Spectral analysis and the Aharonov-Bohm\~ effect on certain almost-Riemannian manifold

We study spectral properties of the Laplace-Beltrami operator on two relevant almost-Riemannian manifolds, namely the Grushin structures on the cylinder and on the sphere. This operator contains first order diverging terms caused by the divergence of the volume. We get explicit descriptions of the spectrum and the eigenfunctions. In particular in both cases we get a Weyl's law with leading term Elog E. We then study the drastic effect of Aharonov-Bohm magnetic potentials on the spectral properties. Other generalised Riemannian structures including conic and anti-conic type manifolds are also studied. In this case, the Aharonov-Bohm magnetic potential may affect the self-adjointness of the Laplace-Beltrami operator.

Advancements in decadal climate predictability: the role of nonoceanic drivers

We review recent progress in understanding the role of sea ice, land surface, stratosphere, and aerosols in decadal-scale predictability and discuss the perspectives for improving the predictive capabilities of current Earth system models (ESMs). These constituents have received relatively little attention because their contribution to the slow climatic manifold is controversial in comparison to that of the large heat capacity of the oceans. Furthermore, their initialization as well as their representation in state-of-the-art climate models remains a challenge. Numerous extraoceanic processes that could be active over the decadal range are proposed. Potential predictability associated with the aforementioned, poorly represented, and scarcely observed constituents of the climate system has been primarily inspected through numerical simulations performed under idealized experimental settings. The impact, however, on practical decadal predictions, conducted with realistically initialized full-fledged climate models, is still largely unexploited. Enhancing initial-value predictability through an improved model initialization appears to be a viable option for land surface, sea ice, and, marginally, the stratosphere. Similarly, capturing future aerosol emission storylines might lead to an improved representation of both global and regional short-term climatic changes. In addition to these factors, a key role on the overall predictive ability of ESMs is expected to be played by an accurate representation of processes associated with specific components of the climate system. These act as “signal carriers,” transferring across the climatic phase space the information associated with the initial state and boundary forcings, and dynamically bridging different (otherwise unconnected) subsystems. Through this mechanism, Earth system components trigger low-frequency variability modes, thus extending the predictability beyond the seasonal scale.

Heterogeneous tensor decomposition for clustering via manifold optimization

Tensor clustering is an important tool that exploits intrinsically rich structures in real-world multiarray or Tensor datasets. Often in dealing with those datasets, standard practice is to use subspace clustering that is based on vectorizing multiarray data. However, vectorization of tensorial data does not exploit complete structure information. In this paper, we propose a subspace clustering algorithm without adopting any vectorization process. Our approach is based on a novel heterogeneous Tucker decomposition model taking into account cluster membership information. We propose a new clustering algorithm that alternates between different modes of the proposed heterogeneous tensor model. All but the last mode have closed-form updates. Updating the last mode reduces to optimizing over the multinomial manifold for which we investigate second order Riemannian geometry and propose a trust-region algorithm. Numerical experiments show that our proposed algorithm compete effectively with state-of-the-art clustering algorithms that are based on tensor factorization.

Sparse density estimation on multinomial manifold combining local component analysis

A new sparse kernel density estimator is introduced based on the minimum integrated square error criterion combining local component analysis for the finite mixture model. We start with a Parzen window estimator which has the Gaussian kernels with a common covariance matrix, the local component analysis is initially applied to find the covariance matrix using expectation maximization algorithm. Since the constraint on the mixing coefficients of a finite mixture model is on the multinomial manifold, we then use the well-known Riemannian trust-region algorithm to find the set of sparse mixing coefficients. The first and second order Riemannian geometry of the multinomial manifold are utilized in the Riemannian trust-region algorithm. Numerical examples are employed to demonstrate that the proposed approach is effective in constructing sparse kernel density estimators with competitive accuracy to existing kernel density estimators.

Effect of Three Methods for Cleaning Dentures on Biofilms Formed In Vitro on Acrylic Resin

Purpose: The aim of this study was to evaluate the effect of three denture hygiene methods against different microbial biofilms formed on acrylic resin specimens. Materials and methods: The set (sterile stainless steel basket and specimens) was contaminated (37 degrees C for 48 hours) by a microbial inoculum with 106 colony-forming units (CFU)/ml (standard strains: Staphylococcus aureus, Streptococcus mutans, Escherichia coli, Candida albicans, Pseudomonas aeruginosa, and Enterococcus faecalis; field strains: S. mutans, C. albicans, C. glabrata, and C. tropicalis). After inoculation, specimens were cleansed by the following methods: (1) chemical: immersion in an alkaline peroxide solution (Bonyplus tablets) for 5 minutes; (2) mechanical: brushing with a dentifrice for removable prostheses (Dentu Creme) for 20 seconds; and (3) a combination of chemical and mechanical methods. Specimens were applied onto a Petri plate with appropriate culture medium for 10 minutes. Afterward, the specimens were removed and the plates incubated at 37 degrees C for 48 hours. Results: Chemical, mechanical, and combination methods showed no significant difference in the reduction of CFU for S. aureus, S. mutans (ATCC and field strain), and P. aeruginosa. Mechanical and combination methods were similar and more effective than the chemical method for E. faecalis, C. albicans (ATCC and field strain), and C. glabrata. The combination method was better than the chemical method for E. coli and C. tropicalis, and the mechanical method showed intermediate results. Conclusion: The three denture hygiene methods showed different effects depending on the type of microbial biofilms formed on acrylic base resin specimens.

Influence of NaHCO(3) Powder on Translucency of Microfilled Composite Resin Immersed in Different Mouthrinses

The regular use of mouthrinses, particularly when combined with the use of air-powder polishing, could affect the appearance of tooth-colored restorations. The current study sought to evaluate the effect of NaHCO(3) powder on translucency of a microfilled composite resin immersed in different mouthrinses, at distinct evaluation periods. Eighty disk-shaped specimens of composite resin (Durafill VS, Heraeus Kulzer GmbH & Co. KG, Hanau, Germany) were prepared. The composite specimens were then randomly allocated into two groups according to the surface treatment: exposure to NaHCO(3) powder (10 seconds) or nonexposure, and they were randomly assigned into four subgroups, according to the mouthrinses employed (N = 10): Periogard (Colgate/Palmolive, Sao Bernardo do Campo, SP, Brazil), Cepacol (Aventis Pharma, Sao Paulo, SP, Brazil), Plax (Colgate/Palmolive), and distilled water (control group). The samples were immersed for 2 minutes daily, 5 days per week, over a 4-month test period. Translucency was measured with a transmission densitometer at seven evaluation periods. Statistical analyses (analysis of variance and Tukey`s test) revealed that: distilled water presented higher translucency values (86.72%); Periogard demonstrated the lowest translucency values (72.70%); and Plax (74.05%) and Cepacol (73.32%) showed intermediate translucency values, which were statistically similar between them (p > 0.01). NaHCO(3) air-powder polishing increased the changes in translucency associated with the mouthrinses. Air-powder polishing alone had no effect on material translucency. Translucency percent was gradually decreased from 1 week of immersion up to 4 months. It may be concluded that the NaHCO(3) powder and the tested mouthrinses have affected the translucency of microfilled composite resin, according to the tested time. CLINICAL SIGNIFICANCE During the last decade, the demand for composite resin restorations has grown considerably, however, controversy persists regarding the effect of surface roughness on color stability.

Effects of Low-Level Laser Therapy (LLLT) in the Development of Exercise-Induced Skeletal Muscle Fatigue and Changes in Biochemical Markers Related to Postexercise Recovery

STUDY DESIGN: Randomized crossover double-blinded placebo-controlled trial. OBJECTIVE: To investigate if low-level laser therapy (LLLT) can affect biceps muscle performance, fatigue development, and biochemical markers of postexercise recovery. BACKGROUND: Cell and animal studies have suggested that LLLT can reduce oxidative stress and inflammatory responses in muscle tissue. But it remains uncertain whether these findings can translate into humans in sport and exercise situations. METHODS: Nine healthy male volleyball players participated in the study. They received either active LLLT (cluster probe with 5 laser diodes; A = 810 nm; 200 mW power output; 30 seconds of irradiation, applied in 2 locations over the biceps of the nondominant arm; 60 J of total energy) or placebo LLLT using an identical cluster probe. The intervention or placebo were applied 3 minutes before the performance of exercise. All subjects performed voluntary elbow flexion repetitions with a workload of 75% of their maximal voluntary contraction force until exhaustion. RESULTS: Active LLLT increased the number of repetitions by 14.5% (mean +/- SD, 39.6 +/- 4.3 versus 34.6 +/- 5.6; P = .037) and the elapsed time before exhaustion by 8.0% (P = .034), when compared to the placebo treatment. The biochemical markers also indicated that recovery may be positively affected by LLLT, as indicated by postexercise blood lactate levels (P<.01), creatine kinase activity (P = .017), and C-reactive protein levels (P = .047), showing a faster recovery with LLLT application prior to the exercise. CONCLUSION: We conclude that pre-exercise irradiation of the biceps with an LLLT dose of 6 J per application location, applied in 2 locations, increased endurance for repeated elbow flexion against resistance and decreased postexercise levels of blood lactate, creatine kinase, and C-reactive protein. LEVEL OF EVIDENCE: Performance enhancement, level 1b. J Orthop Sports Phys Ther 2010;40(8):524-532. doi:10.2519/jospt.2010.3294

Comparison between cold water immersion therapy (CWIT) and light emitting diode therapy (LEDT) in short-term skeletal muscle recovery after high-intensity exercise in athletes-preliminary results

In the last years, phototherapy has becoming a promising tool to improve skeletal muscle recovery after exercise, however, it was not compared with other modalities commonly used with this aim. In the present study we compared the short-term effects of cold water immersion therapy (CWIT) and light emitting diode therapy (LEDT) with placebo LEDT on biochemical markers related to skeletal muscle recovery after high-intensity exercise. A randomized double-blind placebo-controlled crossover trial was performed with six male young futsal athletes. They were treated with CWIT (5A degrees C of temperature [SD +/- 1A degrees]), active LEDT (69 LEDs with wavelengths 660/850 nm, 10/30 mW of output power, 30 s of irradiation time per point, and 41.7 J of total energy irradiated per point, total of ten points irradiated) or an identical placebo LEDT 5 min after each of three Wingate cycle tests. Pre-exercise, post-exercise, and post-treatment measurements were taken of blood lactate levels, creatine kinase (CK) activity, and C-reactive protein (CRP) levels. There were no significant differences in the work performed during the three Wingate tests (p > 0.05). All biochemical parameters increased from baseline values (p < 0.05) after the three exercise tests, but only active LEDT decreased blood lactate levels (p = 0.0065) and CK activity (p = 0.0044) significantly after treatment. There were no significant differences in CRP values after treatments. We concluded that treating the leg muscles with LEDT 5 min after the Wingate cycle test seemed to inhibit the expected post-exercise increase in blood lactate levels and CK activity. This suggests that LEDT has better potential than 5 min of CWIT for improving short-term post-exercise recovery.

ON INTEGRABLE CODIMENSION ONE ANOSOV ACTIONS OF R(k)

In this paper, we consider codimension one Anosov actions of R(k), k >= 1, on closed connected orientable manifolds of dimension n vertical bar k with n >= 3. We show that the fundamental group of the ambient manifold is solvable if and only if the weak foliation of codimension one is transversely affine. We also study the situation where one 1-parameter subgroup of R(k) admits a cross-section, and compare this to the case where the whole action is transverse to a fibration over a manifold of dimension n. As a byproduct, generalizing a Theorem by Ghys in the case k = 1, we show that, under some assumptions about the smoothness of the sub-bundle E(ss) circle plus E(uu), and in the case where the action preserves the volume, it is topologically equivalent to a suspension of a linear Anosov action of Z(k) on T(n).

Transitivity of codimension-one Anosov actions of R(k) on closed manifolds

We consider Anosov actions of R(k), k >= 2, on a closed connected orientable manifold M, of codimension one, i.e. such that the unstable foliation associated to some element of R(k) has dimension one. We prove that if the ambient manifold has dimension greater than k + 2, then the action is topologically transitive. This generalizes a result of Verjovsky for codimension-one Anosov flows.

UNIVERSAL COVERING OF DRIFTLESS CONTROL SYSTEMS

Let M be a finite-dimensional manifold and Sigma be a driftless control system on M of full rank. We prove that for a given initial state x epsilon M, the covering space Gamma(Sigma, x) for a monotonic homotopy of trajectories of Sigma which is recently constructed in [1] coincides with the simply connected universal covering manifold of M and that the terminal projection epsilon(x) : Gamma(Sigma, x) -> M given by epsilon(x) ([alpha]) = alpha(1) is a covering mapping.

Global analytic regularity for structures of co-rank one

We consider real analytic involutive structures V, of co-rank one, defined on a real analytic paracompact orientable manifold M. To each such structure we associate certain connected subsets of M which we call the level sets of V. We prove that analytic regularity propagates along them. With a further assumption on the level sets of V we characterize the global analytic hypoellipticity of a differential operator naturally associated to V. As an application we study a case of tube structures.

On the variations of the Betti numbers of regular levels of Morse flows

We generalize results in Cruz and de Rezende (1999) [7] by completely describing how the Beth numbers of the boundary of an orientable manifold vary after attaching a handle, when the homology coefficients are in Z, Q, R or Z/pZ with p prime. First we apply this result to the Conley index theory of Lyapunov graphs. Next we consider the Ogasa invariant associated with handle decompositions of manifolds. We make use of the above results in order to obtain upper bounds for the Ogasa invariant of product manifolds. (C) 2011 Elsevier B.V. All rights reserved.

Dynamics of a class of ODEs more general than almost periodic

A temporally global solution, if it exists, of a nonautonomous ordinary differential equation need not be periodic, almost periodic or almost automorphic when the forcing term is periodic, almost periodic or almost automorphic, respectively. An alternative class of functions extending periodic and almost periodic functions which has the property that a bounded temporally global solution solution of a nonautonomous ordinary differential equation belongs to this class when the forcing term does is introduced here. Specifically, the class of functions consists of uniformly continuous functions, defined on the real line and taking values in a Banach space, which have pre-compact ranges. Besides periodic and almost periodic functions, this class also includes many nonrecurrent functions. Assuming a hyperbolic structure for the unperturbed linear equation and certain properties for the linear and nonlinear parts, the existence of a special bounded entire solution, as well the existence of stable and unstable manifolds of this solution are established. Moreover, it is shown that this solution and these manifolds inherit the temporal behaviour of the vector field equation. In the stable case it is shown that this special solution is the pullback attractor of the system. A class of infinite dimensional examples involving a linear operator consisting of a time independent part which generates a C(0)-semigroup plus a small time dependent part is presented and applied to systems of coupled heat and beam equations. (C) 2010 Elsevier Ltd. All rights reserved.

In situ impedance spectroscopy study of the electrochemical corrosion of Ti and Ti-6Al-4V in simulated body fluid at 25 degrees C and 37 degrees C

The corrosion resistance of Ti and Ti-6Al-4V was investigated through electrochemical impedance spectroscopy, EIS, potentiodynamic polarisation curves and UV-Vis spectrophotometry. The tests were done in Hank solution at 25 degrees C and 37 degrees C. The EIS measurements were done at the open circuit potential at specific immersion times. An increase of the resistance as a function of the immersion time was observed, for Ti (at 25 degrees C and 37 degrees C), and for Ti-6Al-4V (at 25 degrees C), which was interpreted as the formation and growth of a passive film on the metallic surfaces. (C) 2009 Elsevier Ltd. All rights reserved.