Decomposition and Bayesian analysis of invariant normal linear models

Using the theory of linear group representations, we analyse the normal linear model with known sampling covariance structure invariant under a symmetry group, and sampling mean structure equivariant under the same group. In particular, assuming an invariant normal prior distribution on the parameter space, the problem of Bayesian inference is shown to decompose naturally into several independent subproblems. Within any such subproblem, if additional irreducibility conditions hold, it is shown that the posterior expectation of any parameter is a fixed scalar multiple of its unique unbiased estimator, and similarly the posterior covariance of any two parameters is a fixed scalar multiple of the prior covariance. The theoretical framework is illustrated with reference to experimental designs.     

Dynamical and structural properties of titanium-decorated fullerene: A computer simulation study

We have investigated a material made of C₆₀Ti₆H₁₂ molecules using the classical molecular dynamic simulation. The system was studied in a wide range of temperatures, from solid to fluid. Several physical characteristics of endohedral fullerene were calculated for various temperatures: the mean square displacement, the translational and angular velocity autocorrelation function, the translational diffusion coefficient and the Lindemann index. We have observed a reduction in the rotational freedom of fullerene decorated with TiH₂ functionality groups in comparison with the pure fullerene sample.     

Extendibility of spherical matrix distributions

We investigate the structure of distributions for matrices which can be embedded in arbitrarily large matrices whose distributions have properties of invariance under orthogonal rotations.     

Extrem aufgeweitete Tetrathiafulvalene mit Polyen-Spacern. Carotinoide Tetrathiafulvalene. Polymethin-tetracyanotetrathiafulvalen-Radikalkationen,eine neue Klasse von Violenen

Extremely Expanded Tetrathiafulvalenes with Polyene Spacers. Carotinoid Tetrathiafulvalenes. Polymethin-Tetracyanotetrathiafulvalene Radical Cations, a New Class of Violenes The synthesis of extended tetrathiafulvalenes 11 with di-, tetra-, hexa-, octa-, deca- and dodecamethine spacers is described by a PPh₃-induced Wittig-reaction-like condensation of the corresponding polyenedials 10 with 2-thio-1,3-dithiole-4,5-dicarbonitrile ( 9 ). By the same procedure, the dimethyloctamethine- and the tetramethyl-hexadecamethine-tetrathiafulvalenes 14 and 15 , respectively, were obtained. The extended tetrathiafulvalenes represent multistep vinylogous redox systems of the ‘violene type’. They can be oxidized to give the cyanine-like radical cations, e.g. 11 _sem, 14 _sem, and 15 _sem, and the dications, e.g. 11 _ox, 14 _ox, and 15 _ox; their UV/VIS/NIR spectra are reported. The crystal and molecular structure of (all-E)-2,2′-(octa-2,4,6-trien-1,8-diylidene)bis[1,3-dithiole-4,5-dicarbonitrile] ( 11e ) was determined: it is a rod-like, planar molecule; in the crystal, it forms staples along the longest molecule axis. The CV measurements confirm that the redox potentials of 11, 14 , and 15 decrease asymptotically with the increasing length of the spacer. Because of the close relationship of the extended tetrathiafulvalenes (ETTF's) to the carotinoids, they are named ‘caroviologenes’; they formally belong to the class of molecular wires.     

Mechanically controlled DNA extrusion from a palindromic sequence by single molecule micromanipulation

A magnetic tweezers setup is used to control both the stretching force and the relative linking number DeltaLk of a palindromic DNA molecule. We show here, in absence of divalent ions, that twisting negatively the molecule while stretching it at approximately 1 pN induces the formation of a cruciform DNA structure. Furthermore, once the cruciform DNA structure is formed, the extrusion of several kilo-base pairs of palindromic DNA sequence is directly and reversibly controlled by varying DeltaLk. Indeed the branch point behaves as a nanomechanical gear that links rotation with translation, a feature related to the helicity of DNA. We obtain experimentally a very good linear relationship between the extension of the molecule and DeltaLk. We use then this experiment to obtain a precise measurement of the pitch of B-DNA in solution: 3.61 +/- 0.03 nm/turn.     

Electrocatalytic Carbon Dioxide Reduction by Using Cationic Pentamethylcyclopentadienyl–Iridium Complexes with Unsymmetrically Substituted Bipyridine Ligands

Eight [Ir(bpy)Cp*Cl]⁺‐type complexes (bpy= bipyridine, Cp*=1,2,3,4,5‐pentamethylcyclopentadienyl) containing differently substituted bipyridine ligands were synthesized and characterized. Cyclic voltammetry (CV) of the complexes in Ar‐saturated acetonitrile solutions showed that the redox behavior of the complexes could be fine tuned by the electronic properties of the substituted bipyridine ligands. Further CV in CO₂‐saturated MeCN/H₂O (9:1, v/v) solutions showed catalytic currents for CO₂ reduction. In controlled potential electrolysis experiments (MeCN/MeOH (1:1, v/v), E_app=?1.80 V vs Ag/AgCl), all of the complexes showed moderate activity in the electrocatalytic reduction of CO₂ with good stability over at least 15 hours. This electrocatalytic process was selective toward formic acid, with only traces of dihydrogen or carbon monoxide and occasionally formaldehyde as byproducts. However, the turnover frequencies and current efficiencies were quite low. No direct correlation between the redox potentials of the complexes and their catalytic activity was observed.     

Photoinduced Mo−CN Bond Breakage in Octacyanomolybdate Leading to Spin Triplet Trapping

The photoinduced properties of the octacoordinated complex K₄Mo^IV(CN)₈⋅2 H₂O were studied by theoretical calculations, crystallography, and optical and magnetic measurements. The crystal structure recorded at 10 K after blue light irradiation reveals an heptacoordinated Mo(CN)₇ species originating from the light-induced cleavage of one Mo−CN bond, concomitant with the photoinduced formation of a paramagnetic signal. When this complex is heated to 70 K, it returns to its original diamagnetic ground state, demonstrating full reversibility. The photomagnetic properties show a partial conversion into a triplet state possessing significant magnetic anisotropy, which is in agreement with theoretical studies. Inspired by these results, we isolated the new compound [K(crypt-222)]₃[Mo^IV(CN)₇]⋅3 CH₃CN using a photochemical pathway, confirming that photodissociation leads to a stable heptacyanomolybdate(IV) species in solution.