A normal form for excitable media

We present a normal form for traveling waves in one-dimensional excitable media in the form of a differential delay equation. The normal form is built around the well-known saddle-node bifurcation generically present in excitable media. Finite wavelength effects are captured by a delay. The normal form describes the behavior of single pulses in a periodic domain and also the richer behavior of wave trains. The normal form exhibits a symmetry preserving Hopf bifurcation which may coalesce with the saddle node in a Bogdanov-Takens point, and a symmetry-breaking spatially inhomogeneous pitchfork bifurcation. We verify the existence of these bifurcations in numerical simulations. The parameters of the normal form are determined and its predictions are tested against numerical simulations of partial differential equation models of excitable media with good agreement.     

Oligonucleotide Analogues with Integrated Bases and Backbone. Part 30

The protected G*[s ]C*[s ]U*[s ]A*[s ]U*[s ]A*[s ]G*[s ]C* octanucleoside 24 was prepared by S‐alkylation of the thiolate derived from tetranucleoside 23 with the methanesulfonate 22 , and transformed to the silylated and isopropylidenated 25 , and further into the fully deprotected octanucleoside 26 . Compound 22 was derived from the methoxytrityl‐protected tetranucleoside 21 , and 21 was obtained by S‐alkylation of the thiolate derived from the dinucleoside 19 with methanesulfonate 17 derived from 16 by detritylation and mesylation. Similarly, tetranucleoside 23 resulted from S‐alkylation of the thiolate derived from 18 with the methanesulfonate 20 derived from 19 . Dinucleosides 16 and 18 resulted from S‐alkylation of the thiolate derived from the known cytidine‐derived thioacetate 15 with the C(8)‐substituted guanosine‐derived methanesulfonates 12 and 14 , respectively, that were synthesized from the protected precursors 4 and 7 by formylation, reduction, protection, and mesylation. The structures of the duplexes of 25 and 26 were calculated using AMBER* modelling and based on the known structure of the core tetranucleoside U*[s ]A*[s ]U*[s ]A*. The former shows a helix with a bent helix axis and strong buckle and propeller twists, whereas the latter is a regular, right‐handed, and apparently strain‐free helix. In agreement with modelling, the silylated and isopropylidenated octanucleoside 25 in (CDCl₂)₂ solution led to a mixture of associated species possessing at most four Watson? Crick base pairs, while the fully deprotected octanucleoside 26 in aqueous medium forms a duplex, as evidenced by a decreasing CD absorption upon increasing the temperature and by a UV‐melting curve with a melting temperature of ca. 10° below the one of the corresponding RNA octamer, indicating cooperativity between base pairing and base‐pair stacking.     

Differential Geometric Aspects of Parametric Estimation Theory for States on Finite-Dimensional C∗-Algebras

A geometrical formulation of estimation theory for finite-dimensional C∗-algebras is presented. This formulation allows to deal with the classical and quantum case in a single, unifying mathematical framework. The derivation of the Cramer–Rao and Helstrom bounds for parametric statistical models with discrete and finite outcome spaces is presented.     

Valence band structure of cellulose and lignin studied by XPS and DFT

In this report, X-ray induced photoelectron spectroscopy (XPS) measurements of the valence band structure of cellulose and lignin are combined with a theoretical reconstruction of the spectra based on density functional theory (DFT) calculations. These calculations involve an analysis of the valence band structures and their respective orbitals in which basic units of cellulose and lignin are considered. In addition, photoionization cross sections are incorporated for reconstruction of the XPS spectra. This combination of theoretical calculations and experimental measurements revealed that an emission present up to 10 eV in the valence band structure is dominated by oxygen rather than by carbon, as reported in literature. Furthermore, a quantitative elemental analysis shows significant carbon contributions at binding energies above 13 eV. The valence band analysis supported by DFT provides a powerful basis for a detailed interpretation of spectroscopic data and enables a profound insight into application relevant processes in future.