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Journal articles on the topic 'Hypergraph Models'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Luqman, Anam, Muhammad Akram, and Ali N. A. Koam. "Granulation of Hypernetwork Models under the q-Rung Picture Fuzzy Environment." Mathematics 7, no. 6 (2019): 496. http://dx.doi.org/10.3390/math7060496.

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In this paper, we define q-rung picture fuzzy hypergraphs and illustrate the formation of granular structures using q-rung picture fuzzy hypergraphs and level hypergraphs. Further, we define the q-rung picture fuzzy equivalence relation and q-rung picture fuzzy hierarchical quotient space structures. In particular, a q-rung picture fuzzy hypergraph and hypergraph combine a set of granules, and a hierarchical structure is formed corresponding to the series of hypergraphs. The mappings between the q-rung picture fuzzy hypergraphs depict the relationships among granules occurring at different levels. The consequences reveal that the representation of the partition of the universal set is more efficient through q-rung picture fuzzy hypergraphs and the q-rung picture fuzzy equivalence relation. We also present an arithmetic example and comparison analysis to signify the superiority and validity of our proposed model.

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Robeva, Elina, and Anna Seigal. "Duality of graphical models and tensor networks." Information and Inference: A Journal of the IMA 8, no. 2 (2018): 273–88. http://dx.doi.org/10.1093/imaiai/iay009.

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Abstract In this article we show the duality between tensor networks and undirected graphical models with discrete variables. We study tensor networks on hypergraphs, which we call tensor hypernetworks. We show that the tensor hypernetwork on a hypergraph exactly corresponds to the graphical model given by the dual hypergraph. We translate various notions under duality. For example, marginalization in a graphical model is dual to contraction in the tensor network. Algorithms also translate under duality. We show that belief propagation corresponds to a known algorithm for tensor network contraction. This article is a reminder that the research areas of graphical models and tensor networks can benefit from interaction.

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DeFranco, Mario DeFranco, and Paul E. Gunnells. "Hypergraph Matrix Models." Moscow Mathematical Journal 21, no. 4 (2021): 737–66. http://dx.doi.org/10.17323/1609-4514-2021-21-4-737-766.

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4

GROSS, ELIZABETH, and SONJA PETROVIĆ. "COMBINATORIAL DEGREE BOUND FOR TORIC IDEALS OF HYPERGRAPHS." International Journal of Algebra and Computation 23, no. 06 (2013): 1503–20. http://dx.doi.org/10.1142/s0218196713500331.

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Associated to any hypergraph is a toric ideal encoding the algebraic relations among its edges. We study these ideals and the combinatorics of their minimal generators, and derive general degree bounds for both uniform and non-uniform hypergraphs in terms of balanced hypergraph bicolorings, separators, and splitting sets. In turn, this provides complexity bounds for algebraic statistical models associated to hypergraphs. As two main applications, we recover a well-known complexity result for Markov bases of arbitrary 3-way tables, and we show that the defining ideal of the tangential variety is generated by quadratics and cubics in cumulant coordinates.

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Hao, Yong-Jing, Ying-Lian Gao, Mi-Xiao Hou, Ling-Yun Dai, and Jin-Xing Liu. "Hypergraph Regularized Discriminative Nonnegative Matrix Factorization on Sample Classification and Co-Differentially Expressed Gene Selection." Complexity 2019 (August 19, 2019): 1–12. http://dx.doi.org/10.1155/2019/7081674.

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Nonnegative Matrix Factorization (NMF) is a significant big data analysis technique. However, standard NMF regularized by simple graph does not have discriminative function, and traditional graph models cannot accurately reflect the problem of multigeometry information between data. To solve the above problem, this paper proposed a new method called Hypergraph Regularized Discriminative Nonnegative Matrix Factorization (HDNMF), which captures intrinsic geometry by constructing hypergraphs rather than simple graphs. The introduction of the hypergraph method allows high-order relationships between samples to be considered, and the introduction of label information enables the method to have discriminative effect. Both the hypergraph Laplace and the discriminative label information are utilized together to learn the projection matrix in the standard method. In addition, we offered a corresponding multiplication update solution for the optimization. Experiments indicate that the method proposed is more effective by comparing with the earlier methods.

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GUNATILLEKA, DANUL K. "COUNTABLE MODELS OF THE THEORIES OF BALDWIN–SHI HYPERGRAPHS AND THEIR REGULAR TYPES." Journal of Symbolic Logic 84, no. 3 (2019): 1007–19. http://dx.doi.org/10.1017/jsl.2019.28.

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AbstractWe continue the study of the theories of Baldwin–Shi hypergraphs from [5]. Restricting our attention to when the rank δ is rational valued, we show that each countable model of the theory of a given Baldwin–Shi hypergraph is isomorphic to a generic structure built from some suitable subclass of the original class used in the construction. We introduce a notion of dimension for a model and show that there is a an elementary chain $\left\{ {\mathfrak{M}_\beta :\beta \leqslant \omega } \right\}$ of countable models of the theory of a fixed Baldwin–Shi hypergraph with $\mathfrak{M}_\beta \preccurlyeq \mathfrak{M}_\gamma $ if and only if the dimension of $\mathfrak{M}_\beta $ is at most the dimension of $\mathfrak{M}_\gamma $ and that each countable model is isomorphic to some $\mathfrak{M}_\beta $. We also study the regular types that appear in these theories and show that the dimension of a model is determined by a particular regular type. Further, drawing on a large body of work, we use these structures to give an example of a pseudofinite, ω-stable theory with a nonlocally modular regular type, answering a question of Pillay in [11].

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Mikov, A. I., and A. A. Mikov. "Connectivity and routes in large geometric network hypergraphs." Informatization and communication, no. 2 (February 16, 2021): 76–80. http://dx.doi.org/10.34219/2078-8320-2021-12-2-76-80.

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Random geometric hypergraphs are considered as mathematical models of large wireless computer networks. The dependences of the mathematical expectation of the number of hyper-edges in random geometric hypergraphs on the radii of reliable reception / transmission of radio signals by network nodes, as well as on the number of vertices in the hyper- graph are studied. The concepts of the shortest route in a geometric hypergraph are discussed. Calculations of the probabil- ity of connectivity of large random geometric hypergraphs, the mathematical expectation of the diameter of hypergraphs and its change with a change in the radii of the nodes are carried out. The presentation of the results is accompanied by graphs.

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8

Laguna, Miguel, José Marqués, and Guillermo Rodríguez-Cano. "Feature diagram formalization based on directed hypergraphs." Computer Science and Information Systems 8, no. 3 (2011): 611–33. http://dx.doi.org/10.2298/csis100804016l.

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Feature models are used to represent the variability and commonality of software product lines (SPL), and to decide on the configuration of specific applications. Several variants based on tree or graph hierarchical structures have been proposed. These structures are completed with additional constraints, generally expressed in parallel with the feature diagram. This paper proposes the use of hypergraphs to integrate both concepts in a unique characterization. Therefore, the definition, validation and selection of feature configurations can be internally based on the hypergraph properties and well-known algorithms, while the concrete visual syntax remains unchanged for domain engineers. The implemented hypergraph algorithms have been tested using a complete set of feature diagrams. Finally a feature meta-model can be derived directly from the formal definitions, providing the foundations for building feature modeling tools.

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9

Owrang O., M. M. "Query Translation Based on Hypergraph Models." Computer Journal 31, no. 2 (1988): 155–64. http://dx.doi.org/10.1093/comjnl/31.2.155.

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10

Chung, Fan, and Alexander Tsiatas. "Hypergraph Coloring Games and Voter Models." Internet Mathematics 10, no. 1-2 (2014): 66–86. http://dx.doi.org/10.1080/15427951.2013.833676.

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Mikov, Alexander I., and Alexander A. Mikov. "Properties of geometric hypergraphs of wireless computer networks." Informatization and communication 4 (November 2020): 60–66. http://dx.doi.org/10.34219/2078-8320-2020-11-4-60-66.

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Mathematical models of wireless computer networks are considered, reflecting two types of interaction between nodes of the same network — broadcast and routing. A natural form of representation of such a network is a hypergraph, in which the direct links between nodes that do not require routing are specified by the hyper-edges. The routes are chains of hyper-edges. The concepts of geometric and random hypergraphs are introduced, the dependences of the probabilistic characteristics of random geometric hypergraphs on the number of vertices and radii of reliable reception / transmission of radio signals by network nodes are studied — the mathematical expectation and standard deviation of the number of hyperedges, degrees of hyperedges. The properties of dynamic geometric hypergraphs are discussed, their influence on the connectivity of a computer network, and the requirements for algorithms for managing connectivity in terms of hypergraphs are formulated.

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12

Sarkar, S., and K. N. Sivarajan. "Hypergraph models for cellular mobile communication systems." IEEE Transactions on Vehicular Technology 47, no. 2 (1998): 460–71. http://dx.doi.org/10.1109/25.669084.

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13

Guzzo, Antonella, Andrea Pugliese, Antonino Rullo, Domenico Sacca, and Antonio Piccolo. "Malevolent Activity Detection with Hypergraph-Based Models." IEEE Transactions on Knowledge and Data Engineering 29, no. 5 (2017): 1115–28. http://dx.doi.org/10.1109/tkde.2017.2658621.

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14

Uçar, Bora, and Cevdet Aykanat. "Revisiting Hypergraph Models for Sparse Matrix Partitioning." SIAM Review 49, no. 4 (2007): 595–603. http://dx.doi.org/10.1137/060662459.

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15

Sechi, Giovanni M., and Paola Zuddas. "Multiperiod Hypergraph Models for Water Systems Optimization." Water Resources Management 22, no. 3 (2007): 307–20. http://dx.doi.org/10.1007/s11269-007-9163-2.

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16

Bouafia, Khawla, and Bálint Molnár. "Hypergraph Application on Business Process Performance." Information 12, no. 9 (2021): 370. http://dx.doi.org/10.3390/info12090370.

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The modeling of the graphical representation of business processes (BP) or workflows in enterprise information systems (IS) is often to represent various activities, entities, relations, functions, and communicate between them in an enterprise to achieve the major goal of operational support. In this work, we decided to use graph representation approaches, especially hypergraphs to depict the complex relationships that exist among the artifacts and constituents of BP for more efficient and accurate manipulations. We used bipartite and further hypergraph formats for storing and curating data. We have investigated the various descriptive languages and representation models of BP as process modeling, workflow and process integration, and object-oriented (OO) languages. We have carried out experiments using different approach combinations, but for observing quiltedrepresentation, we focused on the main consistencies of “DBP”. As the final approach, we used the “DBP” stream and data schemes that are defined by us to proceed with using pure Python for manually generating data and external Python libraries to store, curate, and visualize “DBP”.

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17

Khalil, W., R. Merzouki, B. Ould-Bouamama, and H. Haffaf. "Hypergraph Models for System of Systems Supervision Design." IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans 42, no. 4 (2012): 1005–12. http://dx.doi.org/10.1109/tsmca.2012.2183350.

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18

Landry, Nicholas W., and Juan G. Restrepo. "The effect of heterogeneity on hypergraph contagion models." Chaos: An Interdisciplinary Journal of Nonlinear Science 30, no. 10 (2020): 103117. http://dx.doi.org/10.1063/5.0020034.

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19

Li, Yalan, and Bo Deng. "A New Method to Find the Wiener Index of Hypergraphs." Discrete Dynamics in Nature and Society 2020 (June 11, 2020): 1–6. http://dx.doi.org/10.1155/2020/8138942.

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The Wiener index is defined as the summation of distances between all pairs of vertices in a graph or in a hypergraph. Both models—graph-theoretical and hypergraph-theoretical—are used in mathematical chemistry for quantitatively studying physical and chemical properties of classical and nonclassical organic compounds. In this paper, we consider relationships between hypertrees and trees and hypercycles and cycles with respect to their Wiener indices.

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20

Khardon, R. "Translating between Horn Representations and their Characteristic Models." Journal of Artificial Intelligence Research 3 (December 1, 1995): 349–72. http://dx.doi.org/10.1613/jair.183.

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Characteristic models are an alternative, model based, representation for Horn expressions. It has been shown that these two representations are incomparable and each has its advantages over the other. It is therefore natural to ask what is the cost of translating, back and forth, between these representations. Interestingly, the same translation questions arise in database theory, where it has applications to the design of relational databases. This paper studies the computational complexity of these problems. Our main result is that the two translation problems are equivalent under polynomial reductions, and that they are equivalent to the corresponding decision problem. Namely, translating is equivalent to deciding whether a given set of models is the set of characteristic models for a given Horn expression. We also relate these problems to the hypergraph transversal problem, a well known problem which is related to other applications in AI and for which no polynomial time algorithm is known. It is shown that in general our translation problems are at least as hard as the hypergraph transversal problem, and in a special case they are equivalent to it.

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Reddy, A. Rama Prathap, D. Venkatesh D. Venkatesh, and K. Ramesh K. Ramesh. "Hypergraph Interference Models in Wireless Ad-Hoc Networks with Low Complexity Distributed Scheduling." International Journal of Scientific Research 2, no. 6 (2012): 178–82. http://dx.doi.org/10.15373/22778179/june2013/57.

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22

Bellaachia, Abdelghani, and Mohammed Al-Dhelaan. "Random Walks in Hypergraph." International Journal of Education and Information Technologies 15 (March 10, 2021): 13–20. http://dx.doi.org/10.46300/9109.2021.15.2.

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Random walks on graphs have been extensively used for a variety of graph-based problems such as ranking vertices, predicting links, recommendations, and clustering. However, many complex problems mandate a high-order graph representation to accurately capture the relationship structure inherent in them. Hypergraphs are particularly useful for such models due to the density of information stored in their structure. In this paper, we propose a novel extension to defining random walks on hypergraphs. Our proposed approach combines the weights of destination vertices and hyperedges in a probabilistic manner to accurately capture transition probabilities. We study and analyze our generalized form of random walks suitable for the structure of hypergraphs. We show the effectiveness of our model by conducting a text ranking experiment on a real world data set with a 9% to 33% improvement in precision and a range of 7% to 50% improvement in Bpref over other random walk approaches.

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23

Ozdal, Muhammet Mustafa, and Cevdet Aykanat. "Hypergraph Models and Algorithms for Data-Pattern-Based Clustering." Data Mining and Knowledge Discovery 9, no. 1 (2004): 29–57. http://dx.doi.org/10.1023/b:dami.0000026903.59233.2a.

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24

Ligęza, Antoni. "Models and Tools for Improving Efficiency in Constraint Logic Programming." Decision Making in Manufacturing and Services 5, no. 1 (2011): 69–78. http://dx.doi.org/10.7494/dmms.2011.5.1.69.

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Constraint Satisfaction Problems typically exhibit strong combinatorial explosion. In this paper we present some models and techniques aimed at improving efficiency in Constraint Logic Programming. A hypergraph model of constraints is presented and an outline of strategy planning approach focused on entropy minimization is put forward. An example cryptoaritmetic problem is explored in order to explain the proposed approach.

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Mokrozub, Vladimir, Evgeniy Malygin, and Vladimir Nemtinov. "Information models for problems solving of hardware design of multi-range chemical industries." MATEC Web of Conferences 224 (2018): 02060. http://dx.doi.org/10.1051/matecconf/201822402060.

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The information models for determining sizes of apparatuses in chemical-technological systems and the development of separate technological apparatus are provided. The information model for solving the problem of calculating the determining sizes of apparatuses is based on the representation the structure of the chemical-technological system in the form of oriented polychromatic hypergraph, the edges of which are the products, and the vertices are the stages of the technological process. The information model for solving the problem of developing a separate technological apparatus allows determining its structure, the parameters of its elements and their location in the 3D model of the assembly. The structure of the apparatus is presented as a hierarchical system of hypergraphs, which was built on the base of the «and – or» tree of possible elements of the apparatus and the rules, that allow to select the necessary elements of «and – or» tree, depending on the functions of the apparatus and the conditions of its operation. The location of the elements of apparatus in space is determined by logical conditions describing their position relative to each other in the 3D model of the assembly.

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Imreh, Csanád, and Judit Nagy-György. "Online hypergraph coloring with rejection." Acta Universitatis Sapientiae, Informatica 7, no. 1 (2015): 5–17. http://dx.doi.org/10.1515/ausi-2015-0009.

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Abstract In this paper we investigate the online hypergraph coloring problem with rejection, where the algorithm is allowed to reject a vertex instead of coloring it but each vertex has a penalty which has to be paid if it is not colored. The goal is to minimize the sum of the number of the used colors for the accepted vertices and the total penalty paid for the rejected ones. We study the online problem which means that the algorithm receives the vertices of the hypergraph in some order v1, . . . , vn and it must decide about vi by only looking at the subhypergraph Hi = (Vi, Ei) where Vi = {v1, . . . , vi} and Ei contains the edges of the hypergraph which are subsets of Vi. We consider two models: in the full edge model only the edges where each vertex is accepted must be well-colored, in the trace model the subsets of the edges formed by the accepted vertices must be well colored as well. We consider proper and conflict free colorings. We present in each cases optimal online algorithms in the sense that they achieve asymptotically the smallest possible competitive ratio.

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Luqman, Anam, Muhammad Akram, and Ali Koam. "An m-Polar Fuzzy Hypergraph Model of Granular Computing." Symmetry 11, no. 4 (2019): 483. http://dx.doi.org/10.3390/sym11040483.

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An m-polar fuzzy model plays a vital role in modeling of real-world problems that involve multi-attribute, multi-polar information and uncertainty. The m-polar fuzzy models give increasing precision and flexibility to the system as compared to the fuzzy and bipolar fuzzy models. An m-polar fuzzy set assigns the membership degree to an object belonging to [ 0 , 1 ] m describing the m distinct attributes of that element. Granular computing deals with representing and processing information in the form of information granules. These information granules are collections of elements combined together due to their similarity and functional/physical adjacency. In this paper, we illustrate the formation of granular structures using m-polar fuzzy hypergraphs and level hypergraphs. Further, we define m-polar fuzzy hierarchical quotient space structures. The mappings between the m-polar fuzzy hypergraphs depict the relationships among granules occurring at different levels. The consequences reveal that the representation of the partition of a universal set is more efficient through m-polar fuzzy hypergraphs as compared to crisp hypergraphs. We also present some examples and a real-world problem to signify the validity of our proposed model.

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28

Ma, Jichao, Chunyu Du, Weifeng Liu, and Yanjiang Wang. "Numerical Simulation of Higher-Order Nonlinearity of Human Brain Functional Connectivity Using Hypergraph p-Laplacian." Mathematics 9, no. 18 (2021): 2345. http://dx.doi.org/10.3390/math9182345.

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Unravelling how the human brain structure gives rise to function is a central question in neuroscience and remains partially answered. Recent studies show that the graph Laplacian of the human brain’s structural connectivity (SC) plays a dominant role in shaping the pattern of resting-state functional connectivity (FC). The modeling of FC using the graph Laplacian of the brain’s SC is limited, owing to the sparseness of the Laplacian matrix. It is unable to model the negative functional correlations. We extended the graph Laplacian to the hypergraph p-Laplacian in order to describe better the nonlinear and high-order relations between SC and FC. First we estimated those possible links showing negative correlations between the brain areas shared across subjects by statistical analysis. Then we presented a hypergraph p-Laplacian model by embedding the two matrices referring to the sign of the correlations between the brain areas relying on the brain structural connectome. We tested the model on two experimental connectome datasets and evaluated the predicted FC by estimating its Pearson correlation with the empirical FC matrices. The results showed that the proposed diffusion model based on hypergraph p-Laplacian can predict functional correlations more accurately than the models using graph Laplacian as well as hypergraph Laplacian.

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29

Das, Mayukh, Devendra Singh Dhami, Gautam Kunapuli, Kristian Kersting, and Sriraam Natarajan. "Fast Relational Probabilistic Inference and Learning: Approximate Counting via Hypergraphs." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 7816–24. http://dx.doi.org/10.1609/aaai.v33i01.33017816.

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Counting the number of true instances of a clause is arguably a major bottleneck in relational probabilistic inference and learning. We approximate counts in two steps: (1) transform the fully grounded relational model to a large hypergraph, and partially-instantiated clauses to hypergraph motifs; (2) since the expected counts of the motifs are provably the clause counts, approximate them using summary statistics (in/outdegrees, edge counts, etc). Our experimental results demonstrate the efficiency of these approximations, which can be applied to many complex statistical relational models, and can be significantly faster than state-of-the-art, both for inference and learning, without sacrificing effectiveness.

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DUAN, Houli, Zhiheng LI, and Yi ZHANG. "Generation of Coordinated Control Regions for Road Network using Hypergraph Models." IFAC Proceedings Volumes 42, no. 15 (2009): 576–81. http://dx.doi.org/10.3182/20090902-3-us-2007.0071.

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31

Li, Qiao, and Rohit Negi. "Maximal Scheduling in Wireless Ad Hoc Networks With Hypergraph Interference Models." IEEE Transactions on Vehicular Technology 61, no. 1 (2012): 297–310. http://dx.doi.org/10.1109/tvt.2011.2176520.

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32

Borndörfer, Ralf, Thomas Eßer, Patrick Frankenberger, et al. "Deutsche Bahn Schedules Train Rotations Using Hypergraph Optimization." INFORMS Journal on Applied Analytics 51, no. 1 (2021): 42–62. http://dx.doi.org/10.1287/inte.2020.1069.

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Deutsche Bahn (DB) operates a large fleet of rolling stock (locomotives, wagons, and train sets) that must be combined into trains to perform rolling stock rotations. This train composition is a special characteristic of railway operations that distinguishes rolling stock rotation planning from the vehicle scheduling problems prevalent in other industries. DB models train compositions using hyperarcs. The resulting hypergraph models are addressed using a novel coarse-to-fine method that implements a hierarchical column generation over three levels of detail. This algorithm is the mathematical core of DB’s fleet employment optimization (FEO) system for rolling stock rotation planning. FEO’s impact within DB’s planning departments has been revolutionary. DB has used it to support the company’s procurements of its newest high-speed passenger train fleet and its intermodal cargo locomotive fleet for crossborder operations. FEO is the key to successful tendering in regional transport and to construction site management in daily operations. DB’s planning departments appreciate FEO’s high-quality results, ability to reoptimize (quickly), and ease of use. Both employees and customers benefit from the increased regularity of operations. DB attributes annual savings of 74 million euro, an annual reduction of 34,000 tons of CO2 emissions, and the elimination of 600 coupling operations in crossborder operations to the implementation of FEO.

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Post, Matt, Yuan Cao, and Gaurav Kumar. "Joshua 6: A phrase-based and hierarchical statistical machine translation system." Prague Bulletin of Mathematical Linguistics 104, no. 1 (2015): 5–16. http://dx.doi.org/10.1515/pralin-2015-0009.

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Abstract We describe the version six release of Joshua, an open-source statistical machine translation toolkit. The main difference from release five is the introduction of a simple, unlexicalized, phrase-based stack decoder. This phrase-based decoder shares a hypergraph format with the syntax-based systems, permitting a tight coupling with the existing codebase of feature functions and hypergraph tools. Joshua 6 also includes a number of large-scale discriminative tuners and a simplified sparse feature function interface with reflection-based loading, which allows new features to be used by writing a single function. Finally, Joshua includes a number of simplifications and improvements focused on usability for both researchers and end-users, including the release of language packs — precompiled models that can be run as black boxes.

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Ajemni, H., R. El, and M. N. "Directed Hypergraph-based Models for the Fault Monitoring of Chemical Reaction Kinetics." International Journal of Computer Applications 166, no. 12 (2017): 1–8. http://dx.doi.org/10.5120/ijca2017914040.

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35

Konstantinova, E. V., and V. A. Skoroboratov. "Graph and hypergraph models of molecular structure: A comparative analysis of indices." Journal of Structural Chemistry 39, no. 6 (1998): 958–66. http://dx.doi.org/10.1007/bf02903615.

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36

Ganesan, Ashwin. "On Some Distributed Scheduling Algorithms for Wireless Networks With Hypergraph Interference Models." IEEE Transactions on Information Theory 67, no. 5 (2021): 2952–57. http://dx.doi.org/10.1109/tit.2021.3059719.

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Fan, Youping, Jingjiao Li, Dai Zhang, Jie Pi, Jiahan Song, and Guo Zhao. "Supporting Sustainable Maintenance of Substations under Cyber-Threats: An Evaluation Method of Cybersecurity Risk for Power CPS." Sustainability 11, no. 4 (2019): 982. http://dx.doi.org/10.3390/su11040982.

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In the increasingly complex cyber-environment, appropriate sustainable maintenance of substation auto systems (SASs) can lead to many positive effects on power cyber-physical systems (CPSs). Evaluating the cybersecurity risk of power CPSs is the first step in creating sustainable maintenance plans for SASs. In this paper, a mathematical framework for evaluating the cybersecurity risk of a power CPS is proposed considering both the probability of successful cyberattacks on SASs and their consequences for the power system. First, the cyberattacks and their countermeasures are introduced, and the probability of successful cyber-intruding on SASs is modeled from the defender’s perspective. Then, a modified hypergraph model of the SAS’s logical structure is established to quantitatively analyze the impacts of cyberattacks on an SAS. The impacts will ultimately act on the physical systems of the power CPS. The modified hypergraph model can describe more information than a graph or hypergraph model and potentially can analyze complex networks like CPSs. Finally, the feasibility and effectiveness of the proposed evaluation method is verified by the IEEE 14-bus system, and the test results demonstrate that this proposed method is more reasonable to assess the cybersecurity risk of power CPS compared with some other models.

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Kim, Hyoungnyoun, and Ji-Hyung Park. "Hypergraph-Based Recognition Memory Model for Lifelong Experience." Computational Intelligence and Neuroscience 2014 (2014): 1–17. http://dx.doi.org/10.1155/2014/354703.

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Cognitive agents are expected to interact with and adapt to a nonstationary dynamic environment. As an initial process of decision making in a real-world agent interaction, familiarity judgment leads the following processes for intelligence. Familiarity judgment includes knowing previously encoded data as well as completing original patterns from partial information, which are fundamental functions of recognition memory. Although previous computational memory models have attempted to reflect human behavioral properties on the recognition memory, they have been focused on static conditions without considering temporal changes in terms of lifelong learning. To provide temporal adaptability to an agent, in this paper, we suggest a computational model for recognition memory that enables lifelong learning. The proposed model is based on a hypergraph structure, and thus it allows a high-order relationship between contextual nodes and enables incremental learning. Through a simulated experiment, we investigate the optimal conditions of the memory model and validate the consistency of memory performance for lifelong learning.

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Cooper, Kendra, and Hassan Khosravi. "Multilevel Topic Dependency Models for Assessment Design and Delivery: A Hypergraph Based Approach." Journal of Visual Language and Computing 2019, no. 2 (2019): 69–82. http://dx.doi.org/10.18293/jvlc2019-n2-018.

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40

Bradley, Jeremy T., Nicholas J. Dingle, William J. Knottenbelt, and Helen J. Wilson. "Hypergraph-based parallel computation of passage time densities in large semi-Markov models." Linear Algebra and its Applications 386 (July 2004): 311–34. http://dx.doi.org/10.1016/j.laa.2003.12.018.

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Higham, Desmond J., and Henry-Louis de Kergorlay. "Epidemics on hypergraphs: spectral thresholds for extinction." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 477, no. 2252 (2021): 20210232. http://dx.doi.org/10.1098/rspa.2021.0232.

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Epidemic spreading is well understood when a disease propagates around a contact graph. In a stochastic susceptible–infected–susceptible setting, spectral conditions characterize whether the disease vanishes. However, modelling human interactions using a graph is a simplification which only considers pairwise relationships. This does not fully represent the more realistic case where people meet in groups. Hyperedges can be used to record higher order interactions, yielding more faithful and flexible models and allowing for the rate of infection of a node to depend on group size and also to vary as a nonlinear function of the number of infectious neighbours. We discuss different types of contagion models in this hypergraph setting and derive spectral conditions that characterize whether the disease vanishes. We study both the exact individual-level stochastic model and a deterministic mean field ODE approximation. Numerical simulations are provided to illustrate the analysis. We also interpret our results and show how the hypergraph model allows us to distinguish between contributions to infectiousness that (i) are inherent in the nature of the pathogen and (ii) arise from behavioural choices (such as social distancing, increased hygiene and use of masks). This raises the possibility of more accurately quantifying the effect of interventions that are designed to contain the spread of a virus.

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Cambazoglu, Berkant Barla, and Cevdet Aykanat. "Hypergraph-Partitioning-Based Remapping Models for Image-Space-Parallel Direct Volume Rendering of Unstructured Grids." IEEE Transactions on Parallel and Distributed Systems 18, no. 1 (2007): 3–16. http://dx.doi.org/10.1109/tpds.2007.253277.

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Abubaker, Nabil, Kadir Akbudak, and Cevdet Aykanat. "Spatiotemporal Graph and Hypergraph Partitioning Models for Sparse Matrix-Vector Multiplication on Many-Core Architectures." IEEE Transactions on Parallel and Distributed Systems 30, no. 2 (2019): 445–58. http://dx.doi.org/10.1109/tpds.2018.2864729.

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Akbudak, Kadir, Enver Kayaaslan, and Cevdet Aykanat. "Hypergraph Partitioning Based Models and Methods for Exploiting Cache Locality in Sparse Matrix-Vector Multiplication." SIAM Journal on Scientific Computing 35, no. 3 (2013): C237—C262. http://dx.doi.org/10.1137/100813956.

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Ran, Maoli, and Xiangyu Bai. "Vehicle Cooperative Network Model Based on Hypergraph in Vehicular Fog Computing." Sensors 20, no. 8 (2020): 2269. http://dx.doi.org/10.3390/s20082269.

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In this paper, we propose an optimization framework of vehicular fog computing and a cooperation vehicular network model. We aim to improve the performance of vehicular fog computing and solve the problem that the data of the vehicle collaborative network is difficult to obtain. This paper applies the hypergraph theory to study the underlying structure, considering the social characteristics of the vehicles and vehicle communication. Since the vehicles join the network in accordance with the Poisson process law, the model is analyzed by using Poisson stochastic process and mean field theory. This paper uses MATLAB to simulate the evolution process of cooperative networks. The results show that the vehicle’s super-degree in vehicular fog computing has scale-free characteristics. Through this model, the vehicle cooperation situation can be analyzed, and the vehicle dynamics can be accurately predicted to further improve the performance of vehicular fog computing. The model can be transformed into some complex network models by adjusting the parameters. It has strong universality and has certain reference significance for the research on the related characteristics of VANETs and the theoretical research of the cooperative network.

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Lanchier, N. "Contact Process with Destruction of Cubes and Hyperplanes: Forest Fires Versus Tornadoes." Journal of Applied Probability 48, no. 02 (2011): 352–65. http://dx.doi.org/10.1017/s0021900200007920.

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Nonspatial stochastic models of populations subject to catastrophic events result in the common conclusion that the survival probability of the population is nondecreasing with respect to the random number of individuals removed at each catastrophe. The purpose of this paper is to prove that such a monotonic relationship is not true for simple spatial models based on Harris' contact processes, whose dynamics are described by hypergraph structures rather than traditional graph structures. More precisely, it is proved that, for a wide range of parameters, the destruction of (infinite) hyperplanes does not affect the existence of a nontrivial invariant measure, whereas the destruction of large (finite) cubes drives the population to extinction, a result that we depict by using the biological picture: forest fires are more devastating than tornadoes. This indicates that the geometry of the subsets struck by catastrophes is somewhat more important than their area, thus the need to consider spatial rather than nonspatial models in this context.

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Lanchier, N. "Contact Process with Destruction of Cubes and Hyperplanes: Forest Fires Versus Tornadoes." Journal of Applied Probability 48, no. 2 (2011): 352–65. http://dx.doi.org/10.1239/jap/1308662632.

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Abstract:

Nonspatial stochastic models of populations subject to catastrophic events result in the common conclusion that the survival probability of the population is nondecreasing with respect to the random number of individuals removed at each catastrophe. The purpose of this paper is to prove that such a monotonic relationship is not true for simple spatial models based on Harris' contact processes, whose dynamics are described by hypergraph structures rather than traditional graph structures. More precisely, it is proved that, for a wide range of parameters, the destruction of (infinite) hyperplanes does not affect the existence of a nontrivial invariant measure, whereas the destruction of large (finite) cubes drives the population to extinction, a result that we depict by using the biological picture: forest fires are more devastating than tornadoes. This indicates that the geometry of the subsets struck by catastrophes is somewhat more important than their area, thus the need to consider spatial rather than nonspatial models in this context.

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Dingle, Nicholas J., Peter G. Harrison, and William J. Knottenbelt. "Uniformization and hypergraph partitioning for the distributed computation of response time densities in very large Markov models." Journal of Parallel and Distributed Computing 64, no. 8 (2004): 908–20. http://dx.doi.org/10.1016/j.jpdc.2004.03.017.

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Wang, Cui, Jiguo Yu, Dongxiao Yu, Baogui Huang, and Shanshan Yu. "An improved approximation algorithm for the shortest link scheduling in wireless networks under SINR and hypergraph models." Journal of Combinatorial Optimization 32, no. 4 (2015): 1052–67. http://dx.doi.org/10.1007/s10878-015-9908-4.

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Sun, Jing Hao, Ding Diao, Ling Jin Huang, and Ya Kun Meng. "The Effect of AS's Geographic Locations on Internet's Stability." Advanced Materials Research 765-767 (September 2013): 1375–81. http://dx.doi.org/10.4028/www.scientific.net/amr.765-767.1375.

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This paper analyzes how the AS's geographic locations and transmission distances affect on Internet's stability. In contrast to the traditional studies focusing on the future AS network which based on nowadays, this paper emphasizes particularly on the change of AS network's performance under the effect of the economic adjusting or the technology innovation to help make adjusting measures and to lead the technological trend. A double-deck network model of geographic hypergraph and AS network is presented to simulate the geographic locations, which is not reflected in traditional models. The simulate results of our model show that Internets stability ascends with the increase of transmission distances. However, if AS's geographic locations are random, the transmission distances has no obvious effects on Internets stability.

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