On noise reduction methods for chaotic data

Recently proposed noise reduction methods for nonlinear chaotic time sequences with additive noise are analyzed and generalized. All these methods have in common that they work iteratively, and that in each step of the iteration the noise is suppressed by requiring locally linear relations among the delay coordinates, i.e., by moving the delay vectors towards some smooth manifold. The different methods can be compared unambiguously in the case of strictly hyperbolic systems corrupted by measurement noise of infinitesimally low level. It was found that all proposed methods converge in this ideal case, but not equally fast. Different problems arise if the system is not hyperbolic, and at higher noise levels. A new scheme which seems to avoid most of these problems is proposed and tested, and seems to give the best noise reduction so far. Moreover, large improvements are possible within the new scheme and the previous schemes if their parameters are not kept fixed during the iteration, and if corrections are included which take into account the curvature of the attracting manifold. Finally, the fact that comparison with simple low-pass filters tends to overestimate the relative achievements of these nonlinear noise reduction schemes is stressed, and it is suggested that they should be compared to Wiener-type filters.     

Tribochemische und thermische Umwandlungen von LnTa3O9 (Ln = Pr,Nd) – röntgenographische und elektronenmikroskopische Untersuchungen

Tribochemical and Thermal Transitions of LnTa₃O₉ (Ln = Pr, Nd) — X-ray and Electron Microscopic Investigations Upon grinding crystals of M1? LnTa₃O₉ (Ln = Pr, Nd) [3] undergo a tribochemical phase transition. This leads to a new modifikation M2? LnTa₃O₉ with a significant higher density. We tried to find out more about the structure with high resolution electron microscopic investigations. According to electron diffraction and powder patterns the lattice parameters are (CuKα₁, λ = 1,54051 Å): M2? PrTa₃O₉: a = 6.2545(7) Å, b = 7.6736(7) Å, c = 6.5316(8) Å, β = 93.93(9)°; M2? NdTa₃O₉: a = 6.2552(5) Å, b = 7.6598(7) Å, c = 6.5103(4) Å, β = 94.096(7)°; (Z = 2). Using the intensities of powder patterns two structure models were calculated (space group P2₁/m, P2/m; R < 20%, heavy metal positions only). A through focus series of high resolution images was in better agreement with the first model (space group P2₁/m). Both models show a remarkable similarity to the structure of M? CeTa₃O₉ [4]. A thermal phase transition leads to M? PrTa₃O₉ and M? NdTa₃O₉ which are both isostructural to M? CeTa₃O₉.     

A Novel Anti-Inflammatory d-Peptide Inhibits Disease Phenotype Progression in an ALS Mouse Model

Amyotrophic lateral sclerosis (ALS) is a progressive neurodegenerative disease characterised by selective neuronal death in the brain stem and spinal cord. The cause is unknown, but an increasing amount of evidence has firmly certified that neuroinflammation plays a key role in ALS pathogenesis. Neuroinflammation is a pathological hallmark of several neurodegenerative disorders and has been implicated as driver of disease progression. Here, we describe a treatment study demonstrating the therapeutic potential of a tandem version of the well-known all-d-peptide RD2 (RD2RD2) in a transgenic mouse model of ALS (SOD1*G93A). Mice were treated intraperitoneally for four weeks with RD2RD2 vs. placebo. SOD1*G93A mice were tested longitudinally during treatment in various behavioural and motor coordination tests. Brain and spinal cord samples were investigated immunohistochemically for gliosis and neurodegeneration. RD2RD2 treatment in SOD1*G93A mice resulted not only in a reduction of activated astrocytes and microglia in both the brain stem and lumbar spinal cord, but also in a rescue of neurons in the motor cortex. RD2RD2 treatment was able to slow progression of the disease phenotype, especially the motor deficits, to an extent that during the four weeks treatment duration, no significant progression was observed in any of the motor experiments. Based on the presented results, we conclude that RD2RD2 is a potential therapeutic candidate against ALS.     

Fluorometabolite biosynthesis and the fluorinase from Streptomyces cattleya

This review outlines the recent developments in uncovering the enzymes and intermediates involved in fluorometabolite biosyntheses in the bacterium Streptomyces cattleya. A particular emphasis is placed on the purification and characterisation of the fluorinase, the C-F bond forming enzyme which initiates the biosynthesis. Nature has hardly developed a biochemistry around fluorine, yet fluorinated organics are important commercial entities, therefore a biotransformation from inorganic to organic fluorine is novel and of contemporary interest.     

Total Synthesis and Structural Revision of the Antibiotic Tetrapeptide GE81112A

The total synthesis of the naturally occurring antibiotic GE81112A, a densely functionalized tetrapeptide, is reported. Comparison of spectral data with those of the natural product and the lack of biological activity of the synthesized compound led us to revise the published configuration of the 3‐hydroxypipecolic acid moiety. This hypothesis was fully validated by the synthesis of the corresponding epimer.     

Time-dependent photoionization of azulene: competition between ionization and relaxation in highly excited states

Pump-probe photoionization has been used to map the relaxation processes taking place from highly vibrationally excited levels of the S(2) state of azulene, populated directly or via internal conversion from the S(4) state. Photoelectron spectra obtained by 1+2(') two-color time-resolved photoelectron imaging are invariant (apart from in intensity) to the pump-probe time delay and to the pump wavelength. This reveals a photoionization process which is driven by an unstable electronic state (e.g., doubly excited state) lying below the ionization potential. This state is postulated to be populated by a probe transition from S(2) and to rapidly relax via an Auger-like process onto highly vibrationally excited Rydberg states. This accounts for the time invariance of the photoelectron spectrum. The intensity of the photoelectron spectrum is proportional to the population in S(2). An exponential energy gap law is used to describe the internal conversion rate from S(2) to S(0). The vibronic coupling strength is found to be larger than 60+/-5 microeV.