Decomposition theorem on matchable distributive lattices

A distributive lattice structure ${\mathbf M}(G)$ has been established on the set of perfect matchings of a plane bipartite graph $G$. We call a lattice {\em matchable distributive lattice} (simply MDL) if it is isomorphic to such a distributive lattice. It is natural to ask which lattices are MDLs. We show that if a plane bipartite graph $G$ is elementary, then ${\mathbf M}(G)$ is irreducible. Based on this result, a decomposition theorem on MDLs is obtained: a finite distributive lattice $\mathbf{L}$ is an MDL if and only if each factor in any cartesian product decomposition of $\mathbf{L}$ is an MDL. Two types of MDLs are presented: $J(\mathbf{m}\times \mathbf{n})$ and $J(\mathbf{T})$, where $\mathbf{m}\times \mathbf{n}$ denotes the cartesian product between $m$-element chain and $n$-element chain, and $\mathbf{T}$ is a poset implied by any orientation of a tree.Comment: 19 pages, 7 figure

Carbon--The First Frontier of Information Processing

Information is often encoded as an aperiodic chain of building blocks. Modern digital computers use bits as the building blocks, but in general the choice of building blocks depends on the nature of the information to be encoded. What are the optimal building blocks to encode structural information? This can be analysed by substituting the operations of addition and multiplication of conventional arithmetic with translation and rotation. It is argued that at the molecular level, the best component for encoding discretised structural information is carbon. Living organisms discovered this billions of years ago, and used carbon as the back-bone for constructing proteins that function according to their structure. Structural analysis of polypeptide chains shows that an efficient and versatile structural language of 20 building blocks is needed to implement all the tasks carried out by proteins. Properties of amino acids indicate that the present triplet genetic code was preceded by a more primitive one, coding for 10 amino acids using two nucleotide bases.Comment: (v1) 9 pages, revtex. (v2) 10 pages. Several arguments expanded to make the article self-contained and to increase clarity. Applications pointed out. (v3) 11 pages. Published version. Well-known properties of proteins shifted to an appendix. Reformatted according to journal styl

Competing itinerant and localized states in strongly correlated BaVS3_3

The electronic structure of the quasi-lowdimensional vanadium sulfide \bavs3 is investigated for the different phases above the magnetic ordering temperature. By means of density functional theory and its combination with dynamical-mean field theory, we follow the evolution of the relevant low-energy electronic states on cooling. Hence we go in the metallic regime from the room temperature hexagonal phase to the orthorhombic phase after the first structural transition, and close with the monoclinic insulating phase below the metal-insulator transition. Due to the low symmetry and expected intersite correlations, the latter phase is treated within cellular dynamical mean-field theory. It is generally discussed how the intriguing interplay between band-structure and strong-correlation effects leads to the stabilization of the various electronic phases with decreasing temperature.Comment: 12 pages, submitted to PR

Influence of Ibuprofen on Phospholipid Membranes

Basic understanding of biological membranes is of paramount importance as these membranes comprise the very building blocks of life itself. Cells depend in their function on a range of properties of the membrane, which are important for the stability and function of the cell, information and nutrient transport, waste disposal and finally the admission of drugs into the cell and also the deflection of bacteria and viruses. We have investigated the influence of ibuprofen on the structure and dynamics of L-alpha-phosphatidylcholine (SoyPC) membranes by means of grazing incidence small-angle neutron scattering (GISANS), neutron reflectometry and grazing incidence neutron spin echo spectroscopy (GINSES). From the results of these experiments we were able to determine that ibuprofen induces a two-step structuring behavior in the SoyPC films, where the structure evolves from the purely lamellar phase for pure SoyPC over a superposition of two hexagonal phases to a purely hexago- nal phase at high concentrations. Additionally, introduction of ibuprofen stiffens the membranes. This behavior may be instrumental in explaining the toxic behavior of ibuprofen in long-term application.Comment: -Improved indexing in Fig. 4e) -changed concentrations to mol% -improved arguments, however conclusions stay unchange