Edge partitions of optimal 2-plane and 3-plane graphs

A topological graph is a graph drawn in the plane. A topological graph is $k$-plane, $k>0$, if each edge is crossed at most $k$ times. We study the problem of partitioning the edges of a $k$-plane graph such that each partite set forms a graph with a simpler structure. While this problem has been studied for $k=1$, we focus on optimal 2-plane and on optimal 3-plane graphs, which are 2-plane and 3-plane graphs with maximum density. We prove the following results. (i) It is not possible to partition the edges of a simple (i.e., with neither self-loops nor parallel edges) optimal 2-plane graph into a 1-plane graph and a forest, while (ii) an edge partition formed by a 1-plane graph and two plane forests always exists and can be computed in linear time. (iii) There exist efficient algorithms to partition the edges of a simple optimal 2-plane graph into a 1-plane graph and a plane graph with maximum vertex degree at most 12, or with maximum vertex degree at most 8 if the optimal2-plane graph is such that its crossing-free edges form a graph with no separating triangles. (iv) There exists an infinite family of simple optimal 2-plane graphs such that in any edge partition composed of a 1-plane graph and a plane graph, the plane graph has maximum vertex degree at least 6 and the 1-plane graph has maximum vertex degree at least 12. (v) Every optimal 3-plane graph whose crossing-free edges form a biconnected graph can be decomposed, in linear time, into a 2-plane graph and two plane forests.     

Understanding how Lewis acids dope organic semiconductors: a “complex” story

We report on computational studies of the potential of three borane Lewis acids (LAs) (B(C₆F₅)₃ (BCF), BF₃, and BBr₃) to form stable adducts and/or to generate positive polarons with three different semiconducting π-conjugated polymers (PFPT, PCPDTPT and PCPDTBT). Density functional theory (DFT) and time-dependent DFT (TD-DFT) calculations based on range-separated hybrid (RSH) functionals provide insight into changes in the electronic structure and optical properties upon adduct formation between LAs and the two polymers containing pyridine moieties, PFPT and PCPDTPT, unravelling the complex interplay between partial hybridization, charge transfer and changes in the polymer backbone conformation. We then assess the potential of BCF to induce p-doping in PCPDTBT, which does not contain pyridine groups, by computing the energetics of various reaction mechanisms proposed in the literature. We find that reaction of BCF(OH₂) to form protonated PCPDTBT and [BCF(OH)]⁻, followed by electron transfer from a pristine to a protonated PCPDTBT chain is highly endergonic, and thus unlikely at low doping concentration. The theoretical and experimental data can, however, be reconciled if one considers the formation of [BCF(OH)BCF]⁻ or [BCF(OH)(OH₂)BCF]⁻ counterions rather than [BCF(OH)]⁻ and invokes subsequent reactions resulting in the elimination of H₂.

Here we report on DFT calculations investigating the mechanistic aspects in doping organic semiconductors by the use of Lewis acids. Our results highlight the role played by the formation of diboron-containing bridged anions in the doping mechanism.     

Crystalline Quality Evaluation of Carbon Nanotubes by Kinetic Analysis in Quasi‐Isothermal Conditions

We demonstrate that the crystalline quality of multi‐walled carbon nanotubes (MWCNTs) is better estimated by the apparent activation energy of the oxidation reaction, obtained by kinetic analysis in quasi‐isothermal conditions, than by the peak‐temperature position in the derivative mass loss curves. This is proven by the existence of a good correlation, reported for the first time herein, between apparent activation energy and G′‐band to D‐band intensity ratio derived from micro‐Raman spectroscopy, which is largely accepted as an indicator of the overall MWCNT crystalline quality. In contrast, no clear reliance is found between G′/D intensity ratio and the peak‐temperature position in the derivative mass loss curves. These conclusions were drawn after investigation of a large number of commercially available and laboratory prepared MWCNTs.     

Multiple Proton Confinement in the M2 Channel from the Influenza A Virus

The tetrameric M2 protein bundle of the influenza A virus is the proton channel responsible for the acidification of the viral interior, a key step in the infection cycle. Selective proton transport is achieved by successive protonation of the conserved histidine amino acids at position 37. A recent X-ray structure of the tetrameric transmembrane (TM) domain of the protein (residues 22-46) resolved several water clusters in the channel lumen, which suggest possible proton pathways to the His37 residues. To explore this hypothesis, we have carried out molecular dynamics (MD) simulations of a proton traveling towards the His37 side chains using MD with classical and quantum force fields. Diffusion through the first half of the channel to the "entry" water cluster near His37 may be hampered by significant kinetic barriers due to electrostatic repulsion. However, once in the entry cluster, a proton can move to one of the acceptor His37 in a nearly barrierless fashion, as evidenced both by MD simulations and a scan of the potential energy surface (PES). Water molecules of the entry cluster, although confined in the M2 pore and restricted in their motions, can conduct protons with a rate very similar to that of bulk water.     

Novel stereoselective syntheses of (2E,4E)-4-(4,4-dimethylpent-2-ynylidene)-N1,N5-dimethyl-N1,N5-bis(naphthalen-1-ylmethyl)pent-2-ene-1,5-diamine

We report two different synthetic approaches for the stereoselective synthesis of (2E,4E)-4-(4,4-dimethylpent-2-ynylidene)-N¹,N⁵-dimethyl-N¹,N⁵-bis(naphthalen-1-ylmethyl)pent-2-ene-1,5-diamine 1, an important impurity-reference standard for the chemical characterization of terbinafine. The diamine 1 was obtained in only six steps with a good overall yield starting from commercially available glutaconic acid.     

A Neutronics Study of the 1945 Haigerloch B-VIII Nuclear Reactor

We present a neutronics study of the German B-VIII nuclear reactor, which was built in Haigerloch, Germany, between February and April 1945. We used the Monte Carlo code MCNP5 to estimate its effective nuclear-multiplication constant k_eff and its corresponding neutron-multiplication factor M, its neutron energy-distribution spectrum, and its neutron-flux distribution in its central horizontal and veritical planes for both thermal and fast neutrons. Our calculations agree well with the known measurements the German scientists made, who determined M to be 6.7. We also found that the effect on k_eff of impurities in the graphite of its neutron reflector could have been only on the order of few hundredths of a percent.     

Bioinspired,Size‐Tunable Self‐Assembly of Polymer–Lipid Bilayer Nanodiscs

Polymer‐based nanodiscs are valuable tools in biomedical research that can offer a detergent‐free solubilization of membrane proteins maintaining their native lipid environment. Herein, we introduce a novel ca. 1.6 kDa SMA‐based polymer with styrene:maleic acid moieties that can form nanodiscs containing a planar lipid bilayer which are useful to reconstitute membrane proteins for structural and functional studies. The physicochemical properties and the mechanism of formation of polymer‐based nanodiscs are characterized by light scattering, NMR, FT‐IR, and TEM. A remarkable feature is that nanodiscs of different sizes, from nanometer to sub‐micrometer diameter, can be produced by varying the lipid‐to‐polymer ratio. The small‐size nanodiscs (up to ca. 30 nm diameter) can be used for solution NMR spectroscopy studies whereas the magnetic‐alignment of macro‐nanodiscs (diameter of > ca. 40 nm) can be exploited for solid‐state NMR studies on membrane proteins.