Networks that optimize a trade-off between efficiency and dynamical resilience

In this Letter we study networks that have been optimized to realize a trade-off between communication efficiency and dynamical resilience. While the first is related to the average shortest pathlength, we argue that the second can be measured by the largest eigenvalue of the adjacency matrix of the network. Best efficiency is realized in star-like configurations, while enhanced resilience is related to the avoidance of short loops and degree homogeneity. Thus crucially, very efficient networks are not resilient while very resilient networks lack in efficiency. Networks that realize a trade-off between both limiting cases exhibit core-periphery structures, where the average degree of core nodes decreases but core size increases as the weight is gradually shifted from a strong requirement for efficiency and limited resilience towards a smaller requirement for efficiency and a strong demand for resilience. We argue that both, efficiency and resilience are important requirements for network design and highlight how networks can be constructed that allow for both.     

On the Algebraic Index for Riemannian Étale Groupoids

In this paper, we construct an explicit quasi-isomorphism to study the cyclic cohomology of a deformation quantization over a Riemannian étale groupoid. Such a quasi-isomorphism allows us to propose a general algebraic index problem for Riemannian étale groupoids. We discuss solutions to that index problem when the groupoid is proper or defined by a constant Dirac structure on a 3-dimensional torus.     

Oligoporphyrin Arrays Conjugated to [60]Fullerene: Preparation,NMR Analysis,and Photophysical and Electrochemical Properties

We report the synthesis and physical properties of novel fullerene–oligoporphyrin dyads. In these systems, the C‐spheres are singly linked to the terminal tetrapyrrolic macrocycles of rod‐like meso,meso‐linked or triply‐linked oligoporphyrin arrays. Monofullerene–mono(Zn^II porphyrin) conjugate 3 was synthesized to establish a general protocol for the preparation of the target molecules (Scheme 1). The synthesis of the meso,meso‐linked oligopophyrin–bisfullerene conjugates 4 – 6 , extending in size up to 4.1 nm ( 6 ), was accomplished by functionalization (iodination followed by Suzuki cross‐coupling) of the two free meso‐positions in oligomers 21 – 23 (Schemes 2 and 3). The attractive interactions between a fullerene and a Zn^II porphyrin chromophore in these dyads was quantified as ΔG=−3.3 kcal mol⁻¹ by variable‐temperature (VT) ¹H‐NMR spectroscopy (Table 1). As a result of this interaction, the C‐spheres adopt a close tangential orientation relative to the plane of the adjacent porphyrin nucleus, as was unambiguously established by ¹H‐ and ¹³C‐NMR (Figs. 9 and 10), and UV/VIS spectroscopy (Figs. 13–15). The synthesis of triply‐linked diporphyrin–bis[60]fullerene conjugate 8 was accomplished by Bingel cyclopropanation of bis‐malonate 45 with two C₆₀ molecules (Scheme 5). Contrary to the meso,meso‐linked systems 4 – 6 , only a weak chromophoric interaction was observed for 8 by UV/VIS spectroscopy (Fig. 16 and Table 2), and the ¹H‐NMR spectra did not provide any evidence for distinct orientational preferences of the C‐spheres. Comprehensive steady‐state and time‐resolved UV/VIS absorption and emission studies demonstrated that the photophysical properties of 8 differ completely from those of 4 – 6 and the many other known porphyrin–fullerene dyads: photoexcitation of the methano[60]fullerene moieties results in quantitative sensitization of the lowest singlet level of the porphyrin tape, which is low‐lying and very short lived. The meso,meso‐linked oligoporphyrins exhibit ¹O₂ sensitization capability, whereas the triply‐fused systems are unable to sensitize the formation of ¹O₂ because of the low energy content of their lowest excited states (Fig. 18). Electrochemical investigations (Table 3, and Figs. 19 and 20) revealed that all oligoporphyrin arrays, with or without appended methano[60]fullerene moieties, have an exceptional multicharge storage capacity due to the large number of electrons that can be reversibly exchanged. Some of the Zn^II porphyrins prepared in this study form infinite, one‐dimensional supramolecular networks in the solid state, in which the macrocycles interact with each other either through H‐bonding or metal ion coordination (Figs. 6 and 7).     

Polygonal finite element formulations for 2d linear-elastic FE problems

Polygonal finite elements provide great flexibility meshing complex structures and for the refinement of meshes. The actual task in the development of these elements is to offer adequate and secure numerical results compared with regular finite elements at low computational costs. Particulary, finding an efficient and appropriate interpolation of the arbitrary element domain exhibits strong difficulties. Based on the general interpolant equation three element formulations are shown that use different interpolation strategies. The elements' performances are shown with a numerical example considering 2d linear elasticity. The results of the different element formulations are compared among each other, with analytical as well as with regular elements' results. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

(P,M)‐1,2,3,9,10,11‐Hexa­methoxy‐5,7‐di­hydro­dibenz­[c,e]­oxepine and (P,M)‐1,11‐di­methyl‐5,5,7,7‐tetra­phenyl‐5,7‐di­hydro­dibenz­[c,e]­oxepine

The title compounds, C₂₀H₂₄O₇ and C₄₀H₃₂O, respectively, are racemic oxepines, the mol­ecules of which contain a chiral axis. Both mol­ecules possess crystallographic C₂ symmetry and the seven‐membered ring adopts a twisted‐boat confor­mation.     

Application of MEKC and monolithic CEC for the analysis of bioactive naphthoquinones in Eleutherine americana

Two microscale separation techniques for the analysis of bioactive naphthoquinones in Eleutherine americana were developed and validated. By MEKC four compounds (eleuthoside B, isoeleutherin, eleutherol and eleutherinoside A) could be determined in plant extracts using an aqueous electrolyte solution composed of 25 mM sodium tetraborate, 50 mM sodium cholate and 20% THF. CEC on a polymeric methacrylate‐based monolith with strong cationic properties showed promising results, as it additionally enabled the separation of two enantiomers, eleutherin and isoeleutherin. The mobile phase for CEC experiments comprised 3 mM ammonium formate in a mixture of ACN and water. At an applied voltage of ?25 kV, all five markers were baseline separated in less than 12 min. Both methods were successfully validated for linearity (MEKC: R²≥0.999; CEC: R²≥0.997), sensitivity (MEKC: LOD=4–5 μg/mL; CEC: LOD=2–8 μg/mL), accuracy (MEKC: 96.5–102.7% recovery; CEC: 97.1–103.5% recovery) and precision (MEKC: σ_rel≤2.43%; CEC: σ_rel≤2.21%). The quantitative analysis of naphthoquinone derivatives in several E. americana samples showed that both methods are suitable for practical applications, because the results were well comparable to those obtained by established techniques such as HPLC.     

Robust optimization of scoring functions for a target class

Target-specific optimization of scoring functions for protein–ligand docking is an effective method for significantly improving the discrimination of active and inactive molecules in virtual screening applications. Its applicability, however, is limited due to the narrow focus on, e.g., single protein structures. Using an ensemble of protein kinase structures, the publically available directory of useful decoys ligand dataset, and a novel multi-factorial optimization procedure, it is shown here that scoring functions can be tuned to multiple targets of a target class simultaneously. This leads to an improved robustness of the resulting scoring function parameters. Extensive validation experiments clearly demonstrate that (1) virtual screening performance for kinases improves significantly; (2) variations in database content affect this kind of machine-learning strategy to a lesser extent than binary QSAR models, and (3) the reweighting of interaction types is of particular importance for improved screening performance. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Electrochemical synthesis of PEDOT derivatives bearing imidazolium‐ionic liquid moieties

Novel poly(3,4‐ethylenedioxythiophene) (PEDOT) polymers bearing imidazolium‐ionic liquid moieties were synthesized by electrochemical polymerizations. For this purpose, new functional monomers were synthesized having an 3,4‐ethylenedioxythiophene (EDOT) unit and an imidazolium‐ionic liquid with different anions such as tetrafluoroborate (BF), bis(trifluoromethane)sulfonimide ((CF₃SO₂)₂N^?), and hexafluorophosphate (PF). Next, polymer films were obtained by electrochemical synthesis in dicholoromethane solutions. Obtained polymers were characterized, revealing the characteristics of PEDOT in terms of electrochemical and spectroelectrochemical properties, FTIR, ¹H NMR, and AFM microscopy. Interestingly, the hydrophobic character of electropolymerized films could be modified depending on the anion type. The hydrophobicity followed the trend PF > (CF₃SO₂)₂N^? > BF > pure PEDOT as determined by water contact angle measurements. Furthermore, the polymers could be dissolved in a range of polar organic solvents such as dimethylformamide, propylene carbonate, and dimethyl sulfoxide making these polymers interesting candidates for wet processing methods. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 3010–3021, 2009