Probabilistic Inductive Classes of Graphs

A unifying framework—probabilistic inductive classes of graphs (PICGs)—is defined by imposing a probability space on the rules and their left elements from the standard notion of inductive class of graphs. The rules can model the processes creating real-world social networks, such as spread of knowledge, dynamics of acquaintanceships or sexual contacts, and emergence of clusters. We demonstrate the characteristics of PICGs by casting some well-known models of growing networks in this framework. Results regarding expected size and order are derived. For PICG models of connected and 2-connected graphs order, size and asymptotic degree distribution are presented. The approaches used represent analytic alternative to computer simulation, which is mostly used to obtain the properties of evolving graphs.     

Steering in computational science: Mesoscale modelling and simulation

This paper outlines the benefits of computational steering for high performance computing applications. Lattice-Boltzmann mesoscale fluid simulations of binary and ternary amphiphilic fluids in two and three dimensions are used to illustrate the substantial improvements which computational steering offers in terms of resource efficiency and time to discover new physics. We discuss details of our current steering implementations and describe their future outlook with the advent of computational grids.     

First integrals and analytical solutions of the nonlinear fin problem with temperature-dependent thermal conductivity and heat transfer coefficient

Fin materials can be observed in a variety of engineering applications. They are used to ease the dissipation of heat from a heated wall to the surrounding environment. In this work, we consider a nonlinear fin problem with temperature-dependent thermal conductivity and heat transfer coefficient. The equation(s) under study are highly nonlinear. Both the thermal conductivity and the heat transfer coefficient are given as arbitrary functions of temperature. Firstly, we consider the Lie group analysis for different cases of thermal conductivity and the heat transfer coefficients. These classifications are obtained from the Lie group analysis. Then, the first integrals of the nonlinear straight fin problem are constructed by three methods, namely, Noether’s classical method, partial Noether approach and Ibragimov’s nonlocal conservation method. Some exact analytical solutions are also constructed. The obtained result is also compared with the result obtained by other methods.     

Delineating Binding Modes of Gal/GalNAc and Structural Elements of the Molecular Recognition of Tumor‐Associated Mucin Glycopeptides by the Human Macrophage Galactose‐Type Lectin

The human macrophage galactose‐type lectin (MGL) is a key physiological receptor for the carcinoma‐associated Tn antigen (GalNAc‐α‐1‐O‐Ser/Thr) in mucins. NMR and modeling‐based data on the molecular recognition features of synthetic Tn‐bearing glycopeptides by MGL are presented. Cognate epitopes on the sugar and matching key amino acids involved in the interaction were identified by saturation transfer difference (STD) NMR spectroscopy. Only the amino acids close to the glycosylation site in the peptides are involved in lectin contact. Moreover, control experiments with non‐glycosylated MUC1 peptides unequivocally showed that the sugar residue is essential for MGL binding, as is Ca²⁺. NMR data were complemented with molecular dynamics simulations and Corcema‐ST to establish a 3D view on the molecular recognition process between Gal, GalNAc, and the Tn‐presenting glycopeptides and MGL. Gal and GalNAc have a dual binding mode with opposite trend of the main interaction pattern and the differences in affinity can be explained by additional hydrogen bonds and CH–π contacts involving exclusively the NHAc moiety.     

High‐pressure NMR characterization of triacetyl‐β‐cyclodextrin in supercritical carbon dioxide

Cyclodextrins are used in many drug formulations since their cavities provide microenvironments where drug molecules can enter and form inclusion complexes for controlled drug delivery. Supercritical carbon dioxide (scCO₂) is an alternative to organic solvents and a very attractive medium for the preparation of these inclusion complexes. The potential ability of triacetyl‐β‐cyclodextrin (TA‐β‐CD) to form inclusion complexes in addition to its high miscibility in liquid and scCO₂ could offer a chance for an economical and environmental friendly chemical processing. In this work, high‐pressure NMR studies were performed in order to obtain information on the molecular structure and dynamics of TA‐β‐CD in scCO₂ at 313.15 K and 20 MPa and its ability to form inclusion complexes under these conditions was studied. The influence of scCO₂ on a number of NMR spectral parameters, such as chemical shifts, spin‐spin coupling constants, nuclear Overhauser effect (NOE) and spin‐lattice relaxation (T₁) has been studied. We unequivocally show for the first time structural changes of TA‐β‐CD in scCO₂, like acetyl chain orientation and overall shape distortions that can affect its inclusion capability in this medium. The possibility of cavity self‐closure is discussed and the results of two inclusion studies that support cavity self‐closure, with the angiotensin‐converting enzyme inhibitor, captopril, and the nonsteroid anti‐inflammatory drug, flufenamic acid, are presented. Copyright © 2008 John Wiley & Sons, Ltd.     

On regularity of block triangular fuzzy matrices

Necessary and sufficient conditions are given for the regularity of block triangular fuzzy matrices. This leads to characterization of idempotency of a class of triangular Toeplitz matrices. As an application, the existence of group inverse of a block triangular fuzzy matrix is discussed. Equivalent conditions for a regular block triangular fuzzy matrix to be expressed as a sum of regular block fuzzy matrices is derived. Further, fuzzy relational equations consistency is studied.     

Synthesis of a new pyranoanthocyanin dimer linked through a methyl-methine bridge

Two new anthocyanin-derived compounds corresponding to the ethylpyranomalvidin-3-glucoside and the pyranomalvidin-3-glucoside dimer linked through a methyl-methine bridge were synthesized for the first time and their structure characterized by LC-DAD/MS and NMR spectroscopy. The latter was obtained in a hydroalcoholic model solution through the reaction of the carboxypyranomalvidin-3-glucoside with ethylpyranomalvidin-3-glucoside and displays a blue/green color in solution.     

Electrooxidation of pyrrole-terminated self-assembled lipoic acid derivatives

New pyrrole derivatives, pyrrolyl lipoic acid (Py-LA 3) and dipyrrolyl lipoic acid (Py₂-LA 2) have been used for surface attachment and immobilisation on gold surfaces, by self-assembly. The electrooxidation of the surface-confined pyrroles was analysed by cyclic voltammetry and the modified electrodes morphological and thickness changes addressed by scanning probe microscopy and ellipsometry. The data support the formation of oligomers as a result of the pendant-pyrrolyl units ease oxidation but provide no evidence of an effective subsequent polymerisation.     

A pericyclic cascade to the stereocontrolled synthesis of 9-cis-retinoids

A domino reaction that is pericyclic in nature is thought to be triggered upon treatment of alkenynol 10 with arylsulfenyl chlorides. The process comprises an ordered sequence of sigmatropic rearrangements: a reversible [2,3]-allyl sulfenate to allyl sulfoxide shift, followed by a [2,3]-propargyl sulfenate to allenyl sulfoxide rearrangement, and last a stereodifferentiating [1,5]-sigmatropic hydrogen migration leading to polyene 13. The occurrence of the C7 to C11 hydrogen migration has been demonstrated by labeling experiments. The double diastereoselection of the [1,5]-sigmatropic hydrogen shift to afford a single isomer of the final polyene 13 is thought to arise from a combination of the electronic effect of the sulfoxide at one terminus, and the steric effect imparted by the bulky trimethylcyclohexenyl substituent at the other terminus. The overall process thus constitutes a stereoselective synthesis of an E,Z,Z-triene fragment from an alkenynol and, in particular, a retinoid with the 7E,9Z,11Z,13E configuration on the conjugated polyenic side chain. Application of this method to the synthesis of retinoids, including labeled analogues, is straightforward.