Mean Li-Yorke chaos in Banach spaces

We investigate the notion of mean Li-Yorke chaos for operators on Banach spaces. We show that it differs from the notion of distributional chaos of type 2, contrary to what happens in the context of topological dynamics on compact metric spaces. We prove that an operator is mean Li-Yorke chaotic if and only if it has an absolutely mean irregular vector. As a consequence, absolutely Ces\`aro bounded operators are never mean Li-Yorke chaotic. Dense mean Li-Yorke chaos is shown to be equivalent to the existence of a dense (or residual) set of absolutely mean irregular vectors. As a consequence, every mean Li-Yorke chaotic operator is densely mean Li-Yorke chaotic on some infinite-dimensional closed invariant subspace. A (Dense) Mean Li-Yorke Chaos Criterion and a sufficient condition for the existence of a dense absolutely mean irregular manifold are also obtained. Moreover, we construct an example of an invertible hypercyclic operator $T$ such that every nonzero vector is absolutely mean irregular for both $T$ and $T^{-1}$. Several other examples are also presented. Finally, mean Li-Yorke chaos is also investigated for $C_0$-semigroups of operators on Banach spaces.Comment: 26 page

The Specification Property for C0C_0-Semigroups

We study one of the strongest versions of chaos for continuous dynamical systems, namely the specification property. We extend the definition of specification property for operators on a Banach space to strongly continuous one-parameter semigroups of operators, that is, $C_0$-semigroups. In addition, we study the relationships of the specification property for $C_0$-semigroups (SgSP) with other dynamical properties: mixing, Devaney's chaos, distributional chaos and frequent hypercyclicity. Concerning the applications, we provide several examples of semigroups which exhibit the SgSP with particular interest on solution semigroups to certain linear PDEs, which range from the hyperbolic heat equation to the Black-Scholes equation.Comment: 13 page

Frequently hypercyclic semigroups

We study frequent hypercyclicity in the context of strongly continuous semigroups of operators. More precisely, we give a criterion (sufficient condition) for a semigroup to be frequently hypercyclic, whose formulation depends on the Pettis integral. This criterion can be verified in certain cases in terms of the infinitesimal generator of semigroup. Applications are given for semigroups generated by Ornstein-Uhlenbeck operators, and especially for translation semigroups on weighted spaces of $p$-integrable functions, or continuous functions that, multiplied by the weight, vanish at infinity

On the relation between low-energy constants and resonance saturation

Although there are phenomenological indications that the low-energy constants in the chiral lagrangian may be understood in terms of a finite number of hadronic resonances, it remains unclear how this follows from QCD. One of the arguments usually given is that low-energy constants are associated with chiral symmetry breaking, while QCD perturbation theory suggests that at high energy chiral symmetry is unbroken, so that only low-lying resonances contribute to the low-energy constants. We revisit this argument in the limit of large Nc, discussing its validity in particular for the low-energy constant L8, and conclude that QCD may be more subtle that what this argument suggests. We illustrate our considerations in a simple Regge-like model which also applies at finite Nc.Comment: 15 pages, one figur

Resummation of Threshold, Low- and High-Energy Expansions for Heavy-Quark Correlators

With the help of the Mellin-Barnes transform, we show how to simultaneously resum the expansion of a heavy-quark correlator around q^2=0 (low-energy), q^2= 4 m^2 (threshold, where m is the quark mass) and q^2=-\infty (high-energy) in a systematic way. We exemplify the method for the perturbative vector correlator at O(alpha_s^2) and O(alpha_s^3). We show that the coefficients, Omega(n), of the Taylor expansion of the vacuum polarization function in terms of the conformal variable \omega admit, for large n, an expansion in powers of 1/n (up to logarithms of n) that we can calculate exactly. This large-n expansion has a sign-alternating component given by the logarithms of the OPE, and a fixed-sign component given by the logarithms of the threshold expansion in the external momentum q^2.Comment: 27 pages, 8 figures. We fix typos in Eqs. (18), (27), (55) and (56). Results unchange

Relative localization for aerial manipulation with PL-SLAM

The final publication is available at link.springer.comThis chapter explains a precise SLAM technique, PL-SLAM, that allows to simultaneously process points and lines and tackle situations where point-only based methods are prone to fail, like poorly textured scenes or motion blurred images where feature points are vanished out. The method is remarkably robust against image noise, and that it outperforms state-of-the-art methods for point based contour alignment. The method can run in real-time and in a low cost hardware.Peer ReviewedPostprint (author's final draft

Mitochondria-encoded genes contribute to evolution of heat and cold tolerance in yeast

Genetic analysis of phenotypic differences between species is typically limited to interfertile species. Here, we conducted a genome-wide noncomplementation screen to identify genes that contribute to a major difference in thermal growth profile between two reproductively isolated yeast species, Saccharomyces cerevisiae and Saccharomyces uvarum. The screen identified only a single nuclear-encoded gene with a moderate effect on heat tolerance, but, in contrast, revealed a large effect of mitochondrial DNA (mitotype) on both heat and cold tolerance. Recombinant mitotypes indicate that multiple genes contribute to thermal divergence, and we show that protein divergence in COX1 affects both heat and cold tolerance. Our results point to the yeast mitochondrial genome as an evolutionary hotspot for thermal divergence.This work was supported by the NIH (grant GM080669) to J.C.F. Additional support to C.T.H. was provided by the USDA National Institute of Food and Agriculture (Hatch project 1003258), the National Science Foundation (DEB-1253634), and the DOE Great Lakes Bioenergy Research Center (DOE BER Office of Science DE-SC0018409 and DE-FC02-07ER64494 to T. J. Donohue). C.T.H. is a Pew Scholar in the Biomedical Sciences and a Vilas Faculty Early Career Investigator, supported by the Pew Charitable Trusts and the Vilas Trust Estate, respectively. D.P. is a Marie Sklodowska-Curie fellow of the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 747775).Peer reviewe

Human response to vibration in residential environments (NANR209), executive summary

The aim of the Defra-funded project NANR209 ‘Human response to vibration in residential environments’ was to develop exposure-response relationships for vibration experienced in residential environments from sources outside of the residents’ control. The project was performed at the University of Salford between January 2008 and March 2011. The final report was published on the Defra website on 6th September 2012. The NANR209 Final Report consists of the following documents: • Executive summary • Final project report • Technical report 1: Measurement of vibration exposure • Technical report 2: Measurement of response • Technical report 3: Calculation of vibration exposure • Technical report 4: Measurement and calculation of noise exposure • Technical report 5: Analysis of the social survey findings • Technical report 6: Determination of exposure-response relationships This document is the Executive summary