MCQ4Structures to compute similarity of molecule structures

Comparison of molecular structures in order to identify their similarity is an important step in solving various problems derived from computational biology, like structure alignment and modelling, motif search or clustering. Thus, there is a constant need for the development of good measures to determine distances between the structures and tools to display these distances in an easily interpretable form. In the paper we present MCQ4Structures, a new method and tool for structural similarity computation based on molecule tertiary structure representation in torsional angle space. We discuss its unique features as compared with the other measures, including RMSD and LGA, and we show its experimental use in comparison of a number of 3D structures as well as evaluation of models predicted within RNA-Puzzles contest. MCQ4Structures software is available as a free Java WebStart application at: http://www.cs.put.poznan.pl/tzok/mcq/. The source code licensed under BSD can be downloaded from the same website.     

Influence of rhodium additive on hydrogen electrosorption in palladium-rich Pd–Rh alloys

Hydrogen electrosorption into Pd-rich (>80 at.% Pd in the bulk) Pd–Rh alloys has been studied in acidic solutions (0.5 M H₂SO₄) using cyclic voltammetry and chronoamperometry. The influence of temperature (in the range between 283 and 328 K), electrode potential and alloy bulk composition on hydrogen electrosorption properties of Pd–Rh alloys is presented. It has been found that the additive of Rh to Pd–Rh alloys increases the maximum hydrogen solubility (for Rh bulk content below 10 at.%), decreases the potential of absorbed hydrogen oxidation peak and decreases the potential of the α → β phase transition. Increasing temperature decreases the potential of absorbed hydrogen oxidation peak, the maximum hydrogen solubility, and the potential of the α → β phase transition. The amounts of electrosorbed hydrogen for α- and β-phase boundaries, i.e., α_max and β_min, have been determined from the integration of the initial parts of current–time responses in hydrogen absorption and desorption processes. The H/M ratio corresponding to α_max increases with increasing Rh content, while for β_min a maximum of H/M ratio is observed for the alloys containing ca. 95% Rh.

     

Determination of catechin and epicatechin in the peel of apple varieties resistant and non-resistant to apple scab

Catechin and epicatechin were analysed in the peel of six apple cultivars (three resistant and three non-resistant to apple scab). Two methods of analytical sample preparation following extraction were tested: solid phase extraction and column separation with Sephadex LH-20 coupled to a differential refractometric detector. Prior to GC and GC-MS analyses, these compounds were silylized. This permitted co-injection with standards and the comparison of retention values and mass spectra with those recorded for standards. The content of catechin and epicatechin in apple peel is discussed in relation to the resistance of apple trees to scab.     

Circle Maps,Measured Laminations,and Free Group Actions on IR-trees

This paper explores the connection between homeomorphisms of the unit circle, codimension-1 measured laminations on closed surfaces, and free actions of surface groups on IR-trees.     

Conformal Families of Measures for Fibred Systems

In this paper, we give sufficient conditions for the existence of (pseudo) weakly conformal and conformal families of measures for fibred systems. We describe a general construction principle for these families, modelled on the one developed by Denker and Urbanski for conformal measures. For those systems that are fibrewise local homeomorphisms, the constructed families are (pseudo) conformal. If a system is, moreover, weakly topologically exact along fibres, then each measure in the associated family is supported on the whole fibre where it is naturally defined.     

Nonspecular total internal reflection of spatial solitons at the interface between highly birefringent media

We investigate total internal reflection of nonlocal spatial optical solitons at the interface between two differently oriented regions of a highly birefringent nematic liquid crystal. The solitons survive the interaction with an induced index mismatch and undergo nonspecular reflection, with an emerging angle differing appreciably from the incidence angle.     

Folding of the Tau Protein on Microtubules

Microtubules are regulated by microtubule‐associated proteins. However, little is known about the structure of microtubule‐associated proteins in complex with microtubules. Herein we show that the microtubule‐associated protein Tau, which is intrinsically disordered in solution, locally folds into a stable structure upon binding to microtubules. While Tau is highly flexible in solution and adopts a β‐sheet structure in amyloid fibrils, in complex with microtubules the conserved hexapeptides at the beginning of the Tau repeats two and three convert into a hairpin conformation. Thus, binding to microtubules stabilizes a unique conformation in Tau.     

Optimal double control problem for a PDE model of goodwill dynamics

We propose a new optimal control model of product goodwill in a segmented market where the state variable behaviour is described by a partial differential equation of the Lotka–Sharp–McKendrick type. In order to maximize the sum of discounted profits over a finite time horizon, we control the marketing communication activities which influence the state equation and the boundary condition. Moreover, we introduce the mathematical representation of heterogeneous electronic word of mouth. Based on the semigroup approach, we prove the existence and uniqueness of optimal controls. Using a maximum principle, we describe a numerical algorithm to find the optimal solution. Finally, we examine several examples on the optimal goodwill model and discover two types of marketing strategies.