Unravelling the Photoprotection Properties of Garden Cress Sprout Extract

Plants, as with humans, require photoprotection against the potentially damaging effects of overexposure to ultraviolet (UV) radiation. Previously, sinapoyl malate (SM) was identified as the photoprotective agent in thale cress. Here, we seek to identify the photoprotective agent in a similar plant, garden cress, which is currently used in the skincare product Detoxophane nc. To achieve this, we explore the photodynamics of both the garden cress sprout extract and Detoxophane nc with femtosecond transient electronic absorption spectroscopy. With the assistance of liquid chromatography-mass spectrometry, we determine that the main UV-absorbing compound in garden cress sprout extract is SM. Importantly, our studies reveal that the photoprotection properties of the SM in the garden cress sprout extract present in Detoxophane nc are not compromised by the formulation environment. The result suggests that Detoxophane nc containing the garden cress sprout extract may offer additional photoprotection to the end user in the form of a UV filter booster.     

Wheels, wheeling, and the Kontsevich integral of the Unknot

We conjecture an exact formula for the Kontsevich integral of the unknot, and also conjecture a formula (also conjectured independently by Deligne [De]) for the relation between the two natural products on the space of uni-trivalent diagrams. The two formulas use the related notions of “Wheels” and “Wheeing”. We prove these formulas ‘on the level of Lie algebras’ using standard techniques from the theory of Vassiliev invariants and the theory of Lie algebras. In a brief epilogue we report on recent proofs of our full conjectures, by Kontsevich [Ko2] and by DBN, DPT, and T. Q. T. Le, [BLT]. This paper is available electronically     

Investigating the Ultrafast Dynamics and Long-Term Photostability of an Isomer Pair,Usujirene and Palythene,from the Mycosporine-like Amino Acid Family

Mycosporine-like amino acids are a prevalent form of photoprotection in micro- and macro-organisms. Using a combination of natural product extraction/purification and femtosecond transient absorption spectroscopy, we studied the relaxation pathway for a common mycosporine-like amino acid pair, usujirene and its geometric isomer palythene, in the first few nanoseconds following photoexcitation. Our studies show that the electronic excited state lifetimes of these molecules persist for only a few hundred femtoseconds before the excited state population is funneled through an energetically accessible conical intersection with subsequent vibrational energy transfer to the solvent. We found that a minor portion of the isomer pair did not recover to their original state within 3 ns after photoexcitation. We investigated the long-term photostability using continuous irradiation at a single wavelength and with a solar simulator to mimic a more real-life environment; high levels of photostability were observed in both experiments. Finally, we employed computational methods to elucidate the photochemical and photophysical properties of usujirene and palythene as well as to reconcile the photoprotective mechanism.     

Universal elements in some classes of mappings and classes of G-spaces

In the present paper it is proved the existence of topologically universal elements in some classes of mappings and classes of G-spaces generalizing some results from [S.D. Iliadis, Universal Spaces and Mappings, North-Holland Math. Stud., vol. 198, Elsevier, 2005] and [S.D. Iliadis, Universal Borel mappings and Borel actions of groups, Topology Appl., in press, doi:10.1016/j.topol.2007.05.029].     

Nonlinear optical absorption in laser modified regions of fused silica substrates

The presence of strong nonlinear absorption has been observed in laser modified fused silica. Intensity-dependent transmission measurements using 355, 532 and 1064 nm laser pulses were performed in pristine polished regions in fused silica substrates and in locations that were exposed to dielectric breakdown. The experimental results suggest that multiphoton absorption is considerably stronger in the modified regions compared to pristine sites and is strongly dependent on the excitation wavelength.     

Emulation of the evolution of a Bose–Einstein condensate in a time-dependent harmonic trap

We emulate the ground state of a Bose–Einstein condensate in a time-dependent isotropic harmonic trap by constructing analytic simulacra of a transformed wavefunction in the regions around the origin and far from the origin. This transformed wavefunction is obtained through a pseudoconformal transformation and is a function of new spatial and temporal variables, while the simulacra are generalisations of asymptotic solutions of the nonlinear Schrödinger equation and they are matched by requiring continuity not only of the wavefunction and of its slope, but of its curvature as well. The resulting piecewise analytic simulacra coincide almost perfectly with the numerically obtained solutions of the time-dependent nonlinear Schrödinger equation and constitute an easy and accurate analytic method for describing fully the condensate ground state.     

Estimation of an Exponential Quantile under a General Loss and an Alternative Estimator under Quadratic Loss

Estimation of the quantile + of an exponential distribution with parameters (, ) is considered under an arbitrary strictly convex loss function. For obeying a certain condition, the inadmissibility of the best affine equivariant procedure is established by exhibiting a better estimator. The LINEX loss is studied in detail. For quadratic loss, sufficient conditions are given for a scale equivariant estimator to dominate the best affine equivariant one and, when exceeds a lower bound specified below, a new minimax estimator is identified.     

Integrated simulation and optimization models for tracking international fixed income indices

Portfolio managers in the international fixed income markets must address jointly the interest rate risk in each market and the exchange rate volatility across markets. This paper develops integrated simulation and optimization models that address these issues in a common framework. Monte Carlo simulation procedures generate jointly scenarios of interest and exchange rates and, thereby, scenarios of holding period returns of the available securities. The portfolio manager’s risk tolerance is incorporated either through a utility function or a (modified) mean absolute deviation function. The optimization models prescribe asset allocation weights among the different markets and also resolve bond-picking decisions. Therefore several interrelated decisions are cast in a common framework. Two models – an expected utility maximization and a mean absolute deviation minimization – are implemented and tested empirically in tracking a composite index of the international bond markets. Backtesting over the period January 1997 to July 1998 illustrate the efficacy of the optimization models in dealing with uncertainty and tracking effectively the volatile index. Of particular interest is the empirical demostration that the integrative models generate portfolios that dominate the portfolios obtained using classical disintegrated approaches. Received: November 24, 1998 / Accepted: October 1, 2000?Published online December 15, 2000     

Plasmonic response of ordered arrays of gold nanorods immersed within a nematic liquid crystal

We study theoretically the optical properties of a two-dimensional lattice of metallic (gold) nanorods immersed within a nematic liquid crystal (NLC) strongly anchored to the surface of the nanorods. The distribution of the director field of the NLC is found by minimising the corresponding total free energy via simulated annealing. Optical properties such as transmittance, reflectance and absorbance of the structure are found by employing a hybrid discrete-dipole approximation/layer-multiple-scattering technique. We show, in particular, that when the NLC is strongly anchored to the nanorods, light absorbance is more efficient compared to the case where the liquid crystal (LC) is aligned by application of an external field. Also, the alignment of the LC molecules via an external field leads to a significant shift of the surface-plasmon resonance of the gold nanorods relative to the strong-anchoring case, an effect which can be exploited in switching applications. We also report that the rate of light absorption is a non-monotonic function of the height of nanorods due to the guiding of EM waves taking place for long enough nanorods.