Comparison of measurements of phase velocity in human calcaneus to Biot theory

Biot's theory for elastic propagation in porous media has previously been shown to be useful for modeling the dependence of phase velocity on porosity in bovine cancellous bone in vitro. In the present study, Biot's theory is applied to measurements of porosity-dependent phase velocity in 53 human calcanea in vitro. Porosity was measured using microcomputed tomography for some samples (n = 23) and estimated based on bone mineral densitometry for the remaining samples (n = 30). The phase velocity at 500 kHz was measured in a water tank using a through-transmission technique. Biot's theory performed well for the prediction of the dependence of sound speed on porosity. The trend was quasilinear, but both the theory and experiment show similar slight curvature. The root mean square error (RMSE) of predicted versus measured sound speed was 15.8 m/s.     

Generalized McCormick relaxations

Convex and concave relaxations are used extensively in global optimization algorithms. Among the various techniques available for generating relaxations of a given function, McCormick’s relaxations are attractive due to the recursive nature of their definition, which affords wide applicability and easy implementation computationally. Furthermore, these relaxations are typically stronger than those resulting from convexification or linearization procedures. This article leverages the recursive nature of McCormick’s relaxations to define a generalized form which both affords a new framework within which to analyze the properties of McCormick’s relaxations, and extends the applicability of McCormick’s technique to challenging open problems in global optimization. Specifically, relaxations of the parametric solutions of ordinary differential equations are considered in detail, and prospects for relaxations of the parametric solutions of nonlinear algebraic equations are discussed. For the case of ODEs, a complete computational procedure for evaluating convex and concave relaxations of the parametric solutions is described. Through McCormick’s composition rule, these relaxations may be used to construct relaxations for very general optimal control problems.     

Nonsmooth exclusion test for finding all solutions of nonlinear equations

A new approach is proposed for finding all real solutions of systems of nonlinear equations with bound constraints. The zero finding problem is converted to a global optimization problem whose global minima with zero objective value, if any, correspond to all solutions of the original problem. A branch-and-bound algorithm is used with McCormick’s nonsmooth convex relaxations to generate lower bounds. An inclusion relation between the solution set of the relaxed problem and that of the original nonconvex problem is established which motivates a method to generate automatically, starting points for a local Newton-type method. A damped-Newton method with natural level functions employing the restrictive monotonicity test is employed to find solutions robustly and rapidly. Due to the special structure of the objective function, the solution of the convex lower bounding problem yields a nonsmooth root exclusion test which is found to perform better than earlier interval-analysis based exclusion tests. Both the componentwise Krawczyk operator and interval-Newton operator with Gauss-Seidel based root inclusion and exclusion tests are also embedded in the proposed algorithm to refine the variable bounds for efficient fathoming of the search space. The performance of the algorithm on a variety of test problems from the literature is presented, and for most of them, the first solution is found at the first iteration of the algorithm due to the good starting point generation.     

Synthesis of light-sensitive arenesulfonylazido polycarboxylic acids

Several light-sensitive arenesulfonylazido polycarboxylic acids were synthesized by a one-step reaction of a polymeric anhydride with a light-sensitive monofunctional alcohol, or by the reverse reaction, i.e., reaction of a polymeric alcohol with a light-sensitive monofunctional anhydride. The polycarboxylic acids are soluble in polar organic solvents and in aqueous base. Neutralization of part of the carboxyl groups gives rise to the formation of water-soluble polymers. Coreaction of poly(maleic anhydride-co-methyl vinyl ether) with 2-hydroxyethyl 4-sulfonylazidocarbanilate and 2-hydroxyethyl trans-2,5-dimethoxystilbene-4′-carbamate produces a light-sensitive polycarboxylic acid with “built-in” sensitizer.     

Kautschuk

Ohne Zusammenfassung     

Fluorescently Labelled ATP Analogues for Direct Monitoring of Ubiquitin Activation

Simple and robust assays to monitor enzymatic ATP cleavage with high efficiency in real-time are scarce. To address this shortcoming, we developed fluorescently labelled adenosine tri-, tetra- and pentaphosphate analogues of ATP. The novel ATP analogues bear — in contrast to earlier reports — only a single acridone-based dye at the terminal phosphate group. The dye's fluorescence is quenched by the adenine component of the ATP analogue and is restored upon cleavage of the phosphate chain and dissociation of the dye from the adenosine moiety. Thereby the activity of ATP-cleaving enzymes can be followed in real-time. We demonstrate this proficiency for ubiquitin activation by the ubiquitin-activating enzymes UBA1 and UBA6 which represents the first step in an enzymatic cascade leading to the covalent attachment of ubiquitin to substrate proteins, a process that is highly conserved from yeast to humans. We found that the efficiency to serve as cofactor for UBA1/UBA6 very much depends on the length of the phosphate chain of the ATP analogue: triphosphates are used poorly while pentaphosphates are most efficiently processed. Notably, the novel pentaphosphate-harbouring ATP analogue supersedes the efficiency of recently reported dual-dye labelled analogues and thus, is a promising candidate for broad applications.     

Electroweak interactions in chiral molecules: two-component density functional theory study of vibrational frequency shifts in polyhalomethanes

In this paper, a two-component density functional theory study of parity violation-induced vibrational frequency shifts in chiral polyhalomethanes is reported and the prospects to detect in these compounds, for the first time, signals of parity violation in molecular systems are discussed. The recent synthesis of enantiomerically enriched CHClFI has renewed interest in examining electroweak corrections for this class of compounds. Utilizing a (quasi-relativistic) two-component zeroth-order regular approximation approach to molecular parity violation, together with density functional theory, the parity violation-induced relative vibrational frequency splittings Δ ν_pv/ν between the C–F stretching fundamental of polyhalomethane enantiomers are computed. The relative splitting in CHClFI is raised compared with CHBrClF, for which upper bounds were determined experimentally. To facilitate measurement, molecules possessing more pronounced relative splittings are desirable. Therefore, the chiral methane derivative CHAtFI is considered, which exhibits a significantly larger electroweak contribution that induces a vibrational frequency splitting on the order of the experimental resolution previously reported for CHBrClF. Employing compounds containing heavy nuclei such as astatine may thus be necessary with present detection methods.     

Die Blutgerinnung als kolloidchemisches Problem

Ohne Zusammenfassung