Free Meixner states

Free Meixner states are a class of functionals on non-commutative polynomials introduced in math.CO/0410482. They are characterized by a resolvent-type form for the generating function of their orthogonal polynomials, by a recursion relation for those polynomials, or by a second-order non-commutative differential equation satisfied by their free cumulant functional. In this paper, we construct an operator model for free Meixner states. By combinatorial methods, we also derive an operator model for their free cumulant functionals. This, in turn, allows us to construct a number of examples. Many of these examples are shown to be trivial, in the sense of being free products of functionals which depend on only a single variable, or rotations of such free products. On the other hand, the multinomial distribution is a free Meixner state and is not a product. Neither is a large class of tracial free Meixner states which are analogous to the simple quadratic exponential families in statistics.Comment: 30 page

Influence of steps on the tilting and adsorption dynamics of ordered Pn films on vicinal Ag(111) surfaces

Here we present a structural study of pentacene (Pn) thin films on vicinal Ag(111) surfaces by He atom diffraction measurements and density functional theory (DFT) calculations supplemented with van der Waals (vdW) interactions. Our He atom diffraction results suggest initial adsorption at the step edges evidenced by initial slow specular reflection intensity decay rate as a function of Pn deposition time. In parallel with the experimental findings, our DFT+vdW calculations predict the step edges as the most stable adsorption site on the surface. An isolated molecule adsorbs as tilted on the step edge with a binding energy of 1.4 eV. In addition, a complete monolayer (ML) with pentacenes flat on the terraces and tilted only at the step edges is found to be more stable than one with all lying flat or tilted molecules, which in turn influences multilayers. Hence our results suggest that step edges can trap Pn molecules and act as nucleation sites for the growth of ordered thin films with a crystal structure similar to that of bulk Pn.Comment: 4 pages, 4 figures, 1 tabl

Computational design of cyclic peptides for the customized oriented immobilization of globular proteins

The oriented immobilization of proteins, key for the development of novel responsive biomaterials, relies on the availability of effective probes. These are generally provided by standard approaches based on in vivo maturation and in vitro selection of antibodies and/or aptamers. These techniques can suffer technical problems when a non-immunogenic epitope needs to be targeted. Here we propose a strategy to circumvent this issue by in silico design. In our method molecular binders, in the form of cyclic peptides, are computationally evolved by stochastically exploring their sequence and structure space to identify high-affinity peptides for a chosen epitope of a target globular protein: here a solvent-exposed site of β2-microglobulin (β2m). Designed sequences were screened by explicit solvent molecular dynamics simulations (MD) followed by experimental validation. Five candidates gave dose-response surface plasmon resonance signals with dissociation constants in the micromolar range. One of them was further analyzed by means of isothermal titration calorimetry, nuclear magnetic resonance, and 250 ns of MD. Atomic-force microscopy imaging showed that this peptide is able to immobilize β2m on a gold surface. In short, we have shown by a variety of experimental techniques that it is possible to capture a protein through an epitope of choice by computational design

Cognitive skills and literacy performance of Chinese adolescents with and without dyslexia

The present study sought to identify cognitive abilities that might distinguish Hong Kong Chinese adolescents with dyslexia and to assess how these abilities were associated with Chinese word reading, word dictation, and reading comprehension. The cognitive skills of interest were morphological awareness, visual-orthographic knowledge, rapid naming, and verbal working memory. A total of 90 junior secondary school students, 30 dyslexic, 30 chronological age controls, and 30 reading level controls was tested on a range of cognitive and literacy tasks. Dyslexic students were less competent than the control students in all cognitive and literacy measures. The regression analyses also showed that verbal working memory, rapid naming, morphological awareness, and visual-orthographic knowledge were significantly associated with literacy performance. Findings underscore the importance of these cognitive skills for Chinese literacy acquisition. Overall, this study highlights the persistent difficulties of Chinese dyslexic adolescents who seem to have multiple causes for reading and spelling difficulties