Recurrence spectrum in smooth dynamical systems

We prove that for conformal expanding maps the return time does have constant multifractal spectrum. This is the counterpart of the result by Feng and Wu in the symbolic setting

Exponential dichotomies of evolution operators in Banach spaces

This paper considers three dichotomy concepts (exponential dichotomy, uniform exponential dichotomy and strong exponential dichotomy) in the general context of non-invertible evolution operators in Banach spaces. Connections between these concepts are illustrated. Using the notion of Green function, we give necessary conditions and sufficient ones for strong exponential dichotomy. Some illustrative examples are presented to prove that the converse of some implication type theorems are not valid

Universal Banking Post Crisis: Past and Future of International Corporate and Personal Banking

This paper reviews the characteristics of the international incursions by banks since the early 1990s, examines the implications of the US subprime meltdown crisis and ensuing credit crunch for the pursuit of international banking activities, and provides a conceptual framework to help banks assess strategic decisions regarding the scope of their international operations in the years to come. We conclude that international banks, while remaining loyal to universal banking in terms of scope of activities, should become increasingly selective regarding the international reach of each and all components of their financial services offering portfolio

Topological pressure of simultaneous level sets

Multifractal analysis studies level sets of asymptotically defined quantities in a topological dynamical system. We consider the topological pressure function on such level sets, relating it both to the pressure on the entire phase space and to a conditional variational principle. We use this to recover information on the topological entropy and Hausdorff dimension of the level sets. Our approach is thermodynamic in nature, requiring only existence and uniqueness of equilibrium states for a dense subspace of potential functions. Using an idea of Hofbauer, we obtain results for all continuous potentials by approximating them with functions from this subspace. This technique allows us to extend a number of previous multifractal results from the $C^{1+\epsilon}$ case to the $C^1$ case. We consider ergodic ratios $S_n \phi/S_n \psi$ where the function $\psi$ need not be uniformly positive, which lets us study dimension spectra for non-uniformly expanding maps. Our results also cover coarse spectra and level sets corresponding to more general limiting behaviour.Comment: 32 pages, minor changes based on referee's comment

Asymmetry after Hamstring Injury in English Premier League: Issue Resolved, Or Perhaps Not?

Hamstring injuries constitute one of the most concerning injuries in English Premier League football, due to its high primary incidence but also its recurrence. Functional methods assessing hamstring function during high-risk performance tasks such as sprinting are vital to identify potential risk factors. The purpose of this study was to assess horizontal force deficits during maximum sprint running on a non-motorized treadmill in football players with previous history of hamstring strains as a pre-season risk-assessment in a club setting. 17 male football players from one Premier League Club were divided into 2 groups, experimental (n= 6, age = 24.5 ± 2.3 years) and control (n= 11, age = 21.3 ± 1.2 years), according to history of previous hamstring injury. Participants performed a protocol including a 10 seconds maximum sprint on a non-motorized treadmill. Force deficits during acceleration phase and steady state phases of the sprint were assessed between limbs and between groups. The main outcome measures were horizontal and vertical peak forces during the acceleration phase or steady state. There were no significant differences in peak forces between previously injured and non-injured limbs, or between groups, challenging the ideas around functional force deficits in sprint running as a diagnostic measure of hamstring re-injury risk

The observational status of Galileon gravity after Planck

We use the latest CMB data from Planck, together with BAO measurements, to constrain the full parameter space of Galileon gravity. We constrain separately the three main branches of the theory known as the Cubic, Quartic and Quintic models, and find that all yield a very good fit to these data. Unlike in ΛCDM, the Galileon model constraints are compatible with local determinations of the Hubble parameter and predict nonzero neutrino masses at over 5σ significance. We also identify that the low l part of the CMB lensing spectrum may be able to distinguish between ΛCDM and Galileon models. In the Cubic model, the lensing potential deepens at late times on sub-horizon scales, which is at odds with the current observational suggestion of a positive ISW effect. Compared to ΛCDM, the Quartic and Quintic models predict less ISW power in the low l region of the CMB temperature spectrum, and as such are slightly preferred by the Planck data. We illustrate that residual local modifications to gravity in the Quartic and Quintic models may render the Cubic model as the only branch of Galileon gravity that passes Solar System tests

Assessment of oil contamination in the bay of Porto Grande (Cape Verde) using the mullet Chelon bispinosus

Polycyclic aromatic hydrocarbons (PAHs) are a group of persistent organic pollutants, some of which are mutagenic and carcinogenic so PAH concentrations in fish used for human consumption are crucial to assess impact to human health. Total PAH concentrations in muscle and liver of mullets Chelon bispinosus from the Bay of Porto Grande (Cape Verde) (four sites in the bay and a control) ranged from 112.7 to 779.5 and 291.5 to 7548.7 ng/g d. w., respectively. Two and three ring PAHs were the most frequent (72.8 to 90.8% in the muscle and 75.9 to 98.3% in the liver), but levels of carcinogenic PAHs (mainly Dibenzo (a,h) antracene) in certain sites (CN and PG) are of concern. Results reflect a chronic PAH pollution in the bay and sources are a mixture of anthropogenic (petrogenic and pyrolytic) and natural sources, making their identification extremely complex. Although, BaP levels were below the threshold established by Cape Verde and the European Union, BaPEs levels in muscle ranged from 0.28 to 3.66 ng/g w. w. and BAPEs and TPAHs exposure for the average adult was 0.02 to 0.26 and 1.6 to 11.2 μg/day, respectively. Further knowledge of PAH concentrations in other species are necessary for a proper environmental risk assessment policy.Key words: Bay of Porto Grande, Cape Verde, Chelon bispinosus, mullets, PAHs, BaPEs, daily intake

Spherical collapse in Galileon gravity: fifth force solutions, halo mass function and halo bias

We study spherical collapse in the Quartic and Quintic Covariant Galileon gravity models within the framework of the excursion set formalism. We derive the nonlinear spherically symmetric equations in the quasi-static and weak-field limits, focusing on model parameters that fit current CMB, SNIa and BAO data. We demonstrate that the equations of the Quintic model do not admit physical solutions of the fifth force in high density regions, which prevents the study of structure formation in this model. For the Quartic model, we show that the effective gravitational strength deviates from the standard value at late times (zlesssim1), becoming larger if the density is low, but smaller if the density is high. This shows that the Vainshtein mechanism at high densities is not enough to screen all of the modifications of gravity. This makes halos that collapse at zlesssim1 feel an overall weaker gravity, which suppresses halo formation. However, the matter density in the Quartic model is higher than in standard ΛCDM, which boosts structure formation and dominates over the effect of the weaker gravity. In the Quartic model there is a significant overabundance of high-mass halos relative to ΛCDM. Dark matter halos are also less biased than in ΛCDM, with the difference increasing appreciably with halo mass. However, our results suggest that the bias may not be small enough to fully reconcile the predicted matter power spectrum with LRG clustering data

Linear perturbations in K-mouflage cosmologies with massive neutrinos

We present a comprehensive derivation of linear perturbation equations for different matter species, including photons, baryons, cold dark matter, scalar fields, and massless and massive neutrinos in the presence of a generic conformal coupling. Starting from the Lagrangians, we show how the conformal transformation affects the dynamics. In particular, we discuss how to incorporate consistently the scalar coupling in the equations of the Boltzmann hierarchy for massive neutrinos and the subsequent fluid approximations. We use the recently proposed K-mouflage model as an example to demonstrate the numerical implementation of our linear perturbation equations. K-mouflage is a new mechanism to suppress the fifth force between matter particles induced by the scalar coupling, but in the linear regime the fifth force is unsuppressed and can change the clustering of different matter species in different ways. We show how the cosmic microwave background, lensing potential and matter power spectra are affected by the fifth force and find ranges of K-mouflage parameters whose effects could be seen observationally. We also find that the scalar coupling can have the nontrivial effect of shifting the amplitude of the power spectra of the lensing potential and density fluctuations in opposite directions, although both probe the overall clustering of matter. This paper can serve as a reference for those who work on generic coupled scalar field cosmology or those who are interested in the cosmological behavior of the K-mouflage model

Weak lensing by voids in modified lensing potentials

We study lensing by voids in Cubic Galileon and Nonlocal gravity cosmologies, which are examples of theories of gravity that modify the lensing potential. We find voids in the dark matter and halo density fields of N-body simulations and compute their lensing signal analytically from the void density profiles, which we show are well fit by a simple analytical formula. In the Cubic Galileon model, the modifications to gravity inside voids are not screened and they approximately double the size of the lensing effects compared to GR. The difference is largely determined by the direct effects of the fifth force on lensing and less so by the modified density profiles. For this model, we also discuss the subtle impact on the force and lensing calculations caused by the screening effects of haloes that exist in and around voids. In the Nonlocal model, the impact of the modified density profiles and the direct modifications to lensing are comparable, but they boost the lensing signal by only ≈ 10%, compared with that of GR. Overall, our results suggest that lensing by voids is a promising tool to test models of gravity that modify lensing