Oseledets' Splitting of Standard-like Maps

For the class of differentiable maps of the plane and, in particular, for standard-like maps (McMillan form), a simple relation is shown between the directions of the local invariant manifolds of a generic point and its contribution to the finite-time Lyapunov exponents (FTLE) of the associated orbit. By computing also the point-wise curvature of the manifolds, we produce a comparative study between local Lyapunov exponent, manifold's curvature and splitting angle between stable/unstable manifolds. Interestingly, the analysis of the Chirikov-Taylor standard map suggests that the positive contributions to the FTLE average mostly come from points of the orbit where the structure of the manifolds is locally hyperbolic: where the manifolds are flat and transversal, the one-step exponent is predominantly positive and large; this behaviour is intended in a purely statistical sense, since it exhibits large deviations. Such phenomenon can be understood by analytic arguments which, as a by-product, also suggest an explicit way to point-wise approximate the splitting.Comment: 17 pages, 11 figure

Neural Correlates of the False Consensus Effect:Evidence for Motivated Projection and Regulatory Restraint

The false consensus effect (FCE), the tendency to project our attitudes and opinions on to others, is a pervasive bias in social reasoning with a range of ramifications for individuals and society. Research in social psychology has suggested that numerous factors (anchoring and adjustment, accessibility, motivated projection, etc.) may contribute to the FCE. In this study, we examine the neural correlates of the FCE and provide evidence that motivated projection plays a significant role. Activity in reward regions (ventromedial pFC and bilateral nucleus accumbens) during consensus estimation was positively associated with bias, whereas activity in right ventrolateral pFC (implicated in emotion regulation) was inversely associated with bias. Activity in reward and regulatory regions accounted for half of the total variation in consensus bias across participants (R2 = .503). This research complements models of the FCE in social psychology, providing a glimpse into the neural mechanisms underlying this important phenomenon

Non-adiabatic pumping in an oscillating-piston model

We consider the prototypical "piston pump" operating on a ring, where a circulating current is induced by means of an AC driving. This can be regarded as a generalized Fermi-Ulam model, incorporating a finite-height moving wall (piston) and non trivial topology (ring). The amount of particles transported per cycle is determined by a layered structure of phase-space. Each layer is characterized by a different drift velocity. We discuss the differences compared with the adiabatic and Boltzmann pictures, and highlight the significance of the "diabatic" contribution that might lead to a counter-stirring effect.Comment: 6 pages, 4 figures, improved versio

Application of a single-objective, hybrid genetic algorithm approach to pharmacokinetic model building.

A limitation in traditional stepwise population pharmacokinetic model building is the difficulty in handling interactions between model components. To address this issue, a method was previously introduced which couples NONMEM parameter estimation and model fitness evaluation to a single-objective, hybrid genetic algorithm for global optimization of the model structure. In this study, the generalizability of this approach for pharmacokinetic model building is evaluated by comparing (1) correct and spurious covariate relationships in a simulated dataset resulting from automated stepwise covariate modeling, Lasso methods, and single-objective hybrid genetic algorithm approaches to covariate identification and (2) information criteria values, model structures, convergence, and model parameter values resulting from manual stepwise versus single-objective, hybrid genetic algorithm approaches to model building for seven compounds. Both manual stepwise and single-objective, hybrid genetic algorithm approaches to model building were applied, blinded to the results of the other approach, for selection of the compartment structure as well as inclusion and model form of inter-individual and inter-occasion variability, residual error, and covariates from a common set of model options. For the simulated dataset, stepwise covariate modeling identified three of four true covariates and two spurious covariates; Lasso identified two of four true and 0 spurious covariates; and the single-objective, hybrid genetic algorithm identified three of four true covariates and one spurious covariate. For the clinical datasets, the Akaike information criterion was a median of 22.3 points lower (range of 470.5 point decrease to 0.1 point decrease) for the best single-objective hybrid genetic-algorithm candidate model versus the final manual stepwise model: the Akaike information criterion was lower by greater than 10 points for four compounds and differed by less than 10 points for three compounds. The root mean squared error and absolute mean prediction error of the best single-objective hybrid genetic algorithm candidates were a median of 0.2 points higher (range of 38.9 point decrease to 27.3 point increase) and 0.02 points lower (range of 0.98 point decrease to 0.74 point increase), respectively, than that of the final stepwise models. In addition, the best single-objective, hybrid genetic algorithm candidate models had successful convergence and covariance steps for each compound, used the same compartment structure as the manual stepwise approach for 6 of 7 (86 %) compounds, and identified 54 % (7 of 13) of covariates included by the manual stepwise approach and 16 covariate relationships not included by manual stepwise models. The model parameter values between the final manual stepwise and best single-objective, hybrid genetic algorithm models differed by a median of 26.7 % (q₁ = 4.9 % and q₃ = 57.1 %). Finally, the single-objective, hybrid genetic algorithm approach was able to identify models capable of estimating absorption rate parameters for four compounds that the manual stepwise approach did not identify. The single-objective, hybrid genetic algorithm represents a general pharmacokinetic model building methodology whose ability to rapidly search the feasible solution space leads to nearly equivalent or superior model fits to pharmacokinetic data

The area of horizons and the trapped region

This paper considers some fundamental questions concerning marginally trapped surfaces, or apparent horizons, in Cauchy data sets for the Einstein equation. An area estimate for outermost marginally trapped surfaces is proved. The proof makes use of an existence result for marginal surfaces, in the presence of barriers, curvature estimates, together with a novel surgery construction for marginal surfaces. These results are applied to characterize the boundary of the trapped region.Comment: 44 pages, v3: small changes in presentatio

Speech Communication

Contains reports on seven research projects.Contract AF19(604)-2061 with Air Force Cambridge Research CenterContract N5ori-07861 with the Navy (Office of Naval Research)National Science Foundatio

Effect of FK 506 on spontaneous diabetes in BB rats

From days 30-120 after birth, 59 BB rats were treated with water (n = 20) or FK 506 in intragastric doses of 1 mg·kg-1·day-1 (n = 19) or 2 mg·kg-1·day-1 (n = 20). Diabetes developed in 75, 15, and 0% of the 3 groups, respectively. Animals protected from diabetes by FK 506 had normal intraperitoneal glucose tolerance tests, virtual absence histopathologically of autoimmune insulitis, and normal pancreatic insulin content. Forty-five to 75 days after stopping FK 506, ∼75% of the rats that were diabetes free at 120 days remained so

Carotenoids and chlorophyll content in natural soap with addition of vegetative raw material

In the present study, we performed quantitative and qualitative determination of carotenoids and chlorophyll in five samples of natural soap with addition of vegetative raw material: Green tea, Chamerion angustifolium (L.) Holub, Trifolium pratense L., Alchemilla vulgaris L. and Urtica dioica L. There was developed the method of quantitative content of carotenoids and chlorophyll using spectrophotometry with analytical wavelength at 450 nm (carotenoids) and 667 nm (chlorophyll). Qualitative determination was carried out by the comparative TLC analysis. As mobile phases were used in the experiment following a mixed solvent of hexane-acetone (3: 1). Identification of carotenoids was carried out according to standard samples β -carotene and literature data