Singularities of the susceptibility of an SRB measure in the presence of stable-unstable tangencies

Let $\rho$ be an SRB (or "physical"), measure for the discrete time evolution given by a map $f$, and let $\rho(A)$ denote the expectation value of a smooth function $A$. If $f$ depends on a parameter, the derivative $\delta\rho(A)$ of $\rho(A)$ with respect to the parameter is formally given by the value of the so-called susceptibility function $\Psi(z)$ at $z=1$. When $f$ is a uniformly hyperbolic diffeomorphism, it has been proved that the power series $\Psi(z)$ has a radius of convergence $r(\Psi)>1$, and that $\delta\rho(A)=\Psi(1)$, but it is known that $r(\Psi)<1$ in some other cases. One reason why $f$ may fail to be uniformly hyperbolic is if there are tangencies between the stable and unstable manifolds for $(f,\rho)$. The present paper gives a crude, nonrigorous, analysis of this situation in terms of the Hausdorff dimension $d$ of $\rho$ in the stable direction. We find that the tangencies produce singularities of $\Psi(z)$ for $|z|1$ if $d>1/2$. In particular, if $d>1/2$ we may hope that $\Psi(1)$ makes sense, and the derivative $\delta\rho(A)=\Psi(1)$ has thus a chance to be definedComment: 12 page

Simultaneous Continuation of Infinitely Many Sinks Near a Quadratic Homoclinic Tangency

We prove that the $C^3$ diffeomorphisms on surfaces, exhibiting infinitely many sinksnear the generic unfolding of a quadratic homoclinic tangency of a dissipative saddle, can be perturbed along an infinite dimensional manifold of $C^3$ diffeomorphisms such that infinitely many sinks persist simultaneously. On the other hand, if they are perturbed along one-parameter families that unfold generically the quadratic tangencies, then at most a finite number of those sinks have continuation

For Richer or For Poorer? Evidence from Indonesia, South Africa, Spain, and Venezuela

We analyze household income dynamics using longitudinal data from Indonesia, South Africa (KwaZulu-Natal), Spain and Venezuela. In all four countries, households with the lowest reported base-year income experienced the largest absolute income gains. This result is robust to reasonable amounts of measurement error in two of the countries. In three of the four countries, households with the lowest predicted base-year income experienced gains at least as large as their wealthier counterparts. Thus, with one exception, the empirical importance of cumulative advantage, poverty traps, and skill-biased technical change was no greater than structural or macroeconomic changes that favored initially poor households in these four countries

Response of graphene to femtosecond high-intensity laser irradiation

We study the response of graphene to high-intensity 10^11-10^12 Wcm^-2, 50-femtosecond laser pulse excitation. We establish that graphene has a fairly high (~3\times10^12Wcm^-2) single-shot damage threshold. Above this threshold, a single laser pulse cleanly ablates graphene, leaving microscopically defined edges. Below this threshold, we observe laser-induced defect formation that leads to degradation of the lattice over multiple exposures. We identify the lattice modification processes through in-situ Raman microscopy. The effective lifetime of CVD graphene under femtosecond near-IR irradiation and its dependence on laser intensity is determined. These results also define the limits of non-linear applications of graphene in femtosecond high-intensity regime.Comment: 4 pages, 3 figure

Absence of kinetic effects in reaction-diffusion processes in scale-free networks

We show that the chemical reactions of the model systems of A+A->0 and A+B->0 when performed on scale-free networks exhibit drastically different behavior as compared to the same reactions in normal spaces. The exponents characterizing the density evolution as a function of time are considerably higher than 1, implying that both reactions occur at a much faster rate. This is due to the fact that the discerning effects of the generation of a depletion zone (A+A) and the segregation of the reactants (A+B) do not occur at all as in normal spaces. Instead we observe the formation of clusters of A (A+A reaction) and of mixed A and B (A+B reaction) around the hubs of the network. Only at the limit of very sparse networks is the usual behavior recovered.Comment: 4 pages, 4 figures, to be published in Physical Review Letter

The effects of a 10-day altitude training camp at 1828 meters on varsity cross-country runners

International Journal of Exercise Science 10(1): 97-107, 2017. Altitude training has been shown to alter blood lactate (BL) levels due to alterations resulting from acclimatization. This study aims to estimate the impact of altitude training on BL changes immediately following an incremental treadmill test and during recovery before and after 10-day altitude training at approximately 1828 meters. Eight varsity cross-country runners performed an incremental treadmill test (ITT), pre and post-altitude training. Resting and post-warm-up BL values were recorded. During ITT, heart rate (HR), oxygen saturation (SpO2), and time to exhaustion were monitored. BL was also measured post-ITT at 0, 2, 4, 6, and 8 minutes. The average of all BL values was higher following altitude intervention (8.8 ± 4.6 mmol/L) compared to pre-intervention (7.4 ± 3.3 mmol/L). These differences were statistically significant (t(6) = -2.40, p = .026). BL immediately (0 minutes) after the ITT was higher following the altitude intervention (13.6 ± 3.6 mmol/L) compared to pre-intervention (9.7 ± 3.8 mmol/L) and was statistically significant (t(7) = -3.30, p = .006). Average HR during the ITT was lower following the altitude intervention (176.9 ± 11.1 bpm) compared to pre (187 ± 9.5 bpm), these differences were statistically significant (t(28)= 18.07, p

Infinitely Many Stochastically Stable Attractors

Let f be a diffeomorphism of a compact finite dimensional boundaryless manifold M exhibiting infinitely many coexisting attractors. Assume that each attractor supports a stochastically stable probability measure and that the union of the basins of attraction of each attractor covers Lebesgue almost all points of M. We prove that the time averages of almost all orbits under random perturbations are given by a finite number of probability measures. Moreover these probability measures are close to the probability measures supported by the attractors when the perturbations are close to the original map f.Comment: 14 pages, 2 figure

On stochastic sea of the standard map

Consider a generic one-parameter unfolding of a homoclinic tangency of an area preserving surface diffeomorphism. We show that for many parameters (residual subset in an open set approaching the critical value) the corresponding diffeomorphism has a transitive invariant set $\Omega$ of full Hausdorff dimension. The set $\Omega$ is a topological limit of hyperbolic sets and is accumulated by elliptic islands. As an application we prove that stochastic sea of the standard map has full Hausdorff dimension for sufficiently large topologically generic parameters.Comment: 36 pages, 5 figure

Perspective: tobacco manufacturers are now compensating states for smoking-related costs: how will this affect the economy?

Smoking out the social and economic benefits of the 1998 tobacco settlement for Massachusetts.Tobacco industry ; Medical care, Cost of