41 research outputs found

    Learning, Generalization, and Functional Entropy in Random Automata Networks

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    It has been shown \citep{broeck90:physicalreview,patarnello87:europhys} that feedforward Boolean networks can learn to perform specific simple tasks and generalize well if only a subset of the learning examples is provided for learning. Here, we extend this body of work and show experimentally that random Boolean networks (RBNs), where both the interconnections and the Boolean transfer functions are chosen at random initially, can be evolved by using a state-topology evolution to solve simple tasks. We measure the learning and generalization performance, investigate the influence of the average node connectivity KK, the system size NN, and introduce a new measure that allows to better describe the network's learning and generalization behavior. We show that the connectivity of the maximum entropy networks scales as a power-law of the system size NN. Our results show that networks with higher average connectivity KK (supercritical) achieve higher memorization and partial generalization. However, near critical connectivity, the networks show a higher perfect generalization on the even-odd task

    Damage Spreading and Criticality in Finite Random Dynamical Networks

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    We systematically study and compare damage spreading at the sparse percolation (SP) limit for random boolean and threshold networks with perturbations that are independent of the network size NN. This limit is relevant to information and damage propagation in many technological and natural networks. Using finite size scaling, we identify a new characteristic connectivity KsK_s, at which the average number of damaged nodes dˉ\bar d, after a large number of dynamical updates, is independent of NN. Based on marginal damage spreading, we determine the critical connectivity Kcsparse(N)K_c^{sparse}(N) for finite NN at the SP limit and show that it systematically deviates from KcK_c, established by the annealed approximation, even for large system sizes. Our findings can potentially explain the results recently obtained for gene regulatory networks and have important implications for the evolution of dynamical networks that solve specific computational or functional tasks.Comment: 4 pages, 4 eps figure

    Assessing Random Dynamical Network Architectures for Nanoelectronics

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    Independent of the technology, it is generally expected that future nanoscale devices will be built from vast numbers of densely arranged devices that exhibit high failure rates. Other than that, there is little consensus on what type of technology and computing architecture holds most promises to go far beyond today's top-down engineered silicon devices. Cellular automata (CA) have been proposed in the past as a possible class of architectures to the von Neumann computing architecture, which is not generally well suited for future parallel and fine-grained nanoscale electronics. While the top-down engineered semi-conducting technology favors regular and locally interconnected structures, future bottom-up self-assembled devices tend to have irregular structures because of the current lack precise control over these processes. In this paper, we will assess random dynamical networks, namely Random Boolean Networks (RBNs) and Random Threshold Networks (RTNs), as alternative computing architectures and models for future information processing devices. We will illustrate that--from a theoretical perspective--they offer superior properties over classical CA-based architectures, such as inherent robustness as the system scales up, more efficient information processing capabilities, and manufacturing benefits for bottom-up designed devices, which motivates this investigation. We will present recent results on the dynamic behavior and robustness of such random dynamical networks while also including manufacturing issues in the assessment.Comment: 8 pages, 6 figures, IEEE/ACM Symposium on Nanoscale Architectures, NANOARCH 2008, Anaheim, CA, USA, Jun 12-13, 200

    Mapping the evolution of scientific fields

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    Despite the apparent cross-disciplinary interactions among scientific fields, a formal description of their evolution is lacking. Here we describe a novel approach to study the dynamics and evolution of scientific fields using a network-based analysis. We build an idea network consisting of American Physical Society Physics and Astronomy Classification Scheme (PACS) numbers as nodes representing scientific concepts. Two PACS numbers are linked if there exist publications that reference them simultaneously. We locate scientific fields using a community finding algorithm, and describe the time evolution of these fields over the course of 1985-2006. The communities we identify map to known scientific fields, and their age depends on their size and activity. We expect our approach to quantifying the evolution of ideas to be relevant for making predictions about the future of science and thus help to guide its development.Comment: v3: re-ran analysis with new noise parameter choice; 10 pages for main paper; 11 pages for suppl. inf

    Viral Disease Networks

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