An Ergodic Sampling Scheme for Constrained Hamiltonian Systems with Applications to Molecular Dynamics

This article addresses the problem of computing the Gibbs distribution of a Hamiltonian system that is subject to holonomic constraints. In doing so, we extend recent ideas of Cancès et al. (M2AN 41(2), 351–389, 2007) who could prove a Law of Large Numbers for unconstrained molecular systems with a separable Hamiltonian employing a discrete version of Hamilton’s principle. Studying ergodicity for constrained Hamiltonian systems, we specifically focus on the numerical discretization error: even if the continuous system is perfectly ergodic this property is typically not preserved by the numerical discretization. The discretization error is taken care of by means of a hybrid Monte-Carlo algorithm that allows for sampling bias-free expectation values with respect to the Gibbs measure independently of the (stable) step-size. We give a demonstration of the sampling algorithm by calculating the free energy profile of a small peptide.     

2-List-coloring planar graphs without monochromatic triangles

We prove that, for every list-assignment of two colors to every vertex of any planar graph, there is a list-coloring such that there is no monochromatic triangle. This proves and extends a conjecture of B. Mohar and R. ?krekovski and a related conjecture of A. Kündgen and R. Ramamurthi.     

Combination of molecular rods and half-discs: transition from lamellar to columnar order in multichain mononuclear ortho-palladated metallomesogens

Novel ortho-palladated phenylpyrimidine-1,3-diketonato organyls with successively increasing numbers of alkyl chains were synthesized and investigated by polarizing optical microscopy and X-ray diffraction. A discontinuous transition from a lamellar to a columnar organization is observed, dependent on the number of chains: molecules with four or five chains from smectic phases (SmA, SmC), the related compound with six chains in the molecule is nonmesomorphic, whereas molecules with seven or eight chains form hexagonal columnar mesophases.     

Axiomatic Quantum Mechanics and Completeness

The standard axiomatization of quantum mechanics (QM) is not fully explicit about the role of the time-parameter. Especially, the time reference within the probability algorithm (the Born Rule, BR) is unclear. From a probability principle P1 and a second principle P2 affording a most natural way to make BR precise, a logical conflict with the standard expression for the completeness of QM can be derived. Rejecting P1 is implausible. Rejecting P2 leads to unphysical results and to a conflict with a generalization of P2, a principle P3. All three principles are shown to be without alternative. It is thus shown that the standard expression of QM completeness must be revised. An absolutely explicit form of the axioms is provided, including a precise form of the projection postulate. An appropriate expression for QM completeness, reflecting the restrictions of the Gleason and Kochen-Specker theorems is proposed.     

Guanidiniocarbonylpyrrole–Aryl Derivatives: Structure Tuning for Spectrophotometric Recognition of Specific DNA and RNA Sequences and for Antiproliferative Activity

We present a systematic study of different guanidiniocarbonylpyrrole‐aryl derivatives designed to interact with DNA or RNA both through intercalation of an aromatic moiety into the base stack of the nucleotide and through groove binding of a guanidiniocarbonylpyrrole cation. We varied 1) the size of the aromatic ring (benzene, naphthalene, pyrene and acridine), 2) the length and flexibility of the linker connecting the two binding groups, and 3) the total number of positive charges present at different pH values. The compounds and their interactions with DNA and RNA were studied by UV/Vis, fluorescence and CD spectroscopy. Antiproliferative activities against human tumour cell lines were also determined. Our studies show that efficient interaction with, for example, DNA requires a significantly large aromatic ring (pyrene) connected through a flexible linker to the pyrrole moiety. However, a positive charge, as in 12 , is also needed. Compound 12 allows for base‐pair‐selective recognition of ds‐DNA at physiological pH values. The antiproliferative activities of these compounds correlate with their binding affinities towards DNA, suggesting that their biological effects are most probably due to DNA binding.