Numerical Approaches for Linear Left-Invariant Diffusions on $SE(2)$, Their Comparison to Exact Solutions,and Their Applications in Retinal Imaging

Left-invariant PDE-evolutions on the roto-translation group $SE(2)$ (and their resolvent equations) have been widely studied in the fields of cortical modeling and image analysis. They include hypo-elliptic diffusion (for contour enhancement) proposed by Citti & Sarti, and Petitot, and they include the direction process (for contour completion) proposed by Mumford. This paper presents a thorough study and comparison of the many numerical approaches, which, remarkably, are missing in the literature. Existing numerical approaches can be classified into 3 categories: Finite difference methods, Fourier based methods (equivalent to $SE(2)$-Fourier methods), and stochastic methods (Monte Carlo simulations). There are also 3 types of exact solutions to the PDE-evolutions that were derived explicitly (in the spatial Fourier domain) in previous works by Duits and van Almsick in 2005. Here we provide an overview of these 3 types of exact solutions and explain how they relate to each of the 3 numerical approaches. We compute relative errors of all numerical approaches to the exact solutions, and the Fourier based methods show us the best performance with smallest relative errors. We also provide an improvement of Mathematica algorithms for evaluating Mathieu-functions, crucial in implementations of the exact solutions. Furthermore, we include an asymptotical analysis of the singularities within the kernels and we propose a probabilistic extension of underlying stochastic processes that overcomes the singular behavior in the origin of time-integrated kernels. Finally, we show retinal imaging applications of combining left-invariant PDE-evolutions with invertible orientation scores.     

Short-Range Berezinskii-Kosterlitz-Thouless Phase Characterization for the q-State Clock Model

Beyond the usual ferromagnetic and paramagnetic phases present in spin systems, the usual q-state clock model presents an intermediate vortex state when the number of possible orientations q for the system is greater than or equal to 5. Such vortex states give rise to the Berezinskii-Kosterlitz-Thouless (BKT) phase present up to the XY model in the limit q→∞. Based on information theory, we present here an analysis of the classical order parameters plus new short-range parameters defined here. Thus, we show that even using the first nearest neighbors spin-spin correlations only, it is possible to distinguish the two transitions presented by this system for q greater than or equal to 5. Moreover, the appearance at relatively low temperature and disappearance of the BKT phase at a rather fix higher temperature is univocally determined by the short-range interactions recognized by the information content of classical and new parameters.     

Electric field induced phase transition in first order ferroelectrics with large zero point energy

An electric field induced phase transition in first order ferroelectrics with very large zero point energy is studied on the framework of the effective field approach. It is well known that when the zero point energy of a system is relatively large, the ferroelectric behaviour is depressed and no phase transition can be observed. The critical value Ω_cf of zero point energy for whom the phase transition disappears turns out to be dependant on the order of transition. For zero point energies larger than this critical value, a phase transition may be induced applying an external electric field. This temperature dependence of the induced polarization shows a discontinuous step when the applied electric field is weak, but becoming a continuous one at a strong applied electric field. Another critical value of zero point energy Ω_cp>Ω_cf is deduced for which no phase transition at all can be attained.     

Metabolite Profiling to Monitor Organochlorine Pesticide Exposure in HepG2 Cell Culture

Gas chromatography coupled with time of flight mass spectrometry (GC/MS-TOF) was used to profile endogenous metabolites in HepG2 cell cultures to assess the metabolic changes induced by exposure to different organochlorine pesticides, their mixtures and controls (endosulfan, lindane, DDT and aldrin). Cells were cultured in DMEM with Glutamax at 37 °C with 5 % CO₂ for 72 h and then exposed to each pesticide, pesticide mixture or DMSO (as a control) for 24 h, and finally, endogenous metabolites were extracted and analyzed using GC/MS-TOF. The experiment was repeated six times under the same cell passage and culture conditions. PCA, PLS-DA and ROC were performed to analyze the GC/MS-TOF data and identify potential biomarkers. Thirty-five explanatory metabolites were found in both PCA and PLS-DA models, where Q ² was 0.86 and R ² was 0.98. Univariate and multivariate ROC showed potential biomarkers for each treatment, suggesting a general toxic mechanism for organochlorine pesticides that is specific for each type of compound. These results confirmed the effect of OCPs in sugar and amino acid metabolism that are linked with the function of cytochrome P450 in reductive dechlorination and oxidative stress.

     

Ultraviolet Erythematic Radiation Dose Received by Golfers in Winter,in Valencia

This article analyzes Ultraviolet Erythematic Radiation (UVER) dose received by several golf players in winter in Valencia. Playing golf involves spending several hours outdoors because of the length of golf matches and training. Moreover, in Valencia there are many golf players coming from northern Europe, with a phototype very sensitive (I–II). For that reason, these people have an increasing risk while playing. This article shows that harmful effects coming from UVER radiation may occur not only in summer time but also in winter, especially at these latitudes. VioSpor dosimeters have been used to develop this analysis over several golf players on January 2013 between 10:00 h and 15:00 h, local time.     

Methoxycarbonylation of olefins catalyzed by palladium(II) complexes containing naphthyl(diphenyl)phosphine ligands

Palladium(II) complexes containing phosphine donor ligands derived from naphthyl(diphenyl)phosphine were synthesized and characterized by NMR and elemental analysis. The complexes were studied as catalyst precursors in the methoxycarbonylation reaction of several aromatic and aliphatic olefins under mild conditions. The catalysts reported high chemoselectivities (over 96%) and regioselectivities between 44% and 93% for different olefins. The best results were obtained over a styrene substrate with 97% of conversion after 6 h of reaction, with high regioselectivity (93%). Kinetic studies permitted the determination of the rate law (v = k [substrate]^1.21±0.02 [catalyst]^0.94±0.11 [acid]^0.52±0.03 [MeOH]^0.53±0.05 [CO]^0.65±0.03) for methoxycarbonylation of styrene. Copyright © 2014 John Wiley & Sons, Ltd.     

Gas phase thermolysis of benzyl t-butyl sulfide,phenyl t-butyl sulfide,and phenyl t-butyl ether

The pyrolysis kinetics of the title compounds has been studied in a stirred-flow reactor over the temperature range 440–530°C and pressures between 5 and 14 torr. Benzyl t-butyl sulfide and phenyl t-butyl ether formed isobutene as product in over 98% yield, together with the corresponding benzyl thiol and phenol. The benzyl thiol decomposes to a large extent into hydrogen sulfide and bibenzyl. In the pyrolysis of phenyl t-butyl sulfide, the hydrocarbon products consisted of 80 ±5% isobutene plus 20% isobutane, while the sulfur containing products were thiophenol and diphenyl disulfide. Order one kinetics was observed for the consumption of the reactants. The first order rate coefficients, based on isobutene production, followed the Arrhenius equations: Benzyl t-butyl sulfide: Phenyl t-butyl sulfide: Phenyl t-butyl ether: For benzyl t-butyl sulfide and phenyl t-butyl ether, the results suggest a unimolecular mechanism involving polar four center cyclic transition states. For phenyl t-butyl sulfide, the t-butyl-sulfur single bond fission mechanism is a parallel, less important process than the complex fission one.