Chaotic Maps, Control Parameter, and Liapunov Exponent

We describe a one-dimensional chaotic map wherethe Liapunov exponent is a smooth function of a controlparameter.     

Aquachlorobis(4,4′,4′′‐tri‐tert‐butyl‐2,2′;6′,2′′‐terpyridine‐κ3N)terbium(III) diperchlorate ethanol disolvate

In the title compound, [TbCl(C₂₇H₃₅N₃)₂(H₂O)](ClO₄)₂·2C₂H₆O, the Tb^III ion has a coordination number of eight, composed of two tridentate substituted‐ter­pyridine ligands, a water mol­ecule and a bound Cl^? anion. The first coordination shell can be described as a distorted bicapped trigonal prism. The dihedral angles between pyridine rings belonging to the same tpy ligand range from 5.2 (5) to 16.8 (5)°.     

Anodic stripping coulometry at a thin-film mercury electrode

Primary coulometric versions of d.c. anodic stripping voltammetry, performed in a microcell at a mercury-plated rotating glassy carbon electrode, are applied to the determination of cadmium and lead. With exhaustive preelectrolysis of the sample solution, 5–100 ng of the metal can be determined from the charge contained in the stripping signal; precision and accuracy are in the 5% range. An extrapolation procedure that requires only partial metal deposition is evaluated.     

Sequential superparamagnetic clustering for unbiased classification of high-dimensional chemical data

For the clustering of chemical structures that are described by the Similog, ISIS count, and ISIS binary fingerprints, we propose a sequential superparamagnetic clustering approach. To appropriately handle nonbinary feature keys, we introduce an extension of the binary Tanimoto similarity measure. In our applications, data sets composed of structures from seven chemically distinct compound classes are evaluated and correctly clustered. The comparison, with results from leading methods, indicates the superiority of our sequential superparamagnetic clustering approach.     

Fully Entangled Quantum States in C^{N^2 } and Bell Measurement

Entangled quantum states are an important component of quantum computing techniques such as quantum error-correction, dense coding, and quantum teleportation. We describe how to generate fully entangled states in the Hilbert space C ^N C ^N starting from a unitary matrix and show that they form an orthonormal basis in this space.     

Phase transitions in experimental systems

Scaling functions of the support and of the measure have been used to characterize the scaling behavior of a dynamical system. While scaling functions for the scaling of the measure, ƒ(), have been calculated for a number of experimental systems, examples of scaling functions φ(λ) for the scaling of the support are difficult to obtain. In this contribution, we report on a phase-transition-like effect of an experimental p-doped germanium semiconductor sample. It is found that the results obtained from the dynamical scaling function agree with those obtained by Horita et al. from model maps, indicating that scaling functions for the scaling of the support are a powerful method of characterizing experimental dynamical systems.     

Renormalization Approach to Optimal Limiter Control in 1-D Chaotic Systems

Optimal limiter control of chaos in 1-d systems is described by flat-topped maps. When we study the properties of this control by a bifurcation analysis of the latter, we find partial universal behavior. The optimality of the control method is expressed by an exponentially fast control onto selected periodic orbits, making targeting algorithms idle.     

Conjugative Stabilization in an “Antiaromatic” System: The Conformational Mobility of 1,5-Bisdehydro[12]annulene

The isodynamical interconversion between the quasiplanar equilibrium conformers 1b and 1c of 1,5-bisdehydro[12]annulene requires a free energy of activation ΔG^# = 4.5 ± 0.2 kcal/mol (120 K) which was determined by line shape analysis of its temperature-dependent NMR. spectrum. Force field calculations indicate that this barrier reflects the energy needed to disrupt the cyclic π-conjugation in going to the nonplanar transition state 1a .     

Carbon−Fluorine Bond Formation via a Five-Coordinate Fluoro Complex of Ruthenium(II), Preliminary Communication

The 16-electron, five-coordinate fluoro complex [RuF(dppp)₂]PF₆ ( 1a ; dppp=propane-1,3-diylbis[diphenylphosphine] smoothly reacts with 1,3-diphenylallyl bromide (=1,1′-(3-bromoprop-1-ene-1,3-diyl)bis[benzene]) in dry CDCl₃ to give 1,3-diphenylallyl fluoride and [RuBr(dppp)₂]⁺ in nearly quantitative yield. Under similar conditions, bromide (or chloride)/fluoride exchange also occurs with chlorotriphenylmethane, bromodiphenylmethane, and tert-butyl bromide. The crystal structure of 1a is reported.     

The Evolving Contribution of Mass Spectrometry to Integrative Structural Biology

Protein complexes are key catalysts and regulators for the majority of cellular processes. Unveiling their assembly and structure is essential to understanding their function and mechanism of action. Although conventional structural techniques such as X-ray crystallography and NMR have solved the structure of important protein complexes, they cannot consistently deal with dynamic and heterogeneous assemblies, limiting their applications to small scale experiments. A novel methodological paradigm, integrative structural biology, aims at overcoming such limitations by combining complementary data sources into a comprehensive structural model. Recent applications have shown that a range of mass spectrometry (MS) techniques are able to generate interaction and spatial restraints (cross-linking MS) information on native complexes or to study the stoichiometry and connectivity of entire assemblies (native MS) rapidly, reliably, and from small amounts of substrate. Although these techniques by themselves do not solve structures, they do provide invaluable structural information and are thus ideally suited to contribute to integrative modeling efforts. The group of Brian Chait has made seminal contributions in the use of mass spectrometric techniques to study protein complexes. In this perspective, we honor the contributions of the Chait group and discuss concepts and milestones of integrative structural biology. We also review recent examples of integration of structural MS techniques with an emphasis on cross-linking MS. We then speculate on future MS applications that would unravel the dynamic nature of protein complexes upon diverse cellular states.

Open image in new window

Graphical Abstract ?