Investigating nonlinear dynamics from time series: The influence of symmetries and the choice of observables

When a dynamical system is investigated from a time series, one of the most challenging problems is to obtain a model that reproduces the underlying dynamics. Many papers have been devoted to this problem but very few have considered the influence of symmetries in the original system and the choice of the observable. Indeed, it is well known that there are usually some variables that provide a better representation of the underlying dynamics and, consequently, a global model can be obtained with less difficulties starting from such variables. This is connected to the problem of observing the dynamical system from a single time series. The roots of the nonequivalence between the dynamical variables will be investigated in a more systematic way using previously defined observability indices. It turns out that there are two important ingredients which are the complexity of the coupling between the dynamical variables and the symmetry properties of the original system. As will be mentioned, symmetries and the choice of observables also has important consequences in other problems such as synchronization of nonlinear oscillators. (c) 2002 American Institute of Physics.     

Synthesis and structure of isomeric palladium(II)-pyrazole chelate complexes with and without an N-H group as hydrogen bond donor

Four new ligands containing a pyrazole ring and either a phosphine or thioether were prepared and converted to their cis-dichloropalladium(II) complexes. Two of the ligands are especially notable for the attachment of a side chain at pyrazole carbon, rather than at nitrogen. The new metal complexes include dichloro[3-(diphenylphosphinomethyl)pyrazole]palladium(II) (1-PdCl2) and dichloro[3-(methylthiomethyl)pyrazole]palladium(II) (2-PdCl2), which both feature an N-H group as a potential proton or hydrogen bond donor. For comparison, isomeric complexes lacking an NH group were prepared: dichloro[1-(diphenylphosphinomethyl)pyrazole]palladium(II) (3-PdCl2) and dichloro[1-(methylthiomethyl)pyrazole]palladium(II) (4-PdCl2). As determined by X-ray crystallography, all four complexes were found to have slightly distorted square planar geometry. Complexes 1-PdCl2 and 2-PdCl2, which contain an NH group, exhibit both intermolecular and intramolecular hydrogen bonding, whereas isomers 3-PdCl2 and 4-PdCl2 do not. Single-crystal X-ray structure determinations on the following compounds are reported: 1-PdCl2, space group P1, a = 8.4488(9) A, b = 8.9175(13) A, c = 12.731(2) A, Z = 2, V = 871.8(2) A3; 2-PdCl2, space group Pbca, a = 10.8827(10) A, b = 11.7721(7) A, c = 14.874(2) A, Z = 8, V = 1905.6 A3; 3-PdCl2, space group P2(1)/c, a = 20.520(2) A, b = 12.549(2) A, c = 13.9784(13) A, Z = 8, V = 3401.1(6) A3; 4-PdCl2, space group Pbca, a = 10.6545(10) A, b = 12.0205(11) A, c = 14.6474(14) A, Z = 8, V = 1875.9(3) A3.     

Iron homeostasis in neuronal cells: a role for IREG1

Background  

Iron is necessary for neuronal function but in excess generates neurodegeneration. Although most of the components of the iron homeostasis machinery have been described in neurons, little is known about the particulars of their iron homeostasis. In this work we characterized the response of SH-SY5Y neuroblastoma cells and hippocampal neurons to a model of progressive iron accumulation.     

Mode dependent vibrational autoionization of Rydberg states of NO2. II. Comparing the symmetric stretching and bending vibrations

Triple-resonance excitation and high-resolution photoelectron spectroscopy are combined to characterize the mode selectivity of vibrational autoionization of the high Rydberg states of NO2. Photoelectron spectra and vibrational branching fractions are reported for autoionizing Rydberg states converging to the NO2+ X 1Sigmag +(110) state, that is, with one quantum in the symmetric stretch, nu1, and one quantum in the bending vibration, nu2. These results indicate that autoionization proceeds most efficiently through the loss of one quantum from the symmetric stretch rather than from the bending vibration. The implications of this result are discussed in terms of the autoionization mechanism.     

Nafion/tetraruthenated porphyrin glassy carbon-modified electrode: characterization and voltammetric studies of sulfite oxidation in water–ethanol solutions

In this work, the modification of a glassy carbon electrode with tetraruthenated porphyrins electrostatically assembled onto a Nafion film, previously adsorbed on the electrode surface, is reported. This modified electrode was characterized by scanning electron microscopy–energy-dispersive X-ray, Raman spectroscopy, UV-Vis spectroelectrochemistry, and cyclic voltammetry. The Nafion film onto the glassy carbon electrode shows a smooth disposition; when the tetraruthenated porphyrin is incorporated on the Nafion film, the complex is adsorbed in a homogeneous way. The modified electrode catalyzes HSO₃⁻ oxidation in water–ethanol solutions and shows an enhanced stability compared with the electrode modified with the dip coating method. Rotating disk electrode experiments showed a kinetic limitation to the electron transfer controlled by charge propagation in the film. I/E curves show a Tafel slope of 120 mV/decade corresponding to a first electron-transfer reaction, depending on the potential, as the determining step. Spectroelectrochemical experiments demonstrated that Ru(II) is the active site for the electrocatalysis.     

Synthesis and characterization of new complexes of the type [Ru(CO)2Cl2 (2‐phenyl‐1,8‐naphthyridine‐kN) (2‐phenyl‐1,8‐naphthyridine‐kN′)]. Preliminary applications in homogeneous catalysis

Novel ruthenium (II) complexes were prepared containing 2‐phenyl‐1,8‐naphthyridine derivatives. The coordination modes of these ligands were modified by addition of coordinating solvents such as water into the ethanolic reaction media. Under these conditions 1,8‐naphthyridine (napy) moieties act as monodentade ligands forming unusual [Ru(CO)₂Cl₂(η¹‐2‐phenyl‐1,8‐naphthyridine‐ kN )(η¹‐2‐phenyl‐1,8‐naphthyridine‐kN′)] complexes. The reaction was reproducible when different 2‐phenyl‐1,8‐naphthyridine derivatives were used. On the other hand, when dry ethanol was used as the solvent we obtained complexes with napy moieties acting as a chelating ligand. The structures proposed for these complexes were supported by NMR spectra, and the presence of two ligands in the [Ru(CO)₂Cl₂(η¹‐2‐phenyl‐1,8‐naphthyridine‐ kN )(η¹‐2‐phenyl‐1,8‐naphthyridine‐kN′)] type complexes was confirmed using elemental analysis. All complexes were tested as catalysts in the hydroformylation of styrene showing moderate activity in N,N′‐dimethylformamide. Copyright © 2008 John Wiley & Sons, Ltd.     

Struggle for space: viral extinction through competition for cells

The design of protocols to suppress the propagation of viral infections is an enduring enterprise, especially hindered by limited knowledge of the mechanisms leading to viral extinction. Here we report on infection extinction due to intraspecific competition to infect susceptible hosts. Beneficial mutations increase the production of viral progeny, while the host cell may develop defenses against infection. For an unlimited number of host cells, a feedback runaway coevolution between host resistance and progeny production occurs. However, physical space limits the advantage that the virus obtains from increasing offspring numbers; thus, infection clearance may result from an increase in host defenses beyond a finite threshold. Our results might be relevant to devise improved control strategies in environments with mobility constraints or different geometrical properties.     

Hermite pseudospectral approximations. An error estimate

We find an error bound for the pseudospectral approximation of a function in terms of Hermite functions, hn(x)=e−x²Hn(x), in certain weighted Sobolev spaces. We use properties of Hermite polynomials, as well as an asymptotic expression for their largest zeroes to achieve the mentioned estimate.