401 research outputs found

    Robust chaos generation by a perceptron

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    The properties of time series generated by a perceptron with monotonic and non-monotonic transfer function, where the next input vector is determined from past output values, are examined. Analysis of the parameter space reveals the following main finding: a perceptron with a monotonic function can produce fragile chaos only whereas a non-monotonic function can generate robust chaos as well. For non-monotonic functions, the dimension of the attractor can be controlled monotonically by tuning a natural parameter in the model.Comment: 7 pages, 5 figures (reduced quality), accepted for publication in EuroPhysics Letter

    On the Brauer groups of symmetries of abelian Dijkgraaf-Witten theories

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    Symmetries of three-dimensional topological field theories are naturally defined in terms of invertible topological surface defects. Symmetry groups are thus Brauer-Picard groups. We present a gauge theoretic realization of all symmetries of abelian Dijkgraaf-Witten theories. The symmetry group for a Dijkgraaf-Witten theory with gauge group a finite abelian group AA, and with vanishing 3-cocycle, is generated by group automorphisms of AA, by automorphisms of the trivial Chern-Simons 2-gerbe on the stack of AA-bundles, and by partial e-m dualities. We show that transmission functors naturally extracted from extended topological field theories with surface defects give a physical realization of the bijection between invertible bimodule categories of a fusion category and braided auto-equivalences of its Drinfeld center. The latter provides the labels for bulk Wilson lines; it follows that a symmetry is completely characterized by its action on bulk Wilson lines.Comment: 21 pages, 9 figures. v2: Minor changes, typos corrected and references added. v3: Typos correcte

    The Forces Applied by Cilia Depend Linearly on Their Frequency Due to Constant Geometry of the Effective Stroke

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    AbstractMucus propelling cilia are excitable by many stimulants, and have been shown to increase their beating frequency up to threefold, by physiological extracellular stimulants, such as adenosine-triphosphate, acetylcholine, and others. This is thought to represent the evolutionary adaptation of mucociliary systems to the need of rapid and efficient cleansing the airways of foreign particles. However, the mucus transport velocity depends not only on the beat frequency of the cilia, but on their beat pattern as well, especially in the case of mucus bearing cilia that beat in a complex, three-dimensional fashion. In this study, we directly measured the force applied by live ciliary tissues with an atomic force microscope, and found that it increases linearly with the beating frequency. This implies that the arc swept by the cilia during their effective stroke remains unchanged during frequency increase, thus leading to a linear dependence of transport velocity on the beat frequency. Combining the atomic force microscope measurements with optical measurements, we have indications that the recovery stroke is performed on a less inclined plane, leading to an effective shortening of the overall path traveled by the cilia tip during this nontransporting phase of their beat pattern. This effect is observed to be independent of the type of stimulant (temperature or chemical), chemical (adenosine-triphosphate or acetylcholine), or concentration (1μM–100μM), indicating that this behavior may result from internal details of the cilium mechanical structure

    Learning and predicting time series by neural networks

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    Artificial neural networks which are trained on a time series are supposed to achieve two abilities: firstly to predict the series many time steps ahead and secondly to learn the rule which has produced the series. It is shown that prediction and learning are not necessarily related to each other. Chaotic sequences can be learned but not predicted while quasiperiodic sequences can be well predicted but not learned.Comment: 5 page