Merging and splitting in cooperative games: some (im)possibility results

Allocation rules for cooperative games can be manipulated by coalitions merging into single players, or, conversely, players splitting into a number of smaller units. This paper collects some (im)possibility results on merging- and splitting-proofness of (core) allocation rules for cooperative games with side-payments.     

Intermolecular exchange-induction energies without overlap expansion

An approach to evaluate the second-order exchange-induction energies of symmetry-adapted intermolecular perturbation theory (SAPT) for single-determinant ground-state monomer wavefunctions has been derived. This approach is correct to all orders of the intermonomer overlap, that is, it takes multiple electron exchange between the monomers into account. The resulting formulae can be written in a compact way and implemented efficiently. Here, the method is employed to investigate the performance of the S ²- or single-exchange approximation at the Hartree-Fock-SAPT level. The list of test systems comprises the prototypical van der Waals- and hydrogen-bridge complexes Ne₂, Ar–HF, and (H₂O)₂, but also the systems HeCl^?, NeNa⁺ and Li⁺F^? involving closed-shell ions. It was found that the errors introduced by the S ²-approximation are more pronounced for the second-order exchange-induction energy than for the first-order exchange energy. While these errors tend to be negligible throughout the well region of complexes such as the neon dimer, they start to be significant in the repulsive part of the well regions of systems such as the water dimer, and in particular for the ionic lithium fluoride molecule. The consequences of these findings for the Hartree-Fock level estimate of higher-order induction plus exchange-induction energies, which is frequently employed in SAPT are also discussed.     

Single-Round DNA Aptamer Selection by Combined Use of Capillary Electrophoresis and Next Generation Sequencing: An Aptaomics Approach for Identifying Unique Functional Protein-Binding DNA Aptamers

In DNA aptamer selection, existing methods do not discriminate aptamer sequences based on their binding affinity and function and the reproducibility of the selection is often poor, even for the selection of well-known aptamers like those that bind the commonly used model protein thrombin. In the present study, a novel single-round selection method (SR-CE selection) was developed by combining capillary electrophoresis (CE) with next generation sequencing. Using SR-CE selection, a successful semi-quantitative and semi-comprehensive aptamer selection for thrombin was demonstrated with high reproducibility for the first time. Selection rules based on dissociation equilibria and kinetics were devised to obtain families of analogous sequences. Selected sequences of the same family were shown to bind thrombin with high affinity. Furthermore, data acquired from SR-CE selection was mined by creating sub-libraries that were categorized by the functionality of the aptamers (e. g., pre-organized aptamers versus structure-induced aptamers). Using this approach, a novel fluorescent molecular recognition sensor for thrombin with nanomolar detection limits was discovered. Thus, in this proof-of-concept report, we have demonstrated the potential of a “DNA Aptaomics” approach to systematically design functional aptamers as well as to obtain high affinity aptamers.     

Fisher Information of Free-Electron Landau States

An electron in a constant magnetic field has energy levels, known as the Landau levels. One can obtain the corresponding radial wavefunction of free-electron Landau states in cylindrical polar coordinates. However, this system has not been explored so far in terms of an information-theoretical viewpoint. Here, we focus on Fisher information associated with these Landau states specified by the two quantum numbers. Fisher information provides a useful measure of the electronic structure in quantum systems, such as hydrogen-like atoms and under some potentials. By numerically evaluating the generalized Laguerre polynomials in the radial densities, we report that Fisher information increases linearly with the principal quantum number that specifies energy levels, but decreases monotonically with the azimuthal quantum number m. We also present relative Fisher information of the Landau states against the reference density with m=0, which is proportional to the principal quantum number. We compare it with the case when the lowest Landau level state is set as the reference.     

Thermal transformation of polyacrylonitrile deposited on SBA-15 type silica

Thermogravimetry, diffuse reflectance infrared Fourier transform spectroscopy, and X-ray photoelectron spectroscopy (XPS) were used for the studying of thermally induced structural changes of polyacrylonitrile (PAN) deposited on the surface of SBA-15 type mesoporous silica. Polymer was introduced onto the support by the precipitation polymerization of acrylonitrile in aqueous suspension of SBA-15. Low temperature transformation (to 723?K) of the deposited PAN was analyzed. It was found that at about 523?K, exothermic cyclization of polymer chains to the so-called ladder form of PAN occurred. However, the total cyclization of PAN required higher carbonization temperatures, at which gradual dehydrogenation followed by graphitization was initiated. XPS revealed that the cyclic form of PAN and a relatively large amount of carbonyl species, formed during the carbonization of the PAN/SBA-15 composite at 623?K, were responsible for the high sorption capacity in the methyl?Cethyl ketone (MEK) vapor elimination. The efficiency in the MEK adsorption was also influenced by the content of PAN-derived carbon deposited on the SBA-15 surface.     

Synthesis and properties of hyperbranched poly(ether sulfone)s prepared by self‐polycondensation of novel AB2 monomer

Hyperbranched poly(ether sulfone)s were prepared by the self‐polycondensation of the novel AB₂ monomer, 4‐(3,5‐hydroxyphenoxy)‐4′‐fluorodiphenylsulfone. The high‐molecular‐weight polymers were isolated in good yields. The degree of branching (DB) of the resulting polymers was investigated by the preparation of dendritic and linear model compounds. The DB determined by gated decoupling ¹³C NMR measurements was in the range 0.17–0.41 and was dependent on the base used for the self‐polycondensation. It was found that cesium fluoride was an effective base to form the polymer having the DB of 0.41. The resulting hyperbranched poly(ether sulfone)s showed good solubility in organic solvents. The solubility and the glass transition temperature of the polymers were influenced by the terminal functional groups. The unique thermal crosslinking phenomenon was observed during the DSC measurements of the hydroxyl‐terminated hyperbranched poly(ether sulfone) under air condition. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012