Distributional chaos for operators with full scrambled sets

In this article we answer in the negative the question of whether hypercyclicity is sufficient for distributional chaos for a continuous linear operator (we even prove that the mixing property does not suffice). Moreover, we show that an extremal situation is possible: There are (hypercyclic and non-hypercyclic) operators such that the whole space consists, except zero, of distributionally irregular vectors.The research of first and third author was supported by MEC and FEDER, project MTM2010-14909 and by GV, Project PROMETEO/2008/101. The research of second author was supported by the Marie Curie European Reintegration Grant of the European Commission under grant agreement no. PERG08-GA-2010-272297. The financial support of these institutions is hereby gratefully acknowledged. We also want to thank X. Barrachina for pointing out to us a gap in the proof of a previous version of Theorem 3.1.Martínez Jiménez, F.; Oprocha, P.; Peris Manguillot, A. (2013). Distributional chaos for operators with full scrambled sets. Mathematische Zeitschrift. 274(1-2):603-612. https://doi.org/10.1007/s00209-012-1087-8S6036122741-2Banks, J., Brooks, J., Cairns, G., Davis, G., Stacey, P.: On Devaney’s definition of chaos. Am. Math. Monthly 99(4), 332–334 (1992)Barrachina, X., Peris, A.: Distributionally chaotic translation semigroups. J. Differ. Equ. Appl. 18, 751–761 (2012)Beauzamy, B.: Introduction to Operator Theory and Invariant Subspaces. North-Holland, Amsterdam (1988)Bermúdez, T., Bonilla, A., Martínez-Giménez, F., Peris, A.: Li–Yorke and distributionally chaotic operators. J. Math. Anal. Appl. 373, 83–93 (2011)Bayart, F., Matheron, E.: Dynamics of linear operators, vol. 179. Cambridge University Press, London(2009).Costakis, G., Sambarino, M.: Topologically mixing hypercyclic operators. Proc. Am. Math. Soc. 132, 385–389 (2004)Devaney, R.L.: An introduction to chaotic dynamical systems, 2nd edn. Addison-Wesley Studies in Nonlinearity. Addison-Wesley Publishing Company Advanced Book Program. Redwood City (1989)Feldman, N.: Hypercyclicity and supercyclicity for invertible bilateral weighted shifts. Proc. Am. Math. Soc. 131, 479–485 (2003)Grosse-Erdmann, K.-G.: Hypercyclic and chaotic weighted shifts. Studia Math. 139(1), 47–68 (2000)Grosse-Erdmann, K.-G., Peris Manguillot, A.: Linear Chaos. Universitext, Springer, London (2011)Hou, B., Cui, P., Cao, Y.: Chaos for Cowen-Douglas operators. Proc. Am. Math. Soc 138, 929–936 (2010)Hou, B., Tian, G., Shi, L.: Some dynamical properties for linear operators. Ill. J. Math. 53, 857–864 (2009)Li, T.Y., Yorke, J.A.: Period three implies chaos. Am. Math. Monthly 82(10), 985–992 (1975)Martínez-Giménez, F., Oprocha, P., Peris, A.: Distributional chaos for backward shifts. J. Math. Anal. Appl. 351, 607–615 (2009)Müller, V., Peris, A.: A Problem of Beauzamy on Irregular Operators (2011). (Preprint)Oprocha, P.: Distributional chaos revisited. Trans. Am. Math. Soc. 361, 4901–4925 (2009)Oprocha, P.: A quantum harmonic oscillator and strong chaos. J. Phys. A 39(47), 14559–14565 (2006)Schweizer, B., Smítal, J.: Measures of chaos and a spectral decomposition of dynamical systems on the interval. Trans. Am. Math. Soc. 344(2), 737–754 (1994)Wu, X., Zhu, P.: The principal measure of a quantum harmonic oscillator. J. Phys. A 44(505101), 6 (2011

A hysteretic multiscale formulation for nonlinear dynamic analysis of composite materials

This article has been made available through the Brunel Open Access Publishing Fund.A new multiscale finite element formulation is presented for nonlinear dynamic analysis of heterogeneous structures. The proposed multiscale approach utilizes the hysteretic finite element method to model the microstructure. Using the proposed computational scheme, the micro-basis functions, that are used to map the microdisplacement components to the coarse mesh, are only evaluated once and remain constant throughout the analysis procedure. This is accomplished by treating inelasticity at the micro-elemental level through properly defined hysteretic evolution equations. Two types of imposed boundary conditions are considered for the derivation of the multiscale basis functions, namely the linear and periodic boundary conditions. The validity of the proposed formulation as well as its computational efficiency are verified through illustrative numerical experiments

Conserved Orb6 Phosphorylation Sites Are Essential for Polarized Cell Growth in Schizosaccharomyces pombe

The Ndr-related Orb6 kinase is a key regulator of polarized cell growth in fission yeast, however the mechanism of Orb6 activation is unclear. Activation of other Ndr kinases involves both autophosphorylation and phosphorylation by an upstream kinase. Previous reports suggest that the Nak1 kinase functions upstream from Orb6. Supporting this model, we show that HA-Orb6 overexpression partially restored cell polarity in nak1 ts cells. We also demonstrated by coimmunoprecipitation and in vitro binding assays that Nak1 and Orb6 physically interact, and that the Nak1 C-terminal region is required forNak1/Orb6 complex formation in vivo. However, results from in vitro kinase assays did not show phosphorylation of recombinant Orb6 by HA-Nak1, suggesting that Orb6 activation may not involve direct phosphorylation by Nak1. To investigate the role of Orb6 phosphorylation and activity, we substituted Ala at the ATP-binding and conserved phosphorylation sites. Overexpression of kinase-dead HA-Orb6K122A in wild-type cells resulted in a loss of cell polarity, suggesting that it has a dominant-negative effect, and it failed to rescue the polarity defect of nak1 or orb6 ts mutants. Recombinant GST-Orb6S291A did not autophosphorylate in vitro suggesting that Ser291 is the primary autophosphorylation site. HA-Orb6S291A overexpression only partially rescued the orb6 polarity defect and failed to rescue the nak1 defect, suggesting that autophosphorylation is important for Orb6 function. GST-Orb6T456A autophosphorylated in vitro, indicating that the conserved phosphorylation site at Thr456 is not essential for kinase activity. However, HA-Orb6T456A overexpression had similar effects as overexpressing kinase-dead HA-Orb6K122A, suggesting that Thr456 is essential for Orb6 function in vivo. Also, we found that both phosphorylation site mutations impaired the ability of Myc-Nak1 to coimmunoprecipitate with HA-Orb6. Together, our results suggest a model whereby autophosphorylation of Ser291 and phosphorylation of Thr456 by an upstream kinase promote Nak1/Orb6 complex formation and Orb6 activation

Coherent ac spin current transmission across an antiferromagnetic CoO insulator

This is the final version. Available on open access from Nature Research via the DOI in this recordData availability: Data are available from the corresponding author upon reasonable request.The recent discovery of spin current transmission through antiferromagnetic insulating materials opens up vast opportunities for fundamental physics and spintronics applications. The question currently surrounding this topic is: whether and how could THz antiferromagnetic magnons mediate a GHz spin current? This mismatch of frequencies becomes particularly critical for the case of coherent ac spin current, raising the fundamental question of whether a GHz ac spin current can ever keep its coherence inside an antiferromagnetic insulator and so drive the spin precession of another ferromagnet layer coherently? Utilizing element- and time-resolved x-ray pump-probe measurements on Py/Ag/CoO/Ag/Fe75Co25/MgO(001) heterostructures, here we demonstrate that a coherent GHz ac spin current pumped by the Py ferromagnetic resonance can transmit coherently across an antiferromagnetic CoO insulating layer to drive a coherent spin precession of the Fe75Co25 layer. Further measurement results favor thermal magnons rather than evanescent spin waves as the mediator of the coherent ac spin current in CoO.US Department of Energy, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering DivisionNational Science Foundation (NSF)National Research Foundation of KoreaEngineering and Physical Sciences Research Council (EPSRC)National Key Research and Development Program of CHIN

Regulatory feedback response mechanisms to phosphate starvation in rice

Phosphorus is a growth-limiting nutrient for plants. The growing scarcity of phosphate stocks threatens global food security. Phosphate-uptake regulation is so complex and incompletely known that attempts to improve phosphorus use efficiency have had extremely limited success. This study improves our understanding of the molecular mechanisms underlying phosphate uptake by investigating the transcriptional dynamics of two regulators: the Ubiquitin ligase PHO2 and the long non-coding RNA IPS1. Temporal measurements of RNA levels have been integrated into mechanistic mathematical models using advanced statistical techniques. Models based solely on current knowledge could not adequately explain the temporal expression profiles. Further modeling and bioinformatics analysis have led to the prediction of three regulatory features: the PHO2 protein mediates the degradation of its own transcriptional activator to maintain constant PHO2 mRNA levels; the binding affinity of the transcriptional activator of PHO2 is impaired by a phosphate-sensitive transcriptional repressor/inhibitor; and the extremely high levels of IPS1 and its rapid disappearance upon Pi re-supply are best explained by Pi-sensitive RNA protection. This work offers both new opportunities for plant phosphate research that will be essential for informing the development of phosphate efficient crop varieties, and a foundation for the development of models integrating phosphate with other stress responses