Existence of common zeros for commuting vector fields on 33-manifolds

In $64$ E. Lima proved that commuting vector fields on surfaces with non-zero Euler characteristic have common zeros. Such statement is empty in dimension $3$, since all the Euler characteristics vanish. Nevertheless, \cite{Bonatti_analiticos} proposed a local version, replacing the Euler characteristic by the Poincar\'e-Hopf index of a vector field $X$ in a region $U$, denoted by $\operatorname{Ind}(X,U)$; he asked: \emph{Given commuting vector fields $X,Y$ and a region $U$ where $\operatorname{Ind}(X,U)\neq 0$, does $U$ contain a common zero of $X$ and $Y$?} \cite{Bonatti_analiticos} gave a positive answer in the case where $X$ and $Y$ are real analytic. In this paper, we prove the existence of common zeros for commuting $C^1$ vector fields $X$, $Y$ on a $3$-manifold, in any region $U$ such that $\operatorname{Ind}(X,U)\neq 0$, assuming that the set of collinearity of $X$ and $Y$ is contained in a smooth surface. This is a strong indication that the results in \cite{Bonatti_analiticos} should hold for $C^1$-vector fields.Comment: Final version, to appear in Annales de L'Institut Fourie

Public expenditure and consumption volatility

Recent estimates of the welfare cost of consumption volatility find that it is significant in developing nations, where it may reach an equivalent of reducing consumption by 10 percent per year. Hence, examining the determinants of consumption volatility is of utmost relevance. Based on cross-country data for the period 1960-2005, the paper explains consumption volatility using three sets of variables: one refers to the volatility of income and the persistence of income shocks; the second set of variables refers to policy volatility, considering the volatility of public spending and the size of government; while the third set captures the ability of agents to smooth shocks, and includes the depth of the domestic financial markets as well as the degree of integration to international capital markets. To allow for potential endogenous regressors, in particular the volatility of fiscal policy and the size of government, the system is estimated using the instrumental variables method. The results indicate that, besides income volatility, the variables with the largest and most robust impact on consumption volatility are government size and the volatility of public spending. Results also show that deeper and more stable domestic financial markets reduce the volatility of consumption, and that more integrated financial markets to the international capital markets are associated with lower volatility of consumption.Economic Conditions and Volatility,Emerging Markets,Economic Stabilization,Economic Theory&Research,Currencies and Exchange Rates

Mixing-like properties for some generic and robust dynamics

We show that the set of Bernoulli measures of an isolated topologically mixing homoclinic class of a generic diffeomorphism is a dense subset of the set of invariant measures supported on the class. For this, we introduce the large periods property and show that this is a robust property for these classes. We also show that the whole manifold is a homoclinic class for an open and dense subset of the set of robustly transitive diffeomorphisms far away from homoclinic tangencies. In particular, using results from Abdenur and Crovisier, we obtain that every diffeomorphism in this subset is robustly topologically mixing

On the centralizer of vector fields: criteria of triviality and genericity results

In this paper, we investigate the question of whether a typical vector field on a compact connected Riemannian manifold $M^d$ has a `small' centralizer. In the $C^1$ case, we give two criteria, one of which is $C^1$-generic, which guarantees that the centralizer of a $C^1$-generic vector field is indeed small, namely \textit{collinear}. The other criterion states that a $C^1$ \textit{separating} flow has a collinear $C^1$-centralizer. When all the singularities are hyperbolic, we prove that the collinearity property can actually be promoted to a stronger one, refered as \textit{quasi-triviality}. In particular, the $C^1$-centralizer of a $C^1$-generic vector field is quasi-trivial. In certain cases, we obtain the triviality of the centralizer of a $C^1$-generic vector field, which includes $C^1$-generic Axiom A (or sectional Axiom A) vector fields and $C^1$-generic vector fields with countably many chain recurrent classes. For sufficiently regular vector fields, we also obtain various criteria which ensure that the centralizer is \textit{trivial} (as small as it can be), and we show that in higher regularity, collinearity and triviality of the $C^d$-centralizer are equivalent properties for a generic vector field in the $C^d$ topology. We also obtain that in the non-uniformly hyperbolic scenario, with regularity $C^2$, the $C^1$-centralizer is trivial.Comment: This is the final version, accepted in Mathematische Zeitschrift. New introduction and some proofs where rewritten and/or expanded, according to referee's suggestion. Also, a new appendix was adde

Colour-Magnitude Diagrams of candidate age-gap filling LMC clusters

The LMC has a rich star cluster system spanning a wide range of ages and masses. One striking feature of the LMC cluster system is the existence of an age gap between 3-10 Gyrs. Four LMC clusters whose integrated colours are consistent with those of intermediate age simple stellar populations have been imaged with the Optical Imager (SOI) at the Southern Telescope for Astrophysical Research (SOAR). Their colour-magnitude diagrams (CMDs) reach V ~ 24. Isochrone fits, based on Padova evolutionary models, were carried out to these CMDs, after subtraction of field contamination. The preliminary results are as follows: KMK88-38 has an age of ~ 1.3 Gyr, assuming typical LMC metallicity and distance modulus, and a very low redenning. For OGLE-LMC0531, the best eye fits to isochrones yield an age ~ 1.6 Gyr and E(B-V)=0.03. BSDL917 is younger, ~ 150 yrs, and subjected to larger extinction (E(B-V)=0.08). The remaining cluster is currently under analysis. Therefore, we conclude that these clusers are unlikely to fill in the LMC cluster age gap, even when fitting uncertainties in the parameters are considered.Comment: 4 pages, 5 figures, compact form of the poster published online in the proceedings of IAUS256: The Magellanic System: Stars, Gas, and Galaxie

Amelioration of the Impact of Physical Fatigue on Cognitive Performance by Phytochemicals: The Effect of a Blackcurrant Supplement : A thesis presented in partial fulfilment of the requirements for the degree of Masters of Science in Psychology at Massey University, Manawatu, New Zealand

Exercise-induced physical fatigue is thought to impair the cognitive functioning, and therefore mental performance, of the brain. Intervention studies have demonstrated that phytochemical supplementation can facilitate improved cognitive and physical performance. However, little is known about phytochemical supplementations’ ability to ameliorate physical fatigue effects on cognitive performance upon congestion. To investigate this hypothesis, the present study investigated the effects phytochemical compounds, from a blackcurrant supplement, had in regards to reducing physical fatigue effects on cognitive performance while under mental loads. Seventy-two healthy participants completed >10 mins of a high intensity intermittent cycling task (HIIT) (physical fatigue cohort) or >10 mins watching an emotionally neutral documentary (control cohort). Half of the participants in each condition received a blackcurrant supplement one hour before beginning the experimental session. Baseline cognitive tasks and mood questionaries were completed before ingestion of a blackcurrant extract, again before post-task measurements were completed, and also immediately following the experimental session. Analysis of the subjective selfreports revealed that HIIT was successful at inducing physical fatigue, however, had no effect on subsequent cognitive performance. Further analyses demonstrated that supplementation with a blackcurrant extract had no influence on cognitive performance. The null results for an effect of physical fatigue on cognitive performance made interpretation of this finding difficult. Overall, effect size calculations indicated that a larger sample size would not have resulted in statistically significant findings. It was concluded that the specific high intensity intermittent exercise used in the present study, did not induce a level of fatigue in participants’ that would subsequently impair cognitive performance. Blackcurrant supplement did not demonstrate an ability to enhance cognitive performance following a physically fatiguing task. Possible explanations for these findings are discussed and some potentially useful future studies outlined in the second and third chapters

Self-consistent physical parameters for MC clusters from CMD modelling: application to SMC clusters observed with the SOAR telescope

The Magellanic Clouds (MCs) present a rich system of stellar clusters that can be used to probe the dynamical and chemical evolution of these neighboring and interacting irregular galaxies. In particular, these stellar clusters (SCs) present combinations of age and metallicity that are not found for this class of objects in the Milky Way, being therefore very useful templates to test and to calibrate integrated light simple stellar population (SSP) models applied to unresolved distance galaxies. On its turn, the age and metallicity for a cluster can be determined spatially resolving its stars, by means of analysis of its colour-magnitude diagrams (CMDs). In this work we present our method to determine self-consistent physical parameters (age, metallicity, distance modulus and reddening) for a stellar cluster, from CMDs modelling of relatively unstudied SCs in the Small Magellanic Cloud (SMC) imaged in the BVI filters with the 4.1 m SOAR telescope. Our preliminary results confirm our expectations that come from a previous integrated spectra and colour analysis: at least one of them (Lindsay 2) is an intermediate-age stellar cluster with ~ 2.6 Gyr and [Fe/H] ~ -1.3, being therefore a new interesting witness regarding the reactivation of the star formation in the MCs in the last 4 Gyr.Comment: 4 pages, 2 figures. To be published in the proceedings of IAUS256: The Magellanic System: Stars, Gas, and Galaxie

On a Theoretical Background for Computing Reliable Approximations of the Barankin Bound

The Barankin bound is locally the greatest possible lower bound for the variance of any unbiased estimator of a deterministic pa- rameter, under certain relatively mild conditions. Much more essential, Barankin's work determines the su cient and necessary conditions un- der which an unbiased estimator with nite variance exists. Nevertheless, the computing of this bound, along with the proof of existence or non- existence of the estimator, has shown to be extremely challenging in most cases. Thereby, many approaches have been made to attain easily com- putable approximations of the bound, given it exists. Focusing on the rather central matter of existence, we provide a simple theoretical frame within which our approximations of the bound give a clear insight on whether an unbiased estimator does exist.Sociedad Argentina de Informática e Investigación Operativa (SADIO