Metal germylyne complexes [Mtbd1;Ge-R] and metallogermylenes [M-Ge-R]: DFT analysis of the systems [(Cp)(CO)(n)()Mtbd1;GeMe] (M = Cr,Mo, W,Fe(2+), n = 2; M = Fe,n = 1) and [(Cp)(CO)(n)()M-GeMe] (M = Cr,Mo, W,n = 3; M = Fe,n = 2)

Quantum chemical calculations at the gradient corrected DFT level using the exchange correlation functionals BP86 and B3LYP of the geometries of the title compounds are reported. The theoretically predicted bond lengths and angles of the model compounds are in excellent agreement with experiment. The nature of the metal-ligand interactions is quantitatively analyzed with an energy decomposition method. The analysis of the electronic structure of the neutral metal germylyne complexes Ia-Id and the metallogermylenes IIa-IId shows that the former compounds have about the same degree of electrostatic and covalent bonding, while the relative strength of the covalent contributions in the latter molecules is lower (41-42%) than the electrostatic attraction (58-59%). The a' '(pi) bonding contribution in the group-6 germylyne complexes Ia-Ic is rather high (42% of the orbital interactions). In the iron complex Id, it is even higher (53.8%) than the sigma bonding. The pi bonding contributions to the covalent bonding become much less (18-20%) in the metallogermylenes IIa-IId.     

Packed to the Rafters: Filling up C60 with Rare Gas Atoms

How many rare gas atoms can be placed into a fullerene cage until the pressure becomes large enough to break the C₆₀ framework? The answer given by density functional and ab initio computations is surprising and underlines the high stability of this unique carbon structure.     

Suitable reference genes for relative quantification of miRNA expression in prostate cancer

Real time quantitative PCR (qPCR) is the method of choice for miRNA expression studies. For relative quantification of miRNAs, normalization to proper reference genes is mandatory. Currently, no validated reference genes for miRNA qPCR in prostate cancer are available. In this study, the expression of four putative reference genes (hsa-miR-16, hsa-miR-130b, RNU6-2, SNORD7) was examined with regard to their use as normalizer. After SNORD7 was already shown an inappropriate reference gene in preliminary experiments using total RNA pools, we studied the expression of the putative reference genes in tissue and normal adjacent tissue sample pairs from 76 men with untreated prostate carcinoma collected after radical prostatectomy. hsa-miR-130b and RNU6-2 showed no significantly different expression between the matched malignant and non-malignant tissue samples, whereas hsa-miR-16 was significantly underexpressed in malignant tissue. Softwares geNorm and Normfinder predicted hsa- miR-130b and the geometric mean of hsa-miR-130b and RNU6-2 as the most stable reference genes. Normalization of the four miRNAs hsa-miR-96, hsa- miR-125b, hsa-miR-205, and hsa-miR-375, which were previously shown to be regulated, shows that normalization to hsa-mir-16 can lead to biased results. We recommend using hsa-miR-130b or the geometric mean of hsa-miR-130b and small RNA RNU6-2 for normalization in miRNA expression studies of prostate cancer.     

Detection and identification of cheaters in (<Emphasis Type="Italic">t</Emphasis>, <Emphasis Type="Italic">n</Emphasis>) secret sharing scheme

In a (t, n) secret sharing scheme, a secret s is divided into n shares and shared among a set of n shareholders by a mutually trusted dealer in such a way that any t or more than t shares will be able to reconstruct this secret; but fewer than t shares cannot know any information about the secret. When shareholders present their shares in the secret reconstruction phase, dishonest shareholder(s) (i.e. cheater(s)) can always exclusively derive the secret by presenting faked share(s) and thus the other honest shareholders get nothing but a faked secret. Cheater detection and identification are very important to achieve fair reconstruction of a secret. In this paper, we consider the situation that there are more than t shareholders participated in the secret reconstruction. Since there are more than t shares (i.e. it only requires t shares) for reconstructing the secret, the redundant shares can be used for cheater detection and identification. Our proposed scheme uses the shares generated by the dealer to reconstruct the secret and, at the same time, to detect and identify cheaters. We have included discussion on three attacks of cheaters and bounds of detectability and identifiability of our proposed scheme under these three attacks. Our proposed scheme is an extension of Shamir’s secret sharing scheme.      

On the role of symmetries in the theory of photonic crystals

We discuss the role of the symmetries in photonic crystals and classify them according to the Cartan–Altland–Zirnbauer scheme. Of particular importance are complex conjugation C$C$ and time-reversal T$T$, but we identify also other significant symmetries. Borrowing the jargon of the classification theory of topological insulators, we show that C$C$ is a “particle–hole-type symmetry” rather than a “time-reversal symmetry” if one considers the Maxwell operator in the first-order formalism where the dynamical Maxwell equations can be rewritten as a Schrödinger equation; The symmetry which implements physical time-reversal is a “chiral-type symmetry”. We justify by an analysis of the band structure why the first-order formalism seems to be more advantageous than the second-order formalism. Moreover, based on the Schrödinger formalism, we introduce a class of effective (tight-binding) models called Maxwell–Harper operators. Some considerations about the breaking of the “particle–hole-type symmetry” in the case of gyrotropic crystals are added at the end of this paper.     

Effective Light Dynamics in Perturbed Photonic Crystals

In this work, we rigorously derive effective dynamics for light from within a limited frequency range propagating in a photonic crystal that is modulated on the macroscopic level; the perturbation parameter \({\lambda \ll 1}\) quantifies the separation of spatial scales.We do that by rewriting the dynamical Maxwell equations as a Schrödinger-type equation and adapting space-adiabatic perturbation theory. Just like in the case of the Bloch electron, we obtain a simpler, effective Maxwell operator for states from within a relevant almost invariant subspace. A correct physical interpretation for the effective dynamics requires establishing two additional facts about the almost invariant subspace: (1) The source-free condition has to be verified and (2) it has to support real states. The second point also forces one to consider a multiband problem even in the simplest possible setting; This turns out to be a major difficulty for the extension of semiclassical methods to the domain of photonic crystals.