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.     

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.     

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.     

Alkaline-Earth Metal Mediated Benzene-to-Biphenyl Coupling

Complex [(^DIPePBDI)Ca]₂(C₆H₆), with a C₆H₆²⁻ dianion bridging two Ca²⁺ ions, reacts with benzene to yield [(^DIPePBDI)Ca]₂(biphenyl) with a bridging biphenyl²⁻ dianion (^DIPePBDI=HC[C(Me)N-DIPeP]₂; DIPeP=2,6-CH(Et)₂-phenyl). The biphenyl complex was also prepared by reacting [(^DIPePBDI)Ca]₂(C₆H₆) with biphenyl or by reduction of [(^DIPePBDI)CaI]₂ with KC₈ in presence of biphenyl. Benzene-benzene coupling was also observed when the deep purple product of ball-milling [(^DIPPBDI)CaI(THF)]₂ with K/KI was extracted with benzene (DIPP=2,6-CH(Me)₂-phenyl) giving crystalline [(^DIPPBDI)Ca(THF)]₂(biphenyl) (52 % yield). Reduction of [(^DIPePBDI)SrI]₂ with KC₈ gave highly labile [(^DIPePBDI)Sr]₂(C₆H₆) as a black powder (61 % yield) which reacts rapidly and selectively with benzene to [(^DIPePBDI)Sr]₂(biphenyl). DFT calculations show that the most likely route for biphenyl formation is a pathway in which the C₆H₆²⁻ dianion attacks neutral benzene. This is facilitated by metal-benzene coordination.     

Synthesis of aryliminoacetonitriles under FVT conditions or by dehydrogenation of arylaminoacetonitriles: an NMR and UV-photoelectron spectroscopy study

The synthesis of [(E)-arylimino]-acetonitriles 3 has been described. It was found that the title compounds can be obtained on the three ways, namely by: (i) dehydrogenation of arylaminoacetonitriles 1, (ii) thermal fragmentation of 1-aryl-4-cyano-β-lactams 4 and (iii) retro-ene reaction of (allyl-p-methoxyphenyl-amino)-acetonitrile (7a) under FVT conditions. ¹H and ¹³C NMR spectra of compounds 3, 5 and 6, and all their precursors 1 and 4, were recorded and analysed in detail using chemical shifts δ_H and δ_C [from GIAO DFT B3LYP/6-31(d) calculations] and J-couplings predicted at the DFT B3LYP/IGLO-II level. Also, UV-photoelectron spectra of 4a,d and 3a,d were measured and analysed considering the theoretical evaluation of their ionisation potentials.     

Delimiting the Unconceived

It has been argued in Dawid (String theory and the scientific method, Cambridge University Press, Cambridge, [4]) that physicists at times generate substantial trust in an empirically unconfirmed theory based on observations that lie beyond the theory’s intended domain. A crucial role in the reconstruction of this argument of “non-empirical confirmation” is played by limitations to scientific underdetermination. The present paper discusses the question as to how generic the role of limitations to scientific underdetermination really is. It is argued that assessing such limitations is essential for generating trust in any theory’s predictions, be it empirically confirmed or not. The emerging view suggests that empirical and non-empirical confirmation are more closely related to each other than one may expect at first glance.