15,622 research outputs found

    Edge of chaos as critical local symmetry breaking in dissipative nonautonomous systems

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    The fully nonlinear notion of resonance -geometrical resonance\textit{geometrical resonance}- in the general context of dissipative systems subjected to nonsteady\textit{nonsteady} potentials is discussed. It is demonstrated that there is an exact local invariant associated with each geometrical resonance solution which reduces to the system's energy when the potential is steady. The geometrical resonance solutions represent a \textit{local symmetry} whose critical breaking leads to a new analytical criterion for the order-chaos threshold. This physical criterion is deduced in the co-moving frame from the local energy conservation over the shortest significant timescale. Remarkably, the new criterion for the onset of chaos is shown to be valid over large regions of parameter space, thus being useful beyond the perturbative regime and the scope of current mathematical techniques

    Reshaping-induced spatiotemporal chaos in driven, damped sine-Gordon systems

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    Spatiotemporal chaos arising from the competition between sine-Gordon-breather and kink-antikink-pair solitons by reshaping an ac force is demonstrated. After introducing soliton collective coordinates, Melnikov's method is applied to the resulting effective equation of motion to estimate the parameter-space regions of the ac force where homoclinic bifurcations are induced. The analysis reveals that the chaos-order threshold exhibits sensitivity to small changes in the force shape. Computer simulations of the sine-Gordon system show good agreement with these theoretical predictions.Comment: 11 pages, 3 figure

    Ring Learning With Errors: A crossroads between postquantum cryptography, machine learning and number theory

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    The present survey reports on the state of the art of the different cryptographic functionalities built upon the ring learning with errors problem and its interplay with several classical problems in algebraic number theory. The survey is based to a certain extent on an invited course given by the author at the Basque Center for Applied Mathematics in September 2018.Comment: arXiv admin note: text overlap with arXiv:1508.01375 by other authors/ comment of the author: quotation has been added to Theorem 5.

    Adding user interactivity to FreeFem++ with EJS: From teaching to research

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    Conferencia plenaria por invitaciónIn this talk we propose the use of an authoring tool, Easy Java Simulations, to build interactive simulations for pdes where the computing kernel is FreeFem++. This tool allows to play with all the parameters of the pde problem at will, mesh size, pde terms, boundary conditions, etc... and creates applets for the student to play and learn in real time on the influence of these parameters on the solution of the pde.Universidad de Málaga. Campus de Excelencia Internacional Andalucia Tech. Conferencias del plan propio de investigación

    Toeplitz Operators on Weighted Bergman Spaces

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    In this article we characterize the boundedness and compactness of a Toeplitz-type operator on weighted Bergman spaces satisfying the so-called Bekolle-Bonami condition in terms of the Berezin transform

    Drastic disorded-induced reduction of signal amplification in scale-free networks

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    Understanding information transmission across a network is a fundamental task for controlling and manipulating both biological and man-made information processing systems. Here, we show how topological resonant-like amplification effects in scale-free networks of signaling devices are drastically reduced when phase disorder in the external signals is considered. This is demonstrated theoretically by means of a star-like network of overdamped bistable systems, and confirmed numerically by simulations of scale-free networks of such systems. The taming effect of the phase disorder is found to be sensitive to the amplification's strength, while the topology-induced amplification mechanism is robust against this kind of quenched disorder in the sense that it does not significantly change the values of the coupling strength where amplification is maximum in its absence.Comment: 5 pages, 4 (double) figure
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