Optimal state space reconstruction via Monte Carlo decision tree search

Nonlinear Dynamics - A novel idea for an optimal time delay state space reconstruction from uni- and multivariate time series is presented. The entire embedding process is considered as a game, in...     

Models of topological space geometries

We study a special class of models of R³-spaces in the sense of Betten. We single out some of the properties of these models, and use these properties as additional axioms for general R³-spaces. Then we investigate the consequences of these new axioms in general R³-spaces. We prove the continuity of the geometric operations which involve planes, and we characterize the planes in incidence geometric terms. Using these results, we study the topology of the space of planes and of line pencils, and we prove the continuity of collineations. The obtained results are applied to our concrete examples.     

Preferred functionalization of metallic and small-diameter single-walled carbon nanotubes by nucleophilic addition of organolithium and -magnesium compounds followed by reoxidation

Covalent sidewall addition to single-walled nanotubes (SWNTs) of a series of organolithium and organomagnesium compounds (nBuLi, tBuLi, EtLi, nHexLi, nBuMgCl, tBuMgCl) followed by reoxidation is reported. The functionalized R(n)-SWNTs were characterized by Raman and NIR emission spectroscopy. The reaction of SWNTs with organolithium and magnesium compounds exhibits pronounced selectivity: in general, metallic tubes are more reactive than semiconducting ones. The reactivity of SWNTs toward the addition of organometallic compounds is inversely proportional to the diameter of the tubes. This was determined simultaneously and independently for both metallic and semiconducting SWNTs. The reactivity also depends on the steric demands of the addend. Binding of the bulky t-butyl addend is less favorable than addition of primary alkyl groups. Significantly, although tBuLi is less reactive than, for example, nBuLi, it is less selective toward the preferred reaction with metallic tubes. This unexpected behavior is explained by fast electron transfer to the metallic SWNTs having low-lying electronic states close to the Fermi level, a competitive initial process. The NIR emission of weakly functionalized semiconducting SWNTs, also reported for the first time, implies interesting applications of functionalized tubes as novel fluorescent reporter molecules.     

Mechanochemical Cycloreversion of Cyclobutane Observed at the Single Molecule Level

Mechanochemical cycloreversion of cyclobutane is known from ultrasound experiments. It is, however, not clear which forces are required to induce the cycloreversion. In atomic force microscopy (AFM) experiments, on the other hand, it is notoriously difficult to assign the ruptured bond. We have solved this problem through the synthesis of tailored macrocycles, in which the cyclobutane mechanophore is bypassed by an ethylene glycol chain of specific length. This macrocycle is covalently anchored between a glass substrate and an AFM cantilever by polyethylene glycol linkers. Upon mechanical stretching of the macrocycle, cycloreversion occurs, which is identified by a defined length increase of the stretched polymer. The measured length change agrees with the value calculated with the external force explicitly included (EFEI) method. By using two different lengths for the ethylene glycol safety line, the assignment becomes unambiguous. Mechanochemical cycloreversion of cyclobutane is observed at forces above 1.7 nN.     

Covalent 2D Patterning,Local Electronic Structure and Polarization Switching of Graphene at the Nanometer Level

A very facile and efficient protocol for the covalent patterning and properties tuning of graphene is reported. Highly reactive fluorine radicals were added to confined regions of graphene directed by laser writing on graphene coated with 1-fluoro-3,3-dimethylbenziodoxole. This process allows for the realization of exquisite patterns on graphene with resolutions down to 200 nm. The degree of functionalization, ranging from the unfunctionalized graphene to extremely high functionalized graphene, can be precisely tuned by controlling the laser irradiation time. Subsequent substitution of the initially patterned fluorine atoms afforded an unprecedented graphene nanostructure bearing thiophene groups. This substitution led to a complete switch of both the electronic structure and the polarization within the patterned graphene regions. This approach paves the way towards the precise modulation of the structure and properties of nanostructured graphene.     

Interpretation of nuclear resonant vibrational spectra of rubredoxin using a combined quantum mechanics and molecular mechanics approach

Nuclear resonant vibrational spectra of the reduced and oxidized form of a mutant of rubredoxin from Pyrococcus abyssii were measured and are compared with simulated spectra that were calculated by a combined quantum mechanics (QM) and molecular mechanics (MM) method. Density functional theory was used for the QM level. Calculations were performed for different models of rubredoxin. Realistic spectra were simulated with reduced models that include at least the iron center, the four cysteins coordinating it, and the residues connected to the cysteins together with a QM layer that comprises the first two coordination shells of the iron center. Larger QM layers did not lead to significant changes of the simulated spectra.     

Mechanically activated rupture of single covalent bonds: evidence of force induced bond hydrolysis

We have used temperature-dependent single molecule force spectroscopy to stretch covalently anchored carboxymethylated amylose (CMA) polymers attached to an amino-functionalized AFM cantilever. Using an Arrhenius kinetics model based on a Morse potential as a one-dimensional representation of covalent bonds, we have extracted kinetic and structural parameters of the bond rupture process. With 35.5 kJ mol(-1), we found a significantly smaller dissociation energy and with 9.0 × 10(2) s(-1) to 3.6 × 10(3) s(-1) also smaller Arrhenius pre-factors than expected for homolytic bond scission. One possible explanation for the severely reduced dissociation energy and Arrhenius pre-factors is the mechanically activated hydrolysis of covalent bonds. Both the carboxylic acid amide and the siloxane bond in the amino-silane surface linker are in principle prone to bond hydrolysis. Scattering, slope and curvature of the scattered data plots indicate that in fact two competing rupture mechanisms are observed.     

Exonucleolytic degradation of high-density labeled DNA studied by fluorescence correlation spectroscopy

The exonucleolytic degradation of high-density labeled DNA by exonuclease III was monitored using two-color fluorescence correlation spectroscopy (FCS). One strand of the double stranded template DNA was labeled on either one or two base types and additionally at one end via a 5' Cy5 tagged primer. Exonucleolytic degradation was followed via the diffusion time, the brightness of the remaining DNA as well as the concentration of released labeled bases. We found a hydrolyzation rate of about 11 to 17 nucleotides per minute per enzyme (nt/min/enzyme) for high-density labeled DNA, which is by a factor of about 4 slower than for unlabeled DNA. The exonucleolytic degradation of a 488 base pair long double stranded DNA resulted in a short double stranded DNA segment of 112 ± 40 base pairs (bp) length with two single-stranded tails.     

Magnetic fullerenes inside single-wall carbon nanotubes

C(59)N magnetic fullerenes were formed inside single-wall carbon nanotubes by vacuum annealing functionalized C(59)N molecules encapsulated inside the tubes. A hindered, anisotropic rotation of C(59)N was deduced from the temperature dependence of the electron spin resonance spectra near room temperature. Shortening of the spin-lattice relaxation time T(1) of C(59)N indicates a reversible charge transfer toward the host nanotubes above approximately 350 K. Bound C(59)N-C(60) heterodimers are formed at lower temperatures when C(60) is coencapsulated with the functionalized C(59)N. In the 10-300 K range, T(1) of the heterodimer shows a relaxation dominated by the conduction electrons on the nanotubes.