Overlapping Modularity at the Critical Point of k-Clique Percolation

One of the most remarkable social phenomena is the formation of communities in social networks corresponding to families, friendship circles, work teams, etc. Since people usually belong to several different communities at the same time, the induced overlaps result in an extremely complicated web of the communities themselves. Thus, uncovering the intricate community structure of social networks is a non-trivial task with great potential for practical applications, gaining a notable interest in the recent years. The Clique Percolation Method (CPM) is one of the earliest overlapping community finding methods, which was already used in the analysis of several different social networks. In this approach the communities correspond to k-clique percolation clusters, and the general heuristic for setting the parameters of the method is to tune the system just below the critical point of k-clique percolation. However, this rule is based on simple physical principles and its validity was never subject to quantitative analysis. Here we examine the quality of the partitioning in the vicinity of the critical point using recently introduced overlapping modularity measures. According to our results on real social and other networks, the overlapping modularities show a maximum close to the critical point, justifying the original criteria for the optimal parameter settings.     

A diagonal measure and a local distance matrix to display relations between objects and variables

Proper permutation of data matrix rows and columns may result in plots showing striking information on the objects and variables under investigation. To control the permutation first, a diagonal matrix measure D was defined expressing the size relations of the matrix elements. D is essentially the absolute norm of a matrix where the matrix elements are weighted by their distance to the matrix diagonal. Changing the order of rows and columns increases or decreases D. Monte Carlo technique was used to achieve maximum D in the case of the object distance matrix or even minimal D in the case of the variable correlation matrix to get similar objects or variables close together. Secondly, a local distance matrix was defined, where an element reflects the distances of neighboring objects in a limited subspace of the variables. Due to the maximization of D in the local distance matrix by row and column changes of the original data matrix, the similar objects were arranged close to each other and simultaneously the variables responsible for their similarity were collected close to the diagonal part defined by these objects. This combination of the diagonal measure and the local distance matrix seems to be an efficient tool in the exploration of hidden similarities of a data matrix. Copyright © 2009 John Wiley & Sons, Ltd.     

Herstellung und Anionenkonstitution von kristallinen Tetramethylammonium-alumosilicaten und -alumosilicatlösungen

Synthesis and Anion Constitution of Crystalline Tetramethylammonium-aluminosilicates and -aluminosilicate Solutions Crystalline tetramethylammonium aluminosilicates with molar constitutions of wN(CH₃)₄OH · xSiO₂ · y Al₂O₃ · zH₂O and w = 1 to 1.2; x = 1; y = 0.02 to 0.5; z = 8.1 to 9.7 has been obtained from mixtures of diluted TMA aluminate and TMA silicate solutions with different molar Si/Al ratios by concentration and cooling down of the mixtures. Investigations of the TMA aluminosilicates by means of trimethylsilylation method show that the structure of the TMA aluminosilicates consists of double fouring units in analogy to the aluminum free TMA silicates. The arrangement of the Al atoms in the double four-rings agrees in general with Loewenstein's rule and leads to five distinct types of double four-rings with different Al content and Si? Al distribution. By the methods used in this study no distinction can be made between monomeric or polymeric arrangements of the double four-ring units. The existence of aluminosilicate anions in aqueous solutions is discussed.     

Isolation and Characterization of Novel Capsorubin‐Like Carotenoids from the Red Mamey (Pouteria sapota)

From the ripe fruits of red mamey (Pouteria sapota), two new carotenoids, 3′‐deoxycapsorubin and 3,3′‐dideoxycapsorubin, were isolated and identified based on their UV/VIS, CD, ¹H‐NMR, and mass spectral data.     

Monte Carlo structure simulations for aqueous 1,4-dioxane solutions

Monte Carlo simulations in the NpT ensembles have been performed for the structure exploration of aqueous 1,4-dioxane solutions. Three different systems with all-atom dioxane:TIP4P water molar compositions of 2:500 (code:D2), 8:465 (D8), and 17:425 (D17) modeled solutions of 0.22, 0.88, and 1.86 mol/dm3 concentrations, respectively, at T = 298 K and p = 1 atm. The calculated solution densities increase from 0.992 to 1.002 g/cm3 with increasing dioxane concentration and approach the experimentally determined densities within 1%. This close agreement was achieved by utilizing RESP charges fitted to the in-solution IEF-PCM/B3LYP/6-31G* electrostatic potential of dioxane taken in its chair conformation and recently developed C, H steric parameters for ethers for calculations with a 12-6-1 all-atom potential. Solution structure analyses pointed out that the dioxane molecules arrange in the solutions with favorable distances of 4-8 angstroms for the ring symmetry centers. Within this range not only pairs of rings but triangular triads and tetrads have also been observed with center-center distances <8 angstroms. For the D8 system, about 25% of the sampled configurations included such a triad. In the case of the D17 model, two simulations starting from different solution configuration predicted different degrees for the dioxane aggregation in aqueous solution. In the more aggregated structure 3-21 triads are consistently maintained and 1-2 tetrads are formed in 58% of the configurations. Each dioxane oxygen forms about one hydrogen bond, on average, to a water molecule in the 0.22-1.86 molar range. The most likely O(dioxane)...H(water) hydrogen bond distance is 1.75-1.80 angstroms compared to the optimal distance of 1.72 angstroms in the isolated dimer. The optimal dioxane-water interaction energy of -5.65 kcal/mol indicates a remarkable hydrogen-bond acceptor character for dioxane.     

Probing small molecule binding to amyloid fibrils

Much effort has focussed in recent years on probing the interactions of small molecules with amyloid fibrils and other protein aggregates. Understanding and control of such interactions are important for the development of diagnostic and therapeutic strategies in situations where protein aggregation is associated with disease. In this perspective article we give an overview over the toolbox of biophysical methods for the study of such amyloid-small molecule interactions. We discuss in detail two recently developed techniques within this framework: linear dichroism, a promising extension of the more traditional spectroscopic techniques, and biosensing methods, where surface-bound amyloid fibrils are exposed to solutions of small molecules. Both techniques rely on the measurement of physical properties that are very directly linked to the binding of small molecules to amyloid aggregates and therefore provide an attractive route to probe these important interactions.     

Rate constant for the reaction of OH radicals with CH3C(O)Cl determined by direct kinetic method

Summary The fast flow technique with OH resonance fluorescence detection has been applied at T = 298 ± 2 K to study the kinetics of the overall reaction: H + CH₃C(O)Cl → products (1) A rate constant value of k₁ = (1.02 ± 0.12) x 10¹⁰ cm³ mol^-1 s^-1 has been determined which is the first direct kinetic parameter reported for reaction (1) in the literature (the error given refers to 2σ accuracy).     

Mono- and dinuclear iron complexes of bis(1-methylimidazol-2-yl)ketone (bik): structure, magnetic properties, and catalytic oxidation studies

The newly synthesized dinuclear complex [Fe(III)(2)(μ-OH)(2)(bik)(4)](NO(3))(4) (1) (bik, bis(1-methylimidazol-2-yl)ketone) shows rather short Fe···Fe (3.0723(6) ?) and Fe-O distances (1.941(2)/1.949(2) ?) compared to other unsupported Fe(III)(2)(μ-OH)(2) complexes. The bridging hydroxide groups of 1 are strongly hydrogen-bonded to a nitrate anion. The (57)Fe isomer shift (δ = 0.45 mm s(-1)) and quadrupole splitting (ΔE(Q) = 0.26 mm s(-1)) obtained from Mo?ssbauer spectroscopy are consistent with the presence of two identical high-spin iron(III) sites. Variable-temperature magnetic susceptibility studies revealed antiferromagnetic exchange (J = 35.9 cm(-1) and H = JS(1)·S(2)) of the metal ions. The optimized DFT geometry of the cation of 1 in the gas phase agrees well with the crystal structure, but both the Fe···Fe and Fe-OH distances are overestimated (3.281 and 2.034 ?, respectively). The agreement in these parameters improves dramatically (3.074 and 1.966 ?) when the hydrogen-bonded nitrate groups are included, reducing the value calculated for J by 35%. Spontaneous reduction of 1 was observed in methanol, yielding a blue [Fe(II)(bik)(3)](2+) species. Variable-temperature magnetic susceptibility measurements of [Fe(II)(bik)(3)](OTf)(2) (2) revealed spin-crossover behavior. Thermal hysteresis was observed with 2, due to a loss of cocrystallized solvent molecules, as monitored by thermogravimetric analysis. The hysteresis disappears once the solvent is fully depleted by thermal cycling. [Fe(II)(bik)(3)](OTf)(2) (2) catalyzes the oxidation of alkanes with t-BuOOH. High selectivity for tertiary C-H bond oxidation was observed with adamantane (3°/2° value of 29.6); low alcohol/ketone ratios in cyclohexane and ethylbenzene oxidation, a strong dependence of total turnover number on the presence of O(2), and a low retention of configuration in cis-1,2-dimethylcyclohexane oxidation were observed. Stereoselective oxidation of olefins with dihydrogen peroxide yielding epoxides was observed under both limiting oxidant and substrate conditions.