KAM Theory in Configuration Space and Cancellations in the Lindstedt Series

The KAM theorem for analytic quasi-integrable anisochronous Hamiltonian systems yields that the perturbation expansion (Lindstedt series) for any quasi-periodic solution with Diophantine frequency vector converges. If one studies the Lindstedt series by following a perturbation theory approach, one finds that convergence is ultimately related to the presence of cancellations between contributions of the same perturbation order. In turn, this is due to symmetries in the problem. Such symmetries are easily visualised in action-angle coordinates, where the KAM theorem is usually formulated by exploiting the analogy between Lindstedt series and perturbation expansions in quantum field theory and, in particular, the possibility of expressing the solutions in terms of tree graphs, which are the analogue of Feynman diagrams. If the unperturbed system is isochronous, Moser’s modifying terms theorem ensures that an analytic quasi-periodic solution with the same Diophantine frequency vector as the unperturbed Hamiltonian exists for the system obtained by adding a suitable constant (counterterm) to the vector field. Also in this case, one can follow the alternative approach of studying the perturbation expansion for both the solution and the counterterm, and again convergence of the two series is obtained as a consequence of deep cancellations between contributions of the same order. In this paper, we revisit Moser’s theorem, by studying the perturbation expansion one obtains by working in Cartesian coordinates. We investigate the symmetries giving rise to the cancellations which makes possible the convergence of the series. We find that the cancellation mechanism works in a completely different way in Cartesian coordinates, and the interpretation of the underlying symmetries in terms of tree graphs is much more subtle than in the case of action-angle coordinates.     

Wavelet‐based self‐organizing maps for classifying multivariate time series

Following a nonparametric approach, we suggest a time‐series clustering method. Our clustering approach combines the benefits connected to the interpretative power of the nonparametric representation of the time series, and the clustering and vector quantization informational gain produced by the adopted unsupervised neural networks technique, enhanced with the self‐organizing maps ordering and topological preservation abilities. The proposed clustering method takes into account a composite wavelet‐based information of the multivariate time series by adding to the information connected to the wavelet variance, namely the influence of variability of individual univariate components of the multivariate time series across scales, the information associated to wavelet correlation, represented by the interaction between pairs of univariate components of the multivariate time series at each scale, and then suitably tuning the combination of these pieces of information. In order to assess the effectiveness of the proposed clustering approach, a simulation study and an empirical application are shown. Copyright © 2013 John Wiley & Sons, Ltd.     

Importance of platinum(II)-assisted platinum(IV) substitution for the oxidation of guanosine derivatives by platinum(IV) complexes

Guanosine derivatives with a nucleophilic group at the 5' position (G-5') are oxidized by the Pt (IV) complex Pt( d, l)(1,2-(NH 2) 2C 6H 10)Cl 4 ([Pt (IV)(dach)Cl 4]). The overall redox reaction is autocatalytic, consisting of the Pt (II)-catalyzed Pt (IV) substitution and two-electron transfer between Pt (IV) and the bound G-5'. In this paper, we extend the study to improve understanding of the redox reaction, particularly the substitution step. The [Pt (II)(NH 3) 2(CBDCA-O,O')] (CBDCA = cyclobutane-1,1-dicarboxylate) complex effectively accelerates the reactions of [Pt (IV)(dach)Cl 4] with 5'-dGMP and with cGMP, indicating that the Pt (II) complex does not need to be a Pt (IV) analogue to accelerate the substitution. Liquid chromatography/mass spectroscopy (LC/MS) analysis showed that the [Pt (IV)(dach)Cl 4]/[Pt (II)(NH 3) 2(CBDCA-O,O')]/cGMP reaction mixture contained two Pt (IV)cGMP adducts, [Pt (IV)(NH 3) 2(cGMP)(Cl)(CBDCA-O,O')] and [Pt (IV)(dach)(cGMP)Cl 3]. The LC/MS studies also indicated that the trans, cis-[Pt (IV)(dach)( (37)Cl) 2( (35)Cl) 2]/[Pt (II)(en)( (35)Cl) 2]/9-EtG mixture contained two Pt (IV)-9-EtG adducts, [Pt (IV)(en)(9-EtG)( (37)Cl)( (35)Cl) 2] and [Pt (IV)(dach)(9-EtG)( (37)Cl)( (35)Cl) 2]. These Pt (IV)G products are predicted by the Basolo-Pearson (BP) Pt (II)-catalyzed Pt (IV)-substitution scheme. The substitution can be envisioned as an oxidative addition reaction of the planar Pt (II) complex where the entering ligand G and the chloro ligand from the axial position of the Pt (IV) complex are added to Pt (II) in the axial positions. From the point of view of reactant Pt (IV), an axial chloro ligand is thought to be substituted by the entering ligand G. The Pt (IV) complexes without halo axial ligands such as trans, cis-[Pt(en)(OH) 2Cl 2], trans, cis-[Pt(en)(OCOCF 3) 2Cl 2], and cis, trans, cis-[Pt(NH 3)(C 6H 11NH 2)(OCOCH 3) 2Cl 2] ([Pt (IV)(a,cha)(OCOCH 3) 2Cl 2], satraplatin) did not react with 5'-dGMP. The bromo complex, [Pt (IV)(en)Br 4], showed a significantly faster substitution rate than the chloro complexes, [Pt (IV)(en)Cl 4] and [Pt (IV)(dach)Cl 4]. The results indicate that the axial halo ligands are essential for substitution and the Pt (IV) complexes with larger axial halo ligands have faster rates. When the Pt (IV) complexes with different carrier ligands were compared, the substitution rates increased in the order [Pt (IV)(dach)Cl 4] < [Pt (IV)(en)Cl 4] < [Pt (IV)(NH 3) 2Cl 4], which is in reverse order to the carrier ligand size. These axial and carrier ligand effects on the substitution rates are consistent with the BP mechanism. Larger axial halo ligands can form a better bridging ligand, which facilitates the electron-transfer process from the Pt (II) to Pt (IV) center. Smaller carrier ligands exert less steric hindrance for the bridge formation.     

Exponential distance-based fuzzy clustering for interval-valued data

In several real life and research situations data are collected in the form of intervals, the so called interval-valued data. In this paper a fuzzy clustering method to analyse interval-valued data is presented. In particular, we address the problem of interval-valued data corrupted by outliers and noise. In order to cope with the presence of outliers we propose to employ a robust metric based on the exponential distance in the framework of the Fuzzy C-medoids clustering mode, the Fuzzy C-medoids clustering model for interval-valued data with exponential distance. The exponential distance assigns small weights to outliers and larger weights to those points that are more compact in the data set, thus neutralizing the effect of the presence of anomalous interval-valued data. Simulation results pertaining to the behaviour of the proposed approach as well as two empirical applications are provided in order to illustrate the practical usefulness of the proposed method.     

Electron trapping at point defects on hydroxylated silica surfaces

The origin of electron trapping and negative charging of hydroxylated silica surfaces is predicted based on accurate quantum-mechanical calculations. The calculated electron affinities of the two dominant neutral paramagnetic defects, the nonbridging oxygen center, identical with Si-O*, and the silicon dangling bond, identical with Si*, demonstrate that both defects are deep electron traps and can form the corresponding negatively charged defects. We predict the structure and optical absorption energies of these diamagnetic defects.     

Oxidation of organotrifluoroborates via oxone

A method for the oxidation of organotrifluoroborates using Oxone was developed. A variety of aryl-, heteroaryl-, alkenyl-, and alkyltrifluoroborates were converted into the corresponding oxidized products in excellent yields. This method proved to be tolerant of a broad range of functional groups, and in secondary alkyl substrates it was demonstrated to be completely stereospecific.     

Electrochemically induced anatase inhibits bacterial colonization on Titanium Grade 2 and Ti6Al4V alloy for dental and orthopedic devices

Bacterial contamination of implanted devices is a common cause of their failure. The aim of the present study was to assess the capability of electrochemical procedures to: (a) promote the formation of anatase on the surface of commercially pure Grade 2 Ti and Ti Grade 5 (Ti6Al4V) alloy; (b) inhibit in vitro biofilm formation of Staphylococcus aureus, Staphylococcus epidermidis, Streptococcus mutans and Porphyromonas gingivalis and oral plaque in vivo, (c) preserve favorable response of osteoblasts and fibroblasts to materials surfaces. Ti Grade 2 and Ti Grade 5 were respectively anodized at two different voltages: 90 and 130V for pure titanium; 100 and 120V for Ti6Al4V alloy. Surface characterization was performed by scanning electron microscopy (SEM) equipped with EDS probe, laser profilometry and X-ray diffractometry. Bacterial adhesion characterization was performed either in vitro and in vivo in patients. Osteoblast and fibroblast response was evaluated by metabolic activity assessment. The higher voltage applied in the anodization treatment of pure titanium (130V) and Ti6Al4V alloy (120V) surfaces, compared to the untreated pure titanium and Ti6Al4V and to lower voltage treatments, resulted in a greater decrease in bacterial attachment and biofilm formation in both in vitro and in vivo experiments. In contrast, the high voltage treatments were found to promote osteoblasts and fibroblasts proliferation. The observations indicated that the experimented high voltage anodization treatments may contribute to preserve the tissue integration and reduce bacteria colonization of titanium and titanium alloy for implantable applications.     

Donor characteristics of transition-metal-doped oxides: Cr-doped MgO versus Mo-doped CaO

The ability of Mo (Cr) impurities in a CaO (MgO) matrix to act as charge donors to adsorbed gold has been investigated by means of scanning tunneling microscopy and density functional theory. Whereas CaO(Mo) features a robust donor characteristic, as deduced from a charge-transfer-driven crossover in the Au particles' geometry in the presence of dopants, MgO(Cr) is electrically inactive. The superior performance of the CaO(Mo) system is explained by the ability of the Mo ions to evolve from a +2 oxidation state in ideal CaO to a +5 state by transferring up to three electrons to the Au adislands. Cr ions in MgO, on the other hand, are stable only in the +2 and +3 charge states and can provide a single electron at best. Since this electron is likely to be captured by cationic vacancies or morphological defects in the real oxide, no charge transfer to Au particles takes place in this case. On the basis of our findings, we have developed general rules on how to optimize the electron donor characteristics of doped oxide materials.     

Improved spatial resolution in the imaging of biological tissue using desorption electrospray ionization

Desorption electrospray ionization imaging allows biomarker discovery and disease diagnosis through chemical characterization of biological samples in their native environment. Optimization of experimental parameters including emitter capillary size, solvent composition, solvent flow rate, mass spectrometry scan-rate and step-size is shown here to improve the resolution available in the study of biological tissue from 180?μm to about 35?μm using an unmodified commercial mass spectrometer. Mouse brain tissue was used to optimize and measure resolution based on known morphological features and their known relationships to major phospholipid components. Features of approximately 35?μm were resolved and correlations drawn between features in grey matter (principally PS (18:0/22:6), m/z 834) and in white matter (principally ST (24:1), m/z 888). The improved spatial resolution allowed characterization of the temporal changes in lipid profiles occurring within mouse ovaries during the ovulatory cycle. An increase in the production of phosphatidylinositol (PI 38:4) m/z 885 and associated fatty acids such as arachidonic acid (FA 20:4) m/z 303 and adrenic acid (FA 22:4) m/z 331was seen with the postovulatory formation of the corpus luteum.