Continuity of Dynamical Structures for Nonautonomous Evolution Equations Under Singular Perturbations

In this paper we study the continuity of invariant sets for nonautonomous infinite-dimensional dynamical systems under singular perturbations. We extend the existing results on lower-semicontinuity of attractors of autonomous and nonautonomous dynamical systems. This is accomplished through a detailed analysis of the structure of the invariant sets and its behavior under perturbation. We prove that a bounded hyperbolic global solutions persists under singular perturbations and that their nonlinear unstable manifold behave continuously. To accomplish this, we need to establish results on roughness of exponential dichotomies under these singular perturbations. Our results imply that, if the limiting pullback attractor of a nonautonomous dynamical system is the closure of a countable union of unstable manifolds of global bounded hyperbolic solutions, then it behaves continuously (upper and lower) under singular perturbations.

Experimental Assessment of the Sensitiveness of an Electrochemical Oscillator towards Chemical Perturbations

In this study we address the problem of the response of a (electro)chemical oscillator towards chemical perturbations of different magnitudes. The chemical perturbation was achieved by addition of distinct amounts of trifluoromethanesulfonate (TFMSA), a rather stable and non-specifically adsorbing anion, and the system under investigation was the methanol electro-oxidation reaction under both stationary and oscillatory regimes. Increasing the anion concentration resulted in a decrease in the reaction rates of methanol oxidation and a general decrease in the parameter window where oscillations occurred. Furthermore, the addition of TFMSA was found to decrease the induction period and the total duration of oscillations. The mechanism underlying these observations was derived mathematically and revealed that inhibition in the methanol oxidation through blockage of active sites was found to further accelerate the intrinsic non-stationarity of the unperturbed system. Altogether, the presented results are among the few concerning the experimental assessment of the sensitiveness of an oscillator towards chemical perturbations. The universal nature of the complex chemical oscillator investigated here might be used for reference when studying the dynamics of other less accessible perturbed networks of (bio)chemical reactions.

Detection of gait perturbations based on proprioceptive information. Application to Limit Cycle Walkers

Walking on irregular surfaces and in the presence of unexpected events is a challenging problem for bipedal machines. Up to date, their ability to cope with gait disturbances is far less successful than humans': Neither trajectory controlled robots, nor dynamic walking machines (Limit CycleWalkers) are able to handle them satisfactorily. On the contrary, humans reject gait perturbations naturally and efficiently relying on their sensory organs that, if needed, elicit a recovery action. A similar approach may be envisioned for bipedal robots and exoskeletons: An algorithm continuously observes the state of the walker and, if an unexpected event happens, triggers an adequate reaction. This paper presents a monitoring algorithm that provides immediate detection of any type of perturbation based solely on a phase representation of the normal walking of the robot. The proposed method was evaluated in a Limit Cycle Walker prototype that suffered push and trip perturbations at different moments of the gait cycle, providing 100% successful detections for the current experimental apparatus and adequately tuned parameters, with no false positives when the robot is walking unperturbed.

Tidal perturbations of the rotation of the moon: the creep tide approach

In this communication we report results from the application to the study of the rotation of the Moon of the creeping tide theory just proposed (Ferraz-Mello, Cel. Mech. Dyn. Astron., submitted. ArXiv astro-ph 1204.3957). The choice of the Moon for the first application of this new theory is motivated by the fact that the Moon is one of the best observed celestial bodies and the comparison of the theoretical predictions of the theory with observations i may validate the theory or point out the need of further improvements. Particularly, the tidal perturbations of the rotation of the Moon - the physical libration of the Moon - have been detected in the Lunar Laser Ranging measurements (Williams et al. JGR 106, 27933, 2001). The major difficulty in this application comes from the fact that tidal torques in a planet-satellite system are very sensitive to the distance between the two-bodies, which is strongly affected by Solar perturbations. In the case of the Moon, the main solar perturbations - the Evection and the Variation - are more important than most of the Keplerian oscillations, being smaller only than the first Keplerian harmonic (equation of the centre). Besides, two of the three components of the Moon's libration in longitude whose tidal contributions were determined by LLR are related to these perturbations. The results may allow us to determine the main parameter of a possible Moon's creeping tide. The preliminary results point to a relaxation factor (gamma) 2 to 4 times smaller than the one predicted from the often cited values of thr Moon's quality factor Q (between 30 and 40), and points to larger Q values.

Cosmological perturbations in generalized theories of gravity

The first part of the thesis concerns the study of inflation in the context of a theory of gravity called "Induced Gravity" in which the gravitational coupling varies in time according to the dynamics of the very same scalar field (the "inflaton") driving inflation, while taking on the value measured today since the end of inflation. Through the analytical and numerical analysis of scalar and tensor cosmological perturbations we show that the model leads to consistent predictions for a broad variety of symmetry-breaking inflaton's potentials, once that a dimensionless parameter entering into the action is properly constrained. We also discuss the average expansion of the Universe after inflation (when the inflaton undergoes coherent oscillations about the minimum of its potential) and determine the effective equation of state. Finally, we analyze the resonant and perturbative decay of the inflaton during (p)reheating. The second part is devoted to the study of a proposal for a quantum theory of gravity dubbed "Horava-Lifshitz (HL) Gravity" which relies on power-counting renormalizability while explicitly breaking Lorentz invariance. We test a pair of variants of the theory ("projectable" and "non-projectable") on a cosmological background and with the inclusion of scalar field matter. By inspecting the quadratic action for the linear scalar cosmological perturbations we determine the actual number of propagating degrees of freedom and realize that the theory, being endowed with less symmetries than General Relativity, does admit an extra gravitational degree of freedom which is potentially unstable. More specifically, we conclude that in the case of projectable HL Gravity the extra mode is either a ghost or a tachyon, whereas in the case of non-projectable HL Gravity the extra mode can be made well-behaved for suitable choices of a pair of free dimensionless parameters and, moreover, turns out to decouple from the low-energy Physics.

How has climate responded to natural perturbations?

Wolff, E. W.; Harrison, S. P.; Knutti, R.; Sanchez-Goñi, M. F.; Wild, O.; Danlau, A.-L.; Masson-Delmotte, V.; Prentice, I. C.; Spahni, R.

Epidemiology of candidemia in Swiss tertiary care hospitals: secular trends, 1991-2000

Candida species are among the most common bloodstream pathogens in the United States, where the emergence of azole-resistant Candida glabrata and Candida krusei are major concerns. Recent comprehensive longitudinal data from Europe are lacking. We conducted a nationwide survey of candidemia during 1991-2000 in 17 university and university-affiliated hospitals representing 79% of all tertiary care hospital beds in Switzerland. The number of transplantations and bloodstream infections increased significantly (P<.001). A total of 1137 episodes of candidemia were observed: Candida species ranked seventh among etiologic agents (2.9% of all bloodstream isolates). The incidence of candidemia was stable over a 10-year period. C. albicans remained the predominant Candida species recovered (66%), followed by C. glabrata (15%). Candida tropicalis emerged (9%), the incidence of Candida parapsilosis decreased (1%), and recovery of C. krusei remained rare (2%). Fluconazole consumption increased significantly (P<.001). Despite increasing high-risk activities, the incidence of candidemia remained unchanged, and no shift to resistant species occurred.

Copper availability contributes to iron perturbations in human nonalcoholic fatty liver disease

BACKGROUND ; AIMS: Iron perturbations are frequently observed in nonalcoholic fatty liver disease (NAFLD). We aimed to investigate a potential association of copper status with disturbances of iron homeostasis in NAFLD. METHODS: We retrospectively studied 140 NAFLD patients and 25 control subjects. Biochemical and hepatic iron and copper parameters were analyzed. Hepatic expression of iron regulatory molecules was investigated in liver biopsy specimens by reverse-transcription polymerase chain reaction and Western blot analysis. RESULTS: NAFLD patients had lower hepatic copper concentrations than control subjects (21.9 +/- 9.8 vs 29.6 +/- 5.1 microg/g; P = .002). NAFLD patients with low serum and liver copper concentrations presented with higher serum ferritin levels (606.7 +/- 265.8 vs 224.2 +/- 176.0 mg/L; P < .001), increased prevalence of siderosis in liver biopsy specimens (36/46 vs 10/47 patients; P < .001), and with elevated hepatic iron concentrations (1184.4 +/- 842.7 vs 319.9 +/- 451.3 microg/g; P = .020). Lower serum concentrations of the copper-dependent ferroxidase ceruloplasmin (21.7 +/- 4.1 vs 30.4 +/- 6.4 mg/dL; P < .001) and decreased liver ferroportin (FP-1; P = .009) messenger RNA expression were found in these patients compared with NAFLD patients with high liver or serum copper concentrations. Accordingly, in rats, a reduced dietary copper intake was paralleled by a decreased hepatic FP-1 protein expression. CONCLUSIONS: A significant proportion of NAFLD patients should be considered copper deficient. Our results indicate that copper status is linked to iron homeostasis in NAFLD, suggesting that low copper bioavailability causes increased hepatic iron stores via decreased FP-1 expression and ceruloplasmin ferroxidase activity thus blocking liver iron export in copper-deficient subjects.