. We present an introduction to distance-regular graphs for the reader who is unfamiliar with the subject, and then give an overview of some developments in the area of distance-regular graphs since the monograph 'BCN'[Brouwer, A.E., Cohen, A.M., Neumaier,
Fuzzy Graph Language Recognizability
Kalampakas , Antonios; Spartalis , Stefanos; Iliadis , Lazaros
2012-01-01
Part 5: Fuzzy Logic; International audience; Fuzzy graph language recognizability is introduced along the lines of the established theory of syntactic graph language recognizability by virtue of the algebraic structure of magmoids. The main closure properties of the corresponding class are investigated and several interesting examples of fuzzy graph languages are examined.
Brouwer, A.E.; Haemers, W.H.
2012-01-01
This book gives an elementary treatment of the basic material about graph spectra, both for ordinary, and Laplace and Seidel spectra. The text progresses systematically, by covering standard topics before presenting some new material on trees, strongly regular graphs, two-graphs, association
Hell, Pavol
2004-01-01
This is a book about graph homomorphisms. Graph theory is now an established discipline but the study of graph homomorphisms has only recently begun to gain wide acceptance and interest. The subject gives a useful perspective in areas such as graph reconstruction, products, fractional and circular colourings, and has applications in complexity theory, artificial intelligence, telecommunication, and, most recently, statistical physics.Based on the authors' lecture notes for graduate courses, this book can be used as a textbook for a second course in graph theory at 4th year or master's level an
Improved Conflict Detection for Graph Transformation with Attributes
Géza Kulcsár
2015-04-01
Full Text Available In graph transformation, a conflict describes a situation where two alternative transformations cannot be arbitrarily serialized. When enriching graphs with attributes, existing conflict detection techniques typically report a conflict whenever at least one of two transformations manipulates a shared attribute. In this paper, we propose an improved, less conservative condition for static conflict detection of graph transformation with attributes by explicitly taking the semantics of the attribute operations into account. The proposed technique is based on symbolic graphs, which extend the traditional notion of graphs by logic formulas used for attribute handling. The approach is proven complete, i.e., any potential conflict is guaranteed to be detected.
Simplicial complexes of graphs
Jonsson, Jakob
2008-01-01
A graph complex is a finite family of graphs closed under deletion of edges. Graph complexes show up naturally in many different areas of mathematics, including commutative algebra, geometry, and knot theory. Identifying each graph with its edge set, one may view a graph complex as a simplicial complex and hence interpret it as a geometric object. This volume examines topological properties of graph complexes, focusing on homotopy type and homology. Many of the proofs are based on Robin Forman's discrete version of Morse theory. As a byproduct, this volume also provides a loosely defined toolbox for attacking problems in topological combinatorics via discrete Morse theory. In terms of simplicity and power, arguably the most efficient tool is Forman's divide and conquer approach via decision trees; it is successfully applied to a large number of graph and digraph complexes.
Sanghavi, Suniti; Natraj, Vijay
2013-01-01
Fourier decomposition of the phase function is essential to decouple the azimuthal component of the radiative transfer equation for multiple scattering calculations. This decomposition can be carried out by means of a direct numerical method based on the definition of the Fourier transform (numFT), or by an expansion of the phase function in terms of spherical Legendre polynomials (sphFT). numFT requires interpolation of the phase function between discrete angles, leading to spurious errors in the final computations. This error is difficult to quantify by means of intensity-only computations, since it is hard to determine the absolute accuracy of any given approach. We show that a linearization (analytic computation of derivatives) of the intensity with respect to parameters governing the phase function can be compared against results using the finite difference method, thereby providing a self-consistency test for characterizing and quantifying the error. We have applied this approach to two linearized versions of the Matrix Operator Method, which are identical in all respects except that one uses numFT while the other uses sphFT. In both cases, we compute the derivatives of the intensity with respect to aerosol parameters governing scattering in the simulated atmosphere. Comparison of the derivatives against their finite difference estimates shows a reduction of error by several orders of magnitude when Legendre polynomials are employed. We have also examined the effect of the angular resolution of the phase function on the error due to the numFT technique. A general reduction of error is seen with increasing angular resolution, indicating that interpolation is indeed the major error source. Also, we have pointed out a related source of error in numFT computations that occurs when Fourier decomposition is carried out on the composite phase function of a layer consisting of more than one scatterer. We conclude that an expansion of the phase function in terms of
Enabling Graph Appliance for Genome Assembly
Singh, Rina [ORNL; Graves, Jeffrey A [ORNL; Lee, Sangkeun (Matt) [ORNL; Sukumar, Sreenivas R [ORNL; Shankar, Mallikarjun [ORNL
2015-01-01
In recent years, there has been a huge growth in the amount of genomic data available as reads generated from various genome sequencers. The number of reads generated can be huge, ranging from hundreds to billions of nucleotide, each varying in size. Assembling such large amounts of data is one of the challenging computational problems for both biomedical and data scientists. Most of the genome assemblers developed have used de Bruijn graph techniques. A de Bruijn graph represents a collection of read sequences by billions of vertices and edges, which require large amounts of memory and computational power to store and process. This is the major drawback to de Bruijn graph assembly. Massively parallel, multi-threaded, shared memory systems can be leveraged to overcome some of these issues. The objective of our research is to investigate the feasibility and scalability issues of de Bruijn graph assembly on Cray s Urika-GD system; Urika-GD is a high performance graph appliance with a large shared memory and massively multithreaded custom processor designed for executing SPARQL queries over large-scale RDF data sets. However, to the best of our knowledge, there is no research on representing a de Bruijn graph as an RDF graph or finding Eulerian paths in RDF graphs using SPARQL for potential genome discovery. In this paper, we address the issues involved in representing a de Bruin graphs as RDF graphs and propose an iterative querying approach for finding Eulerian paths in large RDF graphs. We evaluate the performance of our implementation on real world ebola genome datasets and illustrate how genome assembly can be accomplished with Urika-GD using iterative SPARQL queries.
Efficient dynamic graph construction for inductive semi-supervised learning.
Dornaika, F; Dahbi, R; Bosaghzadeh, A; Ruichek, Y
2017-10-01
Most of graph construction techniques assume a transductive setting in which the whole data collection is available at construction time. Addressing graph construction for inductive setting, in which data are coming sequentially, has received much less attention. For inductive settings, constructing the graph from scratch can be very time consuming. This paper introduces a generic framework that is able to make any graph construction method incremental. This framework yields an efficient and dynamic graph construction method that adds new samples (labeled or unlabeled) to a previously constructed graph. As a case study, we use the recently proposed Two Phase Weighted Regularized Least Square (TPWRLS) graph construction method. The paper has two main contributions. First, we use the TPWRLS coding scheme to represent new sample(s) with respect to an existing database. The representative coefficients are then used to update the graph affinity matrix. The proposed method not only appends the new samples to the graph but also updates the whole graph structure by discovering which nodes are affected by the introduction of new samples and by updating their edge weights. The second contribution of the article is the application of the proposed framework to the problem of graph-based label propagation using multiple observations for vision-based recognition tasks. Experiments on several image databases show that, without any significant loss in the accuracy of the final classification, the proposed dynamic graph construction is more efficient than the batch graph construction. Copyright © 2017 Elsevier Ltd. All rights reserved.
Graphing trillions of triangles.
Burkhardt, Paul
2017-07-01
The increasing size of Big Data is often heralded but how data are transformed and represented is also profoundly important to knowledge discovery, and this is exemplified in Big Graph analytics. Much attention has been placed on the scale of the input graph but the product of a graph algorithm can be many times larger than the input. This is true for many graph problems, such as listing all triangles in a graph. Enabling scalable graph exploration for Big Graphs requires new approaches to algorithms, architectures, and visual analytics. A brief tutorial is given to aid the argument for thoughtful representation of data in the context of graph analysis. Then a new algebraic method to reduce the arithmetic operations in counting and listing triangles in graphs is introduced. Additionally, a scalable triangle listing algorithm in the MapReduce model will be presented followed by a description of the experiments with that algorithm that led to the current largest and fastest triangle listing benchmarks to date. Finally, a method for identifying triangles in new visual graph exploration technologies is proposed.
Interacting particle systems on graphs
Sood, Vishal
In this dissertation, the dynamics of socially or biologically interacting populations are investigated. The individual members of the population are treated as particles that interact via links on a social or biological network represented as a graph. The effect of the structure of the graph on the properties of the interacting particle system is studied using statistical physics techniques. In the first chapter, the central concepts of graph theory and social and biological networks are presented. Next, interacting particle systems that are drawn from physics, mathematics and biology are discussed in the second chapter. In the third chapter, the random walk on a graph is studied. The mean time for a random walk to traverse between two arbitrary sites of a random graph is evaluated. Using an effective medium approximation it is found that the mean first-passage time between pairs of sites, as well as all moments of this first-passage time, are insensitive to the density of links in the graph. The inverse of the mean-first passage time varies non-monotonically with the density of links near the percolation transition of the random graph. Much of the behavior can be understood by simple heuristic arguments. Evolutionary dynamics, by which mutants overspread an otherwise uniform population on heterogeneous graphs, are studied in the fourth chapter. Such a process underlies' epidemic propagation, emergence of fads, social cooperation or invasion of an ecological niche by a new species. The first part of this chapter is devoted to neutral dynamics, in which the mutant genotype does not have a selective advantage over the resident genotype. The time to extinction of one of the two genotypes is derived. In the second part of this chapter, selective advantage or fitness is introduced such that the mutant genotype has a higher birth rate or a lower death rate. This selective advantage leads to a dynamical competition in which selection dominates for large populations
Paulo Antonio Delgado-Arredondo
2015-01-01
Full Text Available Induction motors are critical components for most industries and the condition monitoring has become necessary to detect faults. There are several techniques for fault diagnosis of induction motors and analyzing the startup transient vibration signals is not as widely used as other techniques like motor current signature analysis. Vibration analysis gives a fault diagnosis focused on the location of spectral components associated with faults. Therefore, this paper presents a comparative study of different time-frequency analysis methodologies that can be used for detecting faults in induction motors analyzing vibration signals during the startup transient. The studied methodologies are the time-frequency distribution of Gabor (TFDG, the time-frequency Morlet scalogram (TFMS, multiple signal classification (MUSIC, and fast Fourier transform (FFT. The analyzed vibration signals are one broken rotor bar, two broken bars, unbalance, and bearing defects. The obtained results have shown the feasibility of detecting faults in induction motors using the time-frequency spectral analysis applied to vibration signals, and the proposed methodology is applicable when it does not have current signals and only has vibration signals. Also, the methodology has applications in motors that are not fed directly to the supply line, in such cases the analysis of current signals is not recommended due to poor current signal quality.
The Partial Mapping of the Web Graph
Kristina Machova
2009-06-01
Full Text Available The paper presents an approach to partial mapping of a web sub-graph. This sub-graph contains the nearest surroundings of an actual web page. Our work deals with acquiring relevant Hyperlinks of a base web site, generation of adjacency matrix, the nearest distance matrix and matrix of converted distances of Hyperlinks, detection of compactness of web representation, and visualization of its graphical representation. The paper introduces an LWP algorithm – a technique for Hyperlink filtration. This work attempts to help users with the orientation within the web graph.
Adriaan R. Soetevent
2010-01-01
This paper extends Hotelling's model of price competition with quadratic transportation costs from a line to graphs. I propose an algorithm to calculate firm-level demand for any given graph, conditional on prices and firm locations. One feature of graph models of price competition is that spatial discontinuities in firm-level demand may occur. I show that the existence result of D'Aspremont et al. (1979) does not extend to simple star graphs. I conjecture that this non-existence result holds...
Pim Heijnen; Adriaan Soetevent
2014-01-01
This paper extends Hotelling's model of price competition with quadratic transportation costs from a line to graphs. We derive an algorithm to calculate firm-level demand for any given graph, conditional on prices and firm locations. These graph models of price competition may lead to spatial discontinuities in firm-level demand. We show that the existence result of D'Aspremont et al. (1979) does not extend to simple star graphs and conjecture that this non-existence result holds more general...
Aleks Kissinger
2014-03-01
Full Text Available String diagrams are a powerful tool for reasoning about physical processes, logic circuits, tensor networks, and many other compositional structures. Dixon, Duncan and Kissinger introduced string graphs, which are a combinatoric representations of string diagrams, amenable to automated reasoning about diagrammatic theories via graph rewrite systems. In this extended abstract, we show how the power of such rewrite systems can be greatly extended by introducing pattern graphs, which provide a means of expressing infinite families of rewrite rules where certain marked subgraphs, called !-boxes ("bang boxes", on both sides of a rule can be copied any number of times or removed. After reviewing the string graph formalism, we show how string graphs can be extended to pattern graphs and how pattern graphs and pattern rewrite rules can be instantiated to concrete string graphs and rewrite rules. We then provide examples demonstrating the expressive power of pattern graphs and how they can be applied to study interacting algebraic structures that are central to categorical quantum mechanics.
Gelfand, I M; Shnol, E E
1969-01-01
The second in a series of systematic studies by a celebrated mathematician I. M. Gelfand and colleagues, this volume presents students with a well-illustrated sequence of problems and exercises designed to illuminate the properties of functions and graphs. Since readers do not have the benefit of a blackboard on which a teacher constructs a graph, the authors abandoned the customary use of diagrams in which only the final form of the graph appears; instead, the book's margins feature step-by-step diagrams for the complete construction of each graph. The first part of the book employs simple fu
Lothian, Joshua [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Powers, Sarah S. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Sullivan, Blair D. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Baker, Matthew B. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Schrock, Jonathan [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Poole, Stephen W. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
2013-10-01
The benchmarking effort within the Extreme Scale Systems Center at Oak Ridge National Laboratory seeks to provide High Performance Computing benchmarks and test suites of interest to the DoD sponsor. The work described in this report is a part of the effort focusing on graph generation. A previously developed benchmark, SystemBurn, allowed the emulation of different application behavior profiles within a single framework. To complement this effort, similar capabilities are desired for graph-centric problems. This report examines existing synthetic graph generator implementations in preparation for further study on the properties of their generated synthetic graphs.
Mansutti, Alessio; Miculan, Marino; Peressotti, Marco
2017-01-01
We introduce loose graph simulations (LGS), a new notion about labelled graphs which subsumes in an intuitive and natural way subgraph isomorphism (SGI), regular language pattern matching (RLPM) and graph simulation (GS). Being a unification of all these notions, LGS allows us to express directly...... also problems which are “mixed” instances of previous ones, and hence which would not fit easily in any of them. After the definition and some examples, we show that the problem of finding loose graph simulations is NP-complete, we provide formal translation of SGI, RLPM, and GS into LGSs, and we give...
Alberto Apostolico
2009-08-01
Full Text Available The Web Graph is a large-scale graph that does not fit in main memory, so that lossless compression methods have been proposed for it. This paper introduces a compression scheme that combines efficient storage with fast retrieval for the information in a node. The scheme exploits the properties of the Web Graph without assuming an ordering of the URLs, so that it may be applied to more general graphs. Tests on some datasets of use achieve space savings of about 10% over existing methods.
Large-Scale Graph Processing Using Apache Giraph
Sakr, Sherif
2017-01-07
This book takes its reader on a journey through Apache Giraph, a popular distributed graph processing platform designed to bring the power of big data processing to graph data. Designed as a step-by-step self-study guide for everyone interested in large-scale graph processing, it describes the fundamental abstractions of the system, its programming models and various techniques for using the system to process graph data at scale, including the implementation of several popular and advanced graph analytics algorithms.
Large-Scale Graph Processing Using Apache Giraph
Sakr, Sherif; Orakzai, Faisal Moeen; Abdelaziz, Ibrahim; Khayyat, Zuhair
2017-01-01
This book takes its reader on a journey through Apache Giraph, a popular distributed graph processing platform designed to bring the power of big data processing to graph data. Designed as a step-by-step self-study guide for everyone interested in large-scale graph processing, it describes the fundamental abstractions of the system, its programming models and various techniques for using the system to process graph data at scale, including the implementation of several popular and advanced graph analytics algorithms.
The Reduction of Directed Cyclic Graph for Task Assignment Problem
Ariffin W.N.M.
2018-01-01
Full Text Available In this paper, a directed cyclic graph (DCG is proposed as the task graph. It is undesirable and impossible to complete the task according to the constraints if the cycle exists. Therefore, an effort should be done in order to eliminate the cycle to obtain a directed acyclic graph (DAG, so that the minimum amount of time required for the entire task can be found. The technique of reducing the complexity of the directed cyclic graph to a directed acyclic graph by reversing the orientation of the path is the main contribution of this study. The algorithm was coded using Java programming and consistently produced good assignment and task schedule.
Genten: Software for Generalized Tensor Decompositions v. 1.0.0
2017-06-22
Tensors, or multidimensional arrays, are a powerful mathematical means of describing multiway data. This software provides computational means for decomposing or approximating a given tensor in terms of smaller tensors of lower dimension, focusing on decomposition of large, sparse tensors. These techniques have applications in many scientific areas, including signal processing, linear algebra, computer vision, numerical analysis, data mining, graph analysis, neuroscience and more. The software is designed to take advantage of parallelism present emerging computer architectures such has multi-core CPUs, many-core accelerators such as the Intel Xeon Phi, and computation-oriented GPUs to enable efficient processing of large tensors.
Graph Theory. 1. Fragmentation of Structural Graphs
Lorentz JÄNTSCHI
2002-12-01
Full Text Available The investigation of structural graphs has many fields of applications in engineering, especially in applied sciences like as applied chemistry and physics, computer sciences and automation, electronics and telecommunication. The main subject of the paper is to express fragmentation criteria in graph using a new method of investigation: terminal paths. Using terminal paths are defined most of the fragmentation criteria that are in use in molecular topology, but the fields of applications are more generally than that, as I mentioned before. Graphical examples of fragmentation are given for every fragmentation criteria. Note that all fragmentation is made with a computer program that implements a routine for every criterion.[1] A web routine for tracing all terminal paths in graph can be found at the address: http://vl.academicdirect.ro/molecular_topology/tpaths/ [1] M. V. Diudea, I. Gutman, L. Jäntschi, Molecular Topology, Nova Science, Commack, New York, 2001, 2002.
Incremental View Maintenance for Deductive Graph Databases Using Generalized Discrimination Networks
Thomas Beyhl
2016-12-01
Full Text Available Nowadays, graph databases are employed when relationships between entities are in the scope of database queries to avoid performance-critical join operations of relational databases. Graph queries are used to query and modify graphs stored in graph databases. Graph queries employ graph pattern matching that is NP-complete for subgraph isomorphism. Graph database views can be employed that keep ready answers in terms of precalculated graph pattern matches for often stated and complex graph queries to increase query performance. However, such graph database views must be kept consistent with the graphs stored in the graph database. In this paper, we describe how to use incremental graph pattern matching as technique for maintaining graph database views. We present an incremental maintenance algorithm for graph database views, which works for imperatively and declaratively specified graph queries. The evaluation shows that our maintenance algorithm scales when the number of nodes and edges stored in the graph database increases. Furthermore, our evaluation shows that our approach can outperform existing approaches for the incremental maintenance of graph query results.
A graph rewriting programming language for graph drawing
Rodgers, Peter
1998-01-01
This paper describes Grrr, a prototype visual graph drawing tool. Previously there were no visual languages for programming graph drawing algorithms despite the inherently visual nature of the process. The languages which gave a diagrammatic view of graphs were not computationally complete and so could not be used to implement complex graph drawing algorithms. Hence current graph drawing tools are all text based. Recent developments in graph rewriting systems have produced computationally com...
Finding Hierarchical and Overlapping Dense Subgraphs using Nucleus Decompositions
Seshadhri, Comandur [The Ohio State Univ., Columbus, OH (United States); Pinar, Ali [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Sariyuce, Ahmet Erdem [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Catalyurek, Umit [The Ohio State Univ., Columbus, OH (United States)
2014-11-01
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 for 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.
de Mol, M.J.; Rensink, Arend; Hunt, James J.
This paper introduces an approach for adding graph transformation-based functionality to existing JAVA programs. The approach relies on a set of annotations to identify the intended graph structure, as well as on user methods to manipulate that structure, within the user’s own JAVA class
Cohen, A.M.; Beineke, L.W.; Wilson, R.J.; Cameron, P.J.
2004-01-01
In this chapter we investigate the classification of distance-transitive graphs: these are graphs whose automorphism groups are transitive on each of the sets of pairs of vertices at distance i, for i = 0, 1,.... We provide an introduction into the field. By use of the classification of finite
Joyner, W David
2017-01-01
This textbook acts as a pathway to higher mathematics by seeking and illuminating the connections between graph theory and diverse fields of mathematics, such as calculus on manifolds, group theory, algebraic curves, Fourier analysis, cryptography and other areas of combinatorics. An overview of graph theory definitions and polynomial invariants for graphs prepares the reader for the subsequent dive into the applications of graph theory. To pique the reader’s interest in areas of possible exploration, recent results in mathematics appear throughout the book, accompanied with examples of related graphs, how they arise, and what their valuable uses are. The consequences of graph theory covered by the authors are complicated and far-reaching, so topics are always exhibited in a user-friendly manner with copious graphs, exercises, and Sage code for the computation of equations. Samples of the book’s source code can be found at github.com/springer-math/adventures-in-graph-theory. The text is geared towards ad...
Perepelitsa, VA; Sergienko, [No Value; Kochkarov, AM
1999-01-01
Definitions of prefractal and fractal graphs are introduced, and they are used to formulate mathematical models in different fields of knowledge. The topicality of fractal-graph recognition from the point of view, of fundamental improvement in the efficiency of the solution of algorithmic problems
Husfeldt, Thore
2015-01-01
This chapter presents an introduction to graph colouring algorithms. The focus is on vertex-colouring algorithms that work for general classes of graphs with worst-case performance guarantees in a sequential model of computation. The presentation aims to demonstrate the breadth of available...
Packing Degenerate Graphs Greedily
Allen, P.; Böttcher, J.; Hladký, J.; Piguet, Diana
2017-01-01
Roč. 61, August (2017), s. 45-51 ISSN 1571-0653 R&D Projects: GA ČR GJ16-07822Y Institutional support: RVO:67985807 Keywords : tree packing conjecture * graph packing * graph processes Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics
Optimizing graph algorithms on pregel-like systems
Salihoglu, Semih
2014-03-01
We study the problem of implementing graph algorithms efficiently on Pregel-like systems, which can be surprisingly challenging. Standard graph algorithms in this setting can incur unnecessary inefficiencies such as slow convergence or high communication or computation cost, typically due to structural properties of the input graphs such as large diameters or skew in component sizes. We describe several optimization techniques to address these inefficiencies. Our most general technique is based on the idea of performing some serial computation on a tiny fraction of the input graph, complementing Pregel\\'s vertex-centric parallelism. We base our study on thorough implementations of several fundamental graph algorithms, some of which have, to the best of our knowledge, not been implemented on Pregel-like systems before. The algorithms and optimizations we describe are fully implemented in our open-source Pregel implementation. We present detailed experiments showing that our optimization techniques improve runtime significantly on a variety of very large graph datasets.
Autoregressive Moving Average Graph Filtering
Isufi, Elvin; Loukas, Andreas; Simonetto, Andrea; Leus, Geert
2016-01-01
One of the cornerstones of the field of signal processing on graphs are graph filters, direct analogues of classical filters, but intended for signals defined on graphs. This work brings forth new insights on the distributed graph filtering problem. We design a family of autoregressive moving average (ARMA) recursions, which (i) are able to approximate any desired graph frequency response, and (ii) give exact solutions for tasks such as graph signal denoising and interpolation. The design phi...
Subgraph detection using graph signals
Chepuri, Sundeep Prabhakar
2017-03-06
In this paper we develop statistical detection theory for graph signals. In particular, given two graphs, namely, a background graph that represents an usual activity and an alternative graph that represents some unusual activity, we are interested in answering the following question: To which of the two graphs does the observed graph signal fit the best? To begin with, we assume both the graphs are known, and derive an optimal Neyman-Pearson detector. Next, we derive a suboptimal detector for the case when the alternative graph is not known. The developed theory is illustrated with numerical experiments.
Subgraph detection using graph signals
Chepuri, Sundeep Prabhakar; Leus, Geert
2017-01-01
In this paper we develop statistical detection theory for graph signals. In particular, given two graphs, namely, a background graph that represents an usual activity and an alternative graph that represents some unusual activity, we are interested in answering the following question: To which of the two graphs does the observed graph signal fit the best? To begin with, we assume both the graphs are known, and derive an optimal Neyman-Pearson detector. Next, we derive a suboptimal detector for the case when the alternative graph is not known. The developed theory is illustrated with numerical experiments.
Probabilistic Graph Layout for Uncertain Network Visualization.
Schulz, Christoph; Nocaj, Arlind; Goertler, Jochen; Deussen, Oliver; Brandes, Ulrik; Weiskopf, Daniel
2017-01-01
We present a novel uncertain network visualization technique based on node-link diagrams. Nodes expand spatially in our probabilistic graph layout, depending on the underlying probability distributions of edges. The visualization is created by computing a two-dimensional graph embedding that combines samples from the probabilistic graph. A Monte Carlo process is used to decompose a probabilistic graph into its possible instances and to continue with our graph layout technique. Splatting and edge bundling are used to visualize point clouds and network topology. The results provide insights into probability distributions for the entire network-not only for individual nodes and edges. We validate our approach using three data sets that represent a wide range of network types: synthetic data, protein-protein interactions from the STRING database, and travel times extracted from Google Maps. Our approach reveals general limitations of the force-directed layout and allows the user to recognize that some nodes of the graph are at a specific position just by chance.
Bollobas, Bela
2004-01-01
The ever-expanding field of extremal graph theory encompasses a diverse array of problem-solving methods, including applications to economics, computer science, and optimization theory. This volume, based on a series of lectures delivered to graduate students at the University of Cambridge, presents a concise yet comprehensive treatment of extremal graph theory.Unlike most graph theory treatises, this text features complete proofs for almost all of its results. Further insights into theory are provided by the numerous exercises of varying degrees of difficulty that accompany each chapter. A
Multiresolution analysis over graphs for a motor imagery based online BCI game.
Asensio-Cubero, Javier; Gan, John Q; Palaniappan, Ramaswamy
2016-01-01
Multiresolution analysis (MRA) over graph representation of EEG data has proved to be a promising method for offline brain-computer interfacing (BCI) data analysis. For the first time we aim to prove the feasibility of the graph lifting transform in an online BCI system. Instead of developing a pointer device or a wheel-chair controller as test bed for human-machine interaction, we have designed and developed an engaging game which can be controlled by means of imaginary limb movements. Some modifications to the existing MRA analysis over graphs for BCI have also been proposed, such as the use of common spatial patterns for feature extraction at the different levels of decomposition, and sequential floating forward search as a best basis selection technique. In the online game experiment we obtained for three classes an average classification rate of 63.0% for fourteen naive subjects. The application of a best basis selection method helps significantly decrease the computing resources needed. The present study allows us to further understand and assess the benefits of the use of tailored wavelet analysis for processing motor imagery data and contributes to the further development of BCI for gaming purposes. Copyright © 2015 Elsevier Ltd. All rights reserved.
Haynes Teresa W.
2014-08-01
Full Text Available A path π = (v1, v2, . . . , vk+1 in a graph G = (V,E is a downhill path if for every i, 1 ≤ i ≤ k, deg(vi ≥ deg(vi+1, where deg(vi denotes the degree of vertex vi ∈ V. The downhill domination number equals the minimum cardinality of a set S ⊆ V having the property that every vertex v ∈ V lies on a downhill path originating from some vertex in S. We investigate downhill domination numbers of graphs and give upper bounds. In particular, we show that the downhill domination number of a graph is at most half its order, and that the downhill domination number of a tree is at most one third its order. We characterize the graphs obtaining each of these bounds
Tailored Random Graph Ensembles
Roberts, E S; Annibale, A; Coolen, A C C
2013-01-01
Tailored graph ensembles are a developing bridge between biological networks and statistical mechanics. The aim is to use this concept to generate a suite of rigorous tools that can be used to quantify and compare the topology of cellular signalling networks, such as protein-protein interaction networks and gene regulation networks. We calculate exact and explicit formulae for the leading orders in the system size of the Shannon entropies of random graph ensembles constrained with degree distribution and degree-degree correlation. We also construct an ergodic detailed balance Markov chain with non-trivial acceptance probabilities which converges to a strictly uniform measure and is based on edge swaps that conserve all degrees. The acceptance probabilities can be generalized to define Markov chains that target any alternative desired measure on the space of directed or undirected graphs, in order to generate graphs with more sophisticated topological features.
Alspach, BR
1985-01-01
This volume deals with a variety of problems involving cycles in graphs and circuits in digraphs. Leading researchers in this area present here 3 survey papers and 42 papers containing new results. There is also a collection of unsolved problems.
Wilson, Robin J
1985-01-01
Graph Theory has recently emerged as a subject in its own right, as well as being an important mathematical tool in such diverse subjects as operational research, chemistry, sociology and genetics. This book provides a comprehensive introduction to the subject.
Hyperbolicity in median graphs
mic problems in hyperbolic spaces and hyperbolic graphs have been .... that in general the main obstacle is that we do not know the location of ...... [25] Jonckheere E and Lohsoonthorn P, A hyperbolic geometry approach to multipath routing,.
Uniform Single Valued Neutrosophic Graphs
S. Broumi
2017-09-01
Full Text Available In this paper, we propose a new concept named the uniform single valued neutrosophic graph. An illustrative example and some properties are examined. Next, we develop an algorithmic approach for computing the complement of the single valued neutrosophic graph. A numerical example is demonstrated for computing the complement of single valued neutrosophic graphs and uniform single valued neutrosophic graph.
Collective Rationality in Graph Aggregation
Endriss, U.; Grandi, U.; Schaub, T.; Friedrich, G.; O'Sullivan, B.
2014-01-01
Suppose a number of agents each provide us with a directed graph over a common set of vertices. Graph aggregation is the problem of computing a single “collective” graph that best represents the information inherent in this profile of individual graphs. We consider this aggregation problem from the
Barra, F.; Gaspard, P.
2001-01-01
We consider the classical evolution of a particle on a graph by using a time-continuous Frobenius-Perron operator that generalizes previous propositions. In this way, the relaxation rates as well as the chaotic properties can be defined for the time-continuous classical dynamics on graphs. These properties are given as the zeros of some periodic-orbit zeta functions. We consider in detail the case of infinite periodic graphs where the particle undergoes a diffusion process. The infinite spatial extension is taken into account by Fourier transforms that decompose the observables and probability densities into sectors corresponding to different values of the wave number. The hydrodynamic modes of diffusion are studied by an eigenvalue problem of a Frobenius-Perron operator corresponding to a given sector. The diffusion coefficient is obtained from the hydrodynamic modes of diffusion and has the Green-Kubo form. Moreover, we study finite but large open graphs that converge to the infinite periodic graph when their size goes to infinity. The lifetime of the particle on the open graph is shown to correspond to the lifetime of a system that undergoes a diffusion process before it escapes
Bollobás, Béla
1998-01-01
The time has now come when graph theory should be part of the education of every serious student of mathematics and computer science, both for its own sake and to enhance the appreciation of mathematics as a whole. This book is an in-depth account of graph theory, written with such a student in mind; it reflects the current state of the subject and emphasizes connections with other branches of pure mathematics. The volume grew out of the author's earlier book, Graph Theory -- An Introductory Course, but its length is well over twice that of its predecessor, allowing it to reveal many exciting new developments in the subject. Recognizing that graph theory is one of several courses competing for the attention of a student, the book contains extensive descriptive passages designed to convey the flavor of the subject and to arouse interest. In addition to a modern treatment of the classical areas of graph theory such as coloring, matching, extremal theory, and algebraic graph theory, the book presents a detailed ...
Quantum complexity of graph and algebraic problems
Doern, Sebastian
2008-01-01
This thesis is organized as follows: In Chapter 2 we give some basic notations, definitions and facts from linear algebra, graph theory, group theory and quantum computation. In Chapter 3 we describe three important methods for the construction of quantum algorithms. We present the quantum search algorithm by Grover, the quantum amplitude amplification and the quantum walk search technique by Magniez et al. These three tools are the basis for the development of our new quantum algorithms for graph and algebra problems. In Chapter 4 we present two tools for proving quantum query lower bounds. We present the quantum adversary method by Ambainis and the polynomial method introduced by Beals et al. The quantum adversary tool is very useful to prove good lower bounds for many graph and algebra problems. The part of the thesis containing the original results is organized in two parts. In the first part we consider the graph problems. In Chapter 5 we give a short summary of known quantum graph algorithms. In Chapter 6 to 8 we study the complexity of our new algorithms for matching problems, graph traversal and independent set problems on quantum computers. In the second part of our thesis we present new quantum algorithms for algebraic problems. In Chapter 9 to 10 we consider group testing problems and prove quantum complexity bounds for important problems from linear algebra. (orig.)
Quantum complexity of graph and algebraic problems
Doern, Sebastian
2008-02-04
This thesis is organized as follows: In Chapter 2 we give some basic notations, definitions and facts from linear algebra, graph theory, group theory and quantum computation. In Chapter 3 we describe three important methods for the construction of quantum algorithms. We present the quantum search algorithm by Grover, the quantum amplitude amplification and the quantum walk search technique by Magniez et al. These three tools are the basis for the development of our new quantum algorithms for graph and algebra problems. In Chapter 4 we present two tools for proving quantum query lower bounds. We present the quantum adversary method by Ambainis and the polynomial method introduced by Beals et al. The quantum adversary tool is very useful to prove good lower bounds for many graph and algebra problems. The part of the thesis containing the original results is organized in two parts. In the first part we consider the graph problems. In Chapter 5 we give a short summary of known quantum graph algorithms. In Chapter 6 to 8 we study the complexity of our new algorithms for matching problems, graph traversal and independent set problems on quantum computers. In the second part of our thesis we present new quantum algorithms for algebraic problems. In Chapter 9 to 10 we consider group testing problems and prove quantum complexity bounds for important problems from linear algebra. (orig.)
Profiling Smart Contracts Interactions with Tensor Decomposition and Graph Mining
Charlier , Jérémy; Lagraa , Sofiane; State , Radu; Francois , Jerome
2017-01-01
International audience; Smart contracts, computer protocols designed for autonomous execution on predefined conditions, arise from the evolution of the Bit-coin's crypto-currency. They provide higher transaction security and allow economy of scale through the automated process. Smart contracts provides inherent benefits for financial institutions such as investment banking, retail banking, and insurance. This technology is widely used within Ethereum, an open source block-chain platform, from...
Searches over graphs representing geospatial-temporal remote sensing data
Brost, Randolph; Perkins, David Nikolaus
2018-03-06
Various technologies pertaining to identifying objects of interest in remote sensing images by searching over geospatial-temporal graph representations are described herein. Graphs are constructed by representing objects in remote sensing images as nodes, and connecting nodes with undirected edges representing either distance or adjacency relationships between objects and directed edges representing changes in time. Geospatial-temporal graph searches are made computationally efficient by taking advantage of characteristics of geospatial-temporal data in remote sensing images through the application of various graph search techniques.
Graph-based clustering and data visualization algorithms
Vathy-Fogarassy, Ágnes
2013-01-01
This work presents a data visualization technique that combines graph-based topology representation and dimensionality reduction methods to visualize the intrinsic data structure in a low-dimensional vector space. The application of graphs in clustering and visualization has several advantages. A graph of important edges (where edges characterize relations and weights represent similarities or distances) provides a compact representation of the entire complex data set. This text describes clustering and visualization methods that are able to utilize information hidden in these graphs, based on
Decomposition of Multi-player Games
Zhao, Dengji; Schiffel, Stephan; Thielscher, Michael
Research in General Game Playing aims at building systems that learn to play unknown games without human intervention. We contribute to this endeavour by generalising the established technique of decomposition from AI Planning to multi-player games. To this end, we present a method for the automatic decomposition of previously unknown games into independent subgames, and we show how a general game player can exploit a successful decomposition for game tree search.
On some covering graphs of a graph
Shariefuddin Pirzada
2016-10-01
Full Text Available For a graph $G$ with vertex set $V(G=\\{v_1, v_2, \\dots, v_n\\}$, let $S$ be the covering set of $G$ having the maximum degree over all the minimum covering sets of $G$. Let $N_S[v]=\\{u\\in S : uv \\in E(G \\}\\cup \\{v\\}$ be the closed neighbourhood of the vertex $v$ with respect to $S.$ We define a square matrix $A_S(G= (a_{ij},$ by $a_{ij}=1,$ if $\\left |N_S[v_i]\\cap N_S[v_j] \\right| \\geq 1, i\
Laplacian Estrada and normalized Laplacian Estrada indices of evolving graphs.
Yilun Shang
Full Text Available 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.
Laplacian Estrada and normalized Laplacian Estrada indices of evolving graphs.
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.
Dense graph limits under respondent-driven sampling
Siva Athreya
Types of network. Food. Political. Social. Linkedin. Protien. Professional. Source: IUPUI Network Sampling course. Page 3. Techniques to Analyse Networks. Network Characteristics: • Distribution: degree, clustering coefficient, hop-plot. ... Hypothesis Testing: H0: Graph is a linkedin network. H1: Graph is a facebook network ...
Decomposing highly edge-connected graphs into homomorphic copies of a fixed tree
Merker, Martin
2016-01-01
far this conjecture has only been verified for paths, stars, and a family of bistars. We prove a weaker version of the Tree Decomposition Conjecture, where we require the subgraphs in the decomposition to be isomorphic to graphs that can be obtained from T by vertex-identifications. We call......The Tree Decomposition Conjecture by Barát and Thomassen states that for every tree T there exists a natural number k(T) such that the following holds: If G is a k(T)-edge-connected simple graph with size divisible by the size of T, then G can be edge-decomposed into subgraphs isomorphic to T. So...... such a subgraph a homomorphic copy of T. This implies the Tree Decomposition Conjecture under the additional constraint that the girth of G is greater than the diameter of T. As an application, we verify the Tree Decomposition Conjecture for all trees of diameter at most 4....
Incremental Frequent Subgraph Mining on Large Evolving Graphs
Abdelhamid, Ehab
2017-08-22
Frequent subgraph mining is a core graph operation used in many domains, such as graph data management and knowledge exploration, bioinformatics and security. Most existing techniques target static graphs. However, modern applications, such as social networks, utilize large evolving graphs. Mining these graphs using existing techniques is infeasible, due to the high computational cost. In this paper, we propose IncGM+, a fast incremental approach for continuous frequent subgraph mining problem on a single large evolving graph. We adapt the notion of “fringe” to the graph context, that is the set of subgraphs on the border between frequent and infrequent subgraphs. IncGM+ maintains fringe subgraphs and exploits them to prune the search space. To boost the efficiency, we propose an efficient index structure to maintain selected embeddings with minimal memory overhead. These embeddings are utilized to avoid redundant expensive subgraph isomorphism operations. Moreover, the proposed system supports batch updates. Using large real-world graphs, we experimentally verify that IncGM+ outperforms existing methods by up to three orders of magnitude, scales to much larger graphs and consumes less memory.
The STAPL Parallel Graph Library
Harshvardhan,
2013-01-01
This paper describes the stapl Parallel Graph Library, a high-level framework that abstracts the user from data-distribution and parallelism details and allows them to concentrate on parallel graph algorithm development. It includes a customizable distributed graph container and a collection of commonly used parallel graph algorithms. The library introduces pGraph pViews that separate algorithm design from the container implementation. It supports three graph processing algorithmic paradigms, level-synchronous, asynchronous and coarse-grained, and provides common graph algorithms based on them. Experimental results demonstrate improved scalability in performance and data size over existing graph libraries on more than 16,000 cores and on internet-scale graphs containing over 16 billion vertices and 250 billion edges. © Springer-Verlag Berlin Heidelberg 2013.
White, AT
1985-01-01
The field of topological graph theory has expanded greatly in the ten years since the first edition of this book appeared. The original nine chapters of this classic work have therefore been revised and updated. Six new chapters have been added, dealing with: voltage graphs, non-orientable imbeddings, block designs associated with graph imbeddings, hypergraph imbeddings, map automorphism groups and change ringing.Thirty-two new problems have been added to this new edition, so that there are now 181 in all; 22 of these have been designated as ``difficult'''' and 9 as ``unsolved''''. Three of the four unsolved problems from the first edition have been solved in the ten years between editions; they are now marked as ``difficult''''.
Ribes, Luis
2017-01-01
This book offers a detailed introduction to graph theoretic methods in profinite groups and applications to abstract groups. It is the first to provide a comprehensive treatment of the subject. The author begins by carefully developing relevant notions in topology, profinite groups and homology, including free products of profinite groups, cohomological methods in profinite groups, and fixed points of automorphisms of free pro-p groups. The final part of the book is dedicated to applications of the profinite theory to abstract groups, with sections on finitely generated subgroups of free groups, separability conditions in free and amalgamated products, and algorithms in free groups and finite monoids. Profinite Graphs and Groups will appeal to students and researchers interested in profinite groups, geometric group theory, graphs and connections with the theory of formal languages. A complete reference on the subject, the book includes historical and bibliographical notes as well as a discussion of open quest...
Subdominant pseudoultrametric on graphs
Dovgoshei, A A; Petrov, E A [Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, Donetsk (Ukraine)
2013-08-31
Let (G,w) be a weighted graph. We find necessary and sufficient conditions under which the weight w:E(G)→R{sup +} can be extended to a pseudoultrametric on V(G), and establish a criterion for the uniqueness of such an extension. We demonstrate that (G,w) is a complete k-partite graph, for k≥2, if and only if for any weight that can be extended to a pseudoultrametric, among all such extensions one can find the least pseudoultrametric consistent with w. We give a structural characterization of graphs for which the subdominant pseudoultrametric is an ultrametric for any strictly positive weight that can be extended to a pseudoultrametric. Bibliography: 14 titles.
Graph mining for next generation sequencing: leveraging the assembly graph for biological insights.
Warnke-Sommer, Julia; Ali, Hesham
2016-05-06
The assembly of Next Generation Sequencing (NGS) reads remains a challenging task. This is especially true for the assembly of metagenomics data that originate from environmental samples potentially containing hundreds to thousands of unique species. The principle objective of current assembly tools is to assemble NGS reads into contiguous stretches of sequence called contigs while maximizing for both accuracy and contig length. The end goal of this process is to produce longer contigs with the major focus being on assembly only. Sequence read assembly is an aggregative process, during which read overlap relationship information is lost as reads are merged into longer sequences or contigs. The assembly graph is information rich and capable of capturing the genomic architecture of an input read data set. We have developed a novel hybrid graph in which nodes represent sequence regions at different levels of granularity. This model, utilized in the assembly and analysis pipeline Focus, presents a concise yet feature rich view of a given input data set, allowing for the extraction of biologically relevant graph structures for graph mining purposes. Focus was used to create hybrid graphs to model metagenomics data sets obtained from the gut microbiomes of five individuals with Crohn's disease and eight healthy individuals. Repetitive and mobile genetic elements are found to be associated with hybrid graph structure. Using graph mining techniques, a comparative study of the Crohn's disease and healthy data sets was conducted with focus on antibiotics resistance genes associated with transposase genes. Results demonstrated significant differences in the phylogenetic distribution of categories of antibiotics resistance genes in the healthy and diseased patients. Focus was also evaluated as a pure assembly tool and produced excellent results when compared against the Meta-velvet, Omega, and UD-IDBA assemblers. Mining the hybrid graph can reveal biological phenomena captured
Kim, Eng-Chan; Cho, Jae-Hwan; Kim, Min-Hye; Kim, Ki-Hong; Choi, Cheon-Woong; Seok, Jong-min; Na, Kil-Ju; Han, Man-Seok
2013-03-01
This study was conducted on 20 patients who had undergone pedicle screw fixation between March and December 2010 to quantitatively compare a conventional fat suppression technique, CHESS (chemical shift selection suppression), and a new technique, IDEAL (iterative decomposition of water and fat with echo asymmetry and least squares estimation). The general efficacy and usefulness of the IDEAL technique was also evaluated. Fat-suppressed transverse-relaxation-weighed images and longitudinal-relaxation-weighted images were obtained before and after contrast injection by using these two techniques with a 1.5T MR (magnetic resonance) scanner. The obtained images were analyzed for image distortion, susceptibility artifacts and homogenous fat removal in the target region. The results showed that the image distortion due to the susceptibility artifacts caused by implanted metal was lower in the images obtained using the IDEAL technique compared to those obtained using the CHESS technique. The results of a qualitative analysis also showed that compared to the CHESS technique, fewer susceptibility artifacts and more homogenous fat removal were found in the images obtained using the IDEAL technique in a comparative image evaluation of the axial plane images before and after contrast injection. In summary, compared to the CHESS technique, the IDEAL technique showed a lower occurrence of susceptibility artifacts caused by metal and lower image distortion. In addition, more homogenous fat removal was shown in the IDEAL technique.
Cheung, King Sing
2014-01-01
Petri nets are a formal and theoretically rich model for the modelling and analysis of systems. A subclass of Petri nets, augmented marked graphs possess a structure that is especially desirable for the modelling and analysis of systems with concurrent processes and shared resources.This monograph consists of three parts: Part I provides the conceptual background for readers who have no prior knowledge on Petri nets; Part II elaborates the theory of augmented marked graphs; finally, Part III discusses the application to system integration. The book is suitable as a first self-contained volume
Dayal, Amit; Brock, David
2018-01-01
Prashant Chandrasekar, a lead developer for the Social Interactome project, has tasked the team with creating a graph representation of the data collected from the social networks involved in that project. The data is currently stored in a MySQL database. The client requested that the graph database be Cayley, but after a literature review, Neo4j was chosen. The reasons for this shift will be explained in the design section. Secondarily, the team was tasked with coming up with three scena...
Thematization of the Calculus Graphing Schema
Cooley, Laurel; Baker, Bernadette; Trigueros, Maria
2003-01-01
This article is the result of an investigation of students' conceptualizations of calculus graphing techniques after they had completed at least two semesters of calculus. The work and responses of 27 students to a series of questions that solicit information about the graphical implications of the first derivative, second derivative, continuity,…
Graph embedding with rich information through heterogeneous graph
Sun, Guolei
2017-01-01
Graph embedding, aiming to learn low-dimensional representations for nodes in graphs, has attracted increasing attention due to its critical application including node classification, link prediction and clustering in social network analysis. Most
Using Graph and Vertex Entropy to Compare Empirical Graphs with Theoretical Graph Models
Tomasz Kajdanowicz
2016-09-01
Full Text Available Over the years, several theoretical graph generation models have been proposed. Among the most prominent are: the Erdős–Renyi random graph model, Watts–Strogatz small world model, Albert–Barabási preferential attachment model, Price citation model, and many more. Often, researchers working with real-world data are interested in understanding the generative phenomena underlying their empirical graphs. They want to know which of the theoretical graph generation models would most probably generate a particular empirical graph. In other words, they expect some similarity assessment between the empirical graph and graphs artificially created from theoretical graph generation models. Usually, in order to assess the similarity of two graphs, centrality measure distributions are compared. For a theoretical graph model this means comparing the empirical graph to a single realization of a theoretical graph model, where the realization is generated from the given model using an arbitrary set of parameters. The similarity between centrality measure distributions can be measured using standard statistical tests, e.g., the Kolmogorov–Smirnov test of distances between cumulative distributions. However, this approach is both error-prone and leads to incorrect conclusions, as we show in our experiments. Therefore, we propose a new method for graph comparison and type classification by comparing the entropies of centrality measure distributions (degree centrality, betweenness centrality, closeness centrality. We demonstrate that our approach can help assign the empirical graph to the most similar theoretical model using a simple unsupervised learning method.
Handbook of graph grammars and computing by graph transformation
Engels, G; Kreowski, H J; Rozenberg, G
1999-01-01
Graph grammars originated in the late 60s, motivated by considerations about pattern recognition and compiler construction. Since then, the list of areas which have interacted with the development of graph grammars has grown quite impressively. Besides the aforementioned areas, it includes software specification and development, VLSI layout schemes, database design, modeling of concurrent systems, massively parallel computer architectures, logic programming, computer animation, developmental biology, music composition, visual languages, and many others.The area of graph grammars and graph tran
Topics in graph theory graphs and their Cartesian product
Imrich, Wilfried; Rall, Douglas F
2008-01-01
From specialists in the field, you will learn about interesting connections and recent developments in the field of graph theory by looking in particular at Cartesian products-arguably the most important of the four standard graph products. Many new results in this area appear for the first time in print in this book. Written in an accessible way, this book can be used for personal study in advanced applications of graph theory or for an advanced graph theory course.
Nutrient Dynamics and Litter Decomposition in Leucaena ...
Nutrient contents and rate of litter decomposition were investigated in Leucaena leucocephala plantation in the University of Agriculture, Abeokuta, Ogun State, Nigeria. Litter bag technique was used to study the pattern and rate of litter decomposition and nutrient release of Leucaena leucocephala. Fifty grams of oven-dried ...
Bisseling, R.H.; Byrka, J.; Cerav-Erbas, S.; Gvozdenovic, N.; Lorenz, M.; Pendavingh, R.A.; Reeves, C.; Röger, M.; Verhoeven, A.; Berg, van den J.B.; Bhulai, S.; Hulshof, J.; Koole, G.; Quant, C.; Williams, J.F.
2006-01-01
Splitting a large software system into smaller and more manageable units has become an important problem for many organizations. The basic structure of a software system is given by a directed graph with vertices representing the programs of the system and arcs representing calls from one program to
Coloring geographical threshold graphs
Bradonjic, Milan [Los Alamos National Laboratory; Percus, Allon [Los Alamos National Laboratory; Muller, Tobias [EINDHOVEN UNIV. OF TECH
2008-01-01
We propose a coloring algorithm for sparse random graphs generated by the geographical threshold graph (GTG) model, a generalization of random geometric graphs (RGG). In a GTG, nodes are distributed in a Euclidean space, and edges are assigned according to a threshold function involving the distance between nodes as well as randomly chosen node weights. The motivation for analyzing this model is that many real networks (e.g., wireless networks, the Internet, etc.) need to be studied by using a 'richer' stochastic model (which in this case includes both a distance between nodes and weights on the nodes). Here, we analyze the GTG coloring algorithm together with the graph's clique number, showing formally that in spite of the differences in structure between GTG and RGG, the asymptotic behavior of the chromatic number is identical: {chi}1n 1n n / 1n n (1 + {omicron}(1)). Finally, we consider the leading corrections to this expression, again using the coloring algorithm and clique number to provide bounds on the chromatic number. We show that the gap between the lower and upper bound is within C 1n n / (1n 1n n){sup 2}, and specify the constant C.
Budhiraja, A.S.; Mukherjee, D.; Wu, R.
2017-01-01
We consider a variation of the supermarket model in which the servers can communicate with their neighbors and where the neighborhood relationships are described in terms of a suitable graph. Tasks with unit-exponential service time distributions arrive at each vertex as independent Poisson
Kucharik, Marcel; Hofacker, Ivo; Stadler, Peter
2014-01-01
of the folding free energy landscape, however, can provide the relevant information. Results We introduce the basin hopping graph (BHG) as a novel coarse-grained model of folding landscapes. Each vertex of the BHG is a local minimum, which represents the corresponding basin in the landscape. Its edges connect...
System dynamics and control with bond graph modeling
Kypuros, Javier
2013-01-01
Part I Dynamic System ModelingIntroduction to System DynamicsIntroductionSystem Decomposition and Model ComplexityMathematical Modeling of Dynamic SystemsAnalysis and Design of Dynamic SystemsControl of Dynamic SystemsDiagrams of Dynamic SystemsA Graph-Centered Approach to ModelingSummaryPracticeExercisesBasic Bond Graph ElementsIntroductionPower and Energy VariablesBasic 1-Port ElementsBasic 2-Ports ElementsJunction ElementsSimple Bond Graph ExamplesSummaryPracticeExercisesBond Graph Synthesis and Equation DerivationIntroductionGeneral GuidelinesMechanical TranslationMechanical RotationElectrical CircuitsHydraulic CircuitsMixed SystemsState Equation DerivationState-Space RepresentationsAlgebraic Loops and Derivative CausalitySummaryPracticeExercisesImpedance Bond GraphsIntroductionLaplace Transform of the State-Space EquationBasic 1-Port ImpedancesImpedance Bond Graph SynthesisJunctions, Transformers, and GyratorsEffort and Flow DividersSign ChangesTransfer Function DerivationAlternative Derivation of Transf...
A graph algebra for scalable visual analytics.
Shaverdian, Anna A; Zhou, Hao; Michailidis, George; Jagadish, Hosagrahar V
2012-01-01
Visual analytics (VA), which combines analytical techniques with advanced visualization features, is fast becoming a standard tool for extracting information from graph data. Researchers have developed many tools for this purpose, suggesting a need for formal methods to guide these tools' creation. Increased data demands on computing requires redesigning VA tools to consider performance and reliability in the context of analysis of exascale datasets. Furthermore, visual analysts need a way to document their analyses for reuse and results justification. A VA graph framework encapsulated in a graph algebra helps address these needs. Its atomic operators include selection and aggregation. The framework employs a visual operator and supports dynamic attributes of data to enable scalable visual exploration of data.
The STAPL Parallel Graph Library
Harshvardhan,; Fidel, Adam; Amato, Nancy M.; Rauchwerger, Lawrence
2013-01-01
This paper describes the stapl Parallel Graph Library, a high-level framework that abstracts the user from data-distribution and parallelism details and allows them to concentrate on parallel graph algorithm development. It includes a customizable
Towards Scalable Graph Computation on Mobile Devices.
Chen, Yiqi; Lin, Zhiyuan; Pienta, Robert; Kahng, Minsuk; Chau, Duen Horng
2014-10-01
Mobile devices have become increasingly central to our everyday activities, due to their portability, multi-touch capabilities, and ever-improving computational power. Such attractive features have spurred research interest in leveraging mobile devices for computation. We explore a novel approach that aims to use a single mobile device to perform scalable graph computation on large graphs that do not fit in the device's limited main memory, opening up the possibility of performing on-device analysis of large datasets, without relying on the cloud. Based on the familiar memory mapping capability provided by today's mobile operating systems, our approach to scale up computation is powerful and intentionally kept simple to maximize its applicability across the iOS and Android platforms. Our experiments demonstrate that an iPad mini can perform fast computation on large real graphs with as many as 272 million edges (Google+ social graph), at a speed that is only a few times slower than a 13″ Macbook Pro. Through creating a real world iOS app with this technique, we demonstrate the strong potential application for scalable graph computation on a single mobile device using our approach.
Towards Scalable Graph Computation on Mobile Devices
Chen, Yiqi; Lin, Zhiyuan; Pienta, Robert; Kahng, Minsuk; Chau, Duen Horng
2015-01-01
Mobile devices have become increasingly central to our everyday activities, due to their portability, multi-touch capabilities, and ever-improving computational power. Such attractive features have spurred research interest in leveraging mobile devices for computation. We explore a novel approach that aims to use a single mobile device to perform scalable graph computation on large graphs that do not fit in the device's limited main memory, opening up the possibility of performing on-device analysis of large datasets, without relying on the cloud. Based on the familiar memory mapping capability provided by today's mobile operating systems, our approach to scale up computation is powerful and intentionally kept simple to maximize its applicability across the iOS and Android platforms. Our experiments demonstrate that an iPad mini can perform fast computation on large real graphs with as many as 272 million edges (Google+ social graph), at a speed that is only a few times slower than a 13″ Macbook Pro. Through creating a real world iOS app with this technique, we demonstrate the strong potential application for scalable graph computation on a single mobile device using our approach. PMID:25859564
Groupies in multitype random graphs
Shang, Yilun
2016-01-01
A groupie in a graph is a vertex whose degree is not less than the average degree of its neighbors. Under some mild conditions, we show that the proportion of groupies is very close to 1/2 in multitype random graphs (such as stochastic block models), which include Erd?s-R?nyi random graphs, random bipartite, and multipartite graphs as special examples. Numerical examples are provided to illustrate the theoretical results.
Groupies in multitype random graphs.
Shang, Yilun
2016-01-01
A groupie in a graph is a vertex whose degree is not less than the average degree of its neighbors. Under some mild conditions, we show that the proportion of groupies is very close to 1/2 in multitype random graphs (such as stochastic block models), which include Erdős-Rényi random graphs, random bipartite, and multipartite graphs as special examples. Numerical examples are provided to illustrate the theoretical results.
Temporal Representation in Semantic Graphs
Levandoski, J J; Abdulla, G M
2007-08-07
A wide range of knowledge discovery and analysis applications, ranging from business to biological, make use of semantic graphs when modeling relationships and concepts. Most of the semantic graphs used in these applications are assumed to be static pieces of information, meaning temporal evolution of concepts and relationships are not taken into account. Guided by the need for more advanced semantic graph queries involving temporal concepts, this paper surveys the existing work involving temporal representations in semantic graphs.
Quantum walks on quotient graphs
Krovi, Hari; Brun, Todd A.
2007-01-01
A discrete-time quantum walk on a graph Γ is the repeated application of a unitary evolution operator to a Hilbert space corresponding to the graph. If this unitary evolution operator has an associated group of symmetries, then for certain initial states the walk will be confined to a subspace of the original Hilbert space. Symmetries of the original graph, given by its automorphism group, can be inherited by the evolution operator. We show that a quantum walk confined to the subspace corresponding to this symmetry group can be seen as a different quantum walk on a smaller quotient graph. We give an explicit construction of the quotient graph for any subgroup H of the automorphism group and illustrate it with examples. The automorphisms of the quotient graph which are inherited from the original graph are the original automorphism group modulo the subgroup H used to construct it. The quotient graph is constructed by removing the symmetries of the subgroup H from the original graph. We then analyze the behavior of hitting times on quotient graphs. Hitting time is the average time it takes a walk to reach a given final vertex from a given initial vertex. It has been shown in earlier work [Phys. Rev. A 74, 042334 (2006)] that the hitting time for certain initial states of a quantum walks can be infinite, in contrast to classical random walks. We give a condition which determines whether the quotient graph has infinite hitting times given that they exist in the original graph. We apply this condition for the examples discussed and determine which quotient graphs have infinite hitting times. All known examples of quantum walks with hitting times which are short compared to classical random walks correspond to systems with quotient graphs much smaller than the original graph; we conjecture that the existence of a small quotient graph with finite hitting times is necessary for a walk to exhibit a quantum speedup
Pattern analysis of directed graphs using DEDICOM: an application to Enron email.
Bader, Brett William; Harshman, Richard A. (University of Western Ontario London, Ontario, Canada); Kolda, Tamara Gibson (Sandia National Labs, Livermore, CA)
2006-12-01
DEDICOM is a linear algebra model for analyzing intrinsically asymmetric relationships, such as trade among nations or the exchange of emails among individuals. DEDICOM decomposes a complex pattern of observed relations among objects into a sum of simpler patterns of inferred relations among latent components of the objects. Three-way DEDICOM is a higher-order extension of the model that incorporates a third mode of the data, such as time, giving it stronger uniqueness properties and consequently enhancing interpretability of solutions. In this paper, we present algorithms for computing these decompositions on large, sparse data as well as a variant for computing an asymmetric nonnegative factorization. When we apply these techniques to adjacency arrays arising from directed graphs with edges labeled by time, we obtain a smaller graph on latent semantic dimensions and gain additional information about their changing relationships over time. We demonstrate these techniques on the Enron email corpus to learn about the social networks and their transient behavior. The mixture of roles assigned to individuals by DEDICOM showed strong correspondence with known job classifications and revealed the patterns of communication between these roles. Changes in the communication pattern over time, e.g., between top executives and the legal department, were also apparent in the solutions.
Multi-rate equivalents of cyclo-static synchronous dataflow graphs
de Groote, Robert; Holzenspies, P.K.F.; Kuper, Jan; Smit, Gerardus Johannes Maria
In this paper, we present a transformation that takes a cyclo-static dataflow (CSDF) graph and produces an equivalent multi-rate synchronous dataflow (MRSDF) graph. This fills a gap in existing analysis techniques for synchronous dataflow graphs; transformations into equivalent homogeneous
A generalization of total graphs
M Afkhami
2018-04-12
Apr 12, 2018 ... product of any lower triangular matrix with the transpose of any element of U belongs to U. The ... total graph of R, which is denoted by T( (R)), is a simple graph with all elements of R as vertices, and ...... [9] Badawi A, On dot-product graph of a commutative ring, Communications in Algebra 43 (2015). 43–50.
Graph transformation tool contest 2008
Rensink, Arend; van Gorp, Pieter
This special section is the outcome of the graph transformation tool contest organised during the Graph-Based Tools (GraBaTs) 2008 workshop, which took place as a satellite event of the International Conference on Graph Transformation (ICGT) 2008. The contest involved two parts: three “off-line case
On dominator colorings in graphs
colors required for a dominator coloring of G is called the dominator .... Theorem 1.3 shows that the complete graph Kn is the only connected graph of order n ... Conversely, if a graph G satisfies condition (i) or (ii), it is easy to see that χd(G) =.
Xuan, Junyu; Lu, Jie; Zhang, Guangquan; Luo, Xiangfeng
2015-12-01
Graph mining has been a popular research area because of its numerous application scenarios. Many unstructured and structured data can be represented as graphs, such as, documents, chemical molecular structures, and images. However, an issue in relation to current research on graphs is that they cannot adequately discover the topics hidden in graph-structured data which can be beneficial for both the unsupervised learning and supervised learning of the graphs. Although topic models have proved to be very successful in discovering latent topics, the standard topic models cannot be directly applied to graph-structured data due to the "bag-of-word" assumption. In this paper, an innovative graph topic model (GTM) is proposed to address this issue, which uses Bernoulli distributions to model the edges between nodes in a graph. It can, therefore, make the edges in a graph contribute to latent topic discovery and further improve the accuracy of the supervised and unsupervised learning of graphs. The experimental results on two different types of graph datasets show that the proposed GTM outperforms the latent Dirichlet allocation on classification by using the unveiled topics of these two models to represent graphs.
Multilinear Graph Embedding: Representation and Regularization for Images.
Chen, Yi-Lei; Hsu, Chiou-Ting
2014-02-01
Given a set of images, finding a compact and discriminative representation is still a big challenge especially when multiple latent factors are hidden in the way of data generation. To represent multifactor images, although multilinear models are widely used to parameterize the data, most methods are based on high-order singular value decomposition (HOSVD), which preserves global statistics but interprets local variations inadequately. To this end, we propose a novel method, called multilinear graph embedding (MGE), as well as its kernelization MKGE to leverage the manifold learning techniques into multilinear models. Our method theoretically links the linear, nonlinear, and multilinear dimensionality reduction. We also show that the supervised MGE encodes informative image priors for image regularization, provided that an image is represented as a high-order tensor. From our experiments on face and gait recognition, the superior performance demonstrates that MGE better represents multifactor images than classic methods, including HOSVD and its variants. In addition, the significant improvement in image (or tensor) completion validates the potential of MGE for image regularization.
Algorithms for Planar Graphs and Graphs in Metric Spaces
Wulff-Nilsen, Christian
structural properties that can be exploited. For instance, a road network or a wire layout on a microchip is typically (near-)planar and distances in the network are often defined w.r.t. the Euclidean or the rectilinear metric. Specialized algorithms that take advantage of such properties are often orders...... of magnitude faster than the corresponding algorithms for general graphs. The first and main part of this thesis focuses on the development of efficient planar graph algorithms. The most important contributions include a faster single-source shortest path algorithm, a distance oracle with subquadratic...... for geometric graphs and graphs embedded in metric spaces. Roughly speaking, the stretch factor is a real value expressing how well a (geo-)metric graph approximates the underlying complete graph w.r.t. distances. We give improved algorithms for computing the stretch factor of a given graph and for augmenting...
Harary, Frank
2015-01-01
Presented in 1962-63 by experts at University College, London, these lectures offer a variety of perspectives on graph theory. Although the opening chapters form a coherent body of graph theoretic concepts, this volume is not a text on the subject but rather an introduction to the extensive literature of graph theory. The seminar's topics are geared toward advanced undergraduate students of mathematics.Lectures by this volume's editor, Frank Harary, include ""Some Theorems and Concepts of Graph Theory,"" ""Topological Concepts in Graph Theory,"" ""Graphical Reconstruction,"" and other introduc
Spectral fluctuations of quantum graphs
Pluhař, Z.; Weidenmüller, H. A.
2014-01-01
We prove the Bohigas-Giannoni-Schmit conjecture in its most general form for completely connected simple graphs with incommensurate bond lengths. We show that for graphs that are classically mixing (i.e., graphs for which the spectrum of the classical Perron-Frobenius operator possesses a finite gap), the generating functions for all (P,Q) correlation functions for both closed and open graphs coincide (in the limit of infinite graph size) with the corresponding expressions of random-matrix theory, both for orthogonal and for unitary symmetry
Dynamic Representations of Sparse Graphs
Brodal, Gerth Stølting; Fagerberg, Rolf
1999-01-01
We present a linear space data structure for maintaining graphs with bounded arboricity—a large class of sparse graphs containing e.g. planar graphs and graphs of bounded treewidth—under edge insertions, edge deletions, and adjacency queries. The data structure supports adjacency queries in worst...... case O(c) time, and edge insertions and edge deletions in amortized O(1) and O(c+log n) time, respectively, where n is the number of nodes in the graph, and c is the bound on the arboricity....
Domination criticality in product graphs
M.R. Chithra
2015-07-01
Full Text Available A connected dominating set is an important notion and has many applications in routing and management of networks. Graph products have turned out to be a good model of interconnection networks. This motivated us to study the Cartesian product of graphs G with connected domination number, γc(G=2,3 and characterize such graphs. Also, we characterize the k−γ-vertex (edge critical graphs and k−γc-vertex (edge critical graphs for k=2,3 where γ denotes the domination number of G. We also discuss the vertex criticality in grids.
Graph Creation, Visualisation and Transformation
Maribel Fernández
2010-03-01
Full Text Available We describe a tool to create, edit, visualise and compute with interaction nets - a form of graph rewriting systems. The editor, called GraphPaper, allows users to create and edit graphs and their transformation rules using an intuitive user interface. The editor uses the functionalities of the TULIP system, which gives us access to a wealth of visualisation algorithms. Interaction nets are not only a formalism for the specification of graphs, but also a rewrite-based computation model. We discuss graph rewriting strategies and a language to express them in order to perform strategic interaction net rewriting.
Study of Chromatic parameters of Line, Total, Middle graphs and Graph operators of Bipartite graph
Nagarathinam, R.; Parvathi, N.
2018-04-01
Chromatic parameters have been explored on the basis of graph coloring process in which a couple of adjacent nodes receives different colors. But the Grundy and b-coloring executes maximum colors under certain restrictions. In this paper, Chromatic, b-chromatic and Grundy number of some graph operators of bipartite graph has been investigat
Graph Sampling for Covariance Estimation
Chepuri, Sundeep Prabhakar
2017-04-25
In this paper the focus is on subsampling as well as reconstructing the second-order statistics of signals residing on nodes of arbitrary undirected graphs. Second-order stationary graph signals may be obtained by graph filtering zero-mean white noise and they admit a well-defined power spectrum whose shape is determined by the frequency response of the graph filter. Estimating the graph power spectrum forms an important component of stationary graph signal processing and related inference tasks such as Wiener prediction or inpainting on graphs. The central result of this paper is that by sampling a significantly smaller subset of vertices and using simple least squares, we can reconstruct the second-order statistics of the graph signal from the subsampled observations, and more importantly, without any spectral priors. To this end, both a nonparametric approach as well as parametric approaches including moving average and autoregressive models for the graph power spectrum are considered. The results specialize for undirected circulant graphs in that the graph nodes leading to the best compression rates are given by the so-called minimal sparse rulers. A near-optimal greedy algorithm is developed to design the subsampling scheme for the non-parametric and the moving average models, whereas a particular subsampling scheme that allows linear estimation for the autoregressive model is proposed. Numerical experiments on synthetic as well as real datasets related to climatology and processing handwritten digits are provided to demonstrate the developed theory.
Canonical Labelling of Site Graphs
Nicolas Oury
2013-06-01
Full Text Available We investigate algorithms for canonical labelling of site graphs, i.e. graphs in which edges bind vertices on sites with locally unique names. We first show that the problem of canonical labelling of site graphs reduces to the problem of canonical labelling of graphs with edge colourings. We then present two canonical labelling algorithms based on edge enumeration, and a third based on an extension of Hopcroft's partition refinement algorithm. All run in quadratic worst case time individually. However, one of the edge enumeration algorithms runs in sub-quadratic time for graphs with "many" automorphisms, and the partition refinement algorithm runs in sub-quadratic time for graphs with "few" bisimulation equivalences. This suite of algorithms was chosen based on the expectation that graphs fall in one of those two categories. If that is the case, a combined algorithm runs in sub-quadratic worst case time. Whether this expectation is reasonable remains an interesting open problem.
Learning heat diffusion graphs
Thanou, Dorina; Dong, Xiaowen; Kressner, Daniel; Frossard, Pascal
2016-01-01
Effective information analysis generally boils down to properly identifying the structure or geometry of the data, which is often represented by a graph. In some applications, this structure may be partly determined by design constraints or pre-determined sensing arrangements, like in road transportation networks for example. In general though, the data structure is not readily available and becomes pretty difficult to define. In particular, the global smoothness assumptions, that most of the...
Syed, M. Qasim; Lovatt, Ian
2014-01-01
This paper is an addition to the series of papers on the exponential function begun by Albert Bartlett. In particular, we ask how the graph of the exponential function y = e[superscript -t/t] would appear if y were plotted versus ln t rather than the normal practice of plotting ln y versus t. In answering this question, we find a new way to…
Understanding Charts and Graphs.
1987-07-28
Farenheit degrees, which have no Onaturalo zero ); finally, ratio scales have numbers that are ordered so that the magnitudes of differences are important and...system. They have to do with the very nature of how marks serve as meaningful symbols. In the ideal case, a chart or graph will be absolutely unambiguous...and these laws comprise this principle (see Stevens, 1974). Absolute discriminability: A minimal magnitude of a mark is necessary for it to be detected
Efficient growth of complex graph states via imperfect path erasure
Campbell, Earl T; Fitzsimons, Joseph; Benjamin, Simon C; Kok, Pieter
2007-01-01
Given a suitably large and well connected (complex) graph state, any quantum algorithm can be implemented purely through local measurements on the individual qubits. Measurements can also be used to create the graph state: path erasure techniques allow one to entangle multiple qubits by determining only global properties of the qubits. Here, this powerful approach is extended by demonstrating that even imperfect path erasure can produce the required graph states with high efficiency. By characterizing the degree of error in each path erasure attempt, one can subsume the resulting imperfect entanglement into an extended graph state formalism. The subsequent growth of the improper graph state can be guided, through a series of strategic decisions, in such a way as to bound the growth of the error and eventually yield a high-fidelity graph state. As an implementation of these techniques, we develop an analytic model for atom (or atom-like) qubits in mismatched cavities, under the double-heralding entanglement procedure of Barrett and Kok (2005 Phys. Rev. A 71 060310). Compared to straightforward post-selection techniques our protocol offers a dramatic improvement in growing complex high-fidelity graph states
Qiu, Fei; Xu, Zhimou
2009-08-01
In this study, the amorphous Ba0.7Sr0.3TiO3 (BST0.7) thin films were grown onto fused quartz and silicon substrates at low temperature by using a metal organic decomposition (MOD)-spin-coating procedure. The optical transmittance spectrum of amorphous BST0.7 thin films on fused quartz substrates has been recorded in the wavelength range 190~900 nm. The films were highly transparent for wavelengths longer than 330 nm; the transmission drops rapidly at 330 nm, and the cutoff wavelength occurs at about 260 nm. In addition, we also report the amorphous BST0.7 thin film groove-buried type waveguides with 90° bent structure fabricated on Si substrates with 1.65 μm thick SiO2 thermal oxide layer. The design, fabrication and optical losses of amorphous BST0.7 optical waveguides were presented. The amorphous BST0.7 thin films were grown onto the SiO2/Si substrates by using a metal organic decomposition (MOD)-spin-coating procedure. The optical propagation losses were about 12.8 and 9.4 dB/cm respectively for the 5 and 10 μm wide waveguides at the wavelength of 632.8 nm. The 90° bent structures with a small curvature of micrometers were designed on the basis of a double corner mirror structure. The bend losses were about 1.2 and 0.9 dB respectively for 5 and 10 μm wide waveguides at the wavelength of 632.8 nm. It is expected for amorphous BST0.7 thin films to be used not only in the passive optical interconnection in monolithic OEICs but also in active waveguide devices on the Si chip.
Graphs cospectral with a friendship graph or its complement
Alireza Abdollahi
2013-12-01
Full Text Available Let $n$ be any positive integer and let $F_n$ be the friendship (or Dutch windmill graph with $2n+1$ vertices and $3n$ edges. Here we study graphs with the same adjacency spectrum as the $F_n$. Two graphs are called cospectral if the eigenvalues multiset of their adjacency matrices are the same. Let $G$ be a graph cospectral with $F_n$. Here we prove that if $G$ has no cycle of length $4$ or $5$, then $Gcong F_n$. Moreover if $G$ is connected and planar then $Gcong F_n$.All but one of connected components of $G$ are isomorphic to $K_2$.The complement $overline{F_n}$ of the friendship graph is determined by its adjacency eigenvalues, that is, if $overline{F_n}$ is cospectral with a graph $H$, then $Hcong overline{F_n}$.
Analyzing locomotion synthesis with feature-based motion graphs.
Mahmudi, Mentar; Kallmann, Marcelo
2013-05-01
We propose feature-based motion graphs for realistic locomotion synthesis among obstacles. Among several advantages, feature-based motion graphs achieve improved results in search queries, eliminate the need of postprocessing for foot skating removal, and reduce the computational requirements in comparison to traditional motion graphs. Our contributions are threefold. First, we show that choosing transitions based on relevant features significantly reduces graph construction time and leads to improved search performances. Second, we employ a fast channel search method that confines the motion graph search to a free channel with guaranteed clearance among obstacles, achieving faster and improved results that avoid expensive collision checking. Lastly, we present a motion deformation model based on Inverse Kinematics applied over the transitions of a solution branch. Each transition is assigned a continuous deformation range that does not exceed the original transition cost threshold specified by the user for the graph construction. The obtained deformation improves the reachability of the feature-based motion graph and in turn also reduces the time spent during search. The results obtained by the proposed methods are evaluated and quantified, and they demonstrate significant improvements in comparison to traditional motion graph techniques.
Decomposing Oriented Graphs into Six Locally Irregular Oriented Graphs
Bensmail, Julien; Renault, Gabriel
2016-01-01
An undirected graph G is locally irregular if every two of its adjacent vertices have distinct degrees. We say that G is decomposable into k locally irregular graphs if there exists a partition E1∪E2∪⋯∪Ek of the edge set E(G) such that each Ei induces a locally irregular graph. It was recently co...
Spectral analysis of growing graphs a quantum probability point of view
Obata, Nobuaki
2017-01-01
This book is designed as a concise introduction to the recent achievements on spectral analysis of graphs or networks from the point of view of quantum (or non-commutative) probability theory. The main topics are spectral distributions of the adjacency matrices of finite or infinite graphs and their limit distributions for growing graphs. The main vehicle is quantum probability, an algebraic extension of the traditional probability theory, which provides a new framework for the analysis of adjacency matrices revealing their non-commutative nature. For example, the method of quantum decomposition makes it possible to study spectral distributions by means of interacting Fock spaces or equivalently by orthogonal polynomials. Various concepts of independence in quantum probability and corresponding central limit theorems are used for the asymptotic study of spectral distributions for product graphs. This book is written for researchers, teachers, and students interested in graph spectra, their (asymptotic) spectr...
Embedded graph invariants in Chern-Simons theory
Major, Seth A.
1999-01-01
Chern-Simons gauge theory, since its inception as a topological quantum field theory, has proved to be a rich source of understanding for knot invariants. In this work the theory is used to explore the definition of the expectation value of a network of Wilson lines -- an embedded graph invariant. Using a generalization of the variational method, lowest-order results for invariants for graphs of arbitrary valence and general vertex tangent space structure are derived. Gauge invariant operators are introduced. Higher order results are found. The method used here provides a Vassiliev-type definition of graph invariants which depend on both the embedding of the graph and the group structure of the gauge theory. It is found that one need not frame individual vertices. However, without a global projection of the graph there is an ambiguity in the relation of the decomposition of distinct vertices. It is suggested that framing may be seen as arising from this ambiguity -- as a way of relating frames at distinct vertices
Proof of the 1-factorization and Hamilton decomposition conjectures
Csaba, Béla; Lo, Allan; Osthus, Deryk; Treglown, Andrew
2016-01-01
In this paper the authors prove the following results (via a unified approach) for all sufficiently large n: (i) [1-factorization conjecture] Suppose that n is even and D\\geq 2\\lceil n/4\\rceil -1. Then every D-regular graph G on n vertices has a decomposition into perfect matchings. Equivalently, \\chi'(G)=D. (ii) [Hamilton decomposition conjecture] Suppose that D \\ge \\lfloor n/2 \\rfloor . Then every D-regular graph G on n vertices has a decomposition into Hamilton cycles and at most one perfect matching. (iii) [Optimal packings of Hamilton cycles] Suppose that G is a graph on n vertices with minimum degree \\delta\\ge n/2. Then G contains at least {\\rm reg}_{\\rm even}(n,\\delta)/2 \\ge (n-2)/8 edge-disjoint Hamilton cycles. Here {\\rm reg}_{\\rm even}(n,\\delta) denotes the degree of the largest even-regular spanning subgraph one can guarantee in a graph on n vertices with minimum degree \\delta. (i) was first explicitly stated by Chetwynd and Hilton. (ii) and the special case \\delta= \\lceil n/2 \\rceil of (iii) answe...
Endomorphisms of graph algebras
Conti, Roberto; Hong, Jeong Hee; Szymanski, Wojciech
2012-01-01
We initiate a systematic investigation of endomorphisms of graph C*-algebras C*(E), extending several known results on endomorphisms of the Cuntz algebras O_n. Most but not all of this study is focused on endomorphisms which permute the vertex projections and globally preserve the diagonal MASA D...... that the restriction to the diagonal MASA of an automorphism which globally preserves both D_E and the core AF-subalgebra eventually commutes with the corresponding one-sided shift. Secondly, we exhibit several properties of proper endomorphisms, investigate invertibility of localized endomorphisms both on C...
Yap, Hian-Poh
1996-01-01
This book provides an up-to-date and rapid introduction to an important and currently active topic in graph theory. The author leads the reader to the forefront of research in this area. Complete and easily readable proofs of all the main theorems, together with numerous examples, exercises and open problems are given. The book is suitable for use as a textbook or as seminar material for advanced undergraduate and graduate students. The references are comprehensive and so it will also be useful for researchers as a handbook.
Graph Algorithm Animation with Grrr
Rodgers, Peter; Vidal, Natalia
2000-01-01
We discuss geometric positioning, highlighting of visited nodes and user defined highlighting that form the algorithm animation facilities in the Grrr graph rewriting programming language. The main purpose of animation was initially for the debugging and profiling of Grrr code, but recently it has been extended for the purpose of teaching algorithms to undergraduate students. The animation is restricted to graph based algorithms such as graph drawing, list manipulation or more traditional gra...
Adaptive visualization for large-scale graph
Nakamura, Hiroko; Shinano, Yuji; Ohzahata, Satoshi
2010-01-01
We propose an adoptive visualization technique for representing a large-scale hierarchical dataset within limited display space. A hierarchical dataset has nodes and links showing the parent-child relationship between the nodes. These nodes and links are described using graphics primitives. When the number of these primitives is large, it is difficult to recognize the structure of the hierarchical data because many primitives are overlapped within a limited region. To overcome this difficulty, we propose an adaptive visualization technique for hierarchical datasets. The proposed technique selects an appropriate graph style according to the nodal density in each area. (author)
Bond graph modeling of nuclear reactor dynamics
Tylee, J.L.
1981-01-01
A tenth-order linear model of a pressurized water reactor (PWR) is developed using bond graph techniques. The model describes the nuclear heat generation process and the transfer of this heat to the reactor coolant. Comparisons between the calculated model response and test data from a small-scale PWR show the model to be an adequate representation of the actual plant dynamics. Possible application of the model in an advanced plant diagnostic system is discussed
Eulerian Graphs and Related Topics
Fleischner, Herbert
1990-01-01
The two volumes comprising Part 1 of this work embrace the theme of Eulerian trails and covering walks. They should appeal both to researchers and students, as they contain enough material for an undergraduate or graduate graph theory course which emphasizes Eulerian graphs, and thus can be read by any mathematician not yet familiar with graph theory. But they are also of interest to researchers in graph theory because they contain many recent results, some of which are only partial solutions to more general problems. A number of conjectures have been included as well. Various problems (such a
Multilevel index decomposition analysis: Approaches and application
Xu, X.Y.; Ang, B.W.
2014-01-01
With the growing interest in using the technique of index decomposition analysis (IDA) in energy and energy-related emission studies, such as to analyze the impacts of activity structure change or to track economy-wide energy efficiency trends, the conventional single-level IDA may not be able to meet certain needs in policy analysis. In this paper, some limitations of single-level IDA studies which can be addressed through applying multilevel decomposition analysis are discussed. We then introduce and compare two multilevel decomposition procedures, which are referred to as the multilevel-parallel (M-P) model and the multilevel-hierarchical (M-H) model. The former uses a similar decomposition procedure as in the single-level IDA, while the latter uses a stepwise decomposition procedure. Since the stepwise decomposition procedure is new in the IDA literature, the applicability of the popular IDA methods in the M-H model is discussed and cases where modifications are needed are explained. Numerical examples and application studies using the energy consumption data of the US and China are presented. - Highlights: • We discuss the limitations of single-level decomposition in IDA applied to energy study. • We introduce two multilevel decomposition models, study their features and discuss how they can address the limitations. • To extend from single-level to multilevel analysis, necessary modifications to some popular IDA methods are discussed. • We further discuss the practical significance of the multilevel models and present examples and cases to illustrate
Random graph states, maximal flow and Fuss-Catalan distributions
Collins, BenoIt; Nechita, Ion; Zyczkowski, Karol
2010-01-01
For any graph consisting of k vertices and m edges we construct an ensemble of random pure quantum states which describe a system composed of 2m subsystems. Each edge of the graph represents a bipartite, maximally entangled state. Each vertex represents a random unitary matrix generated according to the Haar measure, which describes the coupling between subsystems. Dividing all subsystems into two parts, one may study entanglement with respect to this partition. A general technique to derive an expression for the average entanglement entropy of random pure states associated with a given graph is presented. Our technique relies on Weingarten calculus and flow problems. We analyze the statistical properties of spectra of such random density matrices and show for which cases they are described by the free Poissonian (Marchenko-Pastur) distribution. We derive a discrete family of generalized, Fuss-Catalan distributions and explicitly construct graphs which lead to ensembles of random states characterized by these novel distributions of eigenvalues.
Maunz, Peter Lukas Wilhelm [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Sterk, Jonathan David [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Lobser, Daniel [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Parekh, Ojas D. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Ryan-Anderson, Ciaran [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2016-01-01
In recent years, advanced network analytics have become increasingly important to na- tional security with applications ranging from cyber security to detection and disruption of ter- rorist networks. While classical computing solutions have received considerable investment, the development of quantum algorithms to address problems, such as data mining of attributed relational graphs, is a largely unexplored space. Recent theoretical work has shown that quan- tum algorithms for graph analysis can be more efficient than their classical counterparts. Here, we have implemented a trapped-ion-based two-qubit quantum information proces- sor to address these goals. Building on Sandia's microfabricated silicon surface ion traps, we have designed, realized and characterized a quantum information processor using the hyperfine qubits encoded in two 171 Yb + ions. We have implemented single qubit gates using resonant microwave radiation and have employed Gate set tomography (GST) to characterize the quan- tum process. For the first time, we were able to prove that the quantum process surpasses the fault tolerance thresholds of some quantum codes by demonstrating a diamond norm distance of less than 1 . 9 x 10 [?] 4 . We used Raman transitions in order to manipulate the trapped ions' motion and realize two-qubit gates. We characterized the implemented motion sensitive and insensitive single qubit processes and achieved a maximal process infidelity of 6 . 5 x 10 [?] 5 . We implemented the two-qubit gate proposed by Molmer and Sorensen and achieved a fidelity of more than 97 . 7%.
Multigraph: Interactive Data Graphs on the Web
Phillips, M. B.
2010-12-01
Many aspects of geophysical science involve time dependent data that is often presented in the form of a graph. Considering that the web has become a primary means of communication, there are surprisingly few good tools and techniques available for presenting time-series data on the web. The most common solution is to use a desktop tool such as Excel or Matlab to create a graph which is saved as an image and then included in a web page like any other image. This technique is straightforward, but it limits the user to one particular view of the data, and disconnects the graph from the data in a way that makes updating a graph with new data an often cumbersome manual process. This situation is somewhat analogous to the state of mapping before the advent of GIS. Maps existed only in printed form, and creating a map was a laborious process. In the last several years, however, the world of mapping has experienced a revolution in the form of web-based and other interactive computer technologies, so that it is now commonplace for anyone to easily browse through gigabytes of geographic data. Multigraph seeks to bring a similar ease of access to time series data. Multigraph is a program for displaying interactive time-series data graphs in web pages that includes a simple way of configuring the appearance of the graph and the data to be included. It allows multiple data sources to be combined into a single graph, and allows the user to explore the data interactively. Multigraph lets users explore and visualize "data space" in the same way that interactive mapping applications such as Google Maps facilitate exploring and visualizing geography. Viewing a Multigraph graph is extremely simple and intuitive, and requires no instructions. Creating a new graph for inclusion in a web page involves writing a simple XML configuration file and requires no programming. Multigraph can read data in a variety of formats, and can display data from a web service, allowing users to "surf
Asymptote Misconception on Graphing Functions: Does Graphing Software Resolve It?
Mehmet Fatih Öçal
2017-01-01
Full Text Available Graphing function is an important issue in mathematics education due to its use in various areas of mathematics and its potential roles for students to enhance learning mathematics. The use of some graphing software assists students’ learning during graphing functions. However, the display of graphs of functions that students sketched by hand may be relatively different when compared to the correct forms sketched using graphing software. The possible misleading effects of this situation brought a discussion of a misconception (asymptote misconception on graphing functions. The purpose of this study is two- fold. First of all, this study investigated whether using graphing software (GeoGebra in this case helps students to determine and resolve this misconception in calculus classrooms. Second, the reasons for this misconception are sought. The multiple case study was utilized in this study. University students in two calculus classrooms who received instructions with (35 students or without GeoGebra assisted instructions (32 students were compared according to whether they fell into this misconception on graphing basic functions (1/x, lnx, ex. In addition, students were interviewed to reveal the reasons behind this misconception. Data were analyzed by means of descriptive and content analysis methods. The findings indicated that those who received GeoGebra assisted instruction were better in resolving it. In addition, the reasons behind this misconception were found to be teacher-based, exam-based and some other factors.
ON BIPOLAR SINGLE VALUED NEUTROSOPHIC GRAPHS
Said Broumi; Mohamed Talea; Assia Bakali; Florentin Smarandache
2016-01-01
In this article, we combine the concept of bipolar neutrosophic set and graph theory. We introduce the notions of bipolar single valued neutrosophic graphs, strong bipolar single valued neutrosophic graphs, complete bipolar single valued neutrosophic graphs, regular bipolar single valued neutrosophic graphs and investigate some of their related properties.
On the number of subgraphs of the Barabasi-Albert random graph
Ryabchenko, Aleksandr A; Samosvat, Egor A [Moscow Institute of Physics and Technology (State University), Dolgoprudnyi, Moscow Region, Russian Frderation (Russian Federation)
2012-06-30
We study a model of a random graph of the type of the Barabasi-Albert preferential attachment model. We develop a technique that makes it possible to estimate the mathematical expectation for a fairly wide class of random variables in the model under consideration. We use this technique to prove a theorem on the asymptotics of the mathematical expectation of the number of subgraphs isomorphic to a certain fixed graph in the random graphs of this model.
On the number of subgraphs of the Barabási-Albert random graph
Ryabchenko, Aleksandr A; Samosvat, Egor A
2012-01-01
We study a model of a random graph of the type of the Barabási-Albert preferential attachment model. We develop a technique that makes it possible to estimate the mathematical expectation for a fairly wide class of random variables in the model under consideration. We use this technique to prove a theorem on the asymptotics of the mathematical expectation of the number of subgraphs isomorphic to a certain fixed graph in the random graphs of this model.
Complexity of Products of Some Complete and Complete Bipartite Graphs
S. N. Daoud
2013-01-01
Full Text Available The number of spanning trees in graphs (networks is an important invariant; it is also an important measure of reliability of a network. In this paper, we derive simple formulas of the complexity, number of spanning trees, of products of some complete and complete bipartite graphs such as cartesian product, normal product, composition product, tensor product, and symmetric product, using linear algebra and matrix analysis techniques.
Graph Theory. 2. Vertex Descriptors and Graph Coloring
Lorentz JÄNTSCHI
2002-12-01
Full Text Available This original work presents the construction of a set of ten sequence matrices and their applications for ordering vertices in graphs. For every sequence matrix three ordering criteria are applied: lexicographic ordering, based on strings of numbers, corresponding to every vertex, extracted as rows from sequence matrices; ordering by the sum of path lengths from a given vertex; and ordering by the sum of paths, starting from a given vertex. We also examine a graph that has different orderings for the above criteria. We then proceed to demonstrate that every criterion induced its own partition of graph vertex. We propose the following theoretical result: both LAVS and LVDS criteria generate identical partitioning of vertices in any graph. Finally, a coloring of graph vertices according to introduced ordering criteria was proposed.
On an edge partition and root graphs of some classes of line graphs
K Pravas
2017-04-01
Full Text Available The Gallai and the anti-Gallai graphs of a graph $G$ are complementary pairs of spanning subgraphs of the line graph of $G$. In this paper we find some structural relations between these graph classes by finding a partition of the edge set of the line graph of a graph $G$ into the edge sets of the Gallai and anti-Gallai graphs of $G$. Based on this, an optimal algorithm to find the root graph of a line graph is obtained. Moreover, root graphs of diameter-maximal, distance-hereditary, Ptolemaic and chordal graphs are also discussed.
BootGraph: probabilistic fiber tractography using bootstrap algorithms and graph theory.
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
Thermal decomposition of pyrite
Music, S.; Ristic, M.; Popovic, S.
1992-01-01
Thermal decomposition of natural pyrite (cubic, FeS 2 ) has been investigated using X-ray diffraction and 57 Fe Moessbauer spectroscopy. X-ray diffraction analysis of pyrite ore from different sources showed the presence of associated minerals, such as quartz, szomolnokite, stilbite or stellerite, micas and hematite. Hematite, maghemite and pyrrhotite were detected as thermal decomposition products of natural pyrite. The phase composition of the thermal decomposition products depends on the terature, time of heating and starting size of pyrite chrystals. Hematite is the end product of the thermal decomposition of natural pyrite. (author) 24 refs.; 6 figs.; 2 tabs
The planar cubic Cayley graphs
Georgakopoulos, Agelos
2018-01-01
The author obtains a complete description of the planar cubic Cayley graphs, providing an explicit presentation and embedding for each of them. This turns out to be a rich class, comprising several infinite families. He obtains counterexamples to conjectures of Mohar, Bonnington and Watkins. The author's analysis makes the involved graphs accessible to computation, corroborating a conjecture of Droms.
Groupies in random bipartite graphs
Yilun Shang
2010-01-01
A vertex $v$ of a graph $G$ is called a groupie if its degree is notless than the average of the degrees of its neighbors. In thispaper we study the influence of bipartition $(B_1,B_2)$ on groupiesin random bipartite graphs $G(B_1,B_2,p)$ with both fixed $p$ and$p$ tending to zero.
Nested Dynamic Condition Response Graphs
Hildebrandt, Thomas; Mukkamala, Raghava Rao; Slaats, Tijs
2012-01-01
We present an extension of the recently introduced declarative process model Dynamic Condition Response Graphs ( DCR Graphs) to allow nested subgraphs and a new milestone relation between events. The extension was developed during a case study carried out jointly with our industrial partner...
Bell inequalities for graph states
Toth, G.; Hyllus, P.; Briegel, H.J.; Guehne, O.
2005-01-01
Full text: In the last years graph states have attracted an increasing interest in the field of quantum information theory. Graph states form a family of multi-qubit states which comprises many popular states such as the GHZ states and the cluster states. They also play an important role in applications. For instance, measurement based quantum computation uses graph states as resources. From a theoretical point of view, it is remarkable that graph states allow for a simple description in terms of stabilizing operators. In this contribution, we investigate the non-local properties of graph states. We derive a family of Bell inequalities which require three measurement settings for each party and are maximally violated by graph states. In turn, any graph state violates at least one of the inequalities. We show that for certain types of graph states the violation of these inequalities increases exponentially with the number of qubits. We also discuss connections to other entanglement properties such as the positively of the partial transpose or the geometric measure of entanglement. (author)
Graph Sampling for Covariance Estimation
Chepuri, Sundeep Prabhakar; Leus, Geert
2017-01-01
specialize for undirected circulant graphs in that the graph nodes leading to the best compression rates are given by the so-called minimal sparse rulers. A near-optimal greedy algorithm is developed to design the subsampling scheme for the non
Network reconstruction via graph blending
Estrada, Rolando
2016-05-01
Graphs estimated from empirical data are often noisy and incomplete due to the difficulty of faithfully observing all the components (nodes and edges) of the true graph. This problem is particularly acute for large networks where the number of components may far exceed available surveillance capabilities. Errors in the observed graph can render subsequent analyses invalid, so it is vital to develop robust methods that can minimize these observational errors. Errors in the observed graph may include missing and spurious components, as well fused (multiple nodes are merged into one) and split (a single node is misinterpreted as many) nodes. Traditional graph reconstruction methods are only able to identify missing or spurious components (primarily edges, and to a lesser degree nodes), so we developed a novel graph blending framework that allows us to cast the full estimation problem as a simple edge addition/deletion problem. Armed with this framework, we systematically investigate the viability of various topological graph features, such as the degree distribution or the clustering coefficients, and existing graph reconstruction methods for tackling the full estimation problem. Our experimental results suggest that incorporating any topological feature as a source of information actually hinders reconstruction accuracy. We provide a theoretical analysis of this phenomenon and suggest several avenues for improving this estimation problem.
A cluster algorithm for graphs
S. van Dongen
2000-01-01
textabstractA cluster algorithm for graphs called the emph{Markov Cluster algorithm (MCL~algorithm) is introduced. The algorithm provides basically an interface to an algebraic process defined on stochastic matrices, called the MCL~process. The graphs may be both weighted (with nonnegative weight)
Quantum chaos on discrete graphs
Smilansky, Uzy
2007-01-01
Adapting a method developed for the study of quantum chaos on quantum (metric) graphs (Kottos and Smilansky 1997 Phys. Rev. Lett. 79 4794, Kottos and Smilansky 1999 Ann. Phys., NY 274 76), spectral ζ functions and trace formulae for discrete Laplacians on graphs are derived. This is achieved by expressing the spectral secular equation in terms of the periodic orbits of the graph and obtaining functions which belong to the class of ζ functions proposed originally by Ihara (1966 J. Mat. Soc. Japan 18 219) and expanded by subsequent authors (Stark and Terras 1996 Adv. Math. 121 124, Kotani and Sunada 2000 J. Math. Sci. Univ. Tokyo 7 7). Finally, a model of 'classical dynamics' on the discrete graph is proposed. It is analogous to the corresponding classical dynamics derived for quantum graphs (Kottos and Smilansky 1997 Phys. Rev. Lett. 79 4794, Kottos and Smilansky 1999 Ann. Phys., NY 274 76). (fast track communication)
A Hybrid Approach to Processing Big Data Graphs on Memory-Restricted Systems
Harshvardhan,
2015-05-01
With the advent of big-data, processing large graphs quickly has become increasingly important. Most existing approaches either utilize in-memory processing techniques that can only process graphs that fit completely in RAM, or disk-based techniques that sacrifice performance. In this work, we propose a novel RAM-Disk hybrid approach to graph processing that can scale well from a single shared-memory node to large distributed-memory systems. It works by partitioning the graph into sub graphs that fit in RAM and uses a paging-like technique to load sub graphs. We show that without modifying the algorithms, this approach can scale from small memory-constrained systems (such as tablets) to large-scale distributed machines with 16, 000+ cores.
Multidimensional Brain MRI segmentation using graph cuts
Lecoeur, Jeremy
2010-01-01
This thesis deals with the segmentation of multimodal brain MRIs by graph cuts method. First, we propose a method that utilizes three MRI modalities by merging them. The border information given by the spectral gradient is then challenged by a region information, given by the seeds selected by the user, using a graph cut algorithm. Then, we propose three enhancements of this method. The first consists in finding an optimal spectral space because the spectral gradient is based on natural images and then inadequate for multimodal medical images. This results in a learning based segmentation method. We then explore the automation of the graph cut method. Here, the various pieces of information usually given by the user are inferred from a robust expectation-maximization algorithm. We show the performance of these two enhanced versions on multiple sclerosis lesions. Finally, we integrate atlases for the automatic segmentation of deep brain structures. These three new techniques show the adaptability of our method to various problems. Our different segmentation methods are better than most of nowadays techniques, speaking of computation time or segmentation accuracy. (authors)
On characterizing terrain visibility graphs
William Evans
2015-06-01
Full Text Available A terrain is an $x$-monotone polygonal line in the $xy$-plane. Two vertices of a terrain are mutually visible if and only if there is no terrain vertex on or above the open line segment connecting them. A graph whose vertices represent terrain vertices and whose edges represent mutually visible pairs of terrain vertices is called a terrain visibility graph. We would like to find properties that are both necessary and sufficient for a graph to be a terrain visibility graph; that is, we would like to characterize terrain visibility graphs.Abello et al. [Discrete and Computational Geometry, 14(3:331--358, 1995] showed that all terrain visibility graphs are “persistent”. They showed that the visibility information of a terrain point set implies some ordering requirements on the slopes of the lines connecting pairs of points in any realization, and as a step towards showing sufficiency, they proved that for any persistent graph $M$ there is a total order on the slopes of the (pseudo lines in a generalized configuration of points whose visibility graph is $M$.We give a much simpler proof of this result by establishing an orientation to every triple of vertices, reflecting some slope ordering requirements that are consistent with $M$ being the visibility graph, and prove that these requirements form a partial order. We give a faster algorithm to construct a total order on the slopes. Our approach attempts to clarify the implications of the graph theoretic properties on the ordering of the slopes, and may be interpreted as defining properties on an underlying oriented matroid that we show is a restricted type of $3$-signotope.
Graph embedding with rich information through heterogeneous graph
Sun, Guolei
2017-11-12
Graph embedding, aiming to learn low-dimensional representations for nodes in graphs, has attracted increasing attention due to its critical application including node classification, link prediction and clustering in social network analysis. Most existing algorithms for graph embedding only rely on the topology information and fail to use the copious information in nodes as well as edges. As a result, their performance for many tasks may not be satisfactory. In this thesis, we proposed a novel and general framework for graph embedding with rich text information (GERI) through constructing a heterogeneous network, in which we integrate node and edge content information with graph topology. Specially, we designed a novel biased random walk to explore the constructed heterogeneous network with the notion of flexible neighborhood. Our sampling strategy can compromise between BFS and DFS local search on heterogeneous graph. To further improve our algorithm, we proposed semi-supervised GERI (SGERI), which learns graph embedding in an discriminative manner through heterogeneous network with label information. The efficacy of our method is demonstrated by extensive comparison experiments with 9 baselines over multi-label and multi-class classification on various datasets including Citeseer, Cora, DBLP and Wiki. It shows that GERI improves the Micro-F1 and Macro-F1 of node classification up to 10%, and SGERI improves GERI by 5% in Wiki.
Gems of combinatorial optimization and graph algorithms
Skutella, Martin; Stiller, Sebastian; Wagner, Dorothea
2015-01-01
Are you looking for new lectures for your course on algorithms, combinatorial optimization, or algorithmic game theory? Maybe you need a convenient source of relevant, current topics for a graduate student or advanced undergraduate student seminar? Or perhaps you just want an enjoyable look at some beautiful mathematical and algorithmic results, ideas, proofs, concepts, and techniques in discrete mathematics and theoretical computer science? Gems of Combinatorial Optimization and Graph Algorithms is a handpicked collection of up-to-date articles, carefully prepared by a select group of international experts, who have contributed some of their most mathematically or algorithmically elegant ideas. Topics include longest tours and Steiner trees in geometric spaces, cartograms, resource buying games, congestion games, selfish routing, revenue equivalence and shortest paths, scheduling, linear structures in graphs, contraction hierarchies, budgeted matching problems, and motifs in networks. This ...
Analysis and enumeration algorithms for biological graphs
Marino, Andrea
2015-01-01
In this work we plan to revise the main techniques for enumeration algorithms and to show four examples of enumeration algorithms that can be applied to efficiently deal with some biological problems modelled by using biological networks: enumerating central and peripheral nodes of a network, enumerating stories, enumerating paths or cycles, and enumerating bubbles. Notice that the corresponding computational problems we define are of more general interest and our results hold in the case of arbitrary graphs. Enumerating all the most and less central vertices in a network according to their eccentricity is an example of an enumeration problem whose solutions are polynomial and can be listed in polynomial time, very often in linear or almost linear time in practice. Enumerating stories, i.e. all maximal directed acyclic subgraphs of a graph G whose sources and targets belong to a predefined subset of the vertices, is on the other hand an example of an enumeration problem with an exponential number of solutions...
CORECLUSTER: A Degeneracy Based Graph Clustering Framework
Giatsidis , Christos; Malliaros , Fragkiskos; Thilikos , Dimitrios M. ,; Vazirgiannis , Michalis
2014-01-01
International audience; Graph clustering or community detection constitutes an important task forinvestigating the internal structure of graphs, with a plethora of applications in several domains. Traditional tools for graph clustering, such asspectral methods, typically suffer from high time and space complexity. In thisarticle, we present \\textsc{CoreCluster}, an efficient graph clusteringframework based on the concept of graph degeneracy, that can be used along withany known graph clusteri...
Barrera-Osorio, Felipe; Garcia-Moreno, Vicente; Patrinos, Harry Anthony; Porta, Emilio
2011-01-01
The Oaxaca-Blinder technique was originally used in labor economics to decompose earnings gaps and to estimate the level of discrimination. It has been applied since in other social issues, including education, where it can be used to assess how much of a gap is due to differences in characteristics (explained variation) and how much is due to…
Decomposition of Sodium Tetraphenylborate
Barnes, M.J.
1998-01-01
The chemical decomposition of aqueous alkaline solutions of sodium tetraphenylborate (NaTPB) has been investigated. The focus of the investigation is on the determination of additives and/or variables which influence NaTBP decomposition. This document describes work aimed at providing better understanding into the relationship of copper (II), solution temperature, and solution pH to NaTPB stability
Modeling flow and transport in fracture networks using graphs
Karra, S.; O'Malley, D.; Hyman, J. D.; Viswanathan, H. S.; Srinivasan, G.
2018-03-01
the DFN, makes the graph algorithm an ideal technique to incorporate in uncertainty quantification methods.
Thermal decomposition of beryllium perchlorate tetrahydrate
Berezkina, L.G.; Borisova, S.I.; Tamm, N.S.; Novoselova, A.V.
1975-01-01
Thermal decomposition of Be(ClO 4 ) 2 x4H 2 O was studied by the differential flow technique in the helium stream. The kinetics was followed by an exchange reaction of the perchloric acid appearing by the decomposition with potassium carbonate. The rate of CO 2 liberation in this process was recorded by a heat conductivity detector. The exchange reaction yielding CO 2 is quantitative, it is not the limiting one and it does not distort the kinetics of the process of perchlorate decomposition. The solid products of decomposition were studied by infrared and NMR spectroscopy, roentgenography, thermography and chemical analysis. A mechanism suggested for the decomposition involves intermediate formation of hydroxyperchlorate: Be(ClO 4 ) 2 x4H 2 O → Be(OH)ClO 4 +HClO 4 +3H 2 O; Be(OH)ClO 4 → BeO+HClO 4 . Decomposition is accompained by melting of the sample. The mechanism of decomposition is hydrolytic. At room temperature the hydroxyperchlorate is a thick syrup-like compound crystallizing after long storing
A characterization of horizontal visibility graphs and combinatorics on words
Gutin, Gregory; Mansour, Toufik; Severini, Simone
2011-06-01
A Horizontal Visibility Graph (HVG) is defined in association with an ordered set of non-negative reals. HVGs realize a methodology in the analysis of time series, their degree distribution being a good discriminator between randomness and chaos Luque et al. [B. Luque, L. Lacasa, F. Ballesteros, J. Luque, Horizontal visibility graphs: exact results for random time series, Phys. Rev. E 80 (2009), 046103]. We prove that a graph is an HVG if and only if it is outerplanar and has a Hamilton path. Therefore, an HVG is a noncrossing graph, as defined in algebraic combinatorics Flajolet and Noy [P. Flajolet, M. Noy, Analytic combinatorics of noncrossing configurations, Discrete Math., 204 (1999) 203-229]. Our characterization of HVGs implies a linear time recognition algorithm. Treating ordered sets as words, we characterize subfamilies of HVGs highlighting various connections with combinatorial statistics and introducing the notion of a visible pair. With this technique, we determine asymptotically the average number of edges of HVGs.
Nested grids ILU-decomposition (NGILU)
Ploeg, A. van der; Botta, E.F.F.; Wubs, F.W.
1996-01-01
A preconditioning technique is described which shows, in many cases, grid-independent convergence. This technique only requires an ordering of the unknowns based on the different levels of multigrid, and an incomplete LU-decomposition based on a drop tolerance. The method is demonstrated on a
Scalable force directed graph layout algorithms using fast multipole methods
Yunis, Enas Abdulrahman
2012-06-01
We present an extension to ExaFMM, a Fast Multipole Method library, as a generalized approach for fast and scalable execution of the Force-Directed Graph Layout algorithm. The Force-Directed Graph Layout algorithm is a physics-based approach to graph layout that treats the vertices V as repelling charged particles with the edges E connecting them acting as springs. Traditionally, the amount of work required in applying the Force-Directed Graph Layout algorithm is O(|V|2 + |E|) using direct calculations and O(|V| log |V| + |E|) using truncation, filtering, and/or multi-level techniques. Correct application of the Fast Multipole Method allows us to maintain a lower complexity of O(|V| + |E|) while regaining most of the precision lost in other techniques. Solving layout problems for truly large graphs with millions of vertices still requires a scalable algorithm and implementation. We have been able to leverage the scalability and architectural adaptability of the ExaFMM library to create a Force-Directed Graph Layout implementation that runs efficiently on distributed multicore and multi-GPU architectures. © 2012 IEEE.
Hierarchy of modular graph identities
D’Hoker, Eric; Kaidi, Justin
2016-01-01
The low energy expansion of Type II superstring amplitudes at genus one is organized in terms of modular graph functions associated with Feynman graphs of a conformal scalar field on the torus. In earlier work, surprising identities between two-loop graphs at all weights, and between higher-loop graphs of weights four and five were constructed. In the present paper, these results are generalized in two complementary directions. First, all identities at weight six and all dihedral identities at weight seven are obtained and proven. Whenever the Laurent polynomial at the cusp is available, the form of these identities confirms the pattern by which the vanishing of the Laurent polynomial governs the full modular identity. Second, the family of modular graph functions is extended to include all graphs with derivative couplings and worldsheet fermions. These extended families of modular graph functions are shown to obey a hierarchy of inhomogeneous Laplace eigenvalue equations. The eigenvalues are calculated analytically for the simplest infinite sub-families and obtained by Maple for successively more complicated sub-families. The spectrum is shown to consist solely of eigenvalues s(s−1) for positive integers s bounded by the weight, with multiplicities which exhibit rich representation-theoretic patterns.
Hierarchy of modular graph identities
D’Hoker, Eric; Kaidi, Justin [Mani L. Bhaumik Institute for Theoretical Physics, Department of Physics and Astronomy,University of California,Los Angeles, CA 90095 (United States)
2016-11-09
The low energy expansion of Type II superstring amplitudes at genus one is organized in terms of modular graph functions associated with Feynman graphs of a conformal scalar field on the torus. In earlier work, surprising identities between two-loop graphs at all weights, and between higher-loop graphs of weights four and five were constructed. In the present paper, these results are generalized in two complementary directions. First, all identities at weight six and all dihedral identities at weight seven are obtained and proven. Whenever the Laurent polynomial at the cusp is available, the form of these identities confirms the pattern by which the vanishing of the Laurent polynomial governs the full modular identity. Second, the family of modular graph functions is extended to include all graphs with derivative couplings and worldsheet fermions. These extended families of modular graph functions are shown to obey a hierarchy of inhomogeneous Laplace eigenvalue equations. The eigenvalues are calculated analytically for the simplest infinite sub-families and obtained by Maple for successively more complicated sub-families. The spectrum is shown to consist solely of eigenvalues s(s−1) for positive integers s bounded by the weight, with multiplicities which exhibit rich representation-theoretic patterns.
Azimuthal decomposition of optical modes
Dudley, Angela L
2012-07-01
Full Text Available This presentation analyses the azimuthal decomposition of optical modes. Decomposition of azimuthal modes need two steps, namely generation and decomposition. An azimuthally-varying phase (bounded by a ring-slit) placed in the spatial frequency...
Discrete geometric analysis of message passing algorithm on graphs
Watanabe, Yusuke
2010-04-01
We often encounter probability distributions given as unnormalized products of non-negative functions. The factorization structures are represented by hypergraphs called factor graphs. Such distributions appear in various fields, including statistics, artificial intelligence, statistical physics, error correcting codes, etc. Given such a distribution, computations of marginal distributions and the normalization constant are often required. However, they are computationally intractable because of their computational costs. One successful approximation method is Loopy Belief Propagation (LBP) algorithm. The focus of this thesis is an analysis of the LBP algorithm. If the factor graph is a tree, i.e. having no cycle, the algorithm gives the exact quantities. If the factor graph has cycles, however, the LBP algorithm does not give exact results and possibly exhibits oscillatory and non-convergent behaviors. The thematic question of this thesis is "How the behaviors of the LBP algorithm are affected by the discrete geometry of the factor graph?" The primary contribution of this thesis is the discovery of a formula that establishes the relation between the LBP, the Bethe free energy and the graph zeta function. This formula provides new techniques for analysis of the LBP algorithm, connecting properties of the graph and of the LBP and the Bethe free energy. We demonstrate applications of the techniques to several problems including (non) convexity of the Bethe free energy, the uniqueness and stability of the LBP fixed point. We also discuss the loop series initiated by Chertkov and Chernyak. The loop series is a subgraph expansion of the normalization constant, or partition function, and reflects the graph geometry. We investigate theoretical natures of the series. Moreover, we show a partial connection between the loop series and the graph zeta function.
XML Graphs in Program Analysis
Møller, Anders; Schwartzbach, Michael I.
2011-01-01
of XML graphs against different XML schema languages, and provide a software package that enables others to make use of these ideas. We also survey the use of XML graphs for program analysis with four very different languages: XACT (XML in Java), Java Servlets (Web application programming), XSugar......XML graphs have shown to be a simple and effective formalism for representing sets of XML documents in program analysis. It has evolved through a six year period with variants tailored for a range of applications. We present a unified definition, outline the key properties including validation...
Rabern, Landon
2007-01-01
We improve upper bounds on the chromatic number proven independently in \\cite{reedNote} and \\cite{ingo}. Our main lemma gives a sufficient condition for two paths in graph to be completely joined. Using this, we prove that if a graph has an optimal coloring with more than $\\frac{\\omega}{2}$ singleton color classes, then it satisfies $\\chi \\leq \\frac{\\omega + \\Delta + 1}{2}$. It follows that a graph satisfying $n - \\Delta < \\alpha + \\frac{\\omega - 1}{2}$ must also satisfy $\\chi \\leq \\frac{\\ome...
Graphs with Eulerian unit spheres
Knill, Oliver
2015-01-01
d-spheres in graph theory are inductively defined as graphs for which all unit spheres S(x) are (d-1)-spheres and that the removal of one vertex renders the graph contractible. Eulerian d-spheres are geometric d-spheres which are d+1 colorable. We prove here that G is an Eulerian sphere if and only if the degrees of all the (d-2)-dimensional sub-simplices in G are even. This generalizes a Kempe-Heawood result for d=2 and is work related to the conjecture that all d-spheres have chromatic numb...
Steganography based on pixel intensity value decomposition
Abdulla, Alan Anwar; Sellahewa, Harin; Jassim, Sabah A.
2014-05-01
This paper focuses on steganography based on pixel intensity value decomposition. A number of existing schemes such as binary, Fibonacci, Prime, Natural, Lucas, and Catalan-Fibonacci (CF) are evaluated in terms of payload capacity and stego quality. A new technique based on a specific representation is proposed to decompose pixel intensity values into 16 (virtual) bit-planes suitable for embedding purposes. The proposed decomposition has a desirable property whereby the sum of all bit-planes does not exceed the maximum pixel intensity value, i.e. 255. Experimental results demonstrate that the proposed technique offers an effective compromise between payload capacity and stego quality of existing embedding techniques based on pixel intensity value decomposition. Its capacity is equal to that of binary and Lucas, while it offers a higher capacity than Fibonacci, Prime, Natural, and CF when the secret bits are embedded in 1st Least Significant Bit (LSB). When the secret bits are embedded in higher bit-planes, i.e., 2nd LSB to 8th Most Significant Bit (MSB), the proposed scheme has more capacity than Natural numbers based embedding. However, from the 6th bit-plane onwards, the proposed scheme offers better stego quality. In general, the proposed decomposition scheme has less effect in terms of quality on pixel value when compared to most existing pixel intensity value decomposition techniques when embedding messages in higher bit-planes.
Szabó, György; Fáth, Gábor
2007-07-01
Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to those applied in non-equilibrium statistical physics. This review gives a tutorial-type overview of the field for physicists. The first four sections introduce the necessary background in classical and evolutionary game theory from the basic definitions to the most important results. The fifth section surveys the topological complications implied by non-mean-field-type social network structures in general. The next three sections discuss in detail the dynamic behavior of three prominent classes of models: the Prisoner's Dilemma, the Rock-Scissors-Paper game, and Competing Associations. The major theme of the review is in what sense and how the graph structure of interactions can modify and enrich the picture of long term behavioral patterns emerging in evolutionary games.
MetricForensics: A Multi-Level Approach for Mining Volatile Graphs
Henderson, Keith [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Eliassi-Rad, Tina [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Faloutsos, Christos [Carnegie Mellon Univ., Pittsburgh, PA (United States); Akoglu, Leman [Carnegie Mellon Univ., Pittsburgh, PA (United States); Li, Lei [Carnegie Mellon Univ., Pittsburgh, PA (United States); Maruhashi, Koji [Fujitsu Laboratories Ltd., Kanagawa (Japan); Prakash, B. Aditya [Carnegie Mellon Univ., Pittsburgh, PA (United States); Tong, H [Carnegie Mellon Univ., Pittsburgh, PA (United States)
2010-02-08
Advances in data collection and storage capacity have made it increasingly possible to collect highly volatile graph data for analysis. Existing graph analysis techniques are not appropriate for such data, especially in cases where streaming or near-real-time results are required. An example that has drawn significant research interest is the cyber-security domain, where internet communication traces are collected and real-time discovery of events, behaviors, patterns and anomalies is desired. We propose MetricForensics, a scalable framework for analysis of volatile graphs. MetricForensics combines a multi-level “drill down" approach, a collection of user-selected graph metrics and a collection of analysis techniques. At each successive level, more sophisticated metrics are computed and the graph is viewed at a finer temporal resolution. In this way, MetricForensics scales to highly volatile graphs by only allocating resources for computationally expensive analysis when an interesting event is discovered at a coarser resolution first. We test MetricForensics on three real-world graphs: an enterprise IP trace, a trace of legitimate and malicious network traffic from a research institution, and the MIT Reality Mining proximity sensor data. Our largest graph has »3M vertices and »32M edges, spanning 4:5 days. The results demonstrate the scalability and capability of MetricForensics in analyzing volatile graphs; and highlight four novel phenomena in such graphs: elbows, broken correlations, prolonged spikes, and strange stars.
Graph anomalies in cyber communications
Vander Wiel, Scott A [Los Alamos National Laboratory; Storlie, Curtis B [Los Alamos National Laboratory; Sandine, Gary [Los Alamos National Laboratory; Hagberg, Aric A [Los Alamos National Laboratory; Fisk, Michael [Los Alamos National Laboratory
2011-01-11
Enterprises monitor cyber traffic for viruses, intruders and stolen information. Detection methods look for known signatures of malicious traffic or search for anomalies with respect to a nominal reference model. Traditional anomaly detection focuses on aggregate traffic at central nodes or on user-level monitoring. More recently, however, traffic is being viewed more holistically as a dynamic communication graph. Attention to the graph nature of the traffic has expanded the types of anomalies that are being sought. We give an overview of several cyber data streams collected at Los Alamos National Laboratory and discuss current work in modeling the graph dynamics of traffic over the network. We consider global properties and local properties within the communication graph. A method for monitoring relative entropy on multiple correlated properties is discussed in detail.
Open Graphs and Computational Reasoning
Lucas Dixon
2010-06-01
Full Text Available We present a form of algebraic reasoning for computational objects which are expressed as graphs. Edges describe the flow of data between primitive operations which are represented by vertices. These graphs have an interface made of half-edges (edges which are drawn with an unconnected end and enjoy rich compositional principles by connecting graphs along these half-edges. In particular, this allows equations and rewrite rules to be specified between graphs. Particular computational models can then be encoded as an axiomatic set of such rules. Further rules can be derived graphically and rewriting can be used to simulate the dynamics of a computational system, e.g. evaluating a program on an input. Examples of models which can be formalised in this way include traditional electronic circuits as well as recent categorical accounts of quantum information.
Woeginger, G.J.
1998-01-01
In this short note we argue that the toughness of split graphs can be computed in polynomial time. This solves an open problem from a recent paper by Kratsch et al. (Discrete Math. 150 (1996) 231–245).
Cellular decomposition in vikalloys
Belyatskaya, I.S.; Vintajkin, E.Z.; Georgieva, I.Ya.; Golikov, V.A.; Udovenko, V.A.
1981-01-01
Austenite decomposition in Fe-Co-V and Fe-Co-V-Ni alloys at 475-600 deg C is investigated. The cellular decomposition in ternary alloys results in the formation of bcc (ordered) and fcc structures, and in quaternary alloys - bcc (ordered) and 12R structures. The cellular 12R structure results from the emergence of stacking faults in the fcc lattice with irregular spacing in four layers. The cellular decomposition results in a high-dispersion structure and magnetic properties approaching the level of well-known vikalloys [ru
Daverman, Robert J
2007-01-01
Decomposition theory studies decompositions, or partitions, of manifolds into simple pieces, usually cell-like sets. Since its inception in 1929, the subject has become an important tool in geometric topology. The main goal of the book is to help students interested in geometric topology to bridge the gap between entry-level graduate courses and research at the frontier as well as to demonstrate interrelations of decomposition theory with other parts of geometric topology. With numerous exercises and problems, many of them quite challenging, the book continues to be strongly recommended to eve
Graph theory and its applications
Gross, Jonathan L
2006-01-01
Gross and Yellen take a comprehensive approach to graph theory that integrates careful exposition of classical developments with emerging methods, models, and practical needs. Their unparalleled treatment provides a text ideal for a two-semester course and a variety of one-semester classes, from an introductory one-semester course to courses slanted toward classical graph theory, operations research, data structures and algorithms, or algebra and topology.
A faithful functor among algebras and graphs
Falcón Ganfornina, Óscar Jesús; Falcón Ganfornina, Raúl Manuel; Núñez Valdés, Juan; Pacheco Martínez, Ana María; Villar Liñán, María Trinidad; Vigo Aguiar, Jesús (Coordinador)
2016-01-01
The problem of identifying a functor between the categories of algebras and graphs is currently open. Based on a known algorithm that identifies isomorphisms of Latin squares with isomorphism of vertex-colored graphs, we describe here a pair of graphs that enable us to find a faithful functor between finite-dimensional algebras over finite fields and these graphs.
Graphs with branchwidth at most three
Bodlaender, H.L.; Thilikos, D.M.
1997-01-01
In this paper we investigate both the structure of graphs with branchwidth at most three, as well as algorithms to recognise such graphs. We show that a graph has branchwidth at most three, if and only if it has treewidth at most three and does not contain the three-dimensional binary cube graph
A Modal-Logic Based Graph Abstraction
Bauer, J.; Boneva, I.B.; Kurban, M.E.; Rensink, Arend; Ehrig, H; Heckel, R.; Rozenberg, G.; Taentzer, G.
2008-01-01
Infinite or very large state spaces often prohibit the successful verification of graph transformation systems. Abstract graph transformation is an approach that tackles this problem by abstracting graphs to abstract graphs of bounded size and by lifting application of productions to abstract
Graphs whose complement and square are isomorphic
Pedersen, Anders Sune
2014-01-01
We study square-complementary graphs, that is, graphs whose complement and square are isomorphic. We prove several necessary conditions for a graph to be square-complementary, describe ways of building new square-complementary graphs from existing ones, construct infinite families of square-compl...
Acyclicity in edge-colored graphs
Gutin, Gregory; Jones, Mark; Sheng, Bin
2017-01-01
A walk W in edge-colored graphs is called properly colored (PC) if every pair of consecutive edges in W is of different color. We introduce and study five types of PC acyclicity in edge-colored graphs such that graphs of PC acyclicity of type i is a proper superset of graphs of acyclicity of type...
Building Scalable Knowledge Graphs for Earth Science
Ramachandran, Rahul; Maskey, Manil; Gatlin, Patrick; Zhang, Jia; Duan, Xiaoyi; Miller, J. J.; Bugbee, Kaylin; Christopher, Sundar; Freitag, Brian
2017-01-01
Knowledge Graphs link key entities in a specific domain with other entities via relationships. From these relationships, researchers can query knowledge graphs for probabilistic recommendations to infer new knowledge. Scientific papers are an untapped resource which knowledge graphs could leverage to accelerate research discovery. Goal: Develop an end-to-end (semi) automated methodology for constructing Knowledge Graphs for Earth Science.
Port-Hamiltonian Systems on Open Graphs
Schaft, A.J. van der; Maschke, B.M.
2010-01-01
In this talk we discuss how to define in an intrinsic manner port-Hamiltonian dynamics on open graphs. Open graphs are graphs where some of the vertices are boundary vertices (terminals), which allow interconnection with other systems. We show that a directed graph carries two natural Dirac
Constructing Dense Graphs with Unique Hamiltonian Cycles
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…
Skew-adjacency matrices of graphs
Cavers, M.; Cioaba, S.M.; Fallat, S.; Gregory, D.A.; Haemers, W.H.; Kirkland, S.J.; McDonald, J.J.; Tsatsomeros, M.
2012-01-01
The spectra of the skew-adjacency matrices of a graph are considered as a possible way to distinguish adjacency cospectral graphs. This leads to the following topics: graphs whose skew-adjacency matrices are all cospectral; relations between the matchings polynomial of a graph and the characteristic
Chromatic polynomials of random graphs
Van Bussel, Frank; Fliegner, Denny; Timme, Marc; Ehrlich, Christoph; Stolzenberg, Sebastian
2010-01-01
Chromatic polynomials and related graph invariants are central objects in both graph theory and statistical physics. Computational difficulties, however, have so far restricted studies of such polynomials to graphs that were either very small, very sparse or highly structured. Recent algorithmic advances (Timme et al 2009 New J. Phys. 11 023001) now make it possible to compute chromatic polynomials for moderately sized graphs of arbitrary structure and number of edges. Here we present chromatic polynomials of ensembles of random graphs with up to 30 vertices, over the entire range of edge density. We specifically focus on the locations of the zeros of the polynomial in the complex plane. The results indicate that the chromatic zeros of random graphs have a very consistent layout. In particular, the crossing point, the point at which the chromatic zeros with non-zero imaginary part approach the real axis, scales linearly with the average degree over most of the density range. While the scaling laws obtained are purely empirical, if they continue to hold in general there are significant implications: the crossing points of chromatic zeros in the thermodynamic limit separate systems with zero ground state entropy from systems with positive ground state entropy, the latter an exception to the third law of thermodynamics.
Commuting graphs of matrix algebras
Akbari, S.; Bidkhori, H.; Mohammadian, A.
2006-08-01
The commuting graph of a ring R, denoted by Γ(R), is a graph whose vertices are all non- central elements of R and two distinct vertices x and y are adjacent if and only if xy = yx. The commuting graph of a group G, denoted by Γ(G), is similarly defined. In this paper we investigate some graph theoretic properties of Γ(M n (F)), where F is a field and n ≥ 2. Also we study the commuting graphs of some classical groups such as GL n (F) and SL n (F). We show that Γ(M n (F)) is a connected graph if and only if every field extension of F of degree n contains a proper intermediate field. We prove that apart from finitely many fields, a similar result is true for Γ(GL n (F)) and Γ(SL n (F)). Also we show that for two fields E and F and integers m, n ≥> 2, if Γ(M m (E)) ≅ Γ(M n (F)), then m = n and vertical bar E vertical bar = vertical bar F vertical bar. (author)
Multiresolution signal decomposition transforms, subbands, and wavelets
Akansu, Ali N; Haddad, Paul R
2001-01-01
The uniqueness of this book is that it covers such important aspects of modern signal processing as block transforms from subband filter banks and wavelet transforms from a common unifying standpoint, thus demonstrating the commonality among these decomposition techniques. In addition, it covers such ""hot"" areas as signal compression and coding, including particular decomposition techniques and tables listing coefficients of subband and wavelet filters and other important properties.The field of this book (Electrical Engineering/Computer Science) is currently booming, which is, of course
Graph Quasicontinuous Functions and Densely Continuous Forms
Lubica Hola
2017-07-01
Full Text Available Let $X, Y$ be topological spaces. A function $f: X \\to Y$ is said to be graph quasicontinuous if there is a quasicontinuous function $g: X \\to Y$ with the graph of $g$ contained in the closure of the graph of $f$. There is a close relation between the notions of graph quasicontinuous functions and minimal usco maps as well as the notions of graph quasicontinuous functions and densely continuous forms. Every function with values in a compact Hausdorff space is graph quasicontinuous; more generally every locally compact function is graph quasicontinuous.
Mining the inner structure of the Web graph
Donato, Debora; Leonardi, Stefano; Millozzi, Stefano; Tsaparas, Panayiotis
2008-01-01
Despite being the sum of decentralized and uncoordinated efforts by heterogeneous groups and individuals, the World Wide Web exhibits a well-defined structure, characterized by several interesting properties. This structure was clearly revealed by Broder et al (2000 Graph structure in the web Comput. Netw. 33 309) who presented the evocative bow-tie picture of the Web. Although, the bow-tie structure is a relatively clear abstraction of the macroscopic picture of the Web, it is quite uninformative with respect to the finer details of the Web graph. In this paper, we mine the inner structure of the Web graph. We present a series of measurements on the Web, which offer a better understanding of the individual components of the bow-tie. In the process, we develop algorithmic techniques for performing these measurements. We discover that the scale-free properties permeate all the components of the bow-tie which exhibit the same macroscopic properties as the Web graph itself. However, close inspection reveals that their inner structure is quite distinct. We show that the Web graph does not exhibit self similarity within its components, and we propose a possible alternative picture for the Web graph, as it emerges from our experiments
Regular graph construction for semi-supervised learning
Vega-Oliveros, Didier A; Berton, Lilian; Eberle, Andre Mantini; Lopes, Alneu de Andrade; Zhao, Liang
2014-01-01
Semi-supervised learning (SSL) stands out for using a small amount of labeled points for data clustering and classification. In this scenario graph-based methods allow the analysis of local and global characteristics of the available data by identifying classes or groups regardless data distribution and representing submanifold in Euclidean space. Most of methods used in literature for SSL classification do not worry about graph construction. However, regular graphs can obtain better classification accuracy compared to traditional methods such as k-nearest neighbor (kNN), since kNN benefits the generation of hubs and it is not appropriate for high-dimensionality data. Nevertheless, methods commonly used for generating regular graphs have high computational cost. We tackle this problem introducing an alternative method for generation of regular graphs with better runtime performance compared to methods usually find in the area. Our technique is based on the preferential selection of vertices according some topological measures, like closeness, generating at the end of the process a regular graph. Experiments using the global and local consistency method for label propagation show that our method provides better or equal classification rate in comparison with kNN
Photochemical decomposition of catecholamines
Mol, N.J. de; Henegouwen, G.M.J.B. van; Gerritsma, K.W.
1979-01-01
During photochemical decomposition (lambda=254 nm) adrenaline, isoprenaline and noradrenaline in aqueous solution were converted to the corresponding aminochrome for 65, 56 and 35% respectively. In determining this conversion, photochemical instability of the aminochromes was taken into account. Irradiations were performed in such dilute solutions that the neglect of the inner filter effect is permissible. Furthermore, quantum yields for the decomposition of the aminochromes in aqueous solution are given. (Author)
Kenneth L. Weiss
2008-01-01
Full Text Available Background and Purpose: Multi-parametric MRI of the entire spine is technologist-dependent, time consuming, and often limited by inhomogeneous fat suppression. We tested a technique to provide rapid automated total spine MRI screening with improved tissue contrast through optimized fat-water separation.Methods: The entire spine was auto-imaged in two contiguous 35 cm field of view (FOV sagittal stations, utilizing out-of-phase fast gradient echo (FGRE and T1 and/or T2 weighted fast spin echo (FSE IDEAL (Iterative Decomposition of Water and Fat with Echo Asymmetric and Least-squares Estimation sequences. 18 subjects were studied, one twice at 3.0T (pre and post contrast and one at both 1.5 T and 3.0T for a total of 20 spine examinations (8 at 1.5 T and 12 at 3.0T. Images were independently evaluated by two neuroradiologists and run through Automated Spine Survey Iterative Scan Technique (ASSIST analysis software for automated vertebral numbering.Results: In all 20 total spine studies, neuroradiologist and computer ASSIST labeling were concordant. In all cases, IDEAL provided uniform fat and water separation throughout the entire 70 cm FOV imaged. Two subjects demonstrated breast metastases and one had a large presumptive schwannoma. 14 subjects demonstrated degenerative disc disease with associated Modic Type I or II changes at one or more levels. FGRE ASSIST afforded subminute submillimeter in-plane resolution of the entire spine with high contrast between discs and vertebrae at both 1.5 and 3.0T. Marrow signal abnormalities could be particularly well characterized with IDEAL derived images and parametric maps.Conclusion: IDEAL ASSIST is a promising MRI technique affording a rapid automated high resolution, high contrast survey of the entire spine with optimized tissue characterization.
Generating a Tolerogenic Cell Therapy Knowledge Graph from Literature
Andre Lamurias
2017-11-01
Full Text Available Tolerogenic cell therapies provide an alternative to conventional immunosuppressive treatments of autoimmune disease and address, among other goals, the rejection of organ or stem cell transplants. Since various methodologies can be followed to develop tolerogenic therapies, it is important to be aware and up to date on all available studies that may be relevant to their improvement. Recently, knowledge graphs have been proposed to link various sources of information, using text mining techniques. Knowledge graphs facilitate the automatic retrieval of information about the topics represented in the graph. The objective of this work was to automatically generate a knowledge graph for tolerogenic cell therapy from biomedical literature. We developed a system, ICRel, based on machine learning to extract relations between cells and cytokines from abstracts. Our system retrieves related documents from PubMed, annotates each abstract with cell and cytokine named entities, generates the possible combinations of cell–cytokine pairs cooccurring in the same sentence, and identifies meaningful relations between cells and cytokines. The extracted relations were used to generate a knowledge graph, where each edge was supported by one or more documents. We obtained a graph containing 647 cell–cytokine relations, based on 3,264 abstracts. The modules of ICRel were evaluated with cross-validation and manual evaluation of the relations extracted. The relation extraction module obtained an F-measure of 0.789 in a reference database, while the manual evaluation obtained an accuracy of 0.615. Even though the knowledge graph is based on information that was already published in other articles about immunology, the system we present is more efficient than the laborious task of manually reading all the literature to find indirect or implicit relations. The ICRel graph will help experts identify implicit relations that may not be evident in published studies.
Interactive Graph Layout of a Million Nodes
Peng Mi; Maoyuan Sun; Moeti Masiane; Yong Cao; Chris North
2016-01-01
Sensemaking of large graphs, specifically those with millions of nodes, is a crucial task in many fields. Automatic graph layout algorithms, augmented with real-time human-in-the-loop interaction, can potentially support sensemaking of large graphs. However, designing interactive algorithms to achieve this is challenging. In this paper, we tackle the scalability problem of interactive layout of large graphs, and contribute a new GPU-based force-directed layout algorithm that exploits graph to...
Khovanov homology of graph-links
Nikonov, Igor M [M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)
2012-08-31
Graph-links arise as the intersection graphs of turning chord diagrams of links. Speaking informally, graph-links provide a combinatorial description of links up to mutations. Many link invariants can be reformulated in the language of graph-links. Khovanov homology, a well-known and useful knot invariant, is defined for graph-links in this paper (in the case of the ground field of characteristic two). Bibliography: 14 titles.
Multi-label Learning with Missing Labels Using Mixed Dependency Graphs
Wu, Baoyuan
2018-04-06
This work focuses on the problem of multi-label learning with missing labels (MLML), which aims to label each test instance with multiple class labels given training instances that have an incomplete/partial set of these labels (i.e., some of their labels are missing). The key point to handle missing labels is propagating the label information from the provided labels to missing labels, through a dependency graph that each label of each instance is treated as a node. We build this graph by utilizing different types of label dependencies. Specifically, the instance-level similarity is served as undirected edges to connect the label nodes across different instances and the semantic label hierarchy is used as directed edges to connect different classes. This base graph is referred to as the mixed dependency graph, as it includes both undirected and directed edges. Furthermore, we present another two types of label dependencies to connect the label nodes across different classes. One is the class co-occurrence, which is also encoded as undirected edges. Combining with the above base graph, we obtain a new mixed graph, called mixed graph with co-occurrence (MG-CO). The other is the sparse and low rank decomposition of the whole label matrix, to embed high-order dependencies over all labels. Combining with the base graph, the new mixed graph is called as MG-SL (mixed graph with sparse and low rank decomposition). Based on MG-CO and MG-SL, we further propose two convex transductive formulations of the MLML problem, denoted as MLMG-CO and MLMG-SL respectively. In both formulations, the instance-level similarity is embedded through a quadratic smoothness term, while the semantic label hierarchy is used as a linear constraint. In MLMG-CO, the class co-occurrence is also formulated as a quadratic smoothness term, while the sparse and low rank decomposition is incorporated into MLMG-SL, through two additional matrices (one is assumed as sparse, and the other is assumed as low
PRIVATE GRAPHS – ACCESS RIGHTS ON GRAPHS FOR SEAMLESS NAVIGATION
W. Dorner
2016-06-01
Full Text Available After the success of GNSS (Global Navigational Satellite Systems and navigation services for public streets, indoor seems to be the next big development in navigational services, relying on RTLS – Real Time Locating Services (e.g. WIFI and allowing seamless navigation. In contrast to navigation and routing services on public streets, seamless navigation will cause an additional challenge: how to make routing data accessible to defined users or restrict access rights for defined areas or only to parts of the graph to a defined user group? The paper will present case studies and data from literature, where seamless and especially indoor navigation solutions are presented (hospitals, industrial complexes, building sites, but the problem of restricted access rights was only touched from a real world, but not a technical perspective. The analysis of case studies will show, that the objective of navigation and the different target groups for navigation solutions will demand well defined access rights and require solutions, how to make only parts of a graph to a user or application available to solve a navigational task. The paper will therefore introduce the concept of private graphs, which is defined as a graph for navigational purposes covering the street, road or floor network of an area behind a public street and suggest different approaches how to make graph data for navigational purposes available considering access rights and data protection, privacy and security issues as well.
Abedin, Jaynal
2014-01-01
Targeted at those with an existing familiarity with R programming, this practical guide will appeal directly to programmers interested in learning effective data visualization techniques with R and a wide-range of its associated libraries.
Graph-cut based discrete-valued image reconstruction.
Tuysuzoglu, Ahmet; Karl, W Clem; Stojanovic, Ivana; Castañòn, David; Ünlü, M Selim
2015-05-01
Efficient graph-cut methods have been used with great success for labeling and denoising problems occurring in computer vision. Unfortunately, the presence of linear image mappings has prevented the use of these techniques in most discrete-amplitude image reconstruction problems. In this paper, we develop a graph-cut based framework for the direct solution of discrete amplitude linear image reconstruction problems cast as regularized energy function minimizations. We first analyze the structure of discrete linear inverse problem cost functions to show that the obstacle to the application of graph-cut methods to their solution is the variable mixing caused by the presence of the linear sensing operator. We then propose to use a surrogate energy functional that overcomes the challenges imposed by the sensing operator yet can be utilized efficiently in existing graph-cut frameworks. We use this surrogate energy functional to devise a monotonic iterative algorithm for the solution of discrete valued inverse problems. We first provide experiments using local convolutional operators and show the robustness of the proposed technique to noise and stability to changes in regularization parameter. Then we focus on nonlocal, tomographic examples where we consider limited-angle data problems. We compare our technique with state-of-the-art discrete and continuous image reconstruction techniques. Experiments show that the proposed method outperforms state-of-the-art techniques in challenging scenarios involving discrete valued unknowns.
Eigenfunction statistics on quantum graphs
Gnutzmann, S.; Keating, J.P.; Piotet, F.
2010-01-01
We investigate the spatial statistics of the energy eigenfunctions on large quantum graphs. It has previously been conjectured that these should be described by a Gaussian Random Wave Model, by analogy with quantum chaotic systems, for which such a model was proposed by Berry in 1977. The autocorrelation functions we calculate for an individual quantum graph exhibit a universal component, which completely determines a Gaussian Random Wave Model, and a system-dependent deviation. This deviation depends on the graph only through its underlying classical dynamics. Classical criteria for quantum universality to be met asymptotically in the large graph limit (i.e. for the non-universal deviation to vanish) are then extracted. We use an exact field theoretic expression in terms of a variant of a supersymmetric σ model. A saddle-point analysis of this expression leads to the estimates. In particular, intensity correlations are used to discuss the possible equidistribution of the energy eigenfunctions in the large graph limit. When equidistribution is asymptotically realized, our theory predicts a rate of convergence that is a significant refinement of previous estimates. The universal and system-dependent components of intensity correlation functions are recovered by means of an exact trace formula which we analyse in the diagonal approximation, drawing in this way a parallel between the field theory and semiclassics. Our results provide the first instance where an asymptotic Gaussian Random Wave Model has been established microscopically for eigenfunctions in a system with no disorder.
Andreas P. Braun
2016-04-01
Full Text Available Box graphs succinctly and comprehensively characterize singular fibers of elliptic fibrations in codimension two and three, as well as flop transitions connecting these, in terms of representation theoretic data. We develop a framework that provides a systematic map between a box graph and a crepant algebraic resolution of the singular elliptic fibration, thus allowing an explicit construction of the fibers from a singular Weierstrass or Tate model. The key tool is what we call a fiber face diagram, which shows the relevant information of a (partial toric triangulation and allows the inclusion of more general algebraic blowups. We shown that each such diagram defines a sequence of weighted algebraic blowups, thus providing a realization of the fiber defined by the box graph in terms of an explicit resolution. We show this correspondence explicitly for the case of SU(5 by providing a map between box graphs and fiber faces, and thereby a sequence of algebraic resolutions of the Tate model, which realizes each of the box graphs.
Degree-based graph construction
Kim, Hyunju; Toroczkai, Zoltan; Erdos, Peter L; Miklos, Istvan; Szekely, Laszlo A
2009-01-01
Degree-based graph construction is a ubiquitous problem in network modelling (Newman et al 2006 The Structure and Dynamics of Networks (Princeton Studies in Complexity) (Princeton, NJ: Princeton University Press), Boccaletti et al 2006 Phys. Rep. 424 175), ranging from social sciences to chemical compounds and biochemical reaction networks in the cell. This problem includes existence, enumeration, exhaustive construction and sampling questions with aspects that are still open today. Here we give necessary and sufficient conditions for a sequence of nonnegative integers to be realized as a simple graph's degree sequence, such that a given (but otherwise arbitrary) set of connections from an arbitrarily given node is avoided. We then use this result to present a swap-free algorithm that builds all simple graphs realizing a given degree sequence. In a wider context, we show that our result provides a greedy construction method to build all the f-factor subgraphs (Tutte 1952 Can. J. Math. 4 314) embedded within K n setmn S k , where K n is the complete graph and S k is a star graph centred on one of the nodes. (fast track communication)
Integer Flows and Circuit Covers of Graphs and Signed Graphs
Cheng, Jian
The work in Chapter 2 is motivated by Tutte and Jaeger's pioneering work on converting modulo flows into integer-valued flows for ordinary graphs. For a signed graphs (G, sigma), we first prove that for each k ∈ {2, 3}, if (G, sigma) is (k - 1)-edge-connected and contains an even number of negative edges when k = 2, then every modulo k-flow of (G, sigma) can be converted into an integer-valued ( k + 1)-ow with a larger or the same support. We also prove that if (G, sigma) is odd-(2p+1)-edge-connected, then (G, sigma) admits a modulo circular (2 + 1/ p)-flows if and only if it admits an integer-valued circular (2 + 1/p)-flows, which improves all previous result by Xu and Zhang (DM2005), Schubert and Steffen (EJC2015), and Zhu (JCTB2015). Shortest circuit cover conjecture is one of the major open problems in graph theory. It states that every bridgeless graph G contains a set of circuits F such that each edge is contained in at least one member of F and the length of F is at most 7/5∥E(G)∥. This concept was recently generalized to signed graphs by Macajova et al. (JGT2015). In Chapter 3, we improve their upper bound from 11∥E( G)∥ to 14/3 ∥E(G)∥, and if G is 2-edgeconnected and has even negativeness, then it can be further reduced to 11/3 ∥E(G)∥. Tutte's 3-flow conjecture has been studied by many graph theorists in the last several decades. As a new approach to this conjecture, DeVos and Thomassen considered the vectors as ow values and found that there is a close relation between vector S1-flows and integer 3-NZFs. Motivated by their observation, in Chapter 4, we prove that if a graph G admits a vector S1-flow with rank at most two, then G admits an integer 3-NZF. The concept of even factors is highly related to the famous Four Color Theorem. We conclude this dissertation in Chapter 5 with an improvement of a recent result by Chen and Fan (JCTB2016) on the upperbound of even factors. We show that if a graph G contains an even factor, then it
Multithreaded Asynchronous Graph Traversal for In-Memory and Semi-External Memory
Pearce, Roger; Gokhale, Maya; Amato, Nancy M.
2010-01-01
. Our highly parallel asynchronous approach hides data latency due to both poor locality and delays in the underlying graph data storage. We present an experimental study applying our technique to both In-Memory and Semi-External Memory graphs utilizing
Total Decomposition of Environmental Radionuclide Samples with a Microwave Oven
Ramon Garcia, Bernd Kahn
1998-01-01
Closed-vessel microwave assisted acid decomposition was investigated as an alternative to traditional methods of sample dissolution/decomposition. This technique, used in analytical chemistry, has some potential advantages over other procedures. It requires less reagents, it is faster, and it has the potential of achieving total dissolution because of higher temperatures and pressures
Fast modal decomposition for optical fibers using digital holography.
Lyu, Meng; Lin, Zhiquan; Li, Guowei; Situ, Guohai
2017-07-26
Eigenmode decomposition of the light field at the output end of optical fibers can provide fundamental insights into the nature of electromagnetic-wave propagation through the fibers. Here we present a fast and complete modal decomposition technique for step-index optical fibers. The proposed technique employs digital holography to measure the light field at the output end of the multimode optical fiber, and utilizes the modal orthonormal property of the basis modes to calculate the modal coefficients of each mode. Optical experiments were carried out to demonstrate the proposed decomposition technique, showing that this approach is fast, accurate and cost-effective.
Cullum, J. K.; Johnson, K.; Tůma, Miroslav
2003-01-01
Roč. 10, - (2003), s. 445-465 ISSN 1070-5325 R&D Projects: GA ČR GA201/02/0595; GA AV ČR IAA1030103 Institutional research plan: CEZ:AV0Z1030915 Keywords : parallel algorithms * graph partitioning * problem decomposition * rate of convergence Subject RIV: BA - General Mathematics Impact factor: 1.042, year: 2003
Thermoanalytical study of the decomposition of yttrium trifluoroacetate thin films
Eloussifi, H.; Farjas, J.; Roura, P.; Ricart, S.; Puig, T.; Obradors, X.; Dammak, M.
2013-01-01
We present the use of the thermal analysis techniques to study yttrium trifluoroacetate thin films decomposition. In situ analysis was done by means of thermogravimetry, differential thermal analysis, and evolved gas analysis. Solid residues at different stages and the final product have been characterized by X-ray diffraction and scanning electron microscopy. The thermal decomposition of yttrium trifluoroacetate thin films results in the formation of yttria and presents the same succession of intermediates than powder's decomposition, however, yttria and all intermediates but YF 3 appear at significantly lower temperatures. We also observe a dependence on the water partial pressure that was not observed in the decomposition of yttrium trifluoroacetate powders. Finally, a dependence on the substrate chemical composition is discerned. - Highlights: • Thermal decomposition of yttrium trifluoroacetate films. • Very different behavior of films with respect to powders. • Decomposition is enhanced in films. • Application of thermal analysis to chemical solution deposition synthesis of films
Graph modeling systems and methods
Neergaard, Mike
2015-10-13
An apparatus and a method for vulnerability and reliability modeling are provided. The method generally includes constructing a graph model of a physical network using a computer, the graph model including a plurality of terminating vertices to represent nodes in the physical network, a plurality of edges to represent transmission paths in the physical network, and a non-terminating vertex to represent a non-nodal vulnerability along a transmission path in the physical network. The method additionally includes evaluating the vulnerability and reliability of the physical network using the constructed graph model, wherein the vulnerability and reliability evaluation includes a determination of whether each terminating and non-terminating vertex represents a critical point of failure. The method can be utilized to evaluate wide variety of networks, including power grid infrastructures, communication network topologies, and fluid distribution systems.
Feder, Tomá s; Motwani, Rajeev
2009-01-01
Results on graph turnpike problem without distinctness, including its NP-completeness, and an O(m+n log n) algorithm, is presented. The usual turnpike problem has all pairwise distances given, but does not specify which pair of vertices w e corresponds to. There are two other problems that can be viewed as special cases of the graph turnpike problem, including the bandwidth problem and the low-distortion graph embedding problem. The aim for the turnpike problem in the NP-complete is to orient the edges with weights w i in either direction so that when the whole cycle is transversed in the real line, it returns to a chosen starting point for the cycle. An instance of the turnpike problem with or without distinctness is uniquely mappable if there exists at most one solution up to translation and choice of orientation.
Feder, Tomás
2009-06-01
Results on graph turnpike problem without distinctness, including its NP-completeness, and an O(m+n log n) algorithm, is presented. The usual turnpike problem has all pairwise distances given, but does not specify which pair of vertices w e corresponds to. There are two other problems that can be viewed as special cases of the graph turnpike problem, including the bandwidth problem and the low-distortion graph embedding problem. The aim for the turnpike problem in the NP-complete is to orient the edges with weights w i in either direction so that when the whole cycle is transversed in the real line, it returns to a chosen starting point for the cycle. An instance of the turnpike problem with or without distinctness is uniquely mappable if there exists at most one solution up to translation and choice of orientation.
Negation switching invariant signed graphs
Deepa Sinha
2014-04-01
Full Text Available A signed graph (or, $sigraph$ in short is a graph G in which each edge x carries a value $\\sigma(x \\in \\{-, +\\}$ called its sign. Given a sigraph S, the negation $\\eta(S$ of the sigraph S is a sigraph obtained from S by reversing the sign of every edge of S. Two sigraphs $S_{1}$ and $S_{2}$ on the same underlying graph are switching equivalent if it is possible to assign signs `+' (`plus' or `-' (`minus' to vertices of $S_{1}$ such that by reversing the sign of each of its edges that has received opposite signs at its ends, one obtains $S_{2}$. In this paper, we characterize sigraphs which are negation switching invariant and also see for what sigraphs, S and $\\eta (S$ are signed isomorphic.
Rosmanis, Ansis
2011-01-01
I introduce a continuous-time quantum walk on graphs called the quantum snake walk, the basis states of which are fixed-length paths (snakes) in the underlying graph. First, I analyze the quantum snake walk on the line, and I show that, even though most states stay localized throughout the evolution, there are specific states that most likely move on the line as wave packets with momentum inversely proportional to the length of the snake. Next, I discuss how an algorithm based on the quantum snake walk might potentially be able to solve an extended version of the glued trees problem, which asks to find a path connecting both roots of the glued trees graph. To the best of my knowledge, no efficient quantum algorithm solving this problem is known yet.
On Graph Rewriting, Reduction and Evaluation
Zerny, Ian
2010-01-01
We inter-derive two prototypical styles of graph reduction: reduction machines à la Turner and graph rewriting systems à la Barendregt et al. To this end, we adapt Danvy et al.'s mechanical program derivations from the world of terms to the world of graphs. We also outline how to inter-derive a t......We inter-derive two prototypical styles of graph reduction: reduction machines à la Turner and graph rewriting systems à la Barendregt et al. To this end, we adapt Danvy et al.'s mechanical program derivations from the world of terms to the world of graphs. We also outline how to inter...
The fascinating world of graph theory
Benjamin, Arthur; Zhang, Ping
2015-01-01
Graph theory goes back several centuries and revolves around the study of graphs-mathematical structures showing relations between objects. With applications in biology, computer science, transportation science, and other areas, graph theory encompasses some of the most beautiful formulas in mathematics-and some of its most famous problems. The Fascinating World of Graph Theory explores the questions and puzzles that have been studied, and often solved, through graph theory. This book looks at graph theory's development and the vibrant individuals responsible for the field's growth. Introducin
Graph-based modelling in engineering
Rysiński, Jacek
2017-01-01
This book presents versatile, modern and creative applications of graph theory in mechanical engineering, robotics and computer networks. Topics related to mechanical engineering include e.g. machine and mechanism science, mechatronics, robotics, gearing and transmissions, design theory and production processes. The graphs treated are simple graphs, weighted and mixed graphs, bond graphs, Petri nets, logical trees etc. The authors represent several countries in Europe and America, and their contributions show how different, elegant, useful and fruitful the utilization of graphs in modelling of engineering systems can be. .
XML Graphs in Program Analysis
Møller, Anders; Schwartzbach, Michael Ignatieff
2007-01-01
XML graphs have shown to be a simple and effective formalism for representing sets of XML documents in program analysis. It has evolved through a six year period with variants tailored for a range of applications. We present a unified definition, outline the key properties including validation...... of XML graphs against different XML schema languages, and provide a software package that enables others to make use of these ideas. We also survey four very different applications: XML in Java, Java Servlets and JSP, transformations between XML and non-XML data, and XSLT....
Graph topologies on closed multifunctions
Giuseppe Di Maio
2003-10-01
Full Text Available In this paper we study function space topologies on closed multifunctions, i.e. closed relations on X x Y using various hypertopologies. The hypertopologies are in essence, graph topologies i.e topologies on functions considered as graphs which are subsets of X x Y . We also study several topologies, including one that is derived from the Attouch-Wets filter on the range. We state embedding theorems which enable us to generalize and prove some recent results in the literature with the use of known results in the hyperspace of the range space and in the function space topologies of ordinary functions.
Cyclic graphs and Apery's theorem
Sorokin, V N
2002-01-01
This is a survey of results about the behaviour of Hermite-Pade approximants for graphs of Markov functions, and a survey of interpolation problems leading to Apery's result about the irrationality of the value ζ(3) of the Riemann zeta function. The first example is given of a cyclic graph for which the Hermite-Pade problem leads to Apery's theorem. Explicit formulae for solutions are obtained, namely, Rodrigues' formulae and integral representations. The asymptotic behaviour of the approximants is studied, and recurrence formulae are found
Minimum Covers of Fixed Cardinality in Weighted Graphs.
White, Lee J.
Reported is the result of research on combinatorial and algorithmic techniques for information processing. A method is discussed for obtaining minimum covers of specified cardinality from a given weighted graph. By the indicated method, it is shown that the family of minimum covers of varying cardinality is related to the minimum spanning tree of…
Decomposing Nekrasov decomposition
Morozov, A. [ITEP,25 Bolshaya Cheremushkinskaya, Moscow, 117218 (Russian Federation); Institute for Information Transmission Problems,19-1 Bolshoy Karetniy, Moscow, 127051 (Russian Federation); National Research Nuclear University MEPhI,31 Kashirskoe highway, Moscow, 115409 (Russian Federation); Zenkevich, Y. [ITEP,25 Bolshaya Cheremushkinskaya, Moscow, 117218 (Russian Federation); National Research Nuclear University MEPhI,31 Kashirskoe highway, Moscow, 115409 (Russian Federation); Institute for Nuclear Research of Russian Academy of Sciences,6a Prospekt 60-letiya Oktyabrya, Moscow, 117312 (Russian Federation)
2016-02-16
AGT relations imply that the four-point conformal block admits a decomposition into a sum over pairs of Young diagrams of essentially rational Nekrasov functions — this is immediately seen when conformal block is represented in the form of a matrix model. However, the q-deformation of the same block has a deeper decomposition — into a sum over a quadruple of Young diagrams of a product of four topological vertices. We analyze the interplay between these two decompositions, their properties and their generalization to multi-point conformal blocks. In the latter case we explain how Dotsenko-Fateev all-with-all (star) pair “interaction” is reduced to the quiver model nearest-neighbor (chain) one. We give new identities for q-Selberg averages of pairs of generalized Macdonald polynomials. We also translate the slicing invariance of refined topological strings into the language of conformal blocks and interpret it as abelianization of generalized Macdonald polynomials.
Decomposing Nekrasov decomposition
Morozov, A.; Zenkevich, Y.
2016-01-01
AGT relations imply that the four-point conformal block admits a decomposition into a sum over pairs of Young diagrams of essentially rational Nekrasov functions — this is immediately seen when conformal block is represented in the form of a matrix model. However, the q-deformation of the same block has a deeper decomposition — into a sum over a quadruple of Young diagrams of a product of four topological vertices. We analyze the interplay between these two decompositions, their properties and their generalization to multi-point conformal blocks. In the latter case we explain how Dotsenko-Fateev all-with-all (star) pair “interaction” is reduced to the quiver model nearest-neighbor (chain) one. We give new identities for q-Selberg averages of pairs of generalized Macdonald polynomials. We also translate the slicing invariance of refined topological strings into the language of conformal blocks and interpret it as abelianization of generalized Macdonald polynomials.
Symmetric Tensor Decomposition
Brachat, Jerome; Comon, Pierre; Mourrain, Bernard
2010-01-01
We present an algorithm for decomposing a symmetric tensor, of dimension n and order d, as a sum of rank-1 symmetric tensors, extending the algorithm of Sylvester devised in 1886 for binary forms. We recall the correspondence between the decomposition of a homogeneous polynomial in n variables...... of polynomial equations of small degree in non-generic cases. We propose a new algorithm for symmetric tensor decomposition, based on this characterization and on linear algebra computations with Hankel matrices. The impact of this contribution is two-fold. First it permits an efficient computation...... of the decomposition of any tensor of sub-generic rank, as opposed to widely used iterative algorithms with unproved global convergence (e.g. Alternate Least Squares or gradient descents). Second, it gives tools for understanding uniqueness conditions and for detecting the rank....
Methods of filtering the graph images of the functions
Олександр Григорович Бурса
2017-06-01
Full Text Available The theoretical aspects of cleaning raster images of scanned graphs of functions from digital, chromatic and luminance distortions by using computer graphics techniques have been considered. The basic types of distortions characteristic of graph images of functions have been stated. To suppress the distortion several methods, providing for high-quality of the resulting images and saving their topological features, were suggested. The paper describes the techniques developed and improved by the authors: the method of cleaning the image of distortions by means of iterative contrasting, based on the step-by-step increase in image contrast in the graph by 1%; the method of small entities distortion restoring, based on the thinning of the known matrix of contrast increase filter (the allowable dimensions of the nucleus dilution radius convolution matrix, which provide for the retention of the graph lines have been established; integration technique of the noise reduction method by means of contrasting and distortion restoring method of small entities with known σ-filter. Each method in the complex has been theoretically substantiated. The developed methods involve treatment of graph images as the entire image (global processing and its fragments (local processing. The metrics assessing the quality of the resulting image with the global and local processing have been chosen, the substantiation of the choice as well as the formulas have been given. The proposed complex methods of cleaning the graphs images of functions from grayscale image distortions is adaptive to the form of an image carrier, the distortion level in the image and its distribution. The presented results of testing the developed complex of methods for a representative sample of images confirm its effectiveness
Macasek, F.; Buriova, E.
2004-01-01
In this presentation authors present the results of analysis of decomposition products of [ 18 ]fluorodexyglucose. It is concluded that the coupling of liquid chromatography - mass spectrometry with electrospray ionisation is a suitable tool for quantitative analysis of FDG radiopharmaceutical, i.e. assay of basic components (FDG, glucose), impurities (Kryptofix) and decomposition products (gluconic and glucuronic acids etc.); 2-[ 18 F]fluoro-deoxyglucose (FDG) is sufficiently stable and resistant towards autoradiolysis; the content of radiochemical impurities (2-[ 18 F]fluoro-gluconic and 2-[ 18 F]fluoro-glucuronic acids in expired FDG did not exceed 1%
Separable decompositions of bipartite mixed states
Li, Jun-Li; Qiao, Cong-Feng
2018-04-01
We present a practical scheme for the decomposition of a bipartite mixed state into a sum of direct products of local density matrices, using the technique developed in Li and Qiao (Sci. Rep. 8:1442, 2018). In the scheme, the correlation matrix which characterizes the bipartite entanglement is first decomposed into two matrices composed of the Bloch vectors of local states. Then, we show that the symmetries of Bloch vectors are consistent with that of the correlation matrix, and the magnitudes of the local Bloch vectors are lower bounded by the correlation matrix. Concrete examples for the separable decompositions of bipartite mixed states are presented for illustration.
Two Notes on Discrimination and Decomposition
Nielsen, Helena Skyt
1998-01-01
1. It turns out that the Oaxaca-Blinder wage decomposition is inadequate when it comes to calculation of separate contributions for indicator variables. The contributions are not robust against a change of reference group. I extend the Oaxaca-Blinder decomposition to handle this problem. 2. The p....... The paper suggests how to use the logit model to decompose the gender difference in the probability of an occurrence. The technique is illustrated by an analysis of discrimination in child labor in rural Zambia....
Multiple graph regularized protein domain ranking
Wang, Jim Jing-Yan
2012-11-19
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. 2012 Wang et al; licensee BioMed Central Ltd.
Multiple graph regularized protein domain ranking
Wang, Jim Jing-Yan; Bensmail, Halima; Gao, Xin
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. 2012 Wang et al; licensee BioMed Central Ltd.
Multiple graph regularized protein domain ranking.
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
Wang Jim
2012-11-01
Full Text Available Abstract 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.
Spreadsheets, Graphing Calculators and the Line of Best Fit
Bernie O'Sullivan
2003-07-01
One technique that can now be done, almost mindlessly, is the line of best fit. Both the graphing calculator and the Excel spreadsheet produce models for collected data that appear to be very good fits, but upon closer scrutiny, are revealed to be quite poor. This article will examine one such case. I will couch the paper within the framework of a very good classroom investigation that will help generate students’ understanding of the basic principles of curve fitting and will enable them to produce a very accurate model of collected data by combining the technology of the graphing calculator and the spreadsheet.
Proceedings 3rd Workshop on GRAPH Inspection and Traversal Engineering (GRAPHITE 2014)
2014-01-01
is to foster the convergence on research interests from several communities dealing with graph analysis in all its forms in computer science, with a particular attention to software development and analysis. Graphs are used to represent data and processes in many application areas, and they are subjected......These are the proceedings of the Third Workshop on GRAPH Inspection and Traversal Engineering (GRAPHITE 2014), which took place on April 5, 2014 in Grenoble, France, as a satellite event of the 17th European Joint Conferences on Theory and Practice of Software (ETAPS 2014). The aim of GRAPHITE...... to various computational algorithms in order to analyze them. Just restricting the attention to the analysis of software, graph analysis algorithms are used, for instance, to verify properties using model checking techniques that explore the system's state space graph or static analysis techniques based...
A linear graph for digoxin radioimmunoassay
Smith, S.E.; Richter, A.
1975-01-01
The determination of drug or hormone concentrations by radio-immunoassay involves interpolation of values for radioisotope counts within standard curves, a technique which requires some dexterity in curve drawing and which results in some inaccuracy in practice. Most of the procedures designed to overcome these difficulties are complex and time-consuming. In radioimmunoassays involving saturation of the antibody-binding sites a special case exists in that the bound radioactivity is directly proportional to the specific activity of the ligand in the system. Thus a graph of the ratio of radioactivity bound in the absence to that in the presence of added non-radioactive ligand is linear against the concentration of added ligand (Hales,C.N., and Randle, P.J., 1963, Biochem. J., vol. 88, 137). A description is given of a simple and convenient modification of their method, and its application to the routine clinical determination of digoxin using a commercial kit (Lanoxitest β digoxin radioimmunoassay kit, Wellcome Reagents Ltd.). Specially constructed graph paper, which yields linearity with standard solutions, was designed so that it could be used directly without data transmission. The specific activity function appears as the upper arithmetical horizontal scale; corresponding values of the concentration of non-radioactive ligand in the solution added were individually calculated and appear on the lower scale opposite the appropriate values of the upper scale. The linearity of the graphs obtained confirmed that binding of digoxin was approximately constant through the range of clinical concentrations tested (0.5 to 8ng/ml), although binding declined slightly at higher concentrations. (U.K.)
Constructing Knowledge Graphs of Depression
Huang, Zhisheng; Yang, Jie; van Harmelen, Frank; Hu, Qing
2017-01-01
Knowledge Graphs have been shown to be useful tools for integrating multiple medical knowledge sources, and to support such tasks as medical decision making, literature retrieval, determining healthcare quality indicators, co-morbodity analysis and many others. A large number of medical knowledge
Partitioning graphs into connected parts
Hof, van 't P.; Paulusma, D.; Woeginger, G.J.; Frid, A.; Morozov, A.S.; Rybalchenko, A.; Wagner, K.W.
2009-01-01
The 2-DISJOINT CONNECTED SUBGRAPHS problem asks if a given graph has two vertex-disjoint connected subgraphs containing pre-specified sets of vertices. We show that this problem is NP-complete even if one of the sets has cardinality 2. The LONGEST PATH CONTRACTIBILITY problem asks for the largest
Isoperimetric inequalities for minimal graphs
Pacelli Bessa, G.; Montenegro, J.F.
2007-09-01
Based on Markvorsen and Palmer's work on mean time exit and isoperimetric inequalities we establish slightly better isoperimetric inequalities and mean time exit estimates for minimal graphs in N x R. We also prove isoperimetric inequalities for submanifolds of Hadamard spaces with tamed second fundamental form. (author)
Ancestral Genres of Mathematical Graphs
Gerofsky, Susan
2011-01-01
Drawing from sources in gesture studies, cognitive science, the anthropology of religion and art/architecture history, this article explores cultural, bodily and cosmological resonances carried (unintentionally) by mathematical graphs on Cartesian coordinates. Concepts of asymmetric bodily spaces, grids, orthogonality, mapping and sacred spaces…
Humidity Graphs for All Seasons.
Esmael, F.
1982-01-01
In a previous article in this journal (Vol. 17, p358, 1979), a wet-bulb depression table was recommended for two simple experiments to determine relative humidity. However, the use of a graph is suggested because it gives the relative humidity directly from the wet and dry bulb readings. (JN)
Contracting a planar graph efficiently
Holm, Jacob; Italiano, Giuseppe F.; Karczmarz, Adam
2017-01-01
the data structure, we can achieve optimal running times for decremental bridge detection, 2-edge connectivity, maximal 3-edge connected components, and the problem of finding a unique perfect matching for a static planar graph. Furthermore, we improve the running times of algorithms for several planar...
Graph Model Based Indoor Tracking
Jensen, Christian Søndergaard; Lu, Hua; Yang, Bin
2009-01-01
The tracking of the locations of moving objects in large indoor spaces is important, as it enables a range of applications related to, e.g., security and indoor navigation and guidance. This paper presents a graph model based approach to indoor tracking that offers a uniform data management...
A graph with fractional revival
Bernard, Pierre-Antoine; Chan, Ada; Loranger, Érika; Tamon, Christino; Vinet, Luc
2018-02-01
An example of a graph that admits balanced fractional revival between antipodes is presented. It is obtained by establishing the correspondence between the quantum walk on a hypercube where the opposite vertices across the diagonals of each face are connected and, the coherent transport of single excitations in the extension of the Krawtchouk spin chain with next-to-nearest neighbour interactions.
Fixation Time for Evolutionary Graphs
Nie, Pu-Yan; Zhang, Pei-Ai
Evolutionary graph theory (EGT) is recently proposed by Lieberman et al. in 2005. EGT is successful for explaining biological evolution and some social phenomena. It is extremely important to consider the time of fixation for EGT in many practical problems, including evolutionary theory and the evolution of cooperation. This study characterizes the time to asymptotically reach fixation.
Parallel processing for pitch splitting decomposition
Barnes, Levi; Li, Yong; Wadkins, David; Biederman, Steve; Miloslavsky, Alex; Cork, Chris
2009-10-01
Decomposition of an input pattern in preparation for a double patterning process is an inherently global problem in which the influence of a local decomposition decision can be felt across an entire pattern. In spite of this, a large portion of the work can be massively distributed. Here, we discuss the advantages of geometric distribution for polygon operations with limited range of influence. Further, we have found that even the naturally global "coloring" step can, in large part, be handled in a geometrically local manner. In some practical cases, up to 70% of the work can be distributed geometrically. We also describe the methods for partitioning the problem into local pieces and present scaling data up to 100 CPUs. These techniques reduce DPT decomposition runtime by orders of magnitude.
Fingerprint recognition system by use of graph matching
Shen, Wei; Shen, Jun; Zheng, Huicheng
2001-09-01
Fingerprint recognition is an important subject in biometrics to identify or verify persons by physiological characteristics, and has found wide applications in different domains. In the present paper, we present a finger recognition system that combines singular points and structures. The principal steps of processing in our system are: preprocessing and ridge segmentation, singular point extraction and selection, graph representation, and finger recognition by graphs matching. Our fingerprint recognition system is implemented and tested for many fingerprint images and the experimental result are satisfactory. Different techniques are used in our system, such as fast calculation of orientation field, local fuzzy dynamical thresholding, algebraic analysis of connections and fingerprints representation and matching by graphs. Wed find that for fingerprint database that is not very large, the recognition rate is very high even without using a prior coarse category classification. This system works well for both one-to-few and one-to-many problems.
Coloring sums of extensions of certain graphs
Johan Kok
2017-12-01
Full Text Available We recall that the minimum number of colors that allow a proper coloring of graph $G$ is called the chromatic number of $G$ and denoted $\\chi(G$. Motivated by the introduction of the concept of the $b$-chromatic sum of a graph the concept of $\\chi'$-chromatic sum and $\\chi^+$-chromatic sum are introduced in this paper. The extended graph $G^x$ of a graph $G$ was recently introduced for certain regular graphs. This paper furthers the concepts of $\\chi'$-chromatic sum and $\\chi^+$-chromatic sum to extended paths and cycles. Bipartite graphs also receive some attention. The paper concludes with patterned structured graphs. These last said graphs are typically found in chemical and biological structures.
Mathematical Minute: Rotating a Function Graph
Bravo, Daniel; Fera, Joseph
2013-01-01
Using calculus only, we find the angles you can rotate the graph of a differentiable function about the origin and still obtain a function graph. We then apply the solution to odd and even degree polynomials.
Bounds on Gromov hyperbolicity constant in graphs
Infinite graphs; Cartesian product graphs; independence number; domin- ation number; geodesics ... the secure transmission of information through the internet (see [15, 16]). In particular, ..... In particular, δ(G) is an integer multiple of 1/4.
Summary: beyond fault trees to fault graphs
Alesso, H.P.; Prassinos, P.; Smith, C.F.
1984-09-01
Fault Graphs are the natural evolutionary step over a traditional fault-tree model. A Fault Graph is a failure-oriented directed graph with logic connectives that allows cycles. We intentionally construct the Fault Graph to trace the piping and instrumentation drawing (P and ID) of the system, but with logical AND and OR conditions added. Then we evaluate the Fault Graph with computer codes based on graph-theoretic methods. Fault Graph computer codes are based on graph concepts, such as path set (a set of nodes traveled on a path from one node to another) and reachability (the complete set of all possible paths between any two nodes). These codes are used to find the cut-sets (any minimal set of component failures that will fail the system) and to evaluate the system reliability
Torsional rigidity, isospectrality and quantum graphs
Colladay, Don; McDonald, Patrick; Kaganovskiy, Leon
2017-01-01
We study torsional rigidity for graph and quantum graph analogs of well-known pairs of isospectral non-isometric planar domains. We prove that such isospectral pairs are distinguished by torsional rigidity. (paper)
Interactive exploration of large-scale time-varying data using dynamic tracking graphs
Widanagamaachchi, W.
2012-10-01
Exploring and analyzing the temporal evolution of features in large-scale time-varying datasets is a common problem in many areas of science and engineering. One natural representation of such data is tracking graphs, i.e., constrained graph layouts that use one spatial dimension to indicate time and show the "tracks" of each feature as it evolves, merges or disappears. However, for practical data sets creating the corresponding optimal graph layouts that minimize the number of intersections can take hours to compute with existing techniques. Furthermore, the resulting graphs are often unmanageably large and complex even with an ideal layout. Finally, due to the cost of the layout, changing the feature definition, e.g. by changing an iso-value, or analyzing properly adjusted sub-graphs is infeasible. To address these challenges, this paper presents a new framework that couples hierarchical feature definitions with progressive graph layout algorithms to provide an interactive exploration of dynamically constructed tracking graphs. Our system enables users to change feature definitions on-the-fly and filter features using arbitrary attributes while providing an interactive view of the resulting tracking graphs. Furthermore, the graph display is integrated into a linked view system that provides a traditional 3D view of the current set of features and allows a cross-linked selection to enable a fully flexible spatio-temporal exploration of data. We demonstrate the utility of our approach with several large-scale scientific simulations from combustion science. © 2012 IEEE.
Bond graph modeling of centrifugal compression systems
Uddin, Nur; Gravdahl, Jan Tommy
2015-01-01
A novel approach to model unsteady fluid dynamics in a compressor network by using a bond graph is presented. The model is intended in particular for compressor control system development. First, we develop a bond graph model of a single compression system. Bond graph modeling offers a different perspective to previous work by modeling the compression system based on energy flow instead of fluid dynamics. Analyzing the bond graph model explains the energy flow during compressor surge. Two pri...
A Graph Calculus for Predicate Logic
Paulo A. S. Veloso
2013-03-01
Full Text Available We introduce a refutation graph calculus for classical first-order predicate logic, which is an extension of previous ones for binary relations. One reduces logical consequence to establishing that a constructed graph has empty extension, i. e. it represents bottom. Our calculus establishes that a graph has empty extension by converting it to a normal form, which is expanded to other graphs until we can recognize conflicting situations (equivalent to a formula and its negation.
Sphere and dot product representations of graphs
R.J. Kang (Ross); T. Müller (Tobias)
2012-01-01
textabstractA graph $G$ is a $k$-sphere graph if there are $k$-dimensional real vectors $v_1,\\dots,v_n$ such that $ij\\in E(G)$ if and only if the distance between $v_i$ and $v_j$ is at most $1$. A graph $G$ is a $k$-dot product graph if there are $k$-dimensional real vectors $v_1,\\dots,v_n$ such
Constructs for Programming with Graph Rewrites
Rodgers, Peter
2000-01-01
Graph rewriting is becoming increasingly popular as a method for programming with graph based data structures. We present several modifications to a basic serial graph rewriting paradigm and discuss how they improve coding programs in the Grrr graph rewriting programming language. The constructs we present are once only nodes, attractor nodes and single match rewrites. We illustrate the operation of the constructs by example. The advantages of adding these new rewrite modifiers is to reduce t...
Decomposition in conic optimization with partially separable structure
Sun, Yifan; Andersen, Martin Skovgaard; Vandenberghe, Lieven
2014-01-01
Decomposition techniques for linear programming are difficult to extend to conic optimization problems with general nonpolyhedral convex cones because the conic inequalities introduce an additional nonlinear coupling between the variables. However in many applications the convex cones have...
Towards decomposition of live chemical agents by pyrotechnic mixtures
Bouma, R.H.B.; Noort, D.
2012-01-01
The aim of this study is to contribute to improved EOD neutralisation techniques against improvised explosive devices (IEDs) containing chemical agents. The decomposition of dimethyl methylphosphonate (DMMP) when exposed to a burning aluminum/potassium nitrate pyrotechnic mixture is studied
Graceful, harmonious and magic type labelings relations and techniques
López, Susana C
2017-01-01
Aimed toward upper undergraduate and graduate students in mathematics, this book examines the foremost forms of graph labelings including magic, harmonious, and graceful labelings. An overview of basic graph theory concepts and notation is provided along with the origins of graph labeling. Common methods and techniques are presented introducing readers to links between graph labels. A variety of useful techniques are presented to analyze and understand properties of graph labelings. The classical results integrated with new techniques, complete proofs, numerous exercises, and a variety of open problems, will provide readers with a solid understanding of graph labelings.
Bose and Fermi walk configurations on planar graphs
Arrowsmith, D K; Bhatti, F M; Essam, J W
2012-01-01
The number, f C n (H), of n-walk configurations of type C is investigated on certain two-rooted directed planar graphs H which will be always realized as plane graphs in R 2 . C may be Bose or Fermi as defined by Inui and Katori. Both types of configuration are collections of non-crossing walks which follow the directed paths between the roots of the plane graph H. In the case of configurations of Fermi type each walk may be included only once. The number f Bose n (H) is shown to be a polynomial in n of degree n max − 1 where n max is the maximum number of walks in a Fermi configuration. The coefficient of the highest power of n in this polynomial is simply related to the number of maximal Fermi walk configurations. It is also shown that n max = c(H) + 1 where c(H) is the number of finite faces on H. Extension of these results to multi-rooted graphs is also discussed. When H is the union of paths between two sites of the directed square lattice subject to various boundary conditions Kreweras showed that the number of Bose configurations is equal to the number of n-element multi-chains on segments of Young’s lattice. He expressed this number as a determinant the elements of which are polynomials in n. We evaluate this determinant by the method of LU decomposition in the case of ‘watermelon’ configurations above a wall. In this case the polynomial is a product of linear factors but on introducing a second wall the polynomial does not completely factorize but has a factor which is the number of watermelon configurations on the largest rectangular subgraph. The number of two-rooted ‘star’ configurations is found to be the product of the numbers of watermelon configurations on the three rectangular subgraphs into which it may be partitioned. (paper)
Tensor decompositions for the analysis of atomic resolution electron energy loss spectra
Spiegelberg, Jakob; Rusz, Ján [Department of Physics and Astronomy, Uppsala University, Box 516, S-751 20 Uppsala (Sweden); Pelckmans, Kristiaan [Department of Information Technology, Uppsala University, Box 337, S-751 05 Uppsala (Sweden)
2017-04-15
A selection of tensor decomposition techniques is presented for the detection of weak signals in electron energy loss spectroscopy (EELS) data. The focus of the analysis lies on the correct representation of the simulated spatial structure. An analysis scheme for EEL spectra combining two-dimensional and n-way decomposition methods is proposed. In particular, the performance of robust principal component analysis (ROBPCA), Tucker Decompositions using orthogonality constraints (Multilinear Singular Value Decomposition (MLSVD)) and Tucker decomposition without imposed constraints, canonical polyadic decomposition (CPD) and block term decompositions (BTD) on synthetic as well as experimental data is examined. - Highlights: • A scheme for compression and analysis of EELS or EDX data is proposed. • Several tensor decomposition techniques are presented for BSS on hyperspectral data. • Robust PCA and MLSVD are discussed for denoising of raw data.
On the sizes of expander graphs and minimum distances of graph codes
Høholdt, Tom; Justesen, Jørn
2014-01-01
We give lower bounds for the minimum distances of graph codes based on expander graphs. The bounds depend only on the second eigenvalue of the graph and the parameters of the component codes. We also give an upper bound on the size of a degree regular graph with given second eigenvalue....
McMillen, Sue; McMillen, Beth
2010-01-01
Connecting stories to qualitative coordinate graphs has been suggested as an effective instructional strategy. Even students who are able to "create" bar graphs may struggle to correctly "interpret" them. Giving children opportunities to work with qualitative graphs can help them develop the skills to interpret, describe, and compare information…
The groupies of random multipartite graphs
Portmann, Marius; Wang, Hongyun
2012-01-01
If a vertex $v$ in a graph $G$ has degree larger than the average of the degrees of its neighbors, we call it a groupie in $G$. In the current work, we study the behavior of groupie in random multipartite graphs with the link probability between sets of nodes fixed. Our results extend the previous ones on random (bipartite) graphs.
Modeling Software Evolution using Algebraic Graph Rewriting
Ciraci, Selim; van den Broek, Pim
We show how evolution requests can be formalized using algebraic graph rewriting. In particular, we present a way to convert the UML class diagrams to colored graphs. Since changes in software may effect the relation between the methods of classes, our colored graph representation also employs the
An intersection graph of straight lines
Thomassen, Carsten
2002-01-01
G. Ehrlich, S. Even, and R.E. Tarjan conjectured that the graph obtained from a complete 3 partite graph K4,4,4 by deleting the edges of four disjoint triangles is not the intersection graph of straight line segments in the plane. We show that it is....
Girth 5 graphs from relative difference sets
Jørgensen, Leif Kjær
2005-01-01
We consider the problem of construction of graphs with given degree $k$ and girth 5 and as few vertices as possible. We give a construction of a family of girth 5 graphs based on relative difference sets. This family contains the smallest known graph of degree 8 and girth 5 which was constructed ...
Cycles in weighted graphs and related topics
Zhang, Shenggui
2002-01-01
This thesis contains results on paths andcycles in graphs andon a more or less relatedtopic, the vulnerability of graphs. In the first part of the thesis, Chapters 2 through 5, we concentrate on paths andcycles in weightedgraphs. A number of sufficient conditions are presentedfor graphs to contain
Graph Transformation Semantics for a QVT Language
Rensink, Arend; Nederpel, Ronald; Bruni, Roberto; Varró, Dániel
It has been claimed by many in the graph transformation community that model transformation, as understood in the context of Model Driven Architecture, can be seen as an application of graph transformation. In this paper we substantiate this claim by giving a graph transformation-based semantics to
Girth 5 graphs from relative difference sets
Jørgensen, Leif Kjær
We consider the problem of construction of graphs with given degree and girth 5 and as few vertices as possible. We give a construction of a family of girth 5 graphs based on relative difference sets. This family contains the smallest known graph of degree 8 and girth 5 which was constructed by G...
Improper colouring of (random) unit disk graphs
Kang, R.J.; Müller, T.; Sereni, J.S.
2008-01-01
For any graph G, the k-improper chromatic number ¿k(G) is the smallest number of colours used in a colouring of G such that each colour class induces a subgraph of maximum degree k. We investigate ¿k for unit disk graphs and random unit disk graphs to generalise results of McDiarmid and Reed
Alliances and Bisection Width for Planar Graphs
Olsen, Martin; Revsbæk, Morten
2013-01-01
An alliance in a graph is a set of vertices (allies) such that each vertex in the alliance has at least as many allies (counting the vertex itself) as non-allies in its neighborhood of the graph. We show that any planar graph with minimum degree at least 4 can be split into two alliances in polyn...
RATGRAPH: Computer Graphing of Rational Functions.
Minch, Bradley A.
1987-01-01
Presents an easy-to-use Applesoft BASIC program that graphs rational functions and any asymptotes that the functions might have. Discusses the nature of rational functions, graphing them manually, employing a computer to graph rational functions, and describes how the program works. (TW)
A new cluster algorithm for graphs
S. van Dongen
1998-01-01
textabstractA new cluster algorithm for graphs called the emph{Markov Cluster algorithm ($MCL$ algorithm) is introduced. The graphs may be both weighted (with nonnegative weight) and directed. Let~$G$~be such a graph. The $MCL$ algorithm simulates flow in $G$ by first identifying $G$ in a
Well-covered graphs and factors
Randerath, Bert; Vestergaard, Preben D.
2006-01-01
A maximum independent set of vertices in a graph is a set of pairwise nonadjacent vertices of largest cardinality α. Plummer defined a graph to be well-covered, if every independent set is contained in a maximum independent set of G. Every well-covered graph G without isolated vertices has a perf...
A new characterization of trivially perfect graphs
Christian Rubio Montiel
2015-03-01
Full Text Available A graph $G$ is \\emph{trivially perfect} if for every induced subgraph the cardinality of the largest set of pairwise nonadjacent vertices (the stability number $\\alpha(G$ equals the number of (maximal cliques $m(G$. We characterize the trivially perfect graphs in terms of vertex-coloring and we extend some definitions to infinite graphs.
47 CFR 80.761 - Conversion graphs.
2010-10-01
... MARITIME SERVICES Standards for Computing Public Coast Station VHF Coverage § 80.761 Conversion graphs. The following graphs must be employed where conversion from one to the other of the indicated types of units is... 47 Telecommunication 5 2010-10-01 2010-10-01 false Conversion graphs. 80.761 Section 80.761...
G. González Rey
2007-09-01
Full Text Available Mediante un modelo matemático son dadas las principales relaciones entre los parámetros geométricos básicos requeridosen la evaluación del diámetro de cresta exterior de un engranaje ortogonal de ruedas cónicas con dientes rectos y suma decorrecciones radiales iguales a cero. Adicionalmente, serán brindados algunos resultados que asocian la correspondenciaentre una geometría racional y la capacidad de carga de un engranaje cónico con restricciones del diámetro de crestaexterior. Para la determinación de los procedimientos de cálculo, los problemas planteados sobre los modelos matemáticoshan sido serán representados por medio de grafos bicromáticos.Palabras claves: Engranajes cónicos, diseño racional, modelo matemático._______________________________________________________________________________Abstract:By means of a mathematical model, the main relations for the evaluation of the outer tip diameter on straight bevelgear with sum of the profile shift coefficients equal to zero are given. Additionally, some results associated with arational geometry and high load capacities of straight bevel gear with restrictions in the outer tip diameter arepresented. For the determination of the calculation procedures based on mathematical models was used thetechnique of representation by means of graphs.Key words: Straight bevel gear, rational design, mathematical models, graphs technique.
Multi-Level Anomaly Detection on Time-Varying Graph Data
Bridges, Robert A [ORNL; Collins, John P [ORNL; Ferragut, Erik M [ORNL; Laska, Jason A [ORNL; Sullivan, Blair D [ORNL
2015-01-01
This work presents a novel modeling and analysis framework for graph sequences which addresses the challenge of detecting and contextualizing anomalies in labelled, streaming graph data. We introduce a generalization of the BTER model of Seshadhri et al. by adding flexibility to community structure, and use this model to perform multi-scale graph anomaly detection. Specifically, probability models describing coarse subgraphs are built by aggregating probabilities at finer levels, and these closely related hierarchical models simultaneously detect deviations from expectation. This technique provides insight into a graph's structure and internal context that may shed light on a detected event. Additionally, this multi-scale analysis facilitates intuitive visualizations by allowing users to narrow focus from an anomalous graph to particular subgraphs or nodes causing the anomaly. For evaluation, two hierarchical anomaly detectors are tested against a baseline Gaussian method on a series of sampled graphs. We demonstrate that our graph statistics-based approach outperforms both a distribution-based detector and the baseline in a labeled setting with community structure, and it accurately detects anomalies in synthetic and real-world datasets at the node, subgraph, and graph levels. To illustrate the accessibility of information made possible via this technique, the anomaly detector and an associated interactive visualization tool are tested on NCAA football data, where teams and conferences that moved within the league are identified with perfect recall, and precision greater than 0.786.
Generating QCD amplitudes in the color-flow basis with MadGraph
Hagiwara, Kaoru; Takaesu, Yoshitaro
2011-01-01
We propose to make use of the off-shell recursive relations with the color-flow decomposition in the calculation of QCD amplitudes on MadGraph. We introduce colored quarks and their interactions with nine gluons in the color-flow basis plus an Abelian gluon on MadGraph, such that it generates helicity amplitudes in the color-flow basis with off-shell recursive formulae for multi-gluon sub-amplitudes. We demonstrate calculations of up to 5-jet processes such as gg→5g, u anti u→5g and uu→uuggg. Although our demonstration is limited, it paves the way to evaluate amplitudes with more quark lines and gluons with MadGraph. (orig.)
On a conjecture concerning helly circle graphs
Durán Guillermo
2003-01-01
Full Text Available We say that G is an e-circle graph if there is a bijection between its vertices and straight lines on the cartesian plane such that two vertices are adjacent in G if and only if the corresponding lines intersect inside the circle of radius one. This definition suggests a method for deciding whether a given graph G is an e-circle graph, by constructing a convenient system S of equations and inequations which represents the structure of G, in such a way that G is an e-circle graph if and only if S has a solution. In fact, e-circle graphs are exactly the circle graphs (intersection graphs of chords in a circle, and thus this method provides an analytic way for recognizing circle graphs. A graph G is a Helly circle graph if G is a circle graph and there exists a model of G by chords such that every three pairwise intersecting chords intersect at the same point. A conjecture by Durán (2000 states that G is a Helly circle graph if and only if G is a circle graph and contains no induced diamonds (a diamond is a graph formed by four vertices and five edges. Many unsuccessful efforts - mainly based on combinatorial and geometrical approaches - have been done in order to validate this conjecture. In this work, we utilize the ideas behind the definition of e-circle graphs and restate this conjecture in terms of an equivalence between two systems of equations and inequations, providing a new, analytic tool to deal with it.
Centrosymmetric Graphs And A Lower Bound For Graph Energy Of Fullerenes
Katona Gyula Y.
2014-11-01
Full Text Available The energy of a molecular graph G is defined as the summation of the absolute values of the eigenvalues of adjacency matrix of a graph G. In this paper, an infinite class of fullerene graphs with 10n vertices, n ≥ 2, is considered. By proving centrosymmetricity of the adjacency matrix of these fullerene graphs, a lower bound for its energy is given. Our method is general and can be extended to other class of fullerene graphs.
Subsampling for graph power spectrum estimation
Chepuri, Sundeep Prabhakar; Leus, Geert
2016-01-01
In this paper we focus on subsampling stationary random signals that reside on the vertices of undirected graphs. Second-order stationary graph signals are obtained by filtering white noise and they admit a well-defined power spectrum. Estimating the graph power spectrum forms a central component of stationary graph signal processing and related inference tasks. We show that by sampling a significantly smaller subset of vertices and using simple least squares, we can reconstruct the power spectrum of the graph signal from the subsampled observations, without any spectral priors. In addition, a near-optimal greedy algorithm is developed to design the subsampling scheme.
On 4-critical t-perfect graphs
Benchetrit, Yohann
2016-01-01
It is an open question whether the chromatic number of $t$-perfect graphs is bounded by a constant. The largest known value for this parameter is 4, and the only example of a 4-critical $t$-perfect graph, due to Laurent and Seymour, is the complement of the line graph of the prism $\\Pi$ (a graph is 4-critical if it has chromatic number 4 and all its proper induced subgraphs are 3-colorable). In this paper, we show a new example of a 4-critical $t$-perfect graph: the complement of the line gra...
Subsampling for graph power spectrum estimation
Chepuri, Sundeep Prabhakar
2016-10-06
In this paper we focus on subsampling stationary random signals that reside on the vertices of undirected graphs. Second-order stationary graph signals are obtained by filtering white noise and they admit a well-defined power spectrum. Estimating the graph power spectrum forms a central component of stationary graph signal processing and related inference tasks. We show that by sampling a significantly smaller subset of vertices and using simple least squares, we can reconstruct the power spectrum of the graph signal from the subsampled observations, without any spectral priors. In addition, a near-optimal greedy algorithm is developed to design the subsampling scheme.
Proving relations between modular graph functions
Basu, Anirban
2016-01-01
We consider modular graph functions that arise in the low energy expansion of the four graviton amplitude in type II string theory. The vertices of these graphs are the positions of insertions of vertex operators on the toroidal worldsheet, while the links are the scalar Green functions connecting the vertices. Graphs with four and five links satisfy several non-trivial relations, which have been proved recently. We prove these relations by using elementary properties of Green functions and the details of the graphs. We also prove a relation between modular graph functions with six links. (paper)
Structuring heterogeneous biological information using fuzzy clustering of k-partite graphs
Theis Fabian J
2010-10-01
Full Text Available Abstract Background Extensive and automated data integration in bioinformatics facilitates the construction of large, complex biological networks. However, the challenge lies in the interpretation of these networks. While most research focuses on the unipartite or bipartite case, we address the more general but common situation of k-partite graphs. These graphs contain k different node types and links are only allowed between nodes of different types. In order to reveal their structural organization and describe the contained information in a more coarse-grained fashion, we ask how to detect clusters within each node type. Results Since entities in biological networks regularly have more than one function and hence participate in more than one cluster, we developed a k-partite graph partitioning algorithm that allows for overlapping (fuzzy clusters. It determines for each node a degree of membership to each cluster. Moreover, the algorithm estimates a weighted k-partite graph that connects the extracted clusters. Our method is fast and efficient, mimicking the multiplicative update rules commonly employed in algorithms for non-negative matrix factorization. It facilitates the decomposition of networks on a chosen scale and therefore allows for analysis and interpretation of structures on various resolution levels. Applying our algorithm to a tripartite disease-gene-protein complex network, we were able to structure this graph on a large scale into clusters that are functionally correlated and biologically meaningful. Locally, smaller clusters enabled reclassification or annotation of the clusters' elements. We exemplified this for the transcription factor MECP2. Conclusions In order to cope with the overwhelming amount of information available from biomedical literature, we need to tackle the challenge of finding structures in large networks with nodes of multiple types. To this end, we presented a novel fuzzy k-partite graph partitioning
Xiong, B.; Oude Elberink, S.; Vosselman, G.
2014-07-01
In the task of 3D building model reconstruction from point clouds we face the problem of recovering a roof topology graph in the presence of noise, small roof faces and low point densities. Errors in roof topology graphs will seriously affect the final modelling results. The aim of this research is to automatically correct these errors. We define the graph correction as a graph-to-graph problem, similar to the spelling correction problem (also called the string-to-string problem). The graph correction is more complex than string correction, as the graphs are 2D while strings are only 1D. We design a strategy based on a dictionary of graph edit operations to automatically identify and correct the errors in the input graph. For each type of error the graph edit dictionary stores a representative erroneous subgraph as well as the corrected version. As an erroneous roof topology graph may contain several errors, a heuristic search is applied to find the optimum sequence of graph edits to correct the errors one by one. The graph edit dictionary can be expanded to include entries needed to cope with errors that were previously not encountered. Experiments show that the dictionary with only fifteen entries already properly corrects one quarter of erroneous graphs in about 4500 buildings, and even half of the erroneous graphs in one test area, achieving as high as a 95% acceptance rate of the reconstructed models.
Decomposition and Simplification of Multivariate Data using Pareto Sets.
Huettenberger, Lars; Heine, Christian; Garth, Christoph
2014-12-01
Topological and structural analysis of multivariate data is aimed at improving the understanding and usage of such data through identification of intrinsic features and structural relationships among multiple variables. We present two novel methods for simplifying so-called Pareto sets that describe such structural relationships. Such simplification is a precondition for meaningful visualization of structurally rich or noisy data. As a framework for simplification operations, we introduce a decomposition of the data domain into regions of equivalent structural behavior and the reachability graph that describes global connectivity of Pareto extrema. Simplification is then performed as a sequence of edge collapses in this graph; to determine a suitable sequence of such operations, we describe and utilize a comparison measure that reflects the changes to the data that each operation represents. We demonstrate and evaluate our methods on synthetic and real-world examples.
Significance evaluation in factor graphs
Madsen, Tobias; Hobolth, Asger; Jensen, Jens Ledet
2017-01-01
in genomics and the multiple-testing issues accompanying them, accurate significance evaluation is of great importance. We here address the problem of evaluating statistical significance of observations from factor graph models. Results Two novel numerical approximations for evaluation of statistical...... significance are presented. First a method using importance sampling. Second a saddlepoint approximation based method. We develop algorithms to efficiently compute the approximations and compare them to naive sampling and the normal approximation. The individual merits of the methods are analysed both from....... Conclusions The applicability of saddlepoint approximation and importance sampling is demonstrated on known models in the factor graph framework. Using the two methods we can substantially improve computational cost without compromising accuracy. This contribution allows analyses of large datasets...
Groups, graphs and random walks
Salvatori, Maura; Sava-Huss, Ecaterina
2017-01-01
An accessible and panoramic account of the theory of random walks on groups and graphs, stressing the strong connections of the theory with other branches of mathematics, including geometric and combinatorial group theory, potential analysis, and theoretical computer science. This volume brings together original surveys and research-expository papers from renowned and leading experts, many of whom spoke at the workshop 'Groups, Graphs and Random Walks' celebrating the sixtieth birthday of Wolfgang Woess in Cortona, Italy. Topics include: growth and amenability of groups; Schrödinger operators and symbolic dynamics; ergodic theorems; Thompson's group F; Poisson boundaries; probability theory on buildings and groups of Lie type; structure trees for edge cuts in networks; and mathematical crystallography. In what is currently a fast-growing area of mathematics, this book provides an up-to-date and valuable reference for both researchers and graduate students, from which future research activities will undoubted...
Flux networks in metabolic graphs
Warren, P B; Queiros, S M Duarte; Jones, J L
2009-01-01
A metabolic model can be represented as a bipartite graph comprising linked reaction and metabolite nodes. Here it is shown how a network of conserved fluxes can be assigned to the edges of such a graph by combining the reaction fluxes with a conserved metabolite property such as molecular weight. A similar flux network can be constructed by combining the primal and dual solutions to the linear programming problem that typically arises in constraint-based modelling. Such constructions may help with the visualization of flux distributions in complex metabolic networks. The analysis also explains the strong correlation observed between metabolite shadow prices (the dual linear programming variables) and conserved metabolite properties. The methods were applied to recent metabolic models for Escherichia coli, Saccharomyces cerevisiae and Methanosarcina barkeri. Detailed results are reported for E. coli; similar results were found for other organisms
3-biplacement of bipartite graphs
Lech Adamus
2008-01-01
Full Text Available Let \\(G=(L,R;E\\ be a bipartite graph with color classes \\(L\\ and \\(R\\ and edge set \\(E\\. A set of two bijections \\(\\{\\varphi_1 , \\varphi_2\\}\\, \\(\\varphi_1 , \\varphi_2 :L \\cup R \\to L \\cup R\\, is said to be a \\(3\\-biplacement of \\(G\\ if \\(\\varphi_1(L= \\varphi_2(L = L\\ and \\(E \\cap \\varphi_1^*(E=\\emptyset\\, \\(E \\cap \\varphi_2^*(E=\\emptyset\\, \\(\\varphi_1^*(E \\cap \\varphi_2^*(E=\\emptyset\\, where \\(\\varphi_1^*\\, \\(\\varphi_2^*\\ are the maps defined on \\(E\\, induced by \\(\\varphi_1\\, \\(\\varphi_2\\, respectively. We prove that if \\(|L| = p\\, \\(|R| = q\\, \\(3 \\leq p \\leq q\\, then every graph \\(G=(L,R;E\\ of size at most \\(p\\ has a \\(3\\-biplacement.
Inverse scale space decomposition
Schmidt, Marie Foged; Benning, Martin; Schönlieb, Carola-Bibiane
2018-01-01
We investigate the inverse scale space flow as a decomposition method for decomposing data into generalised singular vectors. We show that the inverse scale space flow, based on convex and even and positively one-homogeneous regularisation functionals, can decompose data represented...... by the application of a forward operator to a linear combination of generalised singular vectors into its individual singular vectors. We verify that for this decomposition to hold true, two additional conditions on the singular vectors are sufficient: orthogonality in the data space and inclusion of partial sums...... of the subgradients of the singular vectors in the subdifferential of the regularisation functional at zero. We also address the converse question of when the inverse scale space flow returns a generalised singular vector given that the initial data is arbitrary (and therefore not necessarily in the range...
Cacciatori, Sergio L; Marrani, Alessio
2013-01-01
By exploiting a "mixed" non-symmetric Freudenthal-Rozenfeld-Tits magic square, two types of coset decompositions are analyzed for the non-compact special K\\"ahler symmetric rank-3 coset E7(-25)/[(E6(-78) x U(1))/Z_3], occurring in supergravity as the vector multiplets' scalar manifold in N=2, D=4 exceptional Maxwell-Einstein theory. The first decomposition exhibits maximal manifest covariance, whereas the second (triality-symmetric) one is of Iwasawa type, with maximal SO(8) covariance. Generalizations to conformal non-compact, real forms of non-degenerate, simple groups "of type E7" are presented for both classes of coset parametrizations, and relations to rank-3 simple Euclidean Jordan algebras and normed trialities over division algebras are also discussed.
On the centrality of some graphs
Vecdi Aytac
2017-10-01
Full Text Available A central issue in the analysis of complex networks is the assessment of their stability and vulnerability. A variety of measures have been proposed in the literature to quantify the stability of networks and a number of graph-theoretic parameters have been used to derive formulas for calculating network reliability. Different measures for graph vulnerability have been introduced so far to study different aspects of the graph behavior after removal of vertices or links such as connectivity, toughness, scattering number, binding number, residual closeness and integrity. In this paper, we consider betweenness centrality of a graph. Betweenness centrality of a vertex of a graph is portion of the shortest paths all pairs of vertices passing through a given vertex. In this paper, we obtain exact values for betweenness centrality for some wheel related graphs namely gear, helm, sunflower and friendship graphs.
Quantum walk on a chimera graph
Xu, Shu; Sun, Xiangxiang; Wu, Jizhou; Zhang, Wei-Wei; Arshed, Nigum; Sanders, Barry C.
2018-05-01
We analyse a continuous-time quantum walk on a chimera graph, which is a graph of choice for designing quantum annealers, and we discover beautiful quantum walk features such as localization that starkly distinguishes classical from quantum behaviour. Motivated by technological thrusts, we study continuous-time quantum walk on enhanced variants of the chimera graph and on diminished chimera graph with a random removal of vertices. We explain the quantum walk by constructing a generating set for a suitable subgroup of graph isomorphisms and corresponding symmetry operators that commute with the quantum walk Hamiltonian; the Hamiltonian and these symmetry operators provide a complete set of labels for the spectrum and the stationary states. Our quantum walk characterization of the chimera graph and its variants yields valuable insights into graphs used for designing quantum-annealers.
Fibonacci number of the tadpole graph
Joe DeMaio
2014-10-01
Full Text Available In 1982, Prodinger and Tichy defined the Fibonacci number of a graph G to be the number of independent sets of the graph G. They did so since the Fibonacci number of the path graph Pn is the Fibonacci number F(n+2 and the Fibonacci number of the cycle graph Cn is the Lucas number Ln. The tadpole graph Tn,k is the graph created by concatenating Cn and Pk with an edge from any vertex of Cn to a pendant of Pk for integers n=3 and k=0. This paper establishes formulae and identities for the Fibonacci number of the tadpole graph via algebraic and combinatorial methods.
Software for Graph Analysis and Visualization
M. I. Kolomeychenko
2014-01-01
Full Text Available This paper describes the software for graph storage, analysis and visualization. The article presents a comparative analysis of existing software for analysis and visualization of graphs, describes the overall architecture of application and basic principles of construction and operation of the main modules. Furthermore, a description of the developed graph storage oriented to storage and processing of large-scale graphs is presented. The developed algorithm for finding communities and implemented algorithms of autolayouts of graphs are the main functionality of the product. The main advantage of the developed software is high speed processing of large size networks (up to millions of nodes and links. Moreover, the proposed graph storage architecture is unique and has no analogues. The developed approaches and algorithms are optimized for operating with big graphs and have high productivity.
VIGOR: Interactive Visual Exploration of Graph Query Results.
Pienta, Robert; Hohman, Fred; Endert, Alex; Tamersoy, Acar; Roundy, Kevin; Gates, Chris; Navathe, Shamkant; Chau, Duen Horng
2018-01-01
Finding patterns in graphs has become a vital challenge in many domains from biological systems, network security, to finance (e.g., finding money laundering rings of bankers and business owners). While there is significant interest in graph databases and querying techniques, less research has focused on helping analysts make sense of underlying patterns within a group of subgraph results. Visualizing graph query results is challenging, requiring effective summarization of a large number of subgraphs, each having potentially shared node-values, rich node features, and flexible structure across queries. We present VIGOR, a novel interactive visual analytics system, for exploring and making sense of query results. VIGOR uses multiple coordinated views, leveraging different data representations and organizations to streamline analysts sensemaking process. VIGOR contributes: (1) an exemplar-based interaction technique, where an analyst starts with a specific result and relaxes constraints to find other similar results or starts with only the structure (i.e., without node value constraints), and adds constraints to narrow in on specific results; and (2) a novel feature-aware subgraph result summarization. Through a collaboration with Symantec, we demonstrate how VIGOR helps tackle real-world problems through the discovery of security blindspots in a cybersecurity dataset with over 11,000 incidents. We also evaluate VIGOR with a within-subjects study, demonstrating VIGOR's ease of use over a leading graph database management system, and its ability to help analysts understand their results at higher speed and make fewer errors.
Parallel External Memory Graph Algorithms
Arge, Lars Allan; Goodrich, Michael T.; Sitchinava, Nodari
2010-01-01
In this paper, we study parallel I/O efficient graph algorithms in the Parallel External Memory (PEM) model, one o f the private-cache chip multiprocessor (CMP) models. We study the fundamental problem of list ranking which leads to efficient solutions to problems on trees, such as computing lowest...... an optimal speedup of Â¿(P) in parallel I/O complexity and parallel computation time, compared to the single-processor external memory counterparts....
Submanifolds weakly associated with graphs
A CARRIAZO, L M FERN ´ANDEZ and A RODRÍGUEZ-HIDALGO. Department of Geometry and Topology, ..... by means of trees (connected graphs without cycles) and forests (disjoint unions of trees, see [6]) given in [3], by extending it to weak ... CR-submanifold. In this case, every tree is a K2. Finally, Theorem 3.8 of [3] can ...
Topological structure of dictionary graphs
Fuks, Henryk; Krzeminski, Mark
2009-01-01
We investigate the topological structure of the subgraphs of dictionary graphs constructed from WordNet and Moby thesaurus data. In the process of learning a foreign language, the learner knows only a subset of all words of the language, corresponding to a subgraph of a dictionary graph. When this subgraph grows with time, its topological properties change. We introduce the notion of the pseudocore and argue that the growth of the vocabulary roughly follows decreasing pseudocore numbers-that is, one first learns words with a high pseudocore number followed by smaller pseudocores. We also propose an alternative strategy for vocabulary growth, involving decreasing core numbers as opposed to pseudocore numbers. We find that as the core or pseudocore grows in size, the clustering coefficient first decreases, then reaches a minimum and starts increasing again. The minimum occurs when the vocabulary reaches a size between 10 3 and 10 4 . A simple model exhibiting similar behavior is proposed. The model is based on a generalized geometric random graph. Possible implications for language learning are discussed.
Fast approximate convex decomposition using relative concavity
Ghosh, Mukulika; Amato, Nancy M.; Lu, Yanyan; Lien, Jyh-Ming
2013-01-01
Approximate convex decomposition (ACD) is a technique that partitions an input object into approximately convex components. Decomposition into approximately convex pieces is both more efficient to compute than exact convex decomposition and can also generate a more manageable number of components. It can be used as a basis of divide-and-conquer algorithms for applications such as collision detection, skeleton extraction and mesh generation. In this paper, we propose a new method called Fast Approximate Convex Decomposition (FACD) that improves the quality of the decomposition and reduces the cost of computing it for both 2D and 3D models. In particular, we propose a new strategy for evaluating potential cuts that aims to reduce the relative concavity, rather than absolute concavity. As shown in our results, this leads to more natural and smaller decompositions that include components for small but important features such as toes or fingers while not decomposing larger components, such as the torso, that may have concavities due to surface texture. Second, instead of decomposing a component into two pieces at each step, as in the original ACD, we propose a new strategy that uses a dynamic programming approach to select a set of n c non-crossing (independent) cuts that can be simultaneously applied to decompose the component into n c+1 components. This reduces the depth of recursion and, together with a more efficient method for computing the concavity measure, leads to significant gains in efficiency. We provide comparative results for 2D and 3D models illustrating the improvements obtained by FACD over ACD and we compare with the segmentation methods in the Princeton Shape Benchmark by Chen et al. (2009) [31]. © 2012 Elsevier Ltd. All rights reserved.
Fast approximate convex decomposition using relative concavity
Ghosh, Mukulika
2013-02-01
Approximate convex decomposition (ACD) is a technique that partitions an input object into approximately convex components. Decomposition into approximately convex pieces is both more efficient to compute than exact convex decomposition and can also generate a more manageable number of components. It can be used as a basis of divide-and-conquer algorithms for applications such as collision detection, skeleton extraction and mesh generation. In this paper, we propose a new method called Fast Approximate Convex Decomposition (FACD) that improves the quality of the decomposition and reduces the cost of computing it for both 2D and 3D models. In particular, we propose a new strategy for evaluating potential cuts that aims to reduce the relative concavity, rather than absolute concavity. As shown in our results, this leads to more natural and smaller decompositions that include components for small but important features such as toes or fingers while not decomposing larger components, such as the torso, that may have concavities due to surface texture. Second, instead of decomposing a component into two pieces at each step, as in the original ACD, we propose a new strategy that uses a dynamic programming approach to select a set of n c non-crossing (independent) cuts that can be simultaneously applied to decompose the component into n c+1 components. This reduces the depth of recursion and, together with a more efficient method for computing the concavity measure, leads to significant gains in efficiency. We provide comparative results for 2D and 3D models illustrating the improvements obtained by FACD over ACD and we compare with the segmentation methods in the Princeton Shape Benchmark by Chen et al. (2009) [31]. © 2012 Elsevier Ltd. All rights reserved.
Quantum information processing with graph states
Schlingemann, Dirk-Michael
2005-04-01
Graph states are multiparticle states which are associated with graphs. Each vertex of the graph corresponds to a single system or particle. The links describe quantum correlations (entanglement) between pairs of connected particles. Graph states were initiated independently by two research groups: On the one hand, graph states were introduced by Briegel and Raussendorf as a resource for a new model of one-way quantum computing, where algorithms are implemented by a sequence of measurements at single particles. On the other hand, graph states were developed by the author of this thesis and ReinhardWerner in Braunschweig, as a tool to build quantum error correcting codes, called graph codes. The connection between the two approaches was fully realized in close cooperation of both research groups. This habilitation thesis provides a survey of the theory of graph codes, focussing mainly, but not exclusively on the author's own research work. We present the theoretical and mathematical background for the analysis of graph codes. The concept of one-way quantum computing for general graph states is discussed. We explicitly show how to realize the encoding and decoding device of a graph code on a one-way quantum computer. This kind of implementation is to be seen as a mathematical description of a quantum memory device. In addition to that, we investigate interaction processes, which enable the creation of graph states on very large systems. Particular graph states can be created, for instance, by an Ising type interaction between next neighbor particles which sits at the points of an infinitely extended cubic lattice. Based on the theory of quantum cellular automata, we give a constructive characterization of general interactions which create a translationally invariant graph state. (orig.)
Visualizing Dataflow Graphs of Deep Learning Models in TensorFlow.
Wongsuphasawat, Kanit; Smilkov, Daniel; Wexler, James; Wilson, Jimbo; Mane, Dandelion; Fritz, Doug; Krishnan, Dilip; Viegas, Fernanda B; Wattenberg, Martin
2018-01-01
We present a design study of the TensorFlow Graph Visualizer, part of the TensorFlow machine intelligence platform. This tool helps users understand complex machine learning architectures by visualizing their underlying dataflow graphs. The tool works by applying a series of graph transformations that enable standard layout techniques to produce a legible interactive diagram. To declutter the graph, we decouple non-critical nodes from the layout. To provide an overview, we build a clustered graph using the hierarchical structure annotated in the source code. To support exploration of nested structure on demand, we perform edge bundling to enable stable and responsive cluster expansion. Finally, we detect and highlight repeated structures to emphasize a model's modular composition. To demonstrate the utility of the visualizer, we describe example usage scenarios and report user feedback. Overall, users find the visualizer useful for understanding, debugging, and sharing the structures of their models.
Many-core graph analytics using accelerated sparse linear algebra routines
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.
Degree Associated Edge Reconstruction Number of Graphs with Regular Pruned Graph
P. Anusha Devi
2015-10-01
Full Text Available An ecard of a graph $G$ is a subgraph formed by deleting an edge. A da-ecard specifies the degree of the deleted edge along with the ecard. The degree associated edge reconstruction number of a graph $G,~dern(G,$ is the minimum number of da-ecards that uniquely determines $G.$ The adversary degree associated edge reconstruction number of a graph $G, adern(G,$ is the minimum number $k$ such that every collection of $k$ da-ecards of $G$ uniquely determines $G.$ The maximal subgraph without end vertices of a graph $G$ which is not a tree is the pruned graph of $G.$ It is shown that $dern$ of complete multipartite graphs and some connected graphs with regular pruned graph is $1$ or $2.$ We also determine $dern$ and $adern$ of corona product of standard graphs.
Wang, Jim Jing-Yan
2014-09-20
Nonnegative matrix factorization (NMF), a popular part-based representation technique, does not capture the intrinsic local geometric structure of the data space. Graph regularized NMF (GNMF) was recently proposed to avoid this limitation by regularizing NMF with a nearest neighbor graph constructed from the input data set. However, GNMF has two main bottlenecks. First, using the original feature space directly to construct the graph is not necessarily optimal because of the noisy and irrelevant features and nonlinear distributions of data samples. Second, one possible way to handle the nonlinear distribution of data samples is by kernel embedding. However, it is often difficult to choose the most suitable kernel. To solve these bottlenecks, we propose two novel graph-regularized NMF methods, AGNMFFS and AGNMFMK, by introducing feature selection and multiple-kernel learning to the graph regularized NMF, respectively. Instead of using a fixed graph as in GNMF, the two proposed methods learn the nearest neighbor graph that is adaptive to the selected features and learned multiple kernels, respectively. For each method, we propose a unified objective function to conduct feature selection/multi-kernel learning, NMF and adaptive graph regularization simultaneously. We further develop two iterative algorithms to solve the two optimization problems. Experimental results on two challenging pattern classification tasks demonstrate that the proposed methods significantly outperform state-of-the-art data representation methods.
Asynchronous Task-Based Polar Decomposition on Manycore Architectures
Sukkari, Dalal
2016-10-25
This paper introduces the first asynchronous, task-based implementation of the polar decomposition on manycore architectures. Based on a new formulation of the iterative QR dynamically-weighted Halley algorithm (QDWH) for the calculation of the polar decomposition, the proposed implementation replaces the original and hostile LU factorization for the condition number estimator by the more adequate QR factorization to enable software portability across various architectures. Relying on fine-grained computations, the novel task-based implementation is also capable of taking advantage of the identity structure of the matrix involved during the QDWH iterations, which decreases the overall algorithmic complexity. Furthermore, the artifactual synchronization points have been severely weakened compared to previous implementations, unveiling look-ahead opportunities for better hardware occupancy. The overall QDWH-based polar decomposition can then be represented as a directed acyclic graph (DAG), where nodes represent computational tasks and edges define the inter-task data dependencies. The StarPU dynamic runtime system is employed to traverse the DAG, to track the various data dependencies and to asynchronously schedule the computational tasks on the underlying hardware resources, resulting in an out-of-order task scheduling. Benchmarking experiments show significant improvements against existing state-of-the-art high performance implementations (i.e., Intel MKL and Elemental) for the polar decomposition on latest shared-memory vendors\\' systems (i.e., Intel Haswell/Broadwell/Knights Landing, NVIDIA K80/P100 GPUs and IBM Power8), while maintaining high numerical accuracy.
Clustering via Kernel Decomposition
Have, Anna Szynkowiak; Girolami, Mark A.; Larsen, Jan
2006-01-01
Methods for spectral clustering have been proposed recently which rely on the eigenvalue decomposition of an affinity matrix. In this work it is proposed that the affinity matrix is created based on the elements of a non-parametric density estimator. This matrix is then decomposed to obtain...... posterior probabilities of class membership using an appropriate form of nonnegative matrix factorization. The troublesome selection of hyperparameters such as kernel width and number of clusters can be obtained using standard cross-validation methods as is demonstrated on a number of diverse data sets....
Using combinatorial problem decomposition for optimizing plutonium inventory management
Niquil, Y.; Gondran, M.; Voskanian, A.; Paris-11 Univ., 91 - Orsay
1997-03-01
Plutonium Inventory Management Optimization can be modeled as a very large 0-1 linear program. To solve it, problem decomposition is necessary, since other classic techniques are not efficient for such a size. The first decomposition consists in favoring constraints that are the most difficult to reach and variables that have the highest influence on the cost: fortunately, both correspond to stock output decisions. The second decomposition consists in mixing continuous linear program solving and integer linear program solving. Besides, the first decisions to be taken are systematically favored, for they are based on data considered to be sure, when data supporting later decisions in known with less accuracy and confidence. (author)
Replica methods for loopy sparse random graphs
Coolen, ACC
2016-01-01
I report on the development of a novel statistical mechanical formalism for the analysis of random graphs with many short loops, and processes on such graphs. The graphs are defined via maximum entropy ensembles, in which both the degrees (via hard constraints) and the adjacency matrix spectrum (via a soft constraint) are prescribed. The sum over graphs can be done analytically, using a replica formalism with complex replica dimensions. All known results for tree-like graphs are recovered in a suitable limit. For loopy graphs, the emerging theory has an appealing and intuitive structure, suggests how message passing algorithms should be adapted, and what is the structure of theories describing spin systems on loopy architectures. However, the formalism is still largely untested, and may require further adjustment and refinement. (paper)
Chemical Graph Transformation with Stereo-Information
Andersen, Jakob Lykke; Flamm, Christoph; Merkle, Daniel
2017-01-01
Double Pushout graph transformation naturally facilitates the modelling of chemical reactions: labelled undirected graphs model molecules and direct derivations model chemical reactions. However, the most straightforward modelling approach ignores the relative placement of atoms and their neighbo......Double Pushout graph transformation naturally facilitates the modelling of chemical reactions: labelled undirected graphs model molecules and direct derivations model chemical reactions. However, the most straightforward modelling approach ignores the relative placement of atoms...... and their neighbours in space. Stereoisomers of chemical compounds thus cannot be distinguished, even though their chemical activity may differ substantially. In this contribution we propose an extended chemical graph transformation system with attributes that encode information about local geometry. The modelling...... of graph transformation, but we here propose a framework that also allows for partially specified stereoinformation. While there are several stereochemical configurations to be considered, we focus here on the tetrahedral molecular shape, and suggest general principles for how to treat all other chemically...
Danburite decomposition by sulfuric acid
Mirsaidov, U.; Mamatov, E.D.; Ashurov, N.A.
2011-01-01
Present article is devoted to decomposition of danburite of Ak-Arkhar Deposit of Tajikistan by sulfuric acid. The process of decomposition of danburite concentrate by sulfuric acid was studied. The chemical nature of decomposition process of boron containing ore was determined. The influence of temperature on the rate of extraction of boron and iron oxides was defined. The dependence of decomposition of boron and iron oxides on process duration, dosage of H 2 SO 4 , acid concentration and size of danburite particles was determined. The kinetics of danburite decomposition by sulfuric acid was studied as well. The apparent activation energy of the process of danburite decomposition by sulfuric acid was calculated. The flowsheet of danburite processing by sulfuric acid was elaborated.
Thermal decomposition of lutetium propionate
Grivel, Jean-Claude
2010-01-01
The thermal decomposition of lutetium(III) propionate monohydrate (Lu(C2H5CO2)3·H2O) in argon was studied by means of thermogravimetry, differential thermal analysis, IR-spectroscopy and X-ray diffraction. Dehydration takes place around 90 °C. It is followed by the decomposition of the anhydrous...... °C. Full conversion to Lu2O3 is achieved at about 1000 °C. Whereas the temperatures and solid reaction products of the first two decomposition steps are similar to those previously reported for the thermal decomposition of lanthanum(III) propionate monohydrate, the final decomposition...... of the oxycarbonate to the rare-earth oxide proceeds in a different way, which is here reminiscent of the thermal decomposition path of Lu(C3H5O2)·2CO(NH2)2·2H2O...
Direct Visual Editing of Node Attributes in Graphs
Christian Eichner
2016-10-01
Full Text Available There are many expressive visualization techniques for analyzing graphs. Yet, there is only little research on how existing visual representations can be employed to support data editing. An increasingly relevant task when working with graphs is the editing of node attributes. We propose an integrated visualize-and-edit approach to editing attribute values via direct interaction with the visual representation. The visualize part is based on node-link diagrams paired with attribute-dependent layouts. The edit part is as easy as moving nodes via drag-and-drop gestures. We present dedicated interaction techniques for editing quantitative as well as qualitative attribute data values. The benefit of our novel integrated approach is that one can directly edit the data while the visualization constantly provides feedback on the implications of the data modifications. Preliminary user feedback indicates that our integrated approach can be a useful complement to standard non-visual editing via external tools.
STRUCTURAL ANNOTATION OF EM IMAGES BY GRAPH CUT
Chang, Hang; Auer, Manfred; Parvin, Bahram
2009-05-08
Biological images have the potential to reveal complex signatures that may not be amenable to morphological modeling in terms of shape, location, texture, and color. An effective analytical method is to characterize the composition of a specimen based on user-defined patterns of texture and contrast formation. However, such a simple requirement demands an improved model for stability and robustness. Here, an interactive computational model is introduced for learning patterns of interest by example. The learned patterns bound an active contour model in which the traditional gradient descent optimization is replaced by the more efficient optimization of the graph cut methods. First, the energy function is defined according to the curve evolution. Next, a graph is constructed with weighted edges on the energy function and is optimized with the graph cut algorithm. As a result, the method combines the advantages of the level set method and graph cut algorithm, i.e.,"topological" invariance and computational efficiency. The technique is extended to the multi-phase segmentation problem; the method is validated on synthetic images and then applied to specimens imaged by transmission electron microscopy(TEM).
Bond graphs : an integrating tool for design of mechatronic systems
Ould Bouamama, B.
2011-01-01
Bond graph is a powerful tool well known for dynamic modelling of multi physical systems: This is the only modelling technique to generate automatically state space or non-linear models using dedicated software tools (CAMP-G, 20-Sim, Symbols, Dymola...). Recently several fundamental theories have been developed for using a bond graph model not only for modeling but also as a real integrated tool from conceptual ideas to optimal practical realization of mechatronic system. This keynote presents a synthesis of those new theories which exploit some particular properties (such as causal, structural and behavioral) of this graphical methodology. Based on a pedagogical example, it will be shown how from a physical system (not a transfer function or state equation) and using only one representation (Bond graph), the following results can be performed: modeling (formal state equations generation), Control analysis (observability, controllability, Structural I/O decouplability, dynamic decoupling,...) diagnosis analysis (automatic generation of robust fault indicators, sensor placement, structural diagnosability) and finally sizing of actuators. The presentation will be illustrated by real industrial applications. Limits and perspectives of bond graph theory conclude the keynote.
Locating sources within a dense sensor array using graph clustering
Gerstoft, P.; Riahi, N.
2017-12-01
We develop a model-free technique to identify weak sources within dense sensor arrays using graph clustering. No knowledge about the propagation medium is needed except that signal strengths decay to insignificant levels within a scale that is shorter than the aperture. We then reinterpret the spatial coherence matrix of a wave field as a matrix whose support is a connectivity matrix of a graph with sensors as vertices. In a dense network, well-separated sources induce clusters in this graph. The geographic spread of these clusters can serve to localize the sources. The support of the covariance matrix is estimated from limited-time data using a hypothesis test with a robust phase-only coherence test statistic combined with a physical distance criterion. The latter criterion ensures graph sparsity and thus prevents clusters from forming by chance. We verify the approach and quantify its reliability on a simulated dataset. The method is then applied to data from a dense 5200 element geophone array that blanketed of the city of Long Beach (CA). The analysis exposes a helicopter traversing the array and oil production facilities.
Experimental quantum annealing: case study involving the graph isomorphism problem.
Zick, Kenneth M; Shehab, Omar; French, Matthew
2015-06-08
Quantum annealing is a proposed combinatorial optimization technique meant to exploit quantum mechanical effects such as tunneling and entanglement. Real-world quantum annealing-based solvers require a combination of annealing and classical pre- and post-processing; at this early stage, little is known about how to partition and optimize the processing. This article presents an experimental case study of quantum annealing and some of the factors involved in real-world solvers, using a 504-qubit D-Wave Two machine and the graph isomorphism problem. To illustrate the role of classical pre-processing, a compact Hamiltonian is presented that enables a reduced Ising model for each problem instance. On random N-vertex graphs, the median number of variables is reduced from N(2) to fewer than N log2 N and solvable graph sizes increase from N = 5 to N = 13. Additionally, error correction via classical post-processing majority voting is evaluated. While the solution times are not competitive with classical approaches to graph isomorphism, the enhanced solver ultimately classified correctly every problem that was mapped to the processor and demonstrated clear advantages over the baseline approach. The results shed some light on the nature of real-world quantum annealing and the associated hybrid classical-quantum solvers.
Spectral decomposition of tent maps using symmetry considerations
Ordonez, G.E.; Driebe, D.J.
1996-01-01
The spectral decompostion of the Frobenius-Perron operator of maps composed of many tents is determined from symmetry considerations. The eigenstates involve Euler as well as Bernoulli polynomials. The authors have introduced some new techniques, based on symmetry considerations, enabling the construction of spectral decompositions in a much simpler way than previous construction algorithms, Here we utilize these techniques to construct the spectral decomposition for one- dimensional maps of the unit interval composed of many tents. The construction uses the knowledge of the spectral decomposition of the r-adic map, which involves Bernoulli polynomials and their duals. It will be seen that the spectral decomposition of the tent maps involves both Bernoulli polynomials and Euler polynomials along with the appropriate dual states
Reconstructing Topological Graphs and Continua
Gartside, Paul; Pitz, Max F.; Suabedissen, Rolf
2015-01-01
The deck of a topological space $X$ is the set $\\mathcal{D}(X)=\\{[X \\setminus \\{x\\}] \\colon x \\in X\\}$, where $[Z]$ denotes the homeomorphism class of $Z$. A space $X$ is topologically reconstructible if whenever $\\mathcal{D}(X)=\\mathcal{D}(Y)$ then $X$ is homeomorphic to $Y$. It is shown that all metrizable compact connected spaces are reconstructible. It follows that all finite graphs, when viewed as a 1-dimensional cell-complex, are reconstructible in the topological sense, and more genera...
On path hypercompositions in graphs and automata
Massouros Christos G.
2016-01-01
Full Text Available The paths in graphs define hypercompositions in the set of their vertices and therefore it is feasible to associate hypercompositional structures to each graph. Similarly, the strings of letters from their alphabet, define hypercompositions in the automata, which in turn define the associated hypergroups to the automata. The study of the associated hypercompositional structures gives results in both, graphs and automata theory.
Steiner Distance in Graphs--A Survey
Mao, Yaping
2017-01-01
For a connected graph $G$ of order at least $2$ and $S\\subseteq V(G)$, the \\emph{Steiner distance} $d_G(S)$ among the vertices of $S$ is the minimum size among all connected subgraphs whose vertex sets contain $S$. In this paper, we summarize the known results on the Steiner distance parameters, including Steiner distance, Steiner diameter, Steiner center, Steiner median, Steiner interval, Steiner distance hereditary graph, Steiner distance stable graph, average Steiner distance, and Steiner ...
Density conditions for triangles in multipartite graphs
Bondy, Adrian; Shen, Jin; Thomassé, Stephan
2006-01-01
subgraphs in G. We investigate in particular the case where G is a complete multipartite graph. We prove that a finite tripartite graph with all edge densities greater than the golden ratio has a triangle and that this bound is best possible. Also we show that an infinite-partite graph with finite parts has...... a triangle, provided that the edge density between any two parts is greater than 1/2....
Efficient Algorithmic Frameworks via Structural Graph Theory
2016-10-28
constant. For example, they measured that, on large samples of the entire network, the Amazon graph has average degree 17.7, the Facebook graph has average...department heads’ opinions of departments, and generally lack transparency and well-defined measures . On the other hand, the National Research Council (the...Efficient and practical resource block allocation for LTE -based D2D network via graph coloring. Wireless Networks 20(4): 611-624 (2014) 50. Hossein
Multicolored spanning subgraphs in G-colorings of complete graphs
Akbari, S.; Zare, S.
2007-08-01
Let G = {g 1 , ..., g n } be a finite abelian group. Consider the complete graph with the vertex set {g 1 , ..., g n }}. The G-coloring of K n is a proper edge coloring in which the color of edge {g i , g j } is g i + g j , l ≤ i ≤ j ≤ n. We prove that in the G-coloring of the complete graph K n , there exists a multicolored Hamilton path if G is not an elementary abelian 2-group. Furthermore, we show that if n is odd, then the G-coloring of K n can be decomposed into multicolored 2-factors and if l r is the number of elements of order r in G, 3 ≤ r ≤ n. then there are exactly (l r )/2 multicolored r-uniform 2-factors in this decomposition. This provides a generalization of a recent result due to Constantine which states: For any prime number p > 2, there exists a proper edge coloring of K p which is decomposable into multicolored Hamilton cycles. (author)
A HYBRID ALGORITHM FOR THE ROBUST GRAPH COLORING PROBLEM
Román Anselmo Mora Gutiérrez
2016-08-01
Full Text Available A hybridalgorithm which combines mathematical programming techniques (Kruskal’s algorithm and the strategy of maintaining arc consistency to solve constraint satisfaction problem “CSP” and heuristic methods (musical composition method and DSATUR to resolve the robust graph coloring problem (RGCP is proposed in this paper. Experimental result shows that this algorithm is better than the other algorithms presented on the literature.
Universal graphs at $\\aleph_{\\omega_1+1}$
Davis, Jacob
2016-01-01
Starting from a supercompact cardinal we build a model in which $2^{\\aleph_{\\omega_1}}=2^{\\aleph_{\\omega_1+1}}=\\aleph_{\\omega_1+3}$ but there is a jointly universal family of size $\\aleph_{\\omega_1+2}$ of graphs on $\\aleph_{\\omega_1+1}$. The same technique will work for any uncountable cardinal in place of $\\omega_1$.
Polynomial-time computability of the edge-reliability of graphs using Gilbert's formula
Thomas J. Marlowe
1998-01-01
Full Text Available Reliability is an important consideration in analyzing computer and other communication networks, but current techniques are extremely limited in the classes of graphs which can be analyzed efficiently. While Gilbert's formula establishes a theoretically elegant recursive relationship between the edge reliability of a graph and the reliability of its subgraphs, naive evaluation requires consideration of all sequences of deletions of individual vertices, and for many graphs has time complexity essentially Θ (N!. We discuss a general approach which significantly reduces complexity, encoding subgraph isomorphism in a finer partition by invariants, and recursing through the set of invariants.
Equilibrium statistical mechanics on correlated random graphs
Barra, Adriano; Agliari, Elena
2011-02-01
Biological and social networks have recently attracted great attention from physicists. Among several aspects, two main ones may be stressed: a non-trivial topology of the graph describing the mutual interactions between agents and, typically, imitative, weighted, interactions. Despite such aspects being widely accepted and empirically confirmed, the schemes currently exploited in order to generate the expected topology are based on a priori assumptions and, in most cases, implement constant intensities for links. Here we propose a simple shift [-1,+1]\\to [0,+1] in the definition of patterns in a Hopfield model: a straightforward effect is the conversion of frustration into dilution. In fact, we show that by varying the bias of pattern distribution, the network topology (generated by the reciprocal affinities among agents, i.e. the Hebbian rule) crosses various well-known regimes, ranging from fully connected, to an extreme dilution scenario, then to completely disconnected. These features, as well as small-world properties, are, in this context, emergent and no longer imposed a priori. The model is throughout investigated also from a thermodynamics perspective: the Ising model defined on the resulting graph is analytically solved (at a replica symmetric level) by extending the double stochastic stability technique, and presented together with its fluctuation theory for a picture of criticality. Overall, our findings show that, at least at equilibrium, dilution (of whatever kind) simply decreases the strength of the coupling felt by the spins, but leaves the paramagnetic/ferromagnetic flavors unchanged. The main difference with respect to previous investigations is that, within our approach, replicas do not appear: instead of (multi)-overlaps as order parameters, we introduce a class of magnetizations on all the possible subgraphs belonging to the main one investigated: as a consequence, for these objects a closure for a self-consistent relation is achieved.
Equilibrium statistical mechanics on correlated random graphs
Barra, Adriano; Agliari, Elena
2011-01-01
Biological and social networks have recently attracted great attention from physicists. Among several aspects, two main ones may be stressed: a non-trivial topology of the graph describing the mutual interactions between agents and, typically, imitative, weighted, interactions. Despite such aspects being widely accepted and empirically confirmed, the schemes currently exploited in order to generate the expected topology are based on a priori assumptions and, in most cases, implement constant intensities for links. Here we propose a simple shift [-1,+1]→[0,+1] in the definition of patterns in a Hopfield model: a straightforward effect is the conversion of frustration into dilution. In fact, we show that by varying the bias of pattern distribution, the network topology (generated by the reciprocal affinities among agents, i.e. the Hebbian rule) crosses various well-known regimes, ranging from fully connected, to an extreme dilution scenario, then to completely disconnected. These features, as well as small-world properties, are, in this context, emergent and no longer imposed a priori. The model is throughout investigated also from a thermodynamics perspective: the Ising model defined on the resulting graph is analytically solved (at a replica symmetric level) by extending the double stochastic stability technique, and presented together with its fluctuation theory for a picture of criticality. Overall, our findings show that, at least at equilibrium, dilution (of whatever kind) simply decreases the strength of the coupling felt by the spins, but leaves the paramagnetic/ferromagnetic flavors unchanged. The main difference with respect to previous investigations is that, within our approach, replicas do not appear: instead of (multi)-overlaps as order parameters, we introduce a class of magnetizations on all the possible subgraphs belonging to the main one investigated: as a consequence, for these objects a closure for a self-consistent relation is achieved
Decomposing a planar graph into an independent set and a 3-degenerate graph
Thomassen, Carsten
2001-01-01
We prove the conjecture made by O. V. Borodin in 1976 that the vertex set of every planar graph can be decomposed into an independent set and a set inducing a 3-degenerate graph. (C) 2001 Academic Press....
Graph algorithms in the titan toolkit.
McLendon, William Clarence, III; Wylie, Brian Neil
2009-10-01
Graph algorithms are a key component in a wide variety of intelligence analysis activities. The Graph-Based Informatics for Non-Proliferation and Counter-Terrorism project addresses the critical need of making these graph algorithms accessible to Sandia analysts in a manner that is both intuitive and effective. Specifically we describe the design and implementation of an open source toolkit for doing graph analysis, informatics, and visualization that provides Sandia with novel analysis capability for non-proliferation and counter-terrorism.
Xu, Kexiang; Trinajstić, Nenad
2015-01-01
This is the first book to focus on the topological index, the Harary index, of a graph, including its mathematical properties, chemical applications and some related and attractive open problems. This book is dedicated to Professor Frank Harary (1921—2005), the grandmaster of graph theory and its applications. It has be written by experts in the field of graph theory and its applications. For a connected graph G, as an important distance-based topological index, the Harary index H(G) is defined as the sum of the reciprocals of the distance between any two unordered vertices of the graph G. In this book, the authors report on the newest results on the Harary index of a graph. These results mainly concern external graphs with respect to the Harary index; the relations to other topological indices; its properties and applications to pure graph theory and chemical graph theory; and two significant variants, i.e., additively and multiplicatively weighted Harary indices. In the last chapter, we present a number o...
An algebraic approach to graph codes
Pinero, Fernando
This thesis consists of six chapters. The first chapter, contains a short introduction to coding theory in which we explain the coding theory concepts we use. In the second chapter, we present the required theory for evaluation codes and also give an example of some fundamental codes in coding...... theory as evaluation codes. Chapter three consists of the introduction to graph based codes, such as Tanner codes and graph codes. In Chapter four, we compute the dimension of some graph based codes with a result combining graph based codes and subfield subcodes. Moreover, some codes in chapter four...
Jensen, T.R.; Thomassen, Carsten
2000-01-01
If k is a prime power, and G is a graph with n vertices, then a k-coloring of G may be considered as a vector in GF(k)(n). We prove that the subspace of GF(3)(n) spanned by all 3-colorings of a planar triangle-free graph with n vertices has dimension n. In particular, any such graph has at least n...... - 1 nonequivalent 3-colorings, and the addition of any edge or any vertex of degree 3 results in a 3-colorable graph. (C) 2000 John Wiley & Sons, Inc....
Interactive Graph Layout of a Million Nodes
Peng Mi
2016-12-01
Full Text Available Sensemaking of large graphs, specifically those with millions of nodes, is a crucial task in many fields. Automatic graph layout algorithms, augmented with real-time human-in-the-loop interaction, can potentially support sensemaking of large graphs. However, designing interactive algorithms to achieve this is challenging. In this paper, we tackle the scalability problem of interactive layout of large graphs, and contribute a new GPU-based force-directed layout algorithm that exploits graph topology. This algorithm can interactively layout graphs with millions of nodes, and support real-time interaction to explore alternative graph layouts. Users can directly manipulate the layout of vertices in a force-directed fashion. The complexity of traditional repulsive force computation is reduced by approximating calculations based on the hierarchical structure of multi-level clustered graphs. We evaluate the algorithm performance, and demonstrate human-in-the-loop layout in two sensemaking case studies. Moreover, we summarize lessons learned for designing interactive large graph layout algorithms on the GPU.
Text-Filled Stacked Area Graphs
Kraus, Martin
2011-01-01
-filled stacked area graphs; i.e., graphs that feature stacked areas that are filled with small-typed text. Since these graphs allow for computing the text layout automatically, it is possible to include large amounts of textual detail with very little effort. We discuss the most important challenges and some...... solutions for the design of text-filled stacked area graphs with the help of an exemplary visualization of the genres, publication years, and titles of a database of several thousand PC games....
Reconstructing Nearly Simple Polytopes from their Graph
Doolittle, Joseph
2017-01-01
We present a partial description of which polytopes are reconstructible from their graphs. This is an extension of work by Blind and Mani (1987) and Kalai (1988), which showed that simple polytopes can be reconstructed from their graphs. In particular, we introduce a notion of $h$-nearly simple and prove that 1-nearly simple and 2-nearly simple polytopes are reconstructible from their graphs. We also give an example of a 3-nearly simple polytope which is not reconstructible from its graph. Fu...
A Reduction of the Graph Reconstruction Conjecture
Monikandan S.
2014-08-01
Full Text Available A graph is said to be reconstructible if it is determined up to isomor- phism from the collection of all its one-vertex deleted unlabeled subgraphs. Reconstruction Conjecture (RC asserts that all graphs on at least three vertices are reconstructible. In this paper, we prove that interval-regular graphs and some new classes of graphs are reconstructible and show that RC is true if and only if all non-geodetic and non-interval-regular blocks G with diam(G = 2 or diam(Ḡ = diam(G = 3 are reconstructible
Total dominator chromatic number of a graph
Adel P. Kazemi
2015-06-01
Full Text Available Given a graph $G$, the total dominator coloring problem seeks a proper coloring of $G$ with the additional property that every vertex in the graph is adjacent to all vertices of a color class. We seek to minimize the number of color classes. We initiate to study this problem on several classes of graphs, as well as finding general bounds and characterizations. We also compare the total dominator chromatic number of a graph with the chromatic number and the total domination number of it.
Equitable Colorings Of Corona Multiproducts Of Graphs
Furmánczyk Hanna
2017-11-01
Full Text Available A graph is equitably k-colorable if its vertices can be partitioned into k independent sets in such a way that the numbers of vertices in any two sets differ by at most one. The smallest k for which such a coloring exists is known as the equitable chromatic number of G and denoted by =(G. It is known that the problem of computation of =(G is NP-hard in general and remains so for corona graphs. In this paper we consider the same model of coloring in the case of corona multiproducts of graphs. In particular, we obtain some results regarding the equitable chromatic number for the l-corona product G ◦l H, where G is an equitably 3- or 4-colorable graph and H is an r-partite graph, a cycle or a complete graph. Our proofs are mostly constructive in that they lead to polynomial algorithms for equitable coloring of such graph products provided that there is given an equitable coloring of G. Moreover, we confirm the Equitable Coloring Conjecture for corona products of such graphs. This paper extends the results from [H. Furmánczyk, K. Kaliraj, M. Kubale and V.J. Vivin, Equitable coloring of corona products of graphs, Adv. Appl. Discrete Math. 11 (2013 103–120].
VT Digital Line Graph Miscellaneous Transmission Lines
Vermont Center for Geographic Information — (Link to Metadata) This datalayer is comprised of Miscellaineous Transmission Lines. Digital line graph (DLG) data are digital representations of cartographic...
A PARALLEL NONOVERLAPPING DOMAIN DECOMPOSITION METHOD FOR STOKES PROBLEMS
Mei-qun Jiang; Pei-liang Dai
2006-01-01
A nonoverlapping domain decomposition iterative procedure is developed and analyzed for generalized Stokes problems and their finite element approximate problems in RN(N=2,3). The method is based on a mixed-type consistency condition with two parameters as a transmission condition together with a derivative-free transmission data updating technique on the artificial interfaces. The method can be applied to a general multi-subdomain decomposition and implemented on parallel machines with local simple communications naturally.
The complexity of the matching-cut problem for planar graphs and other graph classes
Bonsma, P.S.
2009-01-01
The Matching-Cut problem is the problem to decide whether a graph has an edge cut that is also a matching. Previously this problem was studied under the name of the Decomposable Graph Recognition problem, and proved to be -complete when restricted to graphs with maximum degree four. In this paper it
Liu, Xu; Chen, Langshi; Firoz, Jesun S.; Qiu, Judy; Jiang, Lei
2017-01-01
Intel Xeon Phi many-integrated-core (MIC) architectures usher in a new era of terascale integration. Among emerging killer applications, parallel graph processing has been a critical technique to analyze connected data. In this paper, we empirically evaluate various computing platforms including an Intel Xeon E5 CPU, a Nvidia Geforce GTX1070 GPU and an Xeon Phi 7210 processor codenamed Knights Landing (KNL) in the domain of parallel graph processing. We show that the KNL gains encouraging per...
Probability on graphs random processes on graphs and lattices
Grimmett, Geoffrey
2018-01-01
This introduction to some of the principal models in the theory of disordered systems leads the reader through the basics, to the very edge of contemporary research, with the minimum of technical fuss. Topics covered include random walk, percolation, self-avoiding walk, interacting particle systems, uniform spanning tree, random graphs, as well as the Ising, Potts, and random-cluster models for ferromagnetism, and the Lorentz model for motion in a random medium. This new edition features accounts of major recent progress, including the exact value of the connective constant of the hexagonal lattice, and the critical point of the random-cluster model on the square lattice. The choice of topics is strongly motivated by modern applications, and focuses on areas that merit further research. Accessible to a wide audience of mathematicians and physicists, this book can be used as a graduate course text. Each chapter ends with a range of exercises.
Multiresolution signal decomposition transforms, subbands, and wavelets
Akansu, Ali N
1992-01-01
This book provides an in-depth, integrated, and up-to-date exposition of the topic of signal decomposition techniques. Application areas of these techniques include speech and image processing, machine vision, information engineering, High-Definition Television, and telecommunications. The book will serve as the major reference for those entering the field, instructors teaching some or all of the topics in an advanced graduate course and researchers needing to consult an authoritative source.n The first book to give a unified and coherent exposition of multiresolutional signal decompos
Efficient decomposition and linearization methods for the stochastic transportation problem
Holmberg, K.
1993-01-01
The stochastic transportation problem can be formulated as a convex transportation problem with nonlinear objective function and linear constraints. We compare several different methods based on decomposition techniques and linearization techniques for this problem, trying to find the most efficient method or combination of methods. We discuss and test a separable programming approach, the Frank-Wolfe method with and without modifications, the new technique of mean value cross decomposition and the more well known Lagrangian relaxation with subgradient optimization, as well as combinations of these approaches. Computational tests are presented, indicating that some new combination methods are quite efficient for large scale problems. (authors) (27 refs.)