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  • 1
    Language: English
    In: Communications in Nonlinear Science and Numerical Simulation, July 2012, Vol.17(7), pp.2741-2751
    Description: ► We couple an ensemble of existing models representing a single real-world phenomena. ► Models interactively exchange information during learning and prediction. ► Coupling coefficients are learned from short past data of the observed phenomenon. ► Examination with Lorenz systems with radical imperfections show good approximation. ► The ensemble is reduced to be made useful for models of high complexity. Most of the existing approaches for combining models representing a single real-world phenomenon into a multi-model ensemble combine the models a posteriori. Alternatively, in our method the models are coupled into a supermodel and continuously communicate during learning and prediction. The method learns a set of coupling coefficients from short past data in order to unite the different strengths of the models into a better representation of the observed phenomenon. The method is examined using the Lorenz oscillator, which is altered by introducing parameter and structural differences for creating imperfect models. The short past data is obtained by the standard oscillator, and different weight is assigned to each sample of the past data. The coupling coefficients are learned by using a quasi-Newton method and an evolutionary algorithm. We also introduce a way for reducing the supermodel, which is particularly useful for models of high complexity. The results reveal that the proposed supermodel gives a very good representation of the truth even for substantially imperfect models and short past data, which suggests that the super-modeling is promising in modeling real-world phenomena.
    Keywords: Multi-Model Ensembles ; Chaos ; Coupled Oscillators ; Applied Sciences
    ISSN: 1007-5704
    E-ISSN: 1878-7274
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  • 2
    Language: English
    In: IEEE Transactions on Circuits and Systems I: Regular Papers, February 2014, Vol.61(2), pp.522-529
    Description: We study synchronization and consensus phenomena in state-dependent graphs in which the edges are weighted according to the Hebbian learning rule or its modified version. By exploring the master stability function of the synchronous state, we show that the modified Hebbian function as coupling strength enlarges the stability region of the synchronous state. In terms of consensus, given that the state-dependent weights are always positive, we prove that consensus in a network of multi-agent systems is always reachable. Furthermore, we show that in state-dependent graphs the second smallest eigenvalue of the graph Laplacian matrix has larger values due to the state-dependency, resulting in speed up of the convergence process.
    Keywords: Couplings ; Synchronization ; Oscillators ; Neurons ; Stability Analysis ; Eigenvalues and Eigenfunctions ; Laplace Equations ; Adaptive Coupling ; Consensus ; Hebbian Learning Rule ; Master-Stability Function ; State-Dependent Graphs ; Synchronization ; Engineering
    ISSN: 1549-8328
    E-ISSN: 1558-0806
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  • 3
    Language: English
    In: IEEE Transactions on Circuits and Systems I: Regular Papers, March 2014, Vol.61(3), pp.811-819
    Description: The incipience of synchrony in a diverse population of phase oscillators with non-identical interactions is an intriguing phenomenon. We study frequency synchronization of such oscillators composing networks with arbitrary topology in the context of the Kuramoto model and we show that its synchronization manifold is exponentially stable when the coupling has certain properties. Several example systems with periodic linear, cubic and sinusoidal coupling functions were examined, some including frustration and external fields. The numerical results confirmed the analytic findings and revealed some other interesting occurrences, like phase clustering in a synchronized network of strongly coupled oscillators. We also analyze the effects of the topology by considering random weighted networks.
    Keywords: Couplings ; Oscillators ; Synchronization ; Frequency Synchronization ; Mathematical Model ; Standards ; Sociology ; Complex Networks ; Nonlinear Systems ; Stability Analysis ; Engineering
    ISSN: 1549-8328
    E-ISSN: 1558-0806
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  • 4
    Language: English
    In: IEEE Transactions on Circuits and Systems I: Regular Papers, October 2017, Vol.64(10), pp.2761-2771
    Description: Real networks in our surrounding are usually complex and composite by nature and they consist of many interwoven layers. The commutation of agents (nodes) across layers in these composite multiplex networks heavily influences the underlying dynamical processes, such as information, idea and disease spreading, synchronization, consensus, etc. In order to understand how the agents' dynamics and the compositeness of multiplex networks influence the spreading dynamics, we develop a susceptible-infected-susceptible-based model on the top of these networks, which is integrated with the transition of agents across layers. Moreover, we analytically obtain a critical infection rate for which an epidemic dies out in a multiplex network, and latter show that this rate can be higher compared with the isolated networks. Finally, using numerical simulations we confirm the epidemic threshold and we show some interesting insights into the epidemic onset and the spreading dynamics in several real and generic multiplex networks.
    Keywords: Multiplexing ; Silicon ; Mathematical Model ; Computer Science ; Social Network Services ; Nonhomogeneous Media ; Markov Processes ; Multiplex Networks ; Epidemic Spreading ; Sis Model ; Engineering ; Computer Science
    ISSN: 1549-8328
    E-ISSN: 1558-0806
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  • 5
    Language: English
    In: IEEE Transactions on Circuits and Systems-I-Regular Papers, 2017, Vol.64(10), p.2761(11)
    Keywords: Mathematical Models – Usage ; Computer Science – Research ; Markov Processes – Usage
    ISSN: 1549-8328
    Source: Cengage Learning, Inc.
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  • 6
    Description: We study two types of biased random walk on complex networks, which are based on local information. In the first procedure, the transitions towards neighboring nodes with smaller degrees are favored, while in the second another concept based on a two-hop neighborhood is explored. We have verified by numerical simulations that both procedures reduce the mean searching time of the target. We show theoretically that for well connected networks, where nodes have many neighbors, biasing of the random walk based on inverse of nodes' degrees leads to nearly optimal search for undirected and directed networks.
    Keywords: Physics - Physics And Society ; Condensed Matter - Statistical Mechanics
    Source: Cornell University
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