Network motifs are recurrent, small-scale patterns of interactions observed frequently in a system. They shed light on the interplay between the topology and the dynamics of complex networks across various domains. In...
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Network motifs are recurrent, small-scale patterns of interactions observed frequently in a system. They shed light on the interplay between the topology and the dynamics of complex networks across various domains. In this work, we focus on the problem of counting occurrences of small sub-hypergraph patterns in very large hypergraphs, where higher-order interactions connect arbitrary numbers of system units. We show how directly exploiting higher-order structures speeds up the counting process compared to traditional data mining techniques for exact motif discovery. Moreover, with hyperedge sampling, performance is further improved at the cost of small errors in the estimation of motif frequency. We evaluate our method on several real-world datasets describing face-to-face interactions, co-authorship and human communication. We show that our approximated algorithm allows us to extract higher-order motifs faster and on a larger scale, beyond the computational limits of an exact approach.
A wide variety of complex systems are characterized by interactions of different types involving varying numbers of units. Multiplex hypergraphs serve as a tool to describe such structures, capturing distinct types of...
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A wide variety of complex systems are characterized by interactions of different types involving varying numbers of units. Multiplex hypergraphs serve as a tool to describe such structures, capturing distinct types of higher-order interactions among a collection of units. In this work, we introduce a comprehensive set of measures to describe structural connectivity patterns in multiplex hypergraphs, considering scales from node and hyperedge levels to the system's mesoscale. We validate our measures with three real-world datasets: scientific co-authorship in physics, movie collaborations, and high school interactions. This validation reveals new collaboration patterns, identifies trends within and across movie subfields, and provides insights into daily interaction dynamics. Our framework aims to offer a more nuanced characterization of real-world systems marked by both multiplex and higher-order interactions.
hypergraph as a formal model offers a sound foundation for representing information systems. There are several issues that are worth observing during analysis, design, and operation of information systems such as cons...
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ISBN:
(纸本)9783030204822;9783030204815
hypergraph as a formal model offers a sound foundation for representing information systems. There are several issues that are worth observing during analysis, design, and operation of information systems such as consistency, integrity, soundness of control and security mechanisms. The improvement and advancement of machine learning and data science algorithms provide the opportunity to spot patterns, to predict and to prescript some activities within complex environments that can depict huge sets of data. Our proposal is that the available algorithms can be applied on hypergraphs through profound customization whereby the capability of algorithms can be exploited for Business Information Systems.
The paper describes a new approach for treatment security issues in reconfigurable grids used for computing or communication, in particular, in the semantic web environment. The proposed strategy combines a convenient...
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The paper describes a new approach for treatment security issues in reconfigurable grids used for computing or communication, in particular, in the semantic web environment. The proposed strategy combines a convenient mathematical model, efficient combinatorial algorithms which are robust with respect to changes in the grid structure, and an efficient implementation. The mathematical model uses properties of weighted hypergraphs. Model flexibility enables to describe basic security relations between the nodes such that these relations are preserved under frequent changes in connections of the hypergraph nodes. The algorithms support construction of a grid with embedded security concepts on a given set of nodes. The proposed implementation makes use of the techniques developed for time and space-critical applications in numerical linear algebra. Our combination of the mentioned combined building blocks is targeted to the emerging field of the semantic web, where the security seems to be very important. Nevertheless, the ideas can be generalized to other concepts describable by weighted hypergraphs. The paper concentrates on explaining the model and the algorithms for the chosen application. The consistency of the proposed ideas for security management in the changing grid was verified in a couple of tests with our pilot implementation SECGRID.
We study the problem of testing properties of hypergraphs. The goal of property testing is to distinguish between the case whether a given object has a certain property or is "far away" from the property. We...
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We study the problem of testing properties of hypergraphs. The goal of property testing is to distinguish between the case whether a given object has a certain property or is "far away" from the property. We prove that the fundamental problem of l-colorability of k-uniform hypergraphs, can be tested in time independent of the size of the hypergraph. We present a testing algorithm that examines only (k l/epsilon)(O(k)) entries of the adjacency matrix of the input hypergraph, where epsilon is a distance parameter independent of the size of the hypergraph. The algorithm tests only a constant number of entries in the adjacency matrix provided that l, k, and c are constants. This result is a generalization of previous results about testing graph colorability. (C) 2004 Elsevier B.V. All rights reserved.
We study the problem of testing properties of hypergraphs. The goal of property testing is to distinguish between the case whether a given object has a certain property or is "far away" from the property. We...
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We study the problem of testing properties of hypergraphs. The goal of property testing is to distinguish between the case whether a given object has a certain property or is "far away" from the property. We prove that the fundamental problem of l-colorability of k-uniform hypergraphs, can be tested in time independent of the size of the hypergraph. We present a testing algorithm that examines only (k l/epsilon)(O(k)) entries of the adjacency matrix of the input hypergraph, where epsilon is a distance parameter independent of the size of the hypergraph. The algorithm tests only a constant number of entries in the adjacency matrix provided that l, k, and c are constants. This result is a generalization of previous results about testing graph colorability. (C) 2004 Elsevier B.V. All rights reserved.
We present a technique for analyzing the run time behavior of integrity constraints repair actions, i.e., active database rules specifically designed to correct violations of database integrity. When constraints becom...
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We present a technique for analyzing the run time behavior of integrity constraints repair actions, i.e., active database rules specifically designed to correct violations of database integrity. When constraints become violated due to an incorrect user transaction, rule computation is started to restore the database to a correct state. Since repair actions may be numerous and may conflict with each other, an automated support to the analysis of their run-time behavior is necessary. The proposed technique helps the rule base administrator define a repair rule selection strategy such that the computation terminates for every input transaction, the final database state satisfies all the constraints, and the user's preferences among different ways to restore integrity are taken into account. In addition, it can be used by the rule designer to spot ''dangerous'' rules that may be subject to redesign. This problem is formulated as an optimization problem on directed hypergraphs, which we demonstrate to be NP-hard and solve by means of a heuristic algorithm.
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